\( \ln C a F_{2}, \) the number of electrons \( (s) \) transferred from calcium to fluorine
atoms are two
A. True
B. False


John and Radha were classmates since
childhood. When Radha became eleven
years old, she developed a little swelling on her neck. She visited the doctor who
started medication for her. After a few
years, John also developed a slight
protrusion on his throat. He got worried
and went to the doctor. But, the doctor
assured him that it was a normal
feature in boys while they are growing
up. Which one is the reason for the
difference in diagnosis?
A. Radha's symptom is hyper/hypothyroidism, John's symptom is of puberty i.e. development of Adam's apple
B. Radha's symptom is of puberty i.e., development of Adam's apple, John's symptom is hyper/hypo thyroidism
C. Radha and John's symptoms are of hypothyroidism
D. Radha and John's symptoms are of hyperthyroidism


Calculate the current flowing through
the resistance \( 2 \Omega \)


\( \ln O_{2} \) and \( H_{2} O_{2}, \) the \( O-O \) bond lengths are 1.21 and \( 1.48 \dot{A} \)
respectively. In ozone, the average \( \boldsymbol{O}- \)
O bond length is:
A \( .1 .28 \AA \)
В. 1.18 А
c. \( 1.44 \dot{h} \)
D . \( 1.52 \hat{h} \)


The standard reduction potential for \( C u^{2+} / C u \) is +0.34 V. What will be the
reduction potential at \( \mathrm{pH}=14 ?[ \) Given:
\( \left.\boldsymbol{K}_{s p} \text { of } \boldsymbol{C u}(\boldsymbol{O H})_{2} \text { is } \mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{1 9}}\right] \)
A . \( 2.2 v \)
в. 3.4v
c. \( -0.22 v \)
D . \( -2.2 v \)


What will be the bond order of the
species with electronic configuration
\( 1 s^{2} 2 s^{2} 2 p^{5} ? \)
A. one
B. Two
c. Three
D. zero


Voltage \( V \) and current i in AC circuit is given by \( \mathrm{V}=\mathbf{5 0} \sin (\mathbf{5 0} t) \) volt
\( \mathrm{i}=50 \sin \left(50 t+\frac{\pi}{3}\right) m A . \) The power
dissipated in circuit is:
\( \mathbf{A} \cdot 5.0 W \)
B . \( 2.5 W \)
c. \( 1.25 W \)
D. zero


Solve in positive integers:
\( 23 x+25 y=915 \)
This question has multiple correct options
A. \( x=15, y=6 \)
B. \( x=30, y=9 \)
c. \( x=5, y=32 \)
D. \( x=10, y=8 \)


A monochromatic source of light
operating at \( 200 \mathrm{W} \) emits \( 4 \times 10^{20} \)
photons per second. Find the wavelength of light.
A . 400 nm
B. 200nm
C \( .4 \times 10^{-10} \dot{A} \)
D. None of these


The numerical ratio of displacement to distance for a moving object is
A. always less than 1
B. always equal to 1
c. always more than 1
D. equal or less than 1


The number of water molecules in
hydrated beryllium salt never exceeds:
A. 6
B. 3
\( c \cdot 2 \)
\( D \)


The length of the latusrectum of an ellipse is equal to one-half of its minor axis. Then the eccentricity of the ellipse is :
A \( \cdot \frac{\sqrt{3}}{2} \)
B. \( \frac{\sqrt{2}}{3} \)
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{1}{\sqrt{2}} \)


In a circle with center \( 0, \) chords \( A B \) and
CD are of length \( 5 \mathrm{cm} \) and \( 6 \mathrm{cm} \)
respectively and subtend angle \( x^{\circ} \) and
\( y^{\circ} \) at center of circle respectively then
A \( \cdot x^{\circ}=y^{\circ} \)
В . \( x^{\circ}<y^{\circ} \)
\( \mathbf{c} \cdot x^{\circ}>y^{\circ} \)
D. None of the above


Assertion:
Chemical messenger gives a message to the cell without entering the cell
Reason:
Chemical messenger is received at the binding site of receptor proteins
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct
F. Answer required


Assertion
The highest oxidation state of \( O s \) is +8
Reason Osmium is a 5 d-block element.
Read the above assertion and reason
and choose the correct option from the
following.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the cardiac cycle, diastole is
A. The number of heart beats per minute.
B. The relaxation period after contraction of the heart.
C. The forceful pumping action of the heart
D. The contraction period after relaxation of the heart.


\( N_{2}, C O, C N^{-} \) and \( N O^{+} \) are
isoelectronic but the former is
chemically inert and later three are very reactive, why?


Match the List-I with List-II and choose
the correct answer from the code.
\( \begin{array}{ll}\begin{array}{l}\text { List-I } \\ \text { (Electrolyte) }\end{array} & \begin{array}{l}\text { List-II } \\ \text { (Solubility product) }\end{array} \\ \text { A. } B i_{2} S_{3} & \text { 1. } 4 s^{3} \\ \text { B. } A l(O H)_{3} & \text { 2. } 27 s^{4} \\ \text { C. CdS } & \text { 3. } 108 s^{5} \\ \text { D. } C a F_{2} & \text { 4. } s^{2}\end{array} \)
\( \mathbf{A} \)
\( A-1, B-2, C-3, D-4 \)
B. \( A-2, B-3, C-1, D-4 \)
C \( . A-4, B-3, C-2, D-1 \)
D . \( A-3, B-2, C-4, D-1 \)


What is an annual ring?


Give the order the rotational symmetry
for each figure:


Using IUPAC norms write the formulae for the following:
(a) Potassium trioxalatoaluminate(III)
(b) Dichloridobis(ethane-1, 2diamine)cobalt(III)chloride


The sum of 3 numbers in an AP is 111, and the differences of the squares of the greatest and least is \( 1776 . \) The smallest
number is
A . 37
B. 25
\( c \cdot 49 \)
D. 32


The \( p H \) of a 0.1 molar solution of the
acid \( H A \) is \( 3 . \) The value of the
ionization constant, \( \boldsymbol{K}_{(a)} \) of the acid is:
A. \( 3 \times 10^{-10} \)
В. \( 1 \times 10^{-3} \)
c. \( 1 \times 10^{-5} \)
D. \( 1 \times 10^{-7} \)


The sum of odd integers from 1 to 2001 is
A \( \cdot(1121)^{2} \)
В. \( (1101)^{2} \)
c. \( (1001)^{2} \)
D. \( (1021)^{2} \)
E \( \cdot(1011)^{2} \)


Which of the following defines electromagnetic induction:
A. When magnetic field associated with a coil changes, an induced electric current flows through the coil
B. Electric current induces magnetic field near the wire carrying current.
C. Two permanent magnets exert force on each other
D. Electrolyte disintegrates into ions in a battery.


Which of the following reaction is used to
make a fuel cell ?
\( \mathbf{A} \cdot 2 H_{2}(g)+O_{2}(g) \rightarrow 2 H_{2} O(l) \)
B. \( 2 F e(s)+O_{2}(g)+4 H^{+}(a q) \rightarrow 2 F e^{2+}(a q)+2 H_{2} O(l) \)
\( \mathbf{c} \cdot P b(s)+P b O_{2}(s)+2 H_{2} S O_{4}(a q) \rightarrow 2 P b S O_{4}(s)+ \)
\( H_{2} O(l) \)
D. \( C d(s)+2 N i(O H)_{3}(s) \rightarrow C d O(s)+2 N i(O H)_{2}+ \)
\( 2 H_{2} O(l) \)


Perform the indicated operations:
\( (5+3 i)(3-2 i) \)
A . \( 21-2 i \)
В. \( 19-3 i \)
\( c \cdot 11-2 i \)
D. \( 21-i \)


The number of electrons delivered at the
cathode during electrolysis by a current
of 1 ampere in 60 seconds is :
(charge on an electron is \( 1.60 \times \) \( \left.10^{-19} C\right): \)
\( \mathbf{A} \cdot 3.75 \times 10^{20} \)
B . \( 7.48 \times 10^{23} \)
\( c \cdot 6 \times 10^{23} \)
D. \( 6 \times 10^{20} \)


The average molar mass of air becomes more in presence of which gas if present in air:
A \( . H_{2} \)
в. \( N_{2} \)
c. \( C_{2} H_{6} \)
D. \( C H_{4} \)


The element of electric heater is made
of
A. Iron
B. Nichrome
c. copper
D. Gold


The charge that will flow to earth when
only switch \( S_{1} \) is connected to earth is :
A . \( -(Q / 2) \)
B. \( (Q / 2) \)
c. \( 3 Q / 4 \)
D. \( -Q \)


What is the name given to India's Meteorological Research Satellite launched in \( 2003 ? \)
A. Vikram-1
B. Bhaskara-
c. Kalpana-1
D. Arya Bhatta- -


An amount at certain rate of compound
interest becomes Rs.700 in 3 years and
Rs. 756 in 4 years. Rate of interest is:
A . \( 7 \% \)
B. \( 10 \% \)
\( c .8 \% \)
D. \( 10.5 \% \)


Draw a labelled ray diagram of a reflecting telescope. Mention its two advantages over the refracting telescope


(a) Select the homologous structures from the combinations given below:
(i) Forelimbs of whales and bats
(ii) Tuber of potato and sweet potato
(iii) Eyes of octopus and mammals
(iv) Thorns of Bougainvillea and tendrils
of Cucurbita


A closed vessel contains equal number
of nitrogen and oxygen molecules at a pressure of \( \mathrm{P} \mathrm{mm} \). If nitrogen is removed from the system, then the pressure will be?
A.
в. \( 2 P \)
c. \( P / 2 \)
D. \( P^{2} \)


One of the two forces is double and the
other resultant is equal to the greater force. The angle between then is
\( \mathbf{A} \cdot \cos ^{-1}(1 / 2) \)
B . \( \cos ^{-1}(-1 / 2) \)
c. \( \cos ^{-1}(1 / 4) \)
D. \( \cos ^{-1}(-1 / 4) \)


\( d \)
\( d \)
\( d \)
\( d \)
\( \phi \)


Let \( P, Q, R \) and \( S \) be the points on the plane with position vectors \( (-2 i-j), 4 i \) \( (3 i+3 j) \) and \( (-3 i+2 j) \) respectively. The quadilateral PQRS must be a
A. Parallelogram, which is neither a rhombus nor a rectangle
B. Square
c. Rectangle, but not a square
D. Rhombus, but not a square


State whether the given statement is true or false:
\( \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2} \) is precipitated if \( \left[\boldsymbol{H} \boldsymbol{g}_{2}^{2+}\right]\left[\boldsymbol{C l}^{-}\right]^{2} \)
is greater than \( \boldsymbol{K}_{\boldsymbol{s p}}\left(\boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2}\right) \)


What are the symptoms of puberty?
A. Growth spurt
B. High pitch voice
c. sprouting of pubic hairs
D. All of the above


If strength of magnetic field \( \bar{B}=2 \hat{i}+ \) \( \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) and area vector is \( \overline{\boldsymbol{A}}=\mathbf{3} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}} \)
then find the magnetic flux link with
area vector
A. 4 weber
B. 6 weber
c. 7 weber
D. 5 weber


Amoeba shows
A. Radial symmetry
B. Asymmetry
C. Bilateral symmetry
D. All of the above


Define ecological pyramid


When exposed to air, sodium
carbonate crystals lose water, turn into
\( \mathbf{a}: \)
A. monohydrate
B. nanohydrate
c. decahydrate
D. hexahydrate


Vanda plant is a/an
A. Total parasite.
B. Partial parasite.
c. Epiphyte.
D. saprophyte.


A ship moves at \( 40 \mathrm{kmph} \) due north and
suddenly moves towards east through
\( 90^{0} \) and continues to move with the
same speed. Then the change in velocity
is
A. zero
B. 40 kmph North East
c. \( 40 \mathrm{kmph} \) south west
D. \( 40 \sqrt{2} \) kmph south East


The loosely arranged non-chlorophyllous
parenchyma cells present in lenticels are known as
A. Complementary cells
B. Passage cells
c. water stomata
D. Albuminous cells


We have \( 20 \mathrm{Kg} \) of a block of a substance at its melting point. The substance has a latent heat of fusion of 1500 Joules per
kilogram and a specific heat at of 2500 Joules per kilogram degree Celcius. How much heat is needed to change the block entirely into a liquid?
A. 30000
B. 750 J
c. 1250
D. 3000 J
E. 8000


Give reasons for the following. Squares, rectangles, parallelograms are all quadrilaterals.


Elements with atomic number greater than 92 are called actinides.
A. True
B. False


How is the working of an electric bell affected, if alternating current be used instead of direct current?


Electric doorbell
A. Always consume power
B. Consume power only when switch is pressed
C. Do not consume power practically and needs only starting power
D. cant say


Identify the group \( 14 A \) element that best fits each of the following descriptions:
(a) prefers the +2 oxidation state.
(b) forms the strongest \( \pi \) bonds.
(c)is the second most abundant
element in the earth's crust.
(d)forms the most acidic oxide.
A \( \cdot(a) P b ;(b) C ;(c) S i ;(d) C \)
B. (a) \( P b ; \) (b) \( C ; \) (c) \( P b ; \) (d) \( C \)
\( \mathbf{c} . \) (a) \( P b_{;} \) (b) \( C ; \) (c) \( S i ; \) (d) \( S i \)
D. \( (a) S n ;(b) C ;(c) S i ;(d) C \)


The circum radius of the triangle
formed by the points (1,2,-3),(2,-3,1) and (-3,1,2) is:
A \( \cdot \sqrt{14} \)
B. 14
c. \( \sqrt{13} \)
D.


If \( \mathbf{f}(\mathbf{x})=\mathbf{x} \cdot \sin \frac{\mathbf{1}}{\boldsymbol{x}} \) for \( \boldsymbol{x} \neq \mathbf{0}, \mathbf{f}(\mathbf{0})=\mathbf{0} \)
then?
A. \( f \) is continuous at \( x=0 \)
B. \( f \) is differentiable at \( x=0 \)
\( \mathrm{c} \cdot f^{\prime}\left(0^{-}\right) \) exists but \( f^{\prime}\left(0^{+}\right) \) does not exist
D. \( f \) is discontinuous at \( x=0 \)


Which of the following is a condensation polymer?
A. Teflon
B. PVC
c. Polyester
D. Neoprene


Find the domain and range of the
following function:
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}2-\boldsymbol{x} & \boldsymbol{i f} \quad \mathbf{0}<\boldsymbol{x}<\mathbf{2} \\ \boldsymbol{x}-\mathbf{1} & \boldsymbol{i f} \quad \boldsymbol{3} \leq \boldsymbol{x}<\mathbf{4}\end{array}\right. \)


A man can swim in still water with a
velocity \( 5 \mathrm{m} / \mathrm{s} \). He wants to reach at
directly opposite point on the other bank
of a river which is flowing at a rate of \( 4 m / s . \) River is \( 15 m \) wide and the man can
run with twice the velocity as compared
with velocity of swimming. If he swims perpendicular to river flow and then run
along the bank, then time taken by him to reach the opposite point is:
A. 3 sec
B. less than 3 sec
c. 5 sec
D. 4.2 sec


In ballistic galvanometer, the frame on
which the coil is wound is non-metallic
to:
A. Avoid the production of induced emf
B. Avoid the production of eddy currents
c. Increase the production of eddy currents
D. Increase the production of induced emf


The acceleration of a body may be doubled by doubling its:
A. mass
B. momentum
c. velocity
D. force acting on it


Evaluate: \( \int \frac{5 x-2}{1+2 x+3 x} d x \)


Two copper balls, each weighting \( 10 g \) are kept in air \( 10 \mathrm{cm} \) apart. If one
electron from every \( 10^{6} \) atom is transferred from one ball to the other,
the coulomb force between them is
(atomic weight of copper is 63.5 )
A \( \cdot 2 \times 10^{10} \mathrm{N} \)
B \( .2 \times 10^{4} \mathrm{N} \)
\( \mathbf{c} \cdot 2 \times 10^{8} \mathrm{N} \)
D. \( 2 \times 10^{6} \mathrm{N} \)


\( \boldsymbol{g}(\boldsymbol{x})=\lim _{m \rightarrow \infty} \frac{\boldsymbol{x}^{m} \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{h}(\boldsymbol{x})+\boldsymbol{3}}{\boldsymbol{2} \boldsymbol{x}^{m}+\boldsymbol{4} \boldsymbol{x}+\mathbf{1}} \)
when \( x \neq 1 \) and \( g(1)=e^{3} \) such that
\( f(x), g(x) \) and \( h(x) \) are continuous function at \( \boldsymbol{x}=\mathbf{1} \) and \( \boldsymbol{f}(\mathbf{1})-\boldsymbol{h}(\mathbf{1})= \)
\( a(b-g(1)) \) then \( a+b \) is


The empirical formula of a compound of
molecular mass 120 is \( C H_{2} O . \) The
molecular formula of the compound is:
\( \mathbf{A} \cdot C_{2} H_{2} O_{2} \)
B \( \cdot C_{4} H_{8} O_{4} \)
c. \( C_{3} H_{6} O_{9} \)
D. none of the above


A bag contains some white and some
black balls, all of which are
distinguishable from each other, all combinations of balls being equally likely. The total number of balls in the
bag is \( 10 . \) If three balls are drawn at random and all of them are found to be
black, the probability that the bag contains 1 white and 9 black balls is :
A \( \cdot \frac{14}{55} \)
B. \( \frac{12}{55} \)
c. \( \frac{8}{55} \)
D. \( \frac{2}{11} \)


The sum of \( 4^{\text {th }} \) and \( 8^{\text {th }} \) term of an A.P. is
24 and the sum of \( 6^{\text {th }} \) and \( 10^{\text {th }} \) term is
34. Find the first term and the common
difference of A.P.


Phosgene is a common name for:
A. carbon tetrachloride
B. carbonyl dichloride
c. \( C O_{2} \) and \( P H_{3} \)
D. phosphoryl chloride


In kidney, the high capillary bed is found
A. In Bowman's capsule
B. Around anterior tubules
c. Around loop of Henle
D. Absent


Two waves \( Y_{1}=a \sin \omega t \) and \( Y_{2}= \)
\( \operatorname{asin}(\omega t+\delta) \) are producing
interference, then resultent intensity is:
A \( \cdot a^{2} \cos ^{2} \delta / 2 \)
B . \( 2 a^{2} \cos ^{2} \delta / 2 \)
c. \( 3 a^{2} \cos ^{2} \delta / 2 \)
D. \( 4 a^{2} \cos ^{2} \delta / 2 \)


\( \operatorname{Let} \boldsymbol{I}= \)
\( \left.\int_{3 n \pi}^{\left(n+\frac{1}{n}\right) 3 \pi} \frac{\mathbf{4} \boldsymbol{x} \boldsymbol{d} \boldsymbol{x}}{\left[\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}\right)+\left(\boldsymbol{a}^{2}-\boldsymbol{b}^{2}\right) \cos \frac{2 n \boldsymbol{x}}{3}\right.}\right] \)
(where \( \mathbf{a}, \mathbf{b}>\mathbf{0}) \)
prove that \( \boldsymbol{I}=\frac{\mathbf{9}\left(\mathbf{2} \boldsymbol{n}^{2}+\mathbf{1}\right) \boldsymbol{\pi}}{\boldsymbol{n}^{2}} \frac{\boldsymbol{a}^{2}-\boldsymbol{b}^{2}}{\boldsymbol{a}^{3} \boldsymbol{b}^{3}} \)


A random variable \( \boldsymbol{X} \) has the following probability distribution:
Determine
(i) \( k \)
(ii) \( \boldsymbol{P}(\boldsymbol{X}<\mathbf{3}) \)
(iii) \( \boldsymbol{P}(\boldsymbol{X}>\boldsymbol{6}) \)
(iv) \( \boldsymbol{P}(\mathbf{0}<\boldsymbol{X}<\mathbf{3}) \)
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline \( \mathrm{X} \) & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline \( \mathrm{P}(\mathrm{X}) \) & 0 & \( k \) & \( 2 k \) & \( 2 k \) & \( 3 k \) & \( k^{2} \) & \( 2 k^{2} \) & \( 7 k^{2}+k \) \\
\hline
\end{tabular}


If \( f(x)=2 \tan ^{-1} x+ \)
\( \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right), x>1, \) then \( f(5) \) is
equal to:
A . \( \pi \)
в.
\( \mathbf{c} \cdot 4 \tan ^{1}(5) \)
D. \( \tan ^{-1}\left(\frac{64}{155}\right) \)


We, humans, produce sound by using
A. oesophagus
B. larynx
c. thyroid Gland
D. mouth


Assertion
Statement \( 1: H g C l_{2} \) and \( S n C l_{2} \) exist
together in an aqueous solution.
Reason

Statement \( 2: S n C l_{2} \) is a strong
reducing agent.
A. Statement 1 is true, Statement 2 is true and Statement 2 is correct explanation for Statement
B. Statement 1 is true, Statement 2 is true and Statement 2 is not the correct explanation for Statement
c. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true


The orbital angular momentum
quantum number of the state \( S_{2} \) is:
A . 0
B.
\( c \cdot 2 \)
D. 3


How much water should be added to 20
ounces of a \( 20 \% \) acid solution to reduce
it to a \( 10 \% \) solution?
A. 5 ounces
B. 10 ounces
c. 20 ounces
D. 30 ounces


The trophic efficiency of producers, herbivores and carnivores are
respectively
A. \( 10 \%, 20 \%, 30 \% \)
В. \( 20 \%, 30 \%, 60 \% \)
c. \( 20 \%, 40 \%, 80 \% \)
D. Always \( 10 \% \)


Solve the following inequalities graphically in two-dimensional plane:
\( \boldsymbol{x}-\boldsymbol{y} \leq 2 \)


The formation of polyethylene from
calcium carbide takes places as follows
\( \boldsymbol{C a} \boldsymbol{C}_{2}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4} \)
\( \boldsymbol{n} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \rightarrow\left(\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}\right)_{n} \)
The amount of polyethylene obtained
from 64 kg of \( C a C_{2} \) is :
A. \( 14 \mathrm{kg} \)
B. \( 7 \mathrm{kg} \)
c. \( 21 \mathrm{kg} \)
D. \( 28 \mathrm{kg} \)


What is observed when sulphur dioxide
is passed through, lime water, water?
Also write the chemical equation for the reaction that takes place


Menstrual cycle occurs in
A. Female primates
B. Human females
C. Mammalian females
D. Rabbit


If \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{e}^{\boldsymbol{x}}}{\mathbf{1}+\boldsymbol{e}^{\boldsymbol{x}}}, \boldsymbol{A}=\int_{\boldsymbol{f}(-\boldsymbol{a})}^{f(\boldsymbol{a})} \boldsymbol{x} \boldsymbol{g}\{\boldsymbol{x}(\mathbf{1}- \)
\( \boldsymbol{x})\} \boldsymbol{d} \boldsymbol{x} \) and \( \boldsymbol{B}=\int_{\boldsymbol{f}(-\boldsymbol{a})}^{f(\boldsymbol{a})} \boldsymbol{g}\{\boldsymbol{x}(\boldsymbol{1}-\boldsymbol{x})\} \boldsymbol{d} \boldsymbol{x} \)
then \( \frac{B}{A} \) is equal to
\( A \cdot-1 \)
B . - -
\( c \cdot 2 \)
\( D \)


\( A \) and \( B \) are events with \( P(A)=0.5, P(B)= \)
0.4 and \( P(A \cap B)=0.3 . \) Find the
probability that:
(i) A does not occur
(ii) Neither \( A \) and nor \( B \) occurs


Myoglobin is present in red muscle
fibres to
A. Store oxygen to be utilized during muscle contraction
B. Remove oxygen to help in anerobic respiration
C. Compensate for lack of haemoglobin during anemia
D. Remove pyruvic acid formed during respiration


Which of the following reactions will
give \( \alpha- \) hydroxy acid as a product?
\( \mathbf{A} \cdot C H_{3}-C H O \frac{(i) N a C N / H C l}{(i i) H_{2} O / H^{\oplus} / \Delta} \)
в. \( C H_{3}-C H O+B r-C H_{2}- \)
\( \operatorname{COOC}_{2} H_{5} \frac{(i) Z_{n}}{(i i) N H_{4} C l / H O H} \)
\( (i i i) H O H / H^{\oplus} / \Delta \)
c. \( C H_{3}- \) COOH \( \stackrel{\text { NaOH } / \text { НОН }}{\longrightarrow} \)
D. All of these


Obturator foramen is found in
A. Pectoral girdle of rabbit
B. Pectoral girdle of frog
c. Pelvic girdle of rabbit
D. Pelvic girdle of frog


Treatment of waste water involves
physical, chemical, and biological processes, which remove
matter that contaminates
waste water.
A. physical
B. chemical and biological
c. both \( A \) and \( B \)
D. none of the above


Which one of the following is the correct
statement?
A. Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase
B. \( \mathrm{B}_{2} \mathrm{H}_{6} .2 \mathrm{NH}_{3} \) is known as inorganic benzene
C . Boric acid is a protonic acid
D. Beryllium exhibits coordination number of six


Moments are measured in:
A \( \cdot \frac{k g}{s} \)
B. Nm
c. \( N \times s \)
D. \( \frac{N}{s} \)


Find the mean of the following frequency distribution:
\( \begin{array}{llll}\text { Class } & 0- & 8- & 16 \\ \text { interval: } & 8 & 16 & 2\end{array} \) \( 16- \)
24 32
6 4 Frequency: \( \quad 5 \)


Distance travelled in nth second has the
units of
A. displacement
B. velocity
c. acceleration
D. momentum


Construct a triangle \( A B C \) whose
perimeter \( 12 \mathrm{cm} \) and whose base angles
are \( 50^{\circ} \) and \( 80^{\circ} \)


At \( 527^{\circ} C \) temperature the activation energy is \( 54.7 \mathrm{KJ} / \) mole. The value of
Arrhenius factor is \( 4 \times 10^{10} \). The rate
constant will be
A \( \cdot 12.28 \times 10^{11} \)
B . \( 10^{7} \)
c. \( 12.28 \times 10^{17} \)
D. \( 14.58 \times 10^{-13} \)


Growth/ annual rings are formed by the activity of
A. Cambium
B. Xylem
c. Phloem
D. Both xylem and phloem


Subtract \( 4 a b c \) from \( -6 a b c \)


The \( C-C \) bond length in ethane is:
A \( .1 .54 A^{\circ} \)
B . \( 1.34 A^{\circ} \)
c. \( 1.39 A^{\circ} \)
D. \( 1.2 A^{0} \)


A horizontal rod of length L and mass \( \mathrm{m} \) lying on the floor is fixed at one end and a force \( F \) is applied at an angle \( \theta \) with the horizontal. The torque experienced by the rod is
\( \mathbf{A} \cdot\left(m L^{2} \alpha\right) / 12 \)
В. \( \left(m L^{2} \alpha\right) / 3 \)
c. \( \left(m L^{2} \alpha\right) / 4 \)
D. \( \left(m L^{2} \alpha\right) / 2 \)


An aqueous solution of orthoboric acid
can be titrated against sodium hydroxide using phenolphthalein indicator only in presence of:
A. trans-glycerol
B. catechol
c. cis-glycerol
D. both (B) and (C)


The inequality \( 2^{\sin \theta}+2^{\cos \theta} \geq 2^{1-(1 / \sqrt{2})} \)
holds for all real values of \( \theta \)
A . True
B. False


toppr \( E \)
Q Type your question
If and is
from the given options.
\( A \)
\( B \)
\( c \)
D.


Synthetic fibres having almost common
property are:
A. nylon and polyster
B. nylon and plastics
c. polyster and plastics
D. all of the above


A black body is at a temperature of
\( 2880 \mathrm{K} . \) The energy of radiation emitted
by this body between wavelengths 499
nm and \( 500 \mathrm{nm} \) is \( U_{1} ; \) between \( 999 \mathrm{nm} \)
and \( 1000 \mathrm{nm} \) is \( U_{2} ; \) and between 1499
\( \mathrm{nm} \) and \( 1500 \mathrm{nm} \) is \( U_{3} . \) Then, (Wein's
constant \( \left.\boldsymbol{b}=\mathbf{2 . 8 8} \times \mathbf{1 0}^{\mathbf{6}} \boldsymbol{n m} \boldsymbol{K}\right) \)
A. \( U_{1}=0 \)
в. \( U_{3}=0 \)
\( \mathbf{c} \cdot U_{1}>U_{2} \)
D. \( U_{2}>U_{1} \)


\( [A r] 3 d^{10} 4 s^{1} \) electronic configuration
belongs to :
\( \mathbf{A} \cdot T i \)
B. \( T l \)
c. \( C u \)
D. \( V \)


A power transmission line feeds input at \( 2200 \mathrm{V} \) to a step-down transformer with its primary windings having 3000 turns. find the number of turns in the
secondary to get the power input at 220
\( \mathbf{V} \)


The oxidation number of \( \mathrm{N} \) and \( C l \) in
\( N O C l O_{4} \) respectively are :
\( A \cdot+2 \) and +7
B. +3 and +7
\( c \cdot-3 \) and +5
D. +2 and -7


The four angles of a quadrilateral are equal. Draw this quadrilateral in your notebook. Find each of them.
A. \( 60^{\circ}, 120^{\circ}, 30^{\circ}, 150^{\circ} \)
\( ^{\circ} \)
B. \( 60^{\circ}, 120^{\circ}, 60^{\circ}, 120^{\circ} \)
\( \mathbf{c} \cdot 90^{\circ}, 90^{\circ}, 90^{\circ}, 90^{\circ} \)
D. \( 60^{\circ}, 60^{\circ}, 120^{\circ}, 120^{\circ} \)


Water vapor is present in air only during
the monsoon.
A . True
B. False


Which of the following is not correct regarding electrolytic preparation of
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
A. Lead is used as cathode
B. 50\% \( H_{2} S O_{4} \) is used
c. Hydrogen is libreated as anode
D. Sulphuric acid undergo oxidation


If \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{W}, \boldsymbol{3} \leq \boldsymbol{x}<\mathbf{6}\}, \boldsymbol{B}= \)
\( \{\mathbf{3}, \boldsymbol{5}, \boldsymbol{7}\} \) and \( \boldsymbol{C}=\{\mathbf{2}, \boldsymbol{4}\} \)
find \( : \boldsymbol{n}(\boldsymbol{A}-\boldsymbol{B}) \)


When a coin is tossed at random, then
the probability of getting a head is
A . 0
B. \( \frac{1}{2} \)
\( c .1 \)
D. 2


Nude flower means
A. Absence of androecium
B. Absence of gynoecium
C. Absence of calyx and corolla
D. Both (A) and (B)


Solve:
\( x d y+y d x=x^{2} y d y \)


\( \hat{\text { i }} \) and \( \hat{j} \) are unit vectors along along \( x \) and \( y- \) axis respectively. What is the magnitude and direction of the vectors \( \hat{\mathbf{i}}+\hat{\text { jand }} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}} \) ?What are the
components of a vector \( A=2 \hat{i}+3 \hat{j} \) along the directions of \( \hat{i}+\hat{j} \) and \( \hat{i}-\hat{j} \)
? [You may use graphical method]


State Kirchhoffs law of electrical
networks.


Construct a quadrilateral ABCD, when:
\( \angle A=90^{\circ}, A B=4.6 \mathrm{cm}, B C=5.0 \mathrm{cm}, \mathrm{AD} \)
\( =6.0 \mathrm{cm} \) and \( \mathrm{CD}=4.2 \mathrm{cm} \)


A \( 0.66 k g \) ball is moving with a speed of
\( 100 m / s . \) The associated wavelength
will be:
\( \left(h=6.6 \times 10^{-34} J s\right) \)
В. \( 6.6 \times 10^{-34} m \)
c. \( 1 \times 10^{-35} m \)
D. \( 1 \times 10^{-32} \)


A triangle is formal using three wire \( A B, B C \) and \( C A \) and is placed in a vertical plane. Coefficient of friction for all three
wires is same. If \( \boldsymbol{w}_{1} \) and \( \boldsymbol{w}_{2} \) is the work
done by the friction in moving an object from \( A \) to \( B \) through \( C^{\prime} \) and \( C \)
respectively, then
A \( \cdot w_{1}=w_{2} \)
в. \( w_{1}<w_{2} \)
c. \( w_{1}>w_{2} \)
D. the relation depends on the length AC and BC


The compound \( I F_{7} \) is named as lodine heptafluoride
A. True
B. False


Domain of \( \boldsymbol{y}=\sqrt{\frac{\mathbf{1}-|\boldsymbol{x}|}{\mathbf{2}-|\boldsymbol{x}|} \mid} \)


Two vertices of a rectangle are on the
positive \( \mathbf{x} \) -axis. The other two vertices lie on the lines \( y=4 x \) and \( y=-5 x+6 \)
Then the maximum area of the
rectangle is?
\( A \cdot \frac{2}{3} \)
B. \( \frac{2}{4} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{4}{3} \)


The amount of solute required to prepare 10 litres of decimolar solution is
A . 0.01 mole
B. 0.2 mole
c. 0.05 mole
D. 1.0 mole


The treated water has a very low level of organic material and suspended matter. It is discharged into
A . sea
B. a river or into the ground
c. both \( A \) and \( B \)
D. none of the above


At what temperature do zinc and carbon
have equal affinity for oxygen?
A \( \cdot 1000^{\circ} \mathrm{C} \)
в. \( 1500^{\circ} \mathrm{C} \)
\( c \cdot 500^{\circ} C \)
D. \( 1200^{\circ} \mathrm{C} \)


Daniel cell operates under nonstandard
state conditions. If the equation of the cell reaction is multiplied by 2 then:
A. \( E \) and \( E^{\circ} \) remain unchanged
B. \( E \) is doubled
C. \( n \) remains unchanged in Nernst equation
D. \( Q \) is halved in Nernst equation


\( \ln \triangle A B C, D \) is the mid-point \( B C . \) If a line is drawn in such a way that it
bisects \( A D \) and \( A D \) and \( A C \) at \( E \) and
\( X \) respectively, then prove that \( \frac{\boldsymbol{E} \boldsymbol{X}}{\boldsymbol{B} \boldsymbol{E}}= \)
\( \frac{1}{3} \)


Show on a graph, the variation of
resistivity with temperature for a typical semiconductor.


Using elementary row transformations, find the inverse of the matrix \( \boldsymbol{A}= \)
\( \left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & 5 & 7 \\ -2 & -4 & -5\end{array}\right] \)


\( 1 \mathrm{mm} \mathrm{Hg} \) is equal to
\( A \cdot 1 \) atm
B . \( 1.013 \times 10^{5} \) Pa
c. 133.29 atm
D. \( 1.316 \times 10^{-3} \) atm


Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is?
\( \mathbf{A} \cdot 250 \Omega \)
B. \( 40 \Omega \)
c. \( 500 \Omega \)
D. 25 \Omega


\( C_{3} \) cycle predominantly operates in
A. Cytoplasm and mitochondria
B. Mitochondria and peroxysome
c. stroma
D. Stroma and grana of a chloroplast


The diagonal passing through origin of a quadrilateral formed by \( \boldsymbol{x}=\mathbf{0}, \boldsymbol{y}= \)
\( \mathbf{0}, \boldsymbol{x}+\boldsymbol{y}=\mathbf{1} \) and \( \boldsymbol{6} \boldsymbol{x}+\boldsymbol{y}=\mathbf{3} \) is
A \( .3 x-2 y=0 \)
в. \( 2 x-3 y=0 \)
c. \( 3 x+2 y=0 \)
D. None of these


State True or False.
In an electrode concentration cell, the
cell reaction \( \mathrm{Zn}\left(\mathrm{C}_{1}\right) \rightarrow \mathrm{Zn}\left(\mathrm{C}_{2}\right) \) will be
spontaneous if \( \mathbf{c}_{1}>\mathbf{c}_{2} \)
A. True
B. False


What is a material called, if it does not
allow electric current to flow through it? (Conductor, Insulator)


What happens when a charged balloon is placed near another balloon of the same charge?
A. Attract each other
B. Repel each other
c. Neither attract nor repel
D. All of the above


Diabetes is a disease in which the urine
contains
A. Sugar
B. Salt
\( c . \) Fat
D. Protein


The integral \( \int_{\pi / 12}^{\pi / 4} \frac{8 \cos 2 x}{(\tan x+\cot x)^{3}} d x \)
equals:
A \( \cdot \frac{15}{128} \)
в. \( \frac{15}{64} \)
c. \( \frac{13}{32} \)
D. \( \frac{13}{256} \)


During the first metaphase of meiosis,
the centromeres
A. Undergo division
B. Do not divide
c. Divide but do not separate
D. Are not identical


The enthalpy change of a reaction does not depend on
A. initial and final enthalpy change of reaction
B. state of reactants and products
c. different intermediate reactions
D. nature of reactants and products


If the momentum of a body is doubled, the kinetic energy is
A. Halved
B. Unchanged
c. Doubled
D. Becomes 4 times


A wire is stretched by a force \( F . \) If \( s \) is the strain developed and \( Y \) is Young's modulus of material of wire, then work
done per unit volume is
A \( \cdot \frac{Y s^{2}}{2} \)
B. \( \frac{s^{2}}{2 Y} \)
c. \( \frac{1}{2} F s \)
D. \( \frac{Y}{2 s^{2}} \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \tan ^{-1}\left[\frac{\boldsymbol{x}^{\mathbf{1} / 3}+\boldsymbol{a}^{\mathbf{1} / 3}}{\mathbf{1}-\boldsymbol{x}^{\mathbf{1} / 3} \boldsymbol{a}^{\mathbf{1} / 3}}\right] \)


Assertion: The setting sun appears to be red.
Reason: Scattering of light is directly proportional to the wavelength.
A. both assertion and reason are true but the reason is the correct explanation of assertion
B. both assertion and reason are true but the reason is not the correct explanation of assertion
c. assertion is true but reason is false
D. both the assertion and reason are false
E. reason is true but assertion is false


A student uses a magnetic compass to
perform a laboratory experiment in the Northern Hemisphere. She then carries the same magnetic compass with her to the Southern Hemisphere, taking care not to damage the compass in any way. When she reaches her destination at the equivalent latitude and longitude in the Southern Hemisphere, she prepares to perform the same laboratory experiment. The student looks at the compass before performing the experiment to see if the compass needle has changed. How has the compass changed?
A. The compass needle points \( 90^{\circ} \) to the left of the expected direction
B. The compass needle points \( 90^{\circ} \) to the right of the expected direction
c. The compass needle slowly rotates in a counter clockwise direction
D. The compass needle slowly rotates in a clockwis tion
as been no he co


A colourless salt gives a white ppt (soluble in ammonium acetate) and a
brown coloured pungent gas on reaction with conc. \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \) salt is:
\( \mathbf{A} \cdot B a\left(N O_{3}\right)_{2} \)
B. \( P b\left(N O_{3}\right)_{2} \)
c. \( \operatorname{NaNO}_{3} \)
D. \( N H_{4} N O_{3} \)


Explain Pauling's scale of electronegativity.


\( \lim _{x \rightarrow \infty} \frac{\cos x+\sin ^{2} x}{x+1} \)


What is the function of copper-T?
A. Checks mutation
B. Stops fertilization
c. stops zygote formation
D. Stops oblituation of blastocoel


Boyle's Law can be verified by :
a) Boyle's law apparatus
b) Quill tube apparatus
c) Regnault's apparatus
d) Jolly's bulb apparatus
A \( . \) a \( \& \) b are true
B. a \& c are true
\( c . \) b \& dare true
D. b \& c are true


A tangent \( P Q \) at a point \( P \) of a circle of
radius \( 5 \mathrm{cm} \) meets a line through the
centre \( O \) so that \( O Q=13 \mathrm{cm} . \) Find the
length of \( P Q \)


What is the dimensional formula of
dynamic viscosity?
\( \mathbf{A} \cdot\left[m^{1} L^{-1} T^{-2}\right] \)
B. \( \left[m^{1} L^{1} T^{-1}\right] \)
C. \( \left[m^{1} L^{-1} T^{-1}\right] \)
\( \mathbf{D} \cdot\left[m^{1} L^{1} T^{1}\right] \)


Explain the following terms giving a suitable example for each.
(i) Elastomers
(ii) Condensation polymer
(iii) Addition polymers


Depict the galvanic cell in which the
reaction \( Z n(s)+2 A g^{+}(a q) \rightarrow \)
\( Z n^{2+}(a q)+2 A g(s) \) takes place.
Further show:
(i) Which of the electrode is negatively charged?
(ii) The carriers of the current in the cell
(iii) Individual reaction at each
electrode


DNA differs from RNA in
A. Nature of sugar alone
B. Nature of purines alone
c. Nature of sugar and pyrimidines
D. All the above


In figure, \( \angle P O R=a^{\circ} \) and \( \angle Q O R=b^{\circ} \)
If \( a^{\circ}-b^{\circ}=60^{\circ} . \) Find angle \( a^{\circ} \) and \( b^{\circ} \)
A \( . \angle a=70^{\circ}, \angle b=110^{\circ} \)
В. \( \angle a=90^{\circ}, \angle b=90^{\circ} \)
C . \( \angle a=120^{\circ}, \angle b=60^{\circ} \)
D. \( \angle a=60^{\circ}, \angle b=120^{\circ} \)


A narrow tube is bent in the form of a
circle of radius \( R, \) as shown in the
figure. Two small holes \( S \) and \( D \) are made in the tube at the positions right angle to each other. A source placed at S generated a wave of intensity \( l_{0} \) which
is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point \( D \) where a detector is placed. The maximum value of \( \lambda \) to produce a
maxima at D is given by :
A \( . \pi R \)
В. \( 2 \pi R \)
c. \( \frac{\pi R}{2} \)
D. \( \frac{3 \pi R}{2} \)


The sums of \( n \) terms of two arithmetic
progressions are in the ratio \( 5 n+4 \)
\( 9 n+6 . \) Find the ratio of their 18 th
terms.


Define the term work function of a
metal.


Find \( a_{20} \) of a geometric sequence if the
first few terms of the sequence are \( \operatorname{given} \) by \( -\frac{1}{2}, \frac{1}{4},-\frac{1}{8}, \frac{1}{16}, \dots \)


Chlorine does not show hydrogen bonding in its compounds while nitrogen shows hydrogen bonding in its compounds. Identify the correct reason
A. Chlorine is not as highly electronegative as nitrogen
B. Chlorine has vacant d-orbitals while nitrogen has no vacant'd' sub shell
c. \( H-C l \) bond is stronger than \( N-H \) bond
D. chlorine has larger size than nitrogen


Evaluate \( \lim _{x \rightarrow 2} \frac{x-2}{x^{2}+x-6} \)


The value of \( \frac{6 \pi^{c}}{5} \) in sexagesimal
measure is
A . \( 144^{\circ} \)
B . \( 216^{\circ} \)
\( c \cdot 240^{9} \)
D. \( 120^{9} \)


Which of the following is not a green
house gas?
A. Methane
B. Carbon dioxide
c. Nitrous oxide
D. Ammonia


A \( 100 m L, 0.1 M \) solution of ammonium acetate is diluted by
adding \( 100 m L \) of water. The pH of the
resulting solution will be \( \left(p K_{a} \) of acetic \right.
acid is nearly equal o \( \left.p K_{b} \text { of } N H_{4} O H\right) \)
A . 4.9
B. 5.0
c. 7.0
D. 10.0


An equilateral triangle and a regular hexagon have equal perimeters. If the
area of the triangle is \( 12 d m^{2} \) then the
difference of their areas \( \left(\text { in } d m^{2}\right) \) is :
A .2
B. 4
\( c \cdot 6 \)
D. 18


In the case of uniform circular motion, which one of the following physical quantities does not remain constant?
A . mass
B. speedd
c. linear momentum
D. kinetic energy


A force of \( 1 \mathrm{N} \) acts upon a mass of \( 1 \mathrm{kg} \) for 1 second and gives it a momentum \( P_{1} \) and kinetic energy \( E_{1} . \) The same
force acts upon the same mass for a displacement of \( 1 \mathrm{m} \) and gives it a
momentum \( P_{2} \) and kinetic energy \( E_{2} \) Then, which of the following is correct?
\( \mathbf{A} \cdot P_{1}=P_{2}, E_{1}=E_{2} \)
B. \( P_{1}>P_{2}, E_{1}>E_{2} \)
c. \( P_{1}<P_{2}, E_{1}<E_{2} \)
D. \( P_{1}>P_{2}, E_{1}<E_{2} \)


The side of a rhombus is \( 10 \mathrm{cm} \) and one
diagonal is \( 16 \mathrm{cm} . \) The area of the
rhombus is
\( \mathbf{A} \cdot 96 c m^{2} \)
B. \( 95 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 94 c m^{2} \)
D. \( 93 c m^{2} \)


Find the value of \( c \) of Rolle's theorem for
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \) in [-1,1]
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. does not exist


The alkene \( C_{6} H_{10} \) producing
OHC \( \left(C H_{2}\right)_{4} C H O \) on ozonolysis is:
A. 1 -hexene
B. 3-hexene
c. cyclohexene
D. 1-methylcyclohexene


A point ' \( O^{\prime} \) marked on the surface of a
glass sphere of diameter \( 20 \mathrm{cm} \) is
viewed through glass from the position
directly opposite to the point ' \( O \) '. If the
refractive index of the glass is \( 1.5, \) find the position of the image formed. Also, draw the ray diagram for the formation
of the image.


Identify the correct order of \( \alpha, \beta \) and \( \gamma \) with reference to their penetrating power in decreasing order. I) \( \boldsymbol{\alpha} \) -ray II) \( \boldsymbol{\gamma} \)
-ray III) \( \beta \) -ray
\( \mathbf{A} \cdot \) ॥,॥।,
B. ॥,|,|||
c. ।,॥,॥
D. III,,,III


Part of the brain acting as relay centre
is
A. Thalamus
B. Hypothalamus
D. Pituitary


Halide containing halogen attached to
\( s p^{2} \) carbon is/are:
This question has multiple correct options
A. allylic halide
B. benzylic halide
c. aryl halide
D. vinyl halide


Animals eating own faecal matter are
A. sanguivorous
B. Frugivorous
c. coprophagous
D. Deteritivorous


A man sold two paintings at \( R s 924 \)
each. On one he gains \( 20 \% \) and on the
other he loses \( 20 \% \). How much does he
gain or lose in the whole transaction?


If you go on increasing the stretching force on a wire a guitar, its frequency:
A. Increases
B. Decreases
c. Remains unchanged
D. None of the above


\( f f(x)=\left|\begin{array}{ccc}\sin x & 1 & 0 \\ 1 & 2 \sin x & 1 \\ 0 & 1 & 2 \sin x\end{array}\right| \) then
\( \int_{-\pi / 2}^{\pi / 2} f(x) d x \) equals to
\( A \)
B.
\( c \)
D. \( \frac{3 \pi}{2} \)


Name the phenomenon which shows the
quantum nature of electromagnetic radiation.


Two spherical bodies of masses \( 2 M \)
and \( M \) and of radii \( 3 R \) and \( R \)
respectively are held at a distance \( 16 R \)
from each other in free space. When they are released, the start approaching
each other due to the gravitational force of attraction, then find
(a) the ratio of their accelerations
during their motion
(b) their velocities at the time of
impact.


The probability of electrons to be found in the condition band of an intrinsic
semiconductor 6 at a finite
temperature.
A. Increases exponentially with increasing band gap
B. Decreases exponentially with increasing band gap
c. Decreases with increasing temperature
D. Is independent of the temperature and the band gar


On passing white light through a glass prism. Which colour ray will deviate maximum towards its base?
A. Red
B. Yellow
c. Вlue
D. Violet


Find the multiplicative inverse of
\( \frac{\sqrt{3}}{2}-\frac{1}{2} i \)


Solubility of salt \( M_{2} X_{3} \) is \( y \operatorname{mol} d m^{-3} \)
The solubility product of the salt will be:
\( A \cdot 6 y^{4} \)
В . \( 64 y^{4} \)
\( c \cdot 36 y^{5} \)
D. \( 108 y^{5} \)


A transmitter transmits at a wavelength
of \( 300 \mathrm{m} . \) A condenser of capacitance \( 2.4 \mu F \) is being used. The value of the
inductance for the resonant circuit is
approximately
B. \( 10^{-6} \) Н \( z \)
\( c \cdot 10^{-8} \mathrm{Hz} \)
D. \( 10^{-10} \) Н \( z \)


Explain any six principles of green
chemistry.


Draw the structure and write the
formula of methane.


helps in writing with a pen or pencil on a paper
A. Magnetic force
B. Electric charge
c. chemical force
D. Frictional force


In how many ways can 6 boys and 5 girls can be seated in a row such that no two
girls are together?
A . \( 6 ! 5 \)
в. \( 2 \times 5 ! 5 \)
c. \( 6 ! \times^{7} P_{5} \)
D. \( 6 ! 6 ! \)


Consider three vectors \( \overrightarrow{\boldsymbol{p}}=\boldsymbol{i}+\boldsymbol{j}+ \)
\( \boldsymbol{k}, \overrightarrow{\boldsymbol{q}}=2 \boldsymbol{i}+\boldsymbol{4} \boldsymbol{j}-\boldsymbol{k} \) and \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{i}+\boldsymbol{j}+\boldsymbol{3} \boldsymbol{k} . \)
\( p, q \) and \( r \) denotes the position vector of three non-collinear points, then the equation of the plane containing these points is
A. \( 2 x-3 y+1=0 \)
B. \( x-3 y+2 z=0 \)
c. \( 3 x-y+z-3=0 \)
D. \( 3 x-y-2=0 \)


If in a triangle \( A B C, \sin A \cos B=1 / 4 \)
and \( 3 \tan A=\tan B, \) then the triangle
is
A. right angled
B. equilateral
c. isosceles
D. none of these


How many energetically equivalent resonance structures exist for the
oxalate dianion?
\( A \)
B. 2
\( c .3 \)
\( D \)


28. mark the odd one w.r.t kingdom
fungi.
A. They reproduce asexually and sexually
B. They show a great diversity in structure and habitat
C. most of fungi are saprophytic in their mode of nutrition
D. They do not reproduce by zoospores


Fructose is obtained from sweet fruits
and honey.
A . True
B. False


Addition of which solute in 1.0 molar \( K I \)
solution will not cause a change in
vapour pressure:
A \( \cdot I_{2} \)
B. water
c. \( H g I_{2} \)
D. addition of \( N a_{2} S O_{4} \)


If \( y=\sec ^{-1}\left(\frac{1}{2 x^{2}-1}\right) \) then \( \frac{d y}{d x}=? \)
A \( \cdot \frac{-2}{\left(1+x^{2}\right)} \)
B. \( \frac{-2}{\left(1-x^{2}\right)} \)
c. \( \frac{-2}{\sqrt{1-x^{2}}} \)
D. none of these


If \( \boldsymbol{\theta}+\boldsymbol{\phi}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}}, \) then \( (\mathbf{1}+\tan \boldsymbol{\theta})(\mathbf{1}+ \)
\( \tan \phi) \) is equal to
A .
B. 2
\( c \cdot \frac{5}{2} \)
D.


Find the number of the
molecule(s)/ion(s) having tetrahedral
geometry from the following.
\( O P F_{3}, S_{2} O_{3}^{2-}, X e O_{4}, S F_{4}, T e C l_{4}, N H \)


Explain the major classes of enzymes.


A first order reaction is half-completed
in 45 minutes. How long does it need for \( 99.9 \% \) of the reaction to be completed?
\( A \cdot 20 \) hours
B. 10 hours
c. \( 7 \frac{3}{10} \) hours
D. 5 hours


A diffraction pattern is obtained by making blue light incident on a narrow slit. If blue light is replaced by red light, then the diffraction bands
A. disappear
B. become broader
c. become narrower
D. remain same


If \( A \) and \( B \) are square matrices of order
3 such that \( |\boldsymbol{A}|=-\mathbf{1},|\boldsymbol{B}|=\mathbf{3}, \) then
\( |\mathbf{3} \boldsymbol{A} \boldsymbol{B}|= \)
A . -9
B. -81
c. -27
D. 81


Starting from rest, a fan takes ten seconds to attain the maximum speed
of 600 rp (revolutions per minute)
Assuming constant acceleration, find the time taken by the fan in attaining half the maximum speed.


Choose the correct answers from the
alternatives given :
Substrate-level phosphorylation takes place in
A. Krebs cycle and the transition reaction
B. glycolysis and the electron transport system
c. electron transport system and the transition reaction
D. glycolysis and the Krebs cycle


Stand electrode potential are; \( \boldsymbol{F e}^{+2} / \mathrm{Fe} \quad \mathrm{E}=0.44 \)
\( \boldsymbol{F} \boldsymbol{e}^{+\boldsymbol{3}} / \boldsymbol{F} \boldsymbol{e}^{+\mathbf{2}} \quad \mathbf{E}=\mathbf{0 . 7 7} \)
If \( F e^{+2}, F e^{+3} \) and \( \mathrm{Fe} \) block re kept
together, then:
A \( \cdot F e^{+3} \) increases
B. \( F e^{+3} \) decreases
c. \( \frac{F e^{+2}}{F e^{+3}} \) reamins unchanged
D. \( F e^{+2} \) decreases


Dimethyl ether and ethyl alcohol are
A. Chain isomers
B. Position isomers
c. Functional isomers
D. Metamers


What is the concentration of
\( C H_{3} C O O H \) which can be added to 0.5 M HCOOH solution so that dissociation
of both is same.
[Given that \( : \boldsymbol{K}_{\boldsymbol{C H}_{3} \text { COOH}}=\mathbf{1 . 8} \times \)
\( \mathbf{1 0}^{-5}, \quad \boldsymbol{K}_{\boldsymbol{H} \mathrm{COOH}}=\mathbf{2 . 4} \times \mathbf{1 0}^{-4} \mathbf{j} \)
(as nearest integer)


The formula of
dichlorobis(urea)copper(II) is:
A \( \cdot\left[C u\left(O=C\left(N H_{2}\right)_{2}\right)_{2}\right] C l_{2} \)
в. \( \left[C u C l_{2}\left(O=C\left(N H_{2}\right)_{2}\right)_{2}\right] \)
c. \( \left[C u\left(O=C\left(N H_{2}\right)_{2}\right)\right] C l \)
D \( \cdot\left[C u C l_{2}\left(O=C\left(N H_{2}\right)_{2}\right) H_{2}\right] \)


If the latus-rectum of an ellipse is one half of its minor axis, then its
eccentricity is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{\sqrt{2}} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{\sqrt{3}}{4} \)


A function \( f(x) \) is defined as \( f(x)= \)
\( \boldsymbol{x}^{2}+\mathbf{3} . \) Find \( \boldsymbol{f}(\mathbf{0}), \boldsymbol{f}(\mathbf{1}), \boldsymbol{f}\left(\boldsymbol{x}^{2}\right), \boldsymbol{f}(\boldsymbol{x}+\mathbf{1}) \)
and \( \boldsymbol{f}(\boldsymbol{f}(\mathbf{1})) \)


The following question is based on simple arithmetic principles. Find the right answer from the given
alternatives. \( \frac{26}{4}+\frac{14}{3}=? \)
A. 11.0
в. \( _{10} \frac{1}{6} \)
c. \( _{11} \frac{1}{6} \)
D. \( _{12} \frac{1}{5} \)
E \( \cdot 11 \frac{2}{3} \)


A circular pond is of diameter \( 17.5 \mathrm{m} \). It is surrounded by a \( 2 \mathrm{m} \) wide path. Find the cost of constructing the path at the
rate of Rs. 25 per square metre (Use \( \pi= \)
3.14)


Natural rubber or raw rubber consists of
basic material latex which is a
dispersion of isoprene. During the treatment, this isoprene forms a high molecular weight polymer of isoprene. Natural rubber can be obtained from
five hundred different species of plants. Consider the following properties of
rubber,
(i) Tensile strength of vulcanized rubber is almost ten times more than raw
rubber.
(ii) The elasticity of the raw rubber is very high. Choose the correct option.
A \( \cdot \) (i) is true (ii) is false.
B. (i) is false (ii) is true.
c. Both (i) and (ii) are true.
D. Both (i) and (ii) are false.


\( \left(\boldsymbol{C O}+\boldsymbol{H}_{2}\right)+\boldsymbol{H}_{2}^{\boldsymbol{6} 73 \boldsymbol{k}, 300 a t \boldsymbol{m}, / C r_{2}} \overrightarrow{\boldsymbol{O}_{3}-\boldsymbol{Z} n \boldsymbol{O}} \)
The above shown reaction may by used for manufacture of:
A. \( H C H O \)
в. \( C H_{3} \) СООН
с. НСООН
D. \( C H_{3} O H \)


\( f(x)=\tan ^{-1} x-x \) is \( _{-1} \)
\( \boldsymbol{R} \)
A. increasing to \( R \)
B. decreasing to \( R \)
C . increasing on \( R^{+} \)
D. increasing on \( (-\infty, 0) \)


The most acidic oxide among the following is:
A. \( C l_{2} O_{5} \)
в. \( C l_{2} O \)
\( \mathbf{c} \cdot C l_{2} O_{3} \)
D. \( C l_{2} O_{7} \)


The differential equation of all nonhorizontal lines in a plane is:
A \( \cdot \frac{d^{2} y}{d x^{2}}=0 \)
B. \( \frac{d^{2} x}{d y^{2}}=0 \)
c. \( \frac{d y}{d x}=0 \)
D. \( \frac{d x}{d y}=0 \)


ntegrate \( \frac{x^{3}+3 x+2}{\left(x^{2}+1\right)^{2}(x+1)} d x \)


If a cube is split into 'n' equal small cubes, what fraction of the bigger cube is the thermal capacity of the smaller
cubes ?


A die is thrown 400 times, the frequency of the outcomes of the events are given
as under.
outcome ' \( \mathbf{3} \) 3. \( \mathbf{2} \) 4
Frequency 70
65
60 1 75
Find the probability of occurrence of an odd number.
A ' the probability of occurrence of odd number \( =\frac{5}{7} \)
B. The probability of occurrence of odd number \( =\frac{9}{2} \)
C ' the probability of occurrence of odd number \( =\frac{193}{400} \)
D. The probability of occurrence of odd number \( =\frac{200}{299} \)


Assertion \( (A): \ln B r F_{3} \) oxidation state
of \( \boldsymbol{F} \) is \( +\mathbf{3} \)
Reason (R): Electronegativity of \( \boldsymbol{F} \) is more than that of bromine.
A. A and R are true, R is correct explanation of A
B. A and R are true, R is not correct explanation of A
c. A is true, but R is false
D. A is false, but R is true


The graph of the equation \( y=x^{2}- \)
\( 4 x+5 \) has its lowest point at
A \( .(2,1) \)
в. (-2,1)
c. (-2,-1)
D. (2,-1)


For the reaction \( 2 A l+F e_{2} O_{3} \longrightarrow \)
\( 2 F e+A l_{2} O_{3}, \) the standard heat
enthalpy of \( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3} \) and \( \boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{3} \) are
-196.5 and -399.1 kcal respectively.
\( \Delta H^{\circ} \) for the reaction is:
\( \mathbf{A} \cdot-252.4 k c a l \)
в. -135.5 kcal
c. \( -202.6 k c a l \)
D. none of the above


The most useful classification of drugs
for medicinal chemists is
A. on the basis of chemical structure
B. on the basis of drug action
c. on the basis of molecular targets
D. on the basis of pharmacological effect


-CHO group is
A. \( + \) ME and tle group
B. -ME and -IE group
C . +ME and -IE group
D. -ME and +IE group


An ink container of cylindrical shape is filled with ink upto \( 91 \% . \) Ball pen refills of length \( 12 \mathrm{cm} \) and inner diameter 2 \( \mathrm{mm} \) are filled upto \( 84 \% \). If the height and radius of the ink container are 14
\( \mathrm{cm} \) and \( 6 \mathrm{cm} \) respectively, find the number of refills that can be filled with
this ink.


Which group of cone-bearing plants had a fern-like appearence but possessed the primitive type of seed and are fossil seed ferns?
A. Gnetales
B. Coniferales
c. Ginkgoales
D. Cycadofilicales or Pteridospermales


In moist air, iron is oxidized to give:
\( A \cdot \) iron \( [I I] \) oxide
B. iron \( [I I I] \) oxide
c. iron[II] hydroxide
D. iron[II] sulphide


A man walks \( 8 \mathrm{m} \) towards East and then
\( 6 \mathrm{m} \) towards North. His magnitude of displacement is equal to:
A . \( 10 \mathrm{m} \)
B. 14 \( m \)
\( c \cdot 2 m \)
D. zero


Coulomb's law relates two charges and
distance between them describing the electric force as being:
A. proportional to the sum of the charges
B. inversely proportional to the distance between charges
C. proportional to the product of the charges and inversely proportional to the distance
D. proportional to the product of the charges and inversely proportional to the square of the distance


An automobile financier claims to be
lending money at simple interest, but he includes the interest every six
months for calculating the principal. If he is charging an interest of \( 10 \% \), the effective rate of interest becomes
A . \( 10 \% \)
B. \( 10.25 \% \)
c. \( 10.5 \% \)
D. \( 15 \% \)


A flask of \( 4.48 \mathrm{L} \) capacity contains a
mixture of \( N_{2} \) and \( H_{2} \) at \( 0^{\circ} \mathrm{C} \) and 1 atm
pressure. If the mixture is made to react
to form \( N H_{3} \) gas at the same temperature, the pressure in the flask reduces to 0.75 atm. The partial pressure of \( N H_{3} \) gas in the final mixture is?
A. 0.33 atm
B. 0.50 atm
c. 0.66 atm
D. 0.25 atm


\( \lim _{x \rightarrow \infty} x\left(a^{\frac{1}{x}}-b^{\frac{1}{x}}\right)= \)
A .
в. \( \log _{e} a / b \)
c. \( \log _{e}(a b) \)
D.


Algae and other submerged green plants often float in water during
daytime and sink at night because
A. Trapping of oxygen bubbles during the day in their photosynthesis
B. Release of absorbed air by warming of water
c. They become light due to the consumption of food
D. They come up to enjoy sunshine


\( f(x)=\left|\begin{array}{ccc}a^{-x} & e^{x \log _{e} a} & x^{2} \\ a^{-3 x} & e^{3 x \log _{e} a} & x^{4} \\ a^{-5 x} & e^{5 x \log _{e} a} & 1\end{array}\right|, \) then
A \( \cdot g(x)+g(-x)=0 \)
B . \( g(x)-g(-x)=0 \)
C. \( g(x) \times g(-x)=0 \)
D. none of these


Ine v-I grapn ror a conauctor at
temperature \( T_{1} \) and \( T_{2} \) are as shown in
the fig. The term \( \left(T_{2}-T_{1}\right) \) is
proportional to
A \( \cdot \frac{\sin 2 \theta}{\sin ^{2} \theta} \)
B. \( \frac{\cot 2 \theta}{\sin ^{2} \theta} \)
c. \( \frac{\cos 2 \theta}{\sin 2 \theta} \)
D. \( \frac{\tan 2 \theta}{\sin ^{2} \theta} \)


Fill in the blanks
Property of metal by which they can be beaten into sheets


(a) Draw electron dot structure of
Sodium (Na), Oxygen (O) and Magnesium (Mg).
(b) Why do ionic compounds have high melting points?


A bag contains a certain number of
balls, some of which are white;a ball is drawn and replaced, another is then drawn and replaced' and so on. If p be the chance of white balls that is most
likely to have been drawn in n trials. For
\( p=\frac{1}{2} \) and \( n=12, \) the number of white
balls required to be drawn is \( k \). Find the
value of \( k \)


"Methodus plantarum nova" is a famous publication of which one of the following taxonomists?
A. Engler and Prantl
B. Carolus Linnaeus
c. Bentham and Hooker
D. John Ray


The set of all points where the function \( \mathbf{f}(\mathbf{x})=\sqrt{\mathbf{1}-\mathbf{e}^{-\mathbf{x}^{2}}} \) is differentiable is
A. \( (0, \infty) \)
)
B \( \cdot(-\infty, \infty) \)
c. \( (-\infty, \infty)-\{0\} \)
D. \( (-1, \infty) \)


Balance the following equation by ion electron method:
\( \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3}+\boldsymbol{N} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}^{+}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \boldsymbol{H}_{3} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}+\boldsymbol{N} \boldsymbol{O}+\boldsymbol{S} \)


The process of conversion of sodium phenoxide to phenol during the preparation phenol from benzene sulphonic acid is called as
reaction
A. neutralization
B. acidification
c. dehydration
D. none


A high fever is dangerous to human body because it
A. Denatures enzymes
B. Inactivates enzymes
c. coagulates blood
D. Boils fluids inside body


Assertion: A white source of light during interference forms only white and black
fringes. Reason: Width of fringe is inversely proportional to the wavelength of the light used.
A. If both assertion and reason are true but the reason is the correct explanation of assertion
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false
E. If reason is true but assertion is false


Groundwater gets recharged by the
process of:
A. pumping
B. heavy rainfall
c. infiltration
D. None of the above


In a region an electric field \( \mathrm{E}=15 \mathrm{N} / \mathrm{C} \)
making an angle of \( 30^{\circ} \) with the horizontal plane is present. A ball having charge \( 2 \mathrm{C}, \) mass \( 3 \mathrm{kg} \) and coefficient of restitution with ground
\( 1 / 2 \) is projected at an angle of \( 30^{\circ} \) with the horizontal in the direction of electric field with speed \( 20 \mathrm{m} / \mathrm{s} \), the horizontal distance travelled by ball from first drop to the second drop is equal to \( 10 x \sqrt{3} m \) The value of \( x \) is:


Which one of the following molecules has the octahedral structure?
\( \mathbf{A} \cdot B e C l_{2} \)
в. \( \operatorname{Se} F_{6} \)
\( c . B F 3 \)
D. PF5
E . \( C F 4 \)


First successful animal clone was
A. Dolly goat
B. Dolly sheep
c. Molly goat
D. Molly sheep


After absorbing a slowly moving neutron of mass \( m_{N} \) (momentum \( \sim 0 \) )
a nucleus of mass \( M \) breaks into two
nuclei of masses \( m_{1} \) and
\( \mathbf{5} \boldsymbol{m}_{1}\left(\boldsymbol{6} \boldsymbol{m}_{1}=\boldsymbol{M}+\boldsymbol{m}_{N}\right) \) respectively. If
the de-Broglie wavelength of the
nucleus with mass \( m_{1} \) is \( \lambda \), the de
Broglie wavelength of the other nucleus will be:
\( A \cdot \lambda \)
в. \( 25 \lambda \)
\( c \cdot 5 \lambda \)
D. \( \lambda / 5 \)


The molarity of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) in a sample
which has density \( 1.4 \mathrm{g} / \mathrm{mL} \) and mass percentage of \( 63 \% \) is
[Molecular Weight of \( \left.\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}=\boldsymbol{6 3}\right] \)


Oxygen in lungs ultimately reaches
A. Alveoli
B. Trachea
c. Bronchus
D. Bronchioles


Find the cube of the following binomial expressions:
\( 4-\frac{1}{3 x} \)


The value of \( \sin \left(2 \sin ^{-1} \mathbf{0 . 8}\right) \)
A \( \cdot \frac{1}{25} \)
в. \( \frac{25}{24} \)
c. \( \frac{24}{25} \)
D. none


The properties of the elements, as well as the formulae and properties of their compounds depend in a periodic manner on the atomic weights of the elements. This periodic law was given by :
A. J.L. Meyer
B. John A.R. Newlands
c. Dobernier
D. D.I. Mendeleev


Standard deviation is calculated from
the Harmonic Mean (HM)
A . Always
B. Sometimes
c. Never
D. None of these


A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The velocity of the shell is
A \( \cdot 102 \mathrm{ms}^{-1} \)
B. 82 \( m s^{-1} \)
\( \mathbf{c} \cdot \) 41 \( m s^{-} \)
D. \( 120 \mathrm{ms}^{-1} \)


The value of \( \int_{-\pi}^{\pi} \frac{\cos ^{2} x}{1+a^{x}} d x, a>0 \) is
\( \mathbf{A} \cdot \pi / 2 \)
в. \( a \pi \)
c. \( \pi \)
D. \( 2 \pi \)


A coil of area \( 80 \mathrm{cm}^{2} \) and number of
turns 50 is rotating about an axis perpendicular to a magnetic field of 0.05 Tesla at 2000 rotations per minute The maximum value of emf induced in
¡it will be
A . \( 200 \pi \) volt
в. \( \frac{10 \pi}{3} \) volt
c. \( \frac{4 \pi}{3} \) volt
D. \( \frac{2}{3} \) volt


A circular conductor of radius \( 5 \mathrm{cm} \)
produce magnetic field of \( 7 \times 10^{-6} \mathrm{T} \)
The current flows through the conductor is
A. 3.0 A
B. 2.25 A
c. 4.5 A
D. 0.56 A


Activated charcoal is prepared by:
\( \mathbf{A} \cdot \) Adding \( B a_{3}\left(P O_{4}\right)_{2} \) to charcoal
B. Treatment with cone. \( H N O_{3} \)
C. Heating charcoal with steam to make it more porous
D. Adding silica to charcoal


Which of the followings is a tricarboxylic acid?
A . Citric acid
B. Malonic acid
c. succinic acid
D. Malic acid


Choose the correct answers from the
following given. Which of the following components of blood does not enter the nephron?
A. Plasma proteins
B. Glucose
c. sodium \( \left(N a^{+}\right) \) ions
D. urea


Write the formulas for the following coordination compounds:
Tetraamminediaquacobalt
(III) chloride


\( N H_{3} \) can enter into complex formation
due to:
A. hydrogen bonding
B. coordinate bond
c. covalent bond
D. ionic bond


Trimethylamine is a pyramidal molecule and formamide is a planar molecule. Hybridisation of nitrogen in both is:
B . \( s p^{3}, s p^{2} \)
\( \mathrm{c} \cdot s p^{3}, s p^{3} \)
D. \( s p^{2}, s p \)


The perianth term used when
A. Androecium and gynoecium are similar
B. Calyx and corolla are similar
C. Androecium and calyx are similar
D. Corolla and gynoecium are similar


A big irregular shaped vessel container water, the specific conductance of which was \( 2.56 \times 10^{-5} \mathrm{mhocm}^{-1} .500 \mathrm{g} \)
of \( N a C l \) was the added to the water and
the specific conductance after the addition of \( N a C l, \) was found to be
\( 3.10 \times 10^{-5} \mathrm{mhocm}^{-1} . \) The capacity of
the vessel if it is fulfilled with water is :
\( \left(\lambda_{\infty} N a C l=149.9\right) \)
B . \( V=2.59 \times 10^{6} \mathrm{cm}^{-3} \)
c. \( V=3.14 \times 10^{9} \mathrm{cm}^{-3} \)
D. none of the above


Calculate the molality of a solution of
Ethanol \( \left(C_{2} H_{5} O H\right) \) in water in which
the mole fraction of ethanol is 0.040
A. \( 4.42 \mathrm{mol} / \mathrm{kg} \)
B. 2.31 mol/kg
c. \( 5.23 \mathrm{mol} / \mathrm{kg} \)
D. none of these


Define the term and give one example
Bilateral symmetry


Find the acceleration of the point \( \boldsymbol{K} \)
A \( \cdot w=\frac{F\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} \)
B. \( w=\frac{F\left(3 m_{1}+m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} \)
c. \( w=\frac{F\left(m_{1}+m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} \)
D. \( w=\frac{F\left(m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} \)


A solute \( X \) when dissolved in a solvent
associates to form a pentamer. The value of van't Hoff factor ( \( i \) ) for the
solute will be?
A . 0.5
B. 5
\( c .0 .2 \)
D. \( 0 . \)


Which part of the pond ecosystem does not get affected by the temperature?
A. Epilimnion
B. Metalimnion
c. Hypolimnion
D. All of the above


Three cards are drawn from a bag
containing \( \mathrm{m} \) cards marked \( 1,2,3 \ldots . . n \) The probability that they form a
sequence is
A \( \cdot \frac{6}{n(n-1)} \)
B. \( \frac{3}{n(n-3)} \)
c. \( \frac{12}{n(n-2)} \)
D. \( \frac{3}{n(n-1)} \)


If \( \vec{n} \) is a unit vector in the direction of
the vector \( \vec{A}, \) then:
\( \mathbf{A} \cdot \vec{n}=|\vec{A}| / \vec{A} \)
В . \( \vec{n}=\vec{n} \times \vec{n} \)
C \( \cdot \vec{n}=\vec{A} /|\vec{A}| \)
D . \( \vec{n}=\vec{A}|\vec{A}| \)


Pharynx is connected with tympanic
cavity through
A . Glottis
B. Gullet
c. Eustachian tubes
D. Internal naress


A thief in a stolen car passes through a police check post at his top speed of
\( 90 k m h^{-1} . \) A motorcycle cop, reacting after \( 2 s, \) accelerates from rest at \( 5 m s^{-2} . \) His top speed being \( 108 k m h^{-1} . \) Find the maximum
separation between policemen and
thief
\( \mathbf{A} \cdot-112.5 m \)
B. \( 115 \mathrm{m} \)
\( c .116 .5 m \)
D. None of these


Which color should be used to increase
the resolving power of a microscope
A . violet
B. red
c. yellow
D. green


In the metal carbonyls of the general
formula \( M(C O)_{x} \) where \( M= \) metal
\( x=4, \) the metal is bonded to:
A. Carbon and oxygen
B. Carbon
c. oxygen
D. co triple bond


A metal bar of \( 70 \mathrm{cm} \) long and \( 4 \mathrm{kg} \) in mass supported on two knife edges placed \( 20 \mathrm{cm} \) from each end. A \( 6 \mathrm{kg} \) load is suspended at \( 30 \mathrm{cm} \) from on end.
Find the normal reaction at the knife-
edge. (assume it to be of uniform cross
section and homogeneous)
\( A \cdot 55 \mathrm{N} \) at \( K_{1} \) and \( 33 \mathrm{N} \) at \( K_{2} \)
B. \( 45 \mathrm{N} \) at \( K_{1} \) and \( 53 \mathrm{N} \) at \( K_{2} \)
c. \( 55 \mathrm{N} \) at \( K_{1} \) and \( 43 \mathrm{N} \) at \( K_{2} \)
D. 43 N at \( K_{1} \) and \( 55 \mathrm{N} \) at \( K_{2} \)


Upon mixing \( 45.0 m L \) of \( 0.25 M \) lead
nitrate solution with \( 25 m L \) of \( 0.1 M \)
chromic sulphate solution, precipitation of lead sulphate takes
place. How many moles of lead
sulphate are formed? Also, calculate the
molar concentrations of the species left behind in the final solution. Assume
that lead sulphate is completely insoluble.


Prove that the median from the vertex of
an isosceles triangle is the bisector of vertical angle.


Describe the principle involved in each of the following process of metallurgy.
a) Froth Floatation method
b) Electrolytic Refining of Metals
c) Zone refining of Metal


In case of A.C, circuit, Ohm's law holds
good for
a) Peak values of voltage and current
b) Effective values of voltage and
current
c) Instantaneous values of voltage and
current
A. only a is true
B. only a and b are true
c. only c is true
D. a, b anc c are true


The force between two short electric
dipole placed on the same axis at a distance \( R, \) varies as?
\( \mathbf{A} \cdot R^{-1} \)
B. \( R^{-2} \)
\( c \cdot R^{-3} \)
D. \( R^{-4} \)


Choose the correct answer from the
alternatives given.

A plane EM wave travelling along zdirection is described by \( \overrightarrow{\boldsymbol{E}}= \) \( E_{0} \sin (k z-\omega t) \hat{i} \) and \( B=B_{0} \sin (k z- \)
\( \omega t) \hat{j} \)
A. the avrage energy density of the wave is given by \( u_{a v}=\frac{1}{4} \varepsilon_{0} E_{0}^{2}+\frac{1}{4} \frac{B_{0}^{2}}{\mu} \)
B. The time averaged intensity of the wave is given \( I_{a v}= \) \( \frac{1}{2} c \varepsilon_{0} E_{0}^{2} \)
c. Both (a) and (b)
D. None of these


The energy required to excite the electron in the atom from \( n=1 \) to \( n= \)
2, when the ionization enthalpy of a
hydrogen atom is \( 1.312 \times 10^{6} J / \) mol
will be:
(in the unit of \( 10^{5} \) ).
A . 8.53
B. 7.51
c. 8.92
D. 9.86


Which of the following processes
involves fertilization?
A. Asexual reproduction
B. Metamorphosis
c. Sexual reproduction
D. None of the above


Explain the work of an Electric
Generator with diagram.


Draw the structures of the following molecules:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8} \)


State whether the given statement is true/false:
\( \sqrt{\boldsymbol{p}}+\sqrt{\boldsymbol{q}}, \) is irrational, where \( p, q \) are primes.
A . True
B. False


ff \( x=2 k+1 \) and \( y=k \) is a solution of
the equation \( 5 x+3 y-7=0, \) find the
value of \( k \)


The aromatic compounds present as particulates are :
A. Polycyclic aromatic hydrocarbons
B. Benzene
c. Toluene
D. Nitrobenzene


Translocation of food in higher plants is related to the idea of
A. Source and \( \operatorname{sink} \)
B. Ascent of sap
c. Diffusion
D. Cyclosis


(i) Where is the centre of gravity of a uniform ring situated?
(ii) "The position of the centre of gravity of a body remains unchanged even when the body is deformed". State whether this statement is true or false.


If \( G \) is the geometric mean of \( x \) and \( y \)
then
\( t \frac{1}{G^{2}-x^{2}}+\frac{1}{G^{2}-y^{2}}=\frac{1}{G^{2}} \)


Maximum frequency of emission is obtained for the transition:
\( \mathbf{A} \cdot n=2 \) to \( n=1 \)
B. \( n=6 \) to \( n=2 \)
c. \( n=1 \) to \( n=2 \)
D. \( n=2 \) to \( n=6 \)
6


\( 5 \mathrm{Gm} \) of steam at \( 100^{\circ} \mathrm{C} \) is passed into
\( 6 \mathrm{gm} \) of ice at \( 0^{\circ} \mathrm{C} \). If the latent heats of steam and ice n cal per \( \mathrm{gm} \) are 540 and 80 respectively, them the final temperature is:-
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 50^{\circ} C \)
D. \( 30^{\circ} \mathrm{C} \)


Two coherent light beams of intensity and 41 are superposed. The maximum and minimum possible intensities in the resulting beam are.
A. 9| and |
B. 9I and 31
c. 5 । and 1
D. 5 । and 3 ।


Multiplying factors is an example of
A. polynomial
B. quadratic equation
c. division algorithm
D. factorisation


Among the following mixture, maximum dipole-dipole interaction is
present in:
A. benzene and ethanol
B. acetonitrile and acetone
c. \( K C l \) and water
D. benzene and carbon tetra chloride


The friction coefficient between the
board and the floor shown in figure (6
E7) is \( \mu \). Find the maximum force that
the man can exert on the rope so that
the board does not slip on the floor.


A particle is projected up along a rough
plane of inclination \( 45^{0} \) with the horizontal. If the coefficient of friction is
\( 0.5, \) the retardation is \( (g= \) acceleration due to gravity):
A \( \cdot \frac{g}{2} \)
в. \( \frac{g}{2 \sqrt{2}} \)
c. \( \frac{3 g}{2 \sqrt{2}} \)
D. \( \frac{g}{\sqrt{2}} \)


Divide \( 3 x^{4}+2 x^{2}-3 \) by \( (x+1) \) find
quotient and remainder


A Faraday is:
A. the magnitude of the charge of 1 mole of electrons
B. the magnitude of the electric dipole
C. a fundamental constant of nature equal to \( 6.63 \times \) \( 10^{-34} J s / \)photon
D. a constant that accounts for the existence of ions in
solution


If a body of mass \( 200 g \) falls from a
height \( 200 m \) and its total potential
energy is conserved into kinetic energy, at the point of contact of the body with the surface, then decrease in potential
energy of the body at the contact is
\begin{tabular}{l}
A. 9005 \\
\hline
\end{tabular}
в. \( 500 J \)
c. \( 400 J \)
D. \( 200 J \)


In a series LCR circuit connected to an
ac source of variable frequency and
voltage \( \boldsymbol{v}=\boldsymbol{v}_{m} \sin \omega \boldsymbol{t}, \) draw a plot
showing the variation of current \( (\boldsymbol{I}) \)
with angular frequency \( (\omega) \) for two
different values of resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \)
\( \left(R_{1}>R_{2}\right) . \) Write the condition under
which the phenomenon of resonance occurs. For which value of
the resistance out of the two curves a
sharper resonance is produced? Define Q-factor of the circuit and give its
significance.


\( \operatorname{Let} P(A)=0.4 \) and \( P(A \cup B)= \)
\( P(A \cap B), \) find \( 5 P(B) \)


What happens when a mixture of cobalt oxide and borax is heated in a flame on
a loop of platinum wire?
A. A transparent white bead is formed
B. A bright pink coloured \( N a B O_{2} \) bead is formed
C. A blue coloured \( C o\left(B O_{2}\right)_{2} \) bead is formed
D. A red coloured \( C o\left(B O_{2}\right)_{2} \) bead is formed


Which color band in the resistor is
having highest tolerance?
A . Violet
B. Green
c. Blue
D. None of the above


1 \( |\Delta| \) \begin{tabular}{|l|}
\hline\( \Delta \) \\
\hline\( \square \) \\
\hline\( \square \) \\
\hline\( + \) \\
\hline
\end{tabular} \begin{tabular}{|c|}
\hline\( A \) \\
\hline\( \square \) \\
\hline
\end{tabular}


The following substances which possess rigidity modulus
A. Only Solids
B. Only liquids
c. Liquids and Gases
D. solids, Liquids and Gases


If \( f(x) \) satisfies the conditions of Rolle's
theorem in [1,2] and \( f(x) \) is continuous in [1,2] then \( \int_{1}^{2} f^{\prime}(x) d x \) is equal to
A . 3
B. 0
\( c .1 \)
D. 2


Complete activity from the following:
First term and common difference of an
A.P. are 6 and 3 respectively. Find \( S_{27} \)
Solution:

First term \( =a=6, \) common difference
\( =\boldsymbol{d}=\mathbf{3}, \boldsymbol{S}_{27}=? \)
\( \boldsymbol{S}_{\boldsymbol{n}}=\frac{\boldsymbol{n}}{2}[\square+(\boldsymbol{n}-1) \boldsymbol{d}]- \) formula
\( \boldsymbol{S}_{\mathbf{2 7}}=\frac{\mathbf{2 7}}{\mathbf{2}}[\mathbf{1 2}+(\mathbf{2 7}-\mathbf{1}) \square] \)
\( =\frac{27}{2} \times \square \)
\( =27 \times 45 \)
\( \therefore S_{27}=\square \)


Name the colour code of the wire which
is connected to the metallic body of an
appliance.


f the magnetic field in the following figure is increased then
\begin{tabular}{l|lllllll}
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\hline\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\hline
\end{tabular}
\( x x \)
\[
x \times x \times x
\]
A. plate A of the condenser will get positively charged
B. plate B of the condenser will get positively chargec
c. the condenser will not be charged
D. both the plates will be charged alternately


A uniform rod is suspended horizontally from its mid-point. A piece of metal whose weight is \( \boldsymbol{w} \) is suspended at a
distance \( l \) from the mid-point. Another
weight \( W_{1} \) is suspended on the other
side at a distance \( l_{1} \) from the mid-point to bring the rod to a horizontal position. When \( \boldsymbol{w} \) is completely immersed in
water, \( \boldsymbol{w}_{1} \) needs to be kept at a distance
\( l_{2} \) from the mid-point to get the rod
back into horizontal position. The specific gravity of the metal piece is
A \( \cdot \frac{w}{w_{1}} \)
в. \( \frac{w l_{1}}{w l-w_{1} l_{2}} \)
c. \( \frac{l_{1}}{l_{1}-l_{2}} \)
D. \( \frac{l_{1}}{l_{2}} \)


A projectile is thrown into space so as to have the maximum possible
horizontal range equal to \( 400 m \). Taking
the point of projection as the origin, the coordinates of the point where the
velocity of the projectile is minimum
are:
\( \mathbf{A} \cdot(400,100) \)
в. (200,100)
c. (400,200)
D. (200,200)


A rigid container has a hole in its wall. When the container is evacuated, its weight is 100 gm. When someair is filled in it at \( 27 C \), its weight becomes 200 gm. Now the temperature of air inside is
increased by \( \Delta \mathrm{T} \), the weight becomes 150 gm. \( \Delta \) T should be :
A .27
в. \( \frac{27^{\circ}}{4} \) с
\( c .300 \)
D. 327


Fill in the blanks:
The gaseous form of water found in
air


Which one of the following is wrongly
matched?
A. Saponification of \( C H_{3} C O O C_{2} H_{5} \) - second order reaction
B. Hydrolysis of \( C H_{3} C O O C H_{3} \) - pseudo unimolecular reaction
C. Decomposition of \( H_{2} O_{2} \) - first order reaction
D. Combination of \( H_{2} \) and \( B r_{2} \) to give \( H B r \) - first order
reaction


If \( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x})(\boldsymbol{x}-\boldsymbol{a})^{2}, \) where \( \boldsymbol{g}(\boldsymbol{a}) \neq \)
0 and is continuous at \( x=a \), then
A. \( f \) is increasing near \( a \) if \( g(a)>0 \)
B. \( f \) is increasing near \( a \) if \( g(a)<0 \)
c. \( f \) is increasing near \( a \) if \( g(a)=0 \)
D. none of these


Match the orbitals of List-I with the
nodal properties of List-II:


If \( y=\sin ^{-1}\left(x^{2}\right) \) then find \( \frac{d y}{d x} \) using first
principle.
A. \( \frac{2 x}{\sqrt{1-x^{4}}} \)
в. \( \frac{2}{\sqrt{1-x^{2}}} \)
c. \( \frac{x}{\sqrt{1-x^{4}}} \)
D. \( -\frac{1}{\sqrt{1-x^{4}}} \)


The de Broglie wavelength of a particle
of mass 1 gram and velocity 100 ms \( ^{-1} \)
is:
A. \( 6.63 \times 10^{-35} \)
В. \( 6.63 \times 10^{-34} \)
c. \( 6.63 \times 10^{-33} \)
D. \( 6.63 \times 10^{-32} \)


When a photosynthetic plant is transferred to an atmosphere of
enriched \( O_{2} \) its rate of
A. Photosynthesis would increase.
B. Photosynthesis would decrease.
c. Respiration would decrease.
D. osmosis would increase.


Statement (1) : There is ionic bonding in
Sodium chloride compound. Statement (2) : Same elctronegativity is
shown by sodium and chlorine atoms.
A. false, false
B. true, false
c. true, true
D. false, true
E. Statement (1) and statement
(2) are true and statement (2) is the correct explanation of Statement
(1)


Draw Venn diagrams to illustrate \( \boldsymbol{A} \cap \)
\( B^{\prime} \)


The stimulus for phototropic movements is
A. Light
B. Dark
c. water
D. Touch


Evaluate: \( \lim _{x \rightarrow 2} \frac{\sin \left(x^{2}-5 x+6\right)}{x^{2}-7 x+10} \)


The factor which is not limiting in normal conditions for photosynthesis is
A. water
B. chlorophyll
c. light
D. carbon dioxide


Identify the compounds from the following which form primary amines under suitable reduction conditions.
1. \( \boldsymbol{C}_{2} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{N} \boldsymbol{C} \)
2. \( C_{2} H_{6} \)
3. \( C_{2} H_{5} C O N H_{2} \)
4. \( C_{6} H_{5} N O_{2} \)
A \( \cdot 1,4 \)
в. 3,4
c. 1,3,4
D. 2,3,4


tood
sonmon
voe vourg


Twelve pairs of ribs and twelve pairs of cranial nerves are found in
A. Fish
B. Frog
c. Lizard
D. Man


Botanical name of potato is
A. Solanum tuberosum
B. Manihot esculenta
c. Malus pumila


Why is electrical wiring usually made
from copper?
A. Because copper is shiny
B. Because copper conducts electricity
c. Because copper is not magnetic
D. none of these


In the formation of certain compound, the central atom uses its hybrid orbital
and has a bond angle aroumd it as \( 105^{\circ} \)
The percentage of s-character in the
hybrid orbital is likely to be
A. \( 20-25 \% \)
B. \( 35-40 \% \)
c. \( 10-15 \% \)
D. \( 23-25 \% \)


Amount of heat can be measured by
A . \( m c T \)
в. \( m+c T \)
\( \mathrm{c} \cdot m c+T \)
D. \( \frac{m c}{T} \)


Which of the following statements is
not correct?
A. Whenever the amount of magnetic flux linked with a circuit changes, an emf is induced in the circuit.
B. The induced emf lasts so long as the change in magnetic flux continues.
C. The direction of induced emf is given by Lenzs law
D. Lenzs law is a consequence of the law of conservation of momentum.


If a dip circle is placed in a vertical
plane at an angle of \( 30^{\circ} \) to the magnetic meridian, the dip needle makes an angle of \( 45^{\circ} \) with the horizontal. The real
dip at that place is?
A \( \cdot \tan ^{-1}(\sqrt{3} / 2) \)
B. \( \tan ^{-1}(\sqrt{3}) \)
C \( \cdot \tan ^{-1}(\sqrt{3} / \sqrt{2}) \)
D \cdot \( \tan ^{-1}(2 / \sqrt{3}) \)


Mean deviation can be calculated from
A. mean
B. median
c. mode
D. any of the above


An oxide of nitrogen which forms
reddish brown fumes in air is:
A \( \cdot N_{2} O \)
B. NO
\( c \cdot N O_{2} \)
D. \( N_{2} O_{3} \)


The product formed when oxygen and hydrogen are mixed in a test tube at room temperature is:
A. hydrogen peroxide
B. water
\( c . \) a base
D. a zwitterion
E. no reaction takes place


The most likely acid-catalysed aldol
condensation products of each of the
two aldehydes \( I \) and \( I I \) will respectively
be
and
\( A \)
and
B.
and
\( c \)
and
\( D \)
and


If \( x^{y}+y^{x}=a^{b} \) then find that \( \frac{d y}{d x} \)
A. \( -\frac{y x^{x-1}+y^{x} \log y}{x^{y} \log x+x y^{x-1}} \)
B. \( \frac{y x^{x-1}+y^{x} \log y}{x^{y} \log x+x y^{x-1} y^{x}} \)
\( ^{\mathrm{C}}-\frac{y x^{x-1}+y^{x} \log y}{x^{y} \log x+x y^{x}} \)
D. None of these


Degeneracy in genetic code exists
because
A. More than one codon can code for a single amino acid
B. One codon can code for multiple amino acids
C. More than on anticodon can bind to a given codon
D. Only one anticodon can bind to a given codon
E. None of the above


\( \boldsymbol{E} \) and \( \boldsymbol{F} \) are the points on the side \( \boldsymbol{P Q} \)
and \( P R \) respectively of \( \triangle P Q R \) For each
of the following cases, state that \( \boldsymbol{E} \boldsymbol{F} \| \)
\( Q R \) If True type 1 and for False type 0
\( \boldsymbol{P E}=\mathbf{4} \boldsymbol{c m}, \boldsymbol{Q} \boldsymbol{E}=\mathbf{4 . 5} \boldsymbol{c m}, \boldsymbol{P} \boldsymbol{F}= \)
\( 8 c m \) and \( R F=9 c m \)


Define coelom


Ultrapure elements are obtained in which of the following method of metal refining?
A. Electrolysis
B. Poling
c. Liquation
D. Electrolytic refining


The equivalent resistance \( R \) of three
resistors \( R_{1}, R_{2} \) and \( R_{3} \) joined in
parallel is
A \( \cdot R=R_{1}+R_{2}+R_{3} \)
B . \( R=1 / R_{1}+1 / R_{2}+1 / R_{3} \)
\( ^{\mathbf{C}} \cdot_{R}=\frac{R_{1} R_{2} R_{3}}{R_{1} R_{2}+R_{2} R_{3}+R_{3} R_{1}} \)
D. \( R=1 /\left(R_{1}+R_{2}+R_{3}\right) \)


Assertion
The energy profile of the reaction \( \boldsymbol{A}+ \)
\( B \rightleftharpoons C \) is given as above, then the K of
the above equilibrium increases with
increase of temperature
Reason
Endothermic reaction is favoured by
increase of temperature
A. Both assertion and reason are true but reason is the correct explanation for assertion
B. Both assertion and reason are true but reason is not the correct explanation for assertion
c. Assertion is true but reason is false
D. Assertion is false but the reason is true


A person is sitting on a moving train and is facing the engine. He tosses up a coin which falls behind him. The train is
moving:
This question has multiple correct options
A. forward and gaining speed.
B. forward and losing speedd
c. backward and losing speed
D. backward and gaining speed.


Lenticel develops through the activity of
A. vascular cambium
B. Dermatogen
c. Phellogen
D. Intercalary meristem


In which of the following compounds
maximum heat is liberated on
combustion of one mole of the
compound?
A. Hydrogen
B. Methane
c. Ethane
D. Butane


In a series LCR circuit, resoanance frequency if half of the frequency of source. The nature of the circuit is
A. Capacitive
B. Resistive
c. Inductive
D. cannot be defined


Consider the following statements:
1. Rate of a process is directly proportional to its free energy change.
2. The order of an elementary reaction
step can be determined by examining the stoichiometry.
3. The first order reaction describes
exponential time course. Of these statements:
A. 1,2 and 3 are correct
B. 1 and 2 are correct
\( c .2 \) and 3 are correct
D. 1 and 3 are correct


Choose the correct answers from the
alternatives given Which of the following characteristics first developed in reptiles?
A. Amniotic egg
B. Scales on skin
c. Four-legged body
D. Skull and vertebral column


A spring-mass oscillator has a total
energy \( E_{0} \) and an amplitude \( x_{0} . \) For
what value of \( \boldsymbol{x} \) will \( \boldsymbol{K}=\boldsymbol{U} \) ?
A \( . x=x_{0} \)
в. \( x=\frac{x_{0}}{\sqrt{2}} \)
c. \( x=2 \)
D. \( x=0 \)


Calculate the molarity of each of the following: (a) \( 30 g \) of \( C o\left(N O_{3}\right)_{2} .6 H_{2} O \)
in \( 4.3 L \) of solution
(b) \( 30 m L \) of 0.5
\( M H_{2} S O_{4} \) diluted to \( 500 m L \)


An urn contains 11 balls numbered from
to \( 11 . \) If a ball is selected at random,
what is the probabiloity of having a ball with a number which is mutliple of either 2 or \( 3 ? \)
A \( \cdot \frac{7}{11} \)
в. \( \frac{8}{11} \)
c. \( \frac{4}{11} \)
D. \( \frac{6}{11} \)


What is the optimum concentration of flouride required by body?
A. 2 ppm
B. 5 ppm
c. 10 ppm
D. 1 ppm


If \( \bar{a}, \bar{b}, \bar{c}, \) are unit vector such that \( \bar{a}+ \) \( \bar{b}+\bar{c}=\overline{0}, \) then the \( \bar{a} . \bar{b}+\bar{b} . \bar{c}+\bar{c} . \bar{a}= \)
\( A \cdot \frac{3}{2} \)
B. \( -\frac{3}{2} \)
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \)


Which condition can be used to prove
that the given triangles are SAS
congruent?
\( A . \angle B=\angle F, \overline{A B} \cong \overline{D F} \) and \( \overline{A C} \cong \overline{D E} \)
B. \( \angle A=\angle F, \overline{A B} \cong \overline{D C} \) and \( \overline{A C} \cong \overline{D E} \)
\( \mathrm{c} . \angle B=\angle C, \overline{A B} \cong \overline{D C} \) and \( \overline{A C} \cong \overline{D E} \)
D. \( \angle B=\angle F, \overline{A C} \cong \overline{D C} \) and \( \overline{A C} \cong \overline{D E} \)
\( E \)


Solve: \( \sqrt{225} \)


The total \( \operatorname{cost} C_{(x)} \) and the total revenue \( R_{(x)} \) associated with production and
sale of \( x \) units of an item are given by
\( C(x)=0.1 x^{2}+30 x+1000 \) and
\( R(x)=0.2 x^{2}+36 x-100 . \) Find the
marginal cost and the marginal revenue when \( x=20 \)


Water flows through two identical tubes
\( A \) and \( B . A \) volume \( V_{0} \) of water passes
through the tube \( A \) and \( 2 V_{0} \) through \( B \)
in a given time. Which of the following may be correct?
This question has multiple correct options
A. Flow in both the tubes are steady
B. Flow in both the tubes are turbulent
c. Flow is steady in \( A \) but turbulent in \( B \)
D. Flow is steady in \( B \) but turbulent in \( A \)


Find the ratio in which (2,1) divides the
line segment joining \( (\mathbf{1}, \mathbf{4}),(\mathbf{4},-\mathbf{5}) \)


What is a peptide bond?


A particle of mass \( m \) strikes a wall
elastically with speed \( v \) at an angle \( 30^{\circ} \)
with the wall as shown in the figure. The
magnitude of impulse imparted to the
ball by the wall is:
\( A \)
в. \( \frac{m v}{2} \)
\( c \cdot 2 m v \)
D. \( \sqrt{3} \) mv


Find the value of the addition of \( (x- \) \( 3 y+4 z),(y-2 x-8 z),(5 x-2 y- \)
\( 3 z) \)


Draw a graph of potential energy v/s reaction coordinate showing the effect of a catalyst on activation energy.


What is the process involved in making candy?
A. Filtration
B. Crystallisation
c. Sedimentation
D. centrifugation


Choose the correct statement from the
following
This question has multiple correct options
A. Electric lines of force never cross each other
B. Electric lines of force end at a positive
C. The electric field charge inside a conductor are infinity
D. Lines of electric field point towards regions of lower potential


During Krebs cycle, energy from glucose is mostly transferred to
A. NADH and FADH
B. NADPH
c. ADP
D. water


Diffusion of a gas in a room is not reversible because:
A. entropy of a system cannot decrease.
B. entropy of a system remains constant.
c. entropy of universe cannot decrease
D. None of the above


charge distribution will be:
\( A \)
B.
\( c \)
D.


If the points \( \boldsymbol{A}(\mathbf{3},-\mathbf{2}, \mathbf{4}), \boldsymbol{B}(\mathbf{1}, \mathbf{1}, \mathbf{1}) \) and
\( C(-1,4,-2) \) are collinear, then the ratio in which \( C \) divides \( A B \) is
A .1: 2
B . -2: 1
c. -1: 2
D. 4: 0


The sex chromosomes of both male and
female are respectively
A. YY, XX
в. \( Y X, X Y \)
c. \( x y, x x \)
D. All of the above


The anticodon found on the t-RNA for
trytophan amino acid is
A. ucc
B. cuu
c. АСС
D. UGG


What is known as linear magnification of spherical mirrors?
A. Ratio of size of image to size of object
B. Ratio of shape of image to size of object
c. Ratio of size of image to shape of object
D. None


The scientific name of snow leopard is
A. Panthera pardus
B. Panthera uncea
C. Panthera tigris
D. Hylobates hoolock


In the sun hydrogen is converted to
A. Helium
B. Uranium
c. Polonium
D. Radium


When the level of contaminants in air
becomes so much that air becomes
harmful for living beings, it is called
A . air pollution
B. water pollution
c. noise Pollution
D. all of the above


The other end of the diameter through
the point (-1,1) on the circle \( x^{2}+ \) \( y^{2}-6 x+4 y-12=0 \) is :
\( \mathbf{A} \cdot(-7,5) \)
B. (-7,-5)
c. (7,-5)
D. (7,5)


If \( f(x)=x^{2} e^{2 x}(x>0,) \) then find the
local maximum value of \( \boldsymbol{f}(\boldsymbol{x}) \)
\( A \cdot \frac{2}{e^{2}} \)
B. \( \frac{-1}{e^{2}} \)
\( c \cdot e^{2} \)
D. \( \frac{1}{e^{2}} \)


Which of the following is released in the manufacture of calcium silicate
cement \( \left(\boldsymbol{C a} \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{4}\right) ? \)
A. Sulfur trioxide
B. Sulfur dioxide
c. oxygen gas
D. water gas


For spherical symmetrical charge
distribution, variation of electric
potential with distance fro center is
given in diagram. Given that \( : V= \) \( \frac{\boldsymbol{q}}{\mathbf{4} \boldsymbol{\pi} \varepsilon_{0} \boldsymbol{R}_{0}} \) for \( \boldsymbol{r} \leq \boldsymbol{R}_{0} \) and \( \boldsymbol{v}=\frac{\boldsymbol{q}}{\boldsymbol{4} \boldsymbol{\pi} \varepsilon_{0} \boldsymbol{r}} \) for
\( \boldsymbol{r} \geq \boldsymbol{R}_{0} \)
Then which option (s) are correct:
This question has multiple correct options
A. Total charge within \( 2 R_{0} \) is 9
B. Total electrostatic energy for \( r \leq R_{0} \) is non-zer
c. \( A t r=R_{0} \) electric field is discontinuous
D. There will be no charge anywhere except at \( r<R_{0} \)


Froth floatation process is used for the :
A. Oxide ores
B. Sulphide ores
c. chloride ores
D. All of these


What is the cube root of \( -4096 ? \)
A . -64
B. -16
c. 16
D. 64


What will be the initial rate of reaction, if its rate constant is \( 10^{-3} \) min \( ^{-1} \) and
the concentration of reactant is \( 0.2- \)
\( d m^{-3} ? \) How much of reactant will be
converted into product in 200 minutes?


Which of the following is a crystalline allotrope of carbon?
A. Charcoal
B. coal
c. Fullerene
D. Lamp black


How many group are \( o / p \) director in the electrophilic aromatic substitution?


Explain the position of hydrogen in the periodic table on the basis of its
electronic configuration.


\( 2.0 \mathrm{g} \) of bensoic acid dissolved in \( 25.0 \mathrm{g} \) of benzene shows a depression in freezing point to 1.62K. Mollal
depression constant \( \left(K_{f} \) of bezene is \right.
4.9 K.kg. \( m o l^{-1} . \) What is the percentage association of the acid?
A. \( (\alpha)=90.8 \% \)
B. \( (\alpha)=99.2 \% \)
c. \( (\alpha)=9.8 \% \)
D. \( (\alpha)=49.6 \% \)


Find the amplitude response \( \left|\frac{V_{2}}{V_{1}}\right| \) for
the ciircuit shown in figure. Determine
the half-power frequency.
A \( \cdot \frac{1}{B C} \)
B. \( \frac{2}{R C} \)
\( c \cdot \frac{4}{R C} \)
D.


A student heats a beaker containing ice
and water. He measures
the temperature of the content of the
beaker as a function of time. Which of
the following would correctly represent
the result?
\( \mathbf{A} \cdot(a) \)
B. (c)
c. \( (b) \)
D. \( (d) \)


In which of the following statements, the obtained impure semiconductor is of p-type?
A. Germanium is doped with bismuth
B. Silicon is doped with antimony
c. Germanium is doped with gallium
D. Silicon is doped with phosphorus


If \( \boldsymbol{y}=\log \left(1+2 t^{2}+\boldsymbol{t}^{4}\right), \boldsymbol{x}=\tan ^{-1} \boldsymbol{t} \)
find \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)


Identify which of the following element has a mass number of 20 and contains
11 neutrons?
A. copper
B. Gallium
c. Calcium
D. Sodium
E. Fluorine


The molar conductivities of \( \wedge_{N a O A C}^{0} \) and \( \wedge_{H C l}^{0} \) at infinite dilution in water at \( 25^{0} C \) and 91.0 and \( 426.2 \mathrm{Scm}^{2} / \mathrm{mol} \) respectively. To calculate \( \wedge_{H O A c}^{0} \), the additional value required is:
\( \mathbf{A} \cdot \wedge_{N a C l}^{0} \)
B. \( \wedge_{H_{2} O}^{0} \)
c. \( \wedge_{K C l}^{0} \)
D. \( \wedge_{N a O H}^{0} \)


The capacitance of a capacitor
A. filled with a dielectric is lesser than it would be in a
vacuum
B. filled with a dielectric is greater than it would be in a vacuum
c. filled with a dielectric is same as it would be in a
vacuum.
D. none of the above


Types of combustion are:
A. rapid, cracking and dazzling
B. spontaneous, rapid and explosive
C. explosive, dazzling and glowing
D. spontaneous and rapid


If \( A \) is a skew-symmetric matrix and \( n \)
is odd positive integer, then \( A^{n} \) is
A. a skew-symmetric matrix
B. a symmetric matrix
c. a diagonal matrix
D. none of these


The coefficient of variation for the given distribution is
A . 28.6
B. 0.306
c. 30.6
D. 306


In three test tubes \( P, Q \) and \( R \) iron nails
water, oil and anhydrous calcium
chloride is taken. Among these test tubes, in which test tubes corrosion of
nails will not take place?
\( A \cdot P, Q \) and \( R \)
B. P and R
c. P and \( Q \)
D. Q and


What is common between the following molecules?
\( \boldsymbol{S O}_{3}, \boldsymbol{C O}_{3}^{2-}, \boldsymbol{N O}_{3}^{-} \)
A. All have linear shape
B. All have trigonal planar shape
c. All have tetrahedral shape
D. All have trigonal pyramidal shape


Two carbon discs of \( 1.0 g \) each are
1.0 \( c m \) apart have equal and opposite charges. If forces of attraction between
them is \( 1.00 \times 10^{-5} N \), calculate the
ratio of excess electrons to total atoms
on the negatively charged disc. (permitivity constant is \( 9.0 \times 10^{9} N m^{2} \)
\( \left.C^{-2}\right) \)
A \( \cdot 6.68 \times 10^{-33} \)
В. \( 1.6 \times 10^{-14} \)
c. \( 4.17 \times 10^{-12} \)
D. \( 4.17 \times 10^{-14} \)


The time taken by the earth to complete one rotation about is own axis is called
A. Solar day
B. Mean solar day
c. 1 hour
D. None


The ends of major axis of an ellipse are (5,0)(-5,0) and one of the foci lies on \( 3 x-5 y-9=0, \) then the eccentricity
of the ellipse is
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{4}{5} \)
D.


Name the functional groups present in the following compound:
(i) \( \boldsymbol{C H}_{3} \boldsymbol{C H O} \)
(ii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H} \)
(iii) \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
(iv) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \)


For a parallel beam of monochromatic light of wavelength \( ^{\prime} \lambda^{\prime}, \) diffraction is produced by a single slit whose width 'a is of the order of the wavelength of the light. If 'D' is the distance of the screen
from the slit, the width of the central
maxima will be
\( ^{\text {A }} \cdot \frac{D a}{\lambda} \)
B. \( \frac{2 D a}{\lambda} \)
c. \( \frac{2 D \lambda}{a} \)
D. \( \frac{D \lambda}{a} \)


Explain the following terms:
Hardy-schulze's rule


The type of nutrition present in
Entamoeba is
A. Saprozoic
B. Parasitic
c. Autotrophic
D. None of these


In which of the following process
hybridization is not affected?
\( \mathbf{A} \cdot 2 P C l_{5}(s) \stackrel{m e l t}{\longrightarrow} P C l_{4}^{+}+P C l_{6}^{-} \)
B \( \cdot L i H+A l H_{3} \longrightarrow L i A l H_{4} \)
\( \mathbf{C} \cdot \operatorname{Be} F_{2}(g) \frac{\text {hoar frosting}}{ } \operatorname{Be} F_{2}(s) \)
D. \( N H_{3}+H_{2} O \longrightarrow N H_{4} O H \)


From a solid wooden cube of sides
\( 14 \mathrm{cm} \) a biggest hemispherical depression is carved out. What is the total surface area of the remain solid?


A candidate is required to answer 6 out of 10 questions which are divided into two groups each containing 5 questions and he is not permitted to attempt more than 4 from each group. In how many ways can he make up his choice?


The period of oscillation of a simple pendulum is \( T=2 \pi \sqrt{\frac{L}{g}} . \) Measured of \( L \) is \( 20.0 \mathrm{cm} \) known to \( 1 \mathrm{mm} \) accuracy
and time for 100 oscillations of the
pendulum is found to be 90 s using a
wrist watch of \( 1 s \) resolution. The
accuracy in the determination of \( g \) ?
A . \( 2.5 \% \)
в. \( 2.7 \% \)
c. \( 2 \% \)
D. 3\%


The variance of first 50 even natural
numbers is


Match the following and choose the
correct option from below.
A. Cuticle
(i) Guard cells
B. Bulliform cells
(ii) single layer
C. Stomata
(iii) Waxy layer
D. Epidermis
(iv) Empty colourless cell
\( A \cdot A-(\text { iii) }, B-(i v), C-(i), D-(i i) \)
B. A-(i), B-(ii), C-(iii), D-(iv)
C. \( A-(\text { ii }), B-(i i), C-(i v), D-(i) \)
D. A-(iii), B-(ii), C-(i), D-(iv)


In the above circuit diagram, identify
diode(diodes) which is(are) forward
biased.
A. Only \( D_{1} \)
B. Only \( D_{2} \)
c. Both \( D_{1} \) and \( D_{2} \)
D. Neither \( D_{1} \) nor \( D_{2} \)


Among plants, pheromones are secreted by the cells of which of the following plants for the given function?
A. All plants for growth and development
B. Yeast for facilitation mating
c. All fungi for sexual reproduction
D. Rhizopus for the formation of zygospore


\( \ln \triangle A B C, \angle C \) is right angle. D \( \& E \) are
mid points of \( A C \& A B \) of \( A B=10 \& A C= \)
6cm. Find length of DE.
A \( .4 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .3 c m \)
D. \( 6 \mathrm{cm} \)


If the first, second and last terms of an
A.P be \( a, b, 2 a \) respectively, then its sum will be
A \( \cdot \frac{a b}{-a+b} \)
В. \( \frac{a b}{2(b-a)} \)
c. \( \frac{3 a b}{2(b-a)} \)
D. \( \frac{3 a b}{4(b-a)} \)


A metal rod of length \( L \) cross-sectional area A Young's modulus Y and coefficient of linear expansion \( \alpha \) is
heated to \( t^{o} C . \) The work that can be
performed by the rod when heated is:
A \( \cdot \frac{Y A \alpha L t^{2}}{2} \)
B. \( \frac{Y A \alpha^{2} L t^{2}}{2} \)
\( \frac{Y A \alpha^{2} L^{2} t^{2}}{2} \)
D. \( \frac{Y A \alpha L t}{2} \)


A semiconductor is doped with a donor
İmpurity:
This question has multiple correct options
A. the hole concentration increases
B. the hole concentration decreases
C. the electron concentration increases
D. the electron concentration decreases


Select the correct I.U.P.A.C name for
\( \left[\boldsymbol{P} \boldsymbol{t}\left(\boldsymbol{C}_{5} \boldsymbol{H}_{5} \boldsymbol{N}\right)_{4}\right]\left[\boldsymbol{P} \boldsymbol{t} \boldsymbol{C l}_{4}\right] \)
A. Tetrapyridineplatinate
(II) tetrachloridoplatinate
B. Tetrapyridineplatinum
(II) tetrachloridoplatinum
C. Tetrapyridineplatinate
(II) tetrachloridoplatinum
D. Tetrapyridineplatinum
(II) tetrachloridoplatinate


\( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{H} \boldsymbol{S}(s) \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
What is the \( K_{p} \) of the reaction if the total pressure at equilibrium is 30
atm?
A .15 atm\( ^{2} \)
B. 225 atm \( ^{2} \)
c. 30 at \( m^{2} \)
D. 15 atm


A die is thrown twice. Each time the
number appearing on it is recorded. Describe the following events:
\( A= \) Both numbers are odd
\( B= \) Both numbers are even
\( C= \) Sum of the numbers is less than 6
Also, Find \( \boldsymbol{A} \cup \boldsymbol{B}, \boldsymbol{A} \cap \boldsymbol{B}, \boldsymbol{A} \cup \boldsymbol{C}, \boldsymbol{A} \cap \boldsymbol{C} \)
Which pairs of events are mutually exclusive


If the sum of all interior angles of a
polygon is \( 3240^{\circ}, \) how many sides has
the polygon?


were the first group of animals to evolve lung tissue requisite to support their respiratory needs without the use supplementary organs.
A. Trematoda
B. Amphibians
c. Reptiles
D. Aves


The pyramid of energy is the best representation of an ecosystem because it indicates
A. Relation of all plants and animals
B. Total energy present in an ecosystem
C. The rate of flow of energy through the food chain
D. None of the above


Convert \( \frac{16}{50} \) into percentage.
A . \( 32 \% \)
B. \( 34 \% \)
c. \( 36 \% \)
D. \( 38 \% \)


The distance covered by it after \( n \) seconds is directly proportional to
\( \mathbf{A} \cdot n^{2} \)
в.
\( c \cdot 2 n-1 \)
D. \( 2 n^{2}-1 \)


A solution is prepaired by mixing \( 8.5 g \)
of \( C H_{2} C l_{2} \) and \( 11.95 g \) of \( C H C l_{3} \). If
vapour pressure of \( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2} \) and
\( C H C l_{3} \) at \( 4298 K \) are 415 and
\( 200 m m H g \) respectively, the mole
fraction of \( \boldsymbol{C H C l}_{3} \) in vapour form is :
(molar mass of \( \left.\boldsymbol{C l}=\mathbf{3 5 . 5} \boldsymbol{g} \boldsymbol{m o l}^{-1}\right) \)
\( \mathbf{A} \cdot 0.162 \)
B. 0.675
c. 0.325
D. 0.486


The average kinetic energy of a gas molecule at \( 27^{\circ} C \) is \( 6.21 \times 10^{-21} J \)
then its average kinetic energy at
\( 227^{\circ} \mathrm{C} \) is:
A \( \cdot 10.35 \times 10^{-21} J \)
В. \( 11.35 \times 10^{-21} J \)
D. \( 5.22 \times 10^{-21} J \)


What is petrol combustion? Explain in
your words