Give the names of the elements present in the following compounds.
(a) Quick lime
(b) Hydrogen bromide
(c) Baking bromide
\( (d) \) Potassium sulphate.


Subfamilies of Leguminosae family are differentiated on the basis of
A. Gynoecium
B. Corolla and androeium
c. Nature of plant
D. Nature of fruit


Collar bone is known as
A. Scapulal
B. stapes
c. coracoid
D. Clavicle


Cell equation \( : \boldsymbol{A}+\mathbf{2} \boldsymbol{B}^{+} \rightarrow \boldsymbol{A}^{2+}+\mathbf{2} \boldsymbol{B} \)
\( \boldsymbol{A}^{2+}+\boldsymbol{2} \boldsymbol{e} \rightarrow \boldsymbol{A} \boldsymbol{E}^{\circ}=+\mathbf{0 . 3 4} \boldsymbol{V} \)
and \( \log _{10} K=15.6 \) at \( 300 K \) for cell reactions
Find \( \boldsymbol{E}^{\circ} \) for \( \boldsymbol{B}^{+}+\boldsymbol{e} \rightarrow \boldsymbol{B} \)
Given \( \left[\frac{2.303 R T}{n F}=0.059\right]_{a t 300 K} \)
A . 0.80
B. 1.26
c. -0.54
D. +0.94


Find the value of determinant.
(i) \( \left|\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right| \)
(ii) \( \left|\begin{array}{cc}x^{2}-x+1 & x-1 \\ x+1 & x+1\end{array}\right| \)


Which describes an
endothermic reaction?
A. Positive \( \Delta H \)
B. Negative \( \Delta H \)
c. Positive \( \Delta G \)
D. Negative \( \Delta G \)
E. Positive \( \Delta S \)


Find the domain of \( f(x)=\cot x+ \)
\( \cot ^{-1} x \)


Find the volume of a right circular cylinder if the radius of its base is \( 7 \mathrm{cm} \)
and height is \( 15 \mathrm{cm} \)


\( 20 \mathrm{ml} \) of \( 0.2 \mathrm{M} A l_{2}\left(S O_{4}\right)_{3} \) is mixed with
\( 20 \mathrm{ml} \) of \( 6.6 \mathrm{M} \mathrm{BaCl}_{2} \), the concentration
of \( C l^{-} \) in solution is:
A. \( 0.2 \mathrm{M} \)
B. 6.6 \( M \)
c. \( 0.02 \mathrm{M} \)
D. 0.06 м


An object is placed at a distance of 10 \( c m \) from a convex lens of focal length
\( 20 c m . \) Find the position and nature of
the image.


\( H C l \) is soluble in organic solvents such as benzene and toluene.
A. True
B. False


The rate of growth of population of a city at any time is proportional to the size of the population at that time. For a certain city, the consumer of proportionality is \( 0.04 . \) The population of the city after 25 years, if the initia population is 10,000 is \( (e=2.7182) \)
\( \mathbf{A} \cdot 27182 \)
B. 27164
c. 27000
D. 27272


If you watch a burning candle carefully, you will find different colurs in the
flame. Which is the hottest part of the
candle flame?
A. The middle orange partttt
B. The middle, yellow part
c. The outermost portion that is blue
D. The innermost black zone


A sequence is defined by \( a_{n}=n^{3}- \)
\( 6 n^{2}+11 n-6 . \) Show that the first three
terms of the sequence are zero and al other terms are positive.


Adsorption is the phenomenon in which substance :
A. accumulates on the surface of the other substance
B. goes into the body of the other substance
c. remains close to the other substance
D. none is the above


Consider the reaction at \( 300 K \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(\ell)+\frac{\mathbf{1 5}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \mathbf{6} \boldsymbol{C O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\ell) ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{3 2 7 1} \boldsymbol{k} \boldsymbol{J} \)
What is \( \Delta U \) for the combustion of 1.5
mole of benzene at \( 27^{\circ} \mathrm{C} \) ?
A. \( -3267.25 k J \)
\( J \)
в. \( -4900.88 k J \)
c. \( -4906.5 k J \)
D. \( -327.754 k J \)


A gun of mass M fires a bullet of mass \( \mathrm{m} \) with a velocity v relative to the gun. The average force required to bring the gun to rest in 0.5 sec. is
A \( \cdot \frac{2 M m V}{m+M} \)
в. \( \frac{M m V}{2(M+m)} \)
c. \( \frac{3 M m V}{2(M+m)} \)
D. \( \frac{M m V}{(M+m)} \)


Distilled water is:
\( A \). a mixture
B. a compound
c. an element
D. none of these


Choose the correct answers from the
alternatives given :
Which of these is not true
of fermentation?
A. Net gain of only two ATP
B. Occurs in cytosol
C. NADH donates electrons to electron transport systemmmen
D. Begins with glucose


Simplify the multiplication of complex numbers: \( (\boldsymbol{x}, \boldsymbol{y}) \times(\mathbf{0}, \mathbf{0}) \)
A. \( (-x, 0) \)
)
в. \( (0,-y) \)
D. None of these


The following statements concern elements in the periodic table. Which of the following is true?
A. For Group 15 elements, the stability of +5 oxidation state increases down the group
B. Elements of Group 16 have lower ionization enthalpy values compared to those of Group 15 in the corresponding periods
c. The Group 13 elements are all metals
D. All the elements in Group 17 are gases


A coil made of insulated copper wire is
connected to a galvanometer. What will
happen if a bar magnet is withdrawn from inside the coil ?
(iii) Magnet completely inside but stationary, no current flows


If the points \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right) \) and \( \left(x_{3}, y_{3}\right) \) are collinear, show that \( \sum\left(\frac{\boldsymbol{y}_{1}-\boldsymbol{y}_{2}}{\boldsymbol{x}_{1} \boldsymbol{x}_{2}}\right)=\mathbf{0}, \) i.e
\( \frac{\boldsymbol{y}_{1}-\boldsymbol{y}_{2}}{\boldsymbol{x}_{1} \boldsymbol{x}_{2}}+\frac{\boldsymbol{y}_{2}-\boldsymbol{y}_{3}}{\boldsymbol{x}_{2} \boldsymbol{x}_{3}}+\frac{\boldsymbol{y}_{3}-\boldsymbol{y}_{1}}{\boldsymbol{x}_{3} \boldsymbol{x}_{1}}=0 \)


If the points \( \boldsymbol{A}(\boldsymbol{x}, \mathbf{2}), \boldsymbol{B}(-\mathbf{3},-\mathbf{4}) \) and
\( C(7,-5) \) are collinear, then the value of \( x \) is :
A . -63
B. 63
\( c .60 \)
D. - 60


The shaded region in the adjoining
diagram represents
A \( . A-B \)
B. \( B-A \)
\( \mathbf{c} \cdot A \Delta B \)
D. \( A \)


\( \operatorname{Let} \boldsymbol{I}=\int_{\boldsymbol{\pi} / 4}^{\pi / 3} \frac{\sin \boldsymbol{x}}{\boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} . \) Then?
\( ^{\mathrm{A}} \cdot \frac{1}{2} \leq I \leq 1 \)
в. \( 4 \leq I \leq 2 \sqrt{30} \)
\( \frac{\sqrt{3}}{8} \leq I \leq \frac{\sqrt{2}}{6} \)
D. \( 1 \leq I \leq \frac{2 \sqrt{3}}{\sqrt{2}} \)


If two events \( A \) and \( B \) are such that
\( \boldsymbol{P}(\boldsymbol{A})=\cdot \boldsymbol{2}, \boldsymbol{P}(\boldsymbol{B})=\cdot \boldsymbol{3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
\( \cdot 4 \) then \( P(A \cap B) \) equals?
A . 0.2
B. 0.1
\( c \cdot 0.3 \)
D. None of these


Find three different solution of the
equation \( 3 x=7 y-21 \)


At \( 27^{\circ} \mathrm{C} \) it was observed in the
hydrogenation of a reaction, the
pressure of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) decreases from 10 atm to 2 atm in 10 min. Calculate the
rate of reaction in \( \mathrm{M} \) min\( ^{-1} \) (Given \( \mathrm{R}= \)
\( \left.0.08 L \operatorname{atm} K^{-1} m o l^{-1}\right) \)
A. 0.02
2
B. 0.03
\( c .0 .04 \)
D. 0.05


Assertion
\( \operatorname{Let} f(x)=\cot ^{-1}\left(\frac{3 x-x^{3}}{1-3 x^{2}}\right), g(x)= \)
\( \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \operatorname{then} f(x)=g(x) \) if
\( \boldsymbol{x}=\frac{\sqrt{\mathbf{2 5}-\mathbf{1 0} \sqrt{\mathbf{5}}}}{\mathbf{5}} \)
Reason
\( \sin 18^{\circ}=\frac{\sqrt{5}-1}{4} \)
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. Assertion is incorrect but Reason is correct


A planet is revolving in an elliptical orbit around the Sun. Its closest
distance from the Sun is \( r_{\text {min }} \) and the
farthest distance is \( r_{m a x} \). If the velocity
of the planet at the distance of the
closest approach is \( \nu_{1} \) and that at the
farthest distance from the Sun is \( \nu_{2} \)
\( \operatorname{then}\left\{\nu_{1}\right\} /\left\{\nu_{2}\right\} \)
A \( \cdot \frac{r_{\max }}{r_{\min }} \)
B \( \cdot \frac{r_{\min }}{r_{\max }} \)
C. \( \frac{r_{\min }+r_{\max }}{r_{\max }-r_{\min }} \)
D. none


Which of the following statements
is/are correct?
This question has multiple correct options
A. The IUPAC name of amyl alcohol is pentanol
B. The IUPAC name of isoamyl alcohol is 3-methyl butanol
C. Wood spirit is methanol
D. Methyl alcohol is also called carbinol


A closed copper vessel contains water equal to half of its volume when the
temperature. Of the vessel is raised to
\( 447^{0} \mathrm{cthe} \) pressure of steam in the vessel
is (Treat steam as an ideal gas, \( \mathrm{R}=8310 \) \( \mathrm{J} / \mathrm{k} / \mathrm{mole}, \) density of water \( =1000 \mathrm{kg} / \mathrm{m}^{3} \)
molecular weight of water \( =18 \) )
\( A \cdot 33.24 \times 10^{7} \mathrm{pa} \)
B . 16.62 x 10 \( ^{7} \) pa
c. \( 10.31 \times 10^{7} \mathrm{pa} \)
D. \( 8.31 \times 10^{7} \mathrm{pa} \)


Thiosulphate reacts differently with iodine and bromine in the reaction
given below. \( \mathbf{2} \boldsymbol{S}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{3}}^{\mathbf{2}-}+\boldsymbol{I}_{\mathbf{2}} \rightarrow \boldsymbol{S}_{\mathbf{4}} \boldsymbol{O}_{\mathbf{6}}^{\mathbf{2}-}+\mathbf{2} \boldsymbol{I}^{-} \)
\( \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}+\boldsymbol{2} \boldsymbol{B} \boldsymbol{r}_{2}+\mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{4}^{2-}+ \)
\( 2 B r^{-}+10 H^{+} \)
Which of the following statement justifies the above dual behaviour of thiosulphate?
A. Bromine is stronger oxidant than iodine
B. Bromine is weaker oxidant than iodine
c. Thiosulphate undergoes oxidation by bromine and reduction by iodine in above reactions
D. Bromine undergoes oxidation and iodine undergoes reduction in above reactions


How do you find the focal length of a
concave mirror?


Two radioactive elements \( X \) and \( Y \)
have half-lives of 50 and 100 minute
respectively. An initial sample of both the elements has same no. of atoms. The ratio of the remaining number of atoms of \( X \) and \( Y \) after 200 minutes is:
\( A \cdot 2 \)
B. 1/2
\( c \cdot 4 \)
D. \( 1 / 4 \)


Prove the following result by using suitable identities.
\( (x-y)^{2}+(y-z)^{2}+(z-x)^{2}= \)
\( 2\left(x^{2}+y^{2}+z^{2}-x y-y z-z x\right) \)


A simple pendulum of length \( 4 \mathrm{m} \) is
taken to a height \( R \) (radius of the earth)
from the earth's surface.The time period of small oscillations of the pendulum is
\( \left(\boldsymbol{g}_{\text {surface}}=\boldsymbol{\pi}^{2} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A . 2 s
B. 4 s
\( c \cdot 8 s \)
D. 16 s


Line \( \overrightarrow{\boldsymbol{r}}=(\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}})+\boldsymbol{t}(\boldsymbol{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \)
contained in a plane to which vector \( \vec{n}=3 \hat{i}-2 \hat{j}+\lambda \hat{k} \) is normal. Find the
value of \( \lambda \). Also find the vector equation
of the plane.


Two identical plane metallic surface \( \boldsymbol{A} \)
and \( B \) parallel to each other in air
separated by a distance of 1 cm let
surface \( A \) as given a position potential
of \( 10 \mathrm{V} \) and surface \( B \) is earthed.


In Rutherford's scattering experiment if impact parameter is zero then angle
of scatting for \( \alpha \) particleis
A \( .90^{\circ} \)
в. \( 270^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 0^{\circ} \)


In above shown figure, the direction of magnetic force and magnetic field is
given then find out the direction of the
particle velocity, v.
A. To the right
B. Downward, in the plane of the page
c. Upward, in the plane of the page
D. Out of the plane of the page
E. Into the plane of the page


An element ' \( X^{\prime} \) has valency of \( H . \) Write
its formula for oxide?


A body is thrown vertically upwards and takes 5 seconds to reach maximum height. The distance travelled by the body will be same in:
A \( \cdot 1^{s t} \) and \( 10^{t h} \) second
B. \( 2^{n d} \) and \( 8^{t h} \) second
\( \mathrm{c} \cdot 4^{\operatorname{th}} \) and \( 6^{t h} \) second
D. Both (2) and (3)


Using Kirchoff's law how can you find
the potential at \( A \) where potential at \( B \) is
zero


\( N_{2} H_{4} \) reduces \( I O_{3}^{-} \) to \( I^{+} \) in acidic
medium as:
\( N_{2} H_{4}+I O_{3}^{-}+H^{+} \longrightarrow N_{2}+I^{+}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Intermediate in the above reaction is \( I_{2} \)
which can be detected by :
A. taking solvent \( C C I_{4} \) in which \( I_{2} \) is soluble and thus layer becomes violet
B. starch as indicator which turns blue
c. both (a) and (b)
D. None of the above


Subtract:
\( a+2 b-c \) from \( 3 a-b+2 c \)


A steady current flows in a metallic
conductor of non-uniform cross-section.
Which of the following quantities is constant along the conductor?
A . Drift speedd
B. current
c. currently density
D. None of these


Put the following parts of a reflex arc in the correct order beginning with the
sensory receptor:
(A) Motor neuron
(B) Interneuron
(C) Effector
(D) Sensory neuron
(E) Sensory receptor
A \( \cdot(E)(D)(B)(A)(C) \)
B. \( (E)(D)(A)(B)(C) \)
c. \( (A)(B)(C)(D)(E) \)
D. \( (A)(E)(D)(B)(C) \)


toppr
Q Type your question
Which one of the following plot
represents velocity \( v \) in \( m s^{-1} \) versus
time \( t \) in seconds?
\( A \)
B
\( c \)
\( D \)


We have \( 1.6 g C H_{4}, 1.7 g N H_{3} \) and
\( 1.8 g H_{2} O . \) Select correct alternate(s)
This question has multiple correct options
A. There are equal number of moles of each reactant
B. Total number of atoms in \( C H_{4}>N H_{3}>H_{2} O \)
c. Total number of H-atoms are in the ratio of 4: 3: 2
D. Total number of \( C \) -atoms in \( C H_{4}< \) that of \( N- \)
atoms in \( N H_{3}< \)that of \( O \) -atoms in \( H_{2} O \)


Choose the correct answer from the
alternatives given:
Directions for questions 71 to 75 :
Study the following graph carefully and
answer the questions given below.

What is the average number of tyres of
type A manufactured over the years?
\( A \cdot 23 \) lakhs
B. 2.3 lakhs
c. 30 lakhs
D. 22 lakhs


Ligaments are made up
of
A. White fibres and some yellow elastic fibres
B. White fibres only
C. Yellow fibres only
D. Yellow fibres and muscle fibres


(ii)


The differential equation corresponding
to the family of circles given by
\( (x-a)^{2}+(y-b)^{2}=4 \) where a and
are parameters, is
A \( \cdot 4 \frac{d^{2} y}{d x^{2}}+9 y=0 \)
\( 4\left(\frac{d^{2} y}{d x^{2}}\right)^{2}=\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3} \)
\( ^{\mathbf{C}} 4 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=6 y \)
\( 4\left(\frac{d^{2} y}{a x^{2}}\right)^{2}+\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{2}=0 \)


Threshold wavelength for a metal
having work function \( \omega_{0} \) is \( \lambda . \) Then the
threshold wavelength for the metal
having work function \( 2 \omega_{0} \) is
\( A \cdot 4 \lambda \)
B. 2\lambda
\( c \cdot \lambda / 2 \)
D. \( \lambda / 4 \)


Particle has an initial velocity \( (\mathbf{6} \hat{\mathbf{i}}+ \)
\( 8 \hat{j}) m s^{-1} \) and \( (0.8 \hat{i}+0.6 \hat{j}) m s^{-2} \) an
acceleration. Its speed after 10 s is:
A \( \cdot 20 m s^{-1} \)
В. \( 7 \sqrt{2} \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 14 \sqrt{2} \mathrm{ms}^{-1} \)


Bag filters are used for removal of
pollutants from
A. Exhaust emissions
B. Effluent water
c. Sewage water
D. Both B and C


The work done in blowing a soap bubble slowly from a radius of \( 5 \mathrm{cm} \) to a radius of \( 10 \mathrm{cm} \) is...................... Joule (given the
surface tension of water is \( 3.5 \times 10^{-2} \mathrm{N} \)
\( \left.m^{-1}\right) \)
\( A \cdot 6.6 \times 10^{-3} \)
B. 2.2 \( \times 10^{-3} \)
c. \( 4.4 \times 10^{-3} \)
D. 8.8 \( \times 10^{-3} \)


The volume of a liquid flowing per second out of an orifice at the bottom of
a tank does not depend upon
A. the height of the liquid above the orifice
B. the acceleration due to gravity
c. the density of the liquid
D. the area of the orifice


Pick up the correct statements:
This question has multiple correct options
A. The changing (with time) magnetic field need not be in existence at the location of induced electric field.
B. A uniform magnetic field increasing at constant rate, induces an electric field which is constant and non
conservative
C. Non zero force exerted by uniform and constant magnetic field on a moving charged particle does no work but always changes momentum of the particle.
D. All the above statements are wrong.


Say true or false:
The degree of the sum of two polynomials each of degree 5 is always
\( \mathbf{5} \)
A . True
B. False


Assertion
NaBO \( _{3} / O H^{-} \) can be used for
oxidation of \( C r^{3+} \) to \( C r^{6}+ \)
Reason
In alkaline medium \( N a B O_{3} \) produces
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
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


Which of the following is best \( C O_{2} \)
absorber as well as a source of \( O_{2} \) in the
space capsule?
A \( . K O_{2} \)
в. \( K_{2} O_{2} \)
c. КОН
D. \( L i O H \)


A particle executes simple harmonic motion with a frequency f. The frequency with which the kinetic energy oscillates is
\( A \cdot y / 2 \)
B.
\( c \cdot 2 y \)
D. none of these


If
\( * \) is defined on the set \( R \) of all real
numbers by \( *: \boldsymbol{a} * \boldsymbol{b}=\sqrt{\boldsymbol{a}^{2}+\boldsymbol{b}^{2}}, \) find
the identify element, if it exists in \( \boldsymbol{R} \)
with respect to \( * \)


Example for a coordination compound is
\( \mathbf{A} \cdot K C l . M g C l_{2} .6 H_{2} O \)
B \( \cdot K_{2} S O_{4} A l_{2}\left(S O_{3}\right) 24 H_{2} O \)
\( \mathbf{c} \cdot \operatorname{CoCl}_{3} \cdot 6 N H_{3} \)
D. \( F e S O_{4} .\left(N H_{4}\right)_{2} S O_{4} .6 H_{2} O \)


An elevator is descending with uniform acceleration. To measure the
acceleration, a person in the elevator drops a coin at the moment the elevator starts. The coin is \( 6 \mathrm{ft} \) above the floor of the elevator at the time it is dropped
The person observes that the coin
strikes the floor in 1 second. Calculate
from these data the acceleration of the
elevator.


Which of the following statement about
friction is wrong?
A. Frictional force can accelerate a body.
B. Frictional force can be reduced to zero.
C. Kinetic friction is always greater than rolling friction.
D. Frictional force is proportional to the area of contact between the surfaces.


A parallel plate capacitor of capacitance \( C \) is connected to a battery and is charged to a potential difference
V. Another capacitor of capacitance \( 2 C \) is similarly charged to a potential difference 2V. The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is :
A . zero
в. \( \frac{3}{2} C V^{2} \)
c. \( \frac{25}{6} C V^{2} \)
D. \( \frac{9}{2} C V^{2} \)


The number of significant figures in \( \mathbf{5 . 6 9} \times \mathbf{1 0}^{\mathbf{1 5}} \mathbf{k g} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 18


For \( a=0, \) the value of \( d( \) maximum
value of \( \rho \) as shown in the figure) is
\( ^{A} \cdot \frac{3 Z e}{4 \pi R^{3}} \)
в. \( \frac{3 Z}{\pi R^{3}} \)
c. \( \frac{4 Z e}{3 \pi R^{3}} \)
D. \( \frac{Z e}{3 \pi R^{3}} \)


Least paramagnetic property is shown by:
A . \( F e \)
в. \( M n \)
c. \( N i \)
D. \( C u \)


Explain briefly the coil and magnet experiment to demonstrate electromagnetic induction.


The electron pair which forms a bond between two similar non - metallic
atoms will be ?
A. Dissimilar shared between the two
B. By complete transfer from one atom to other
c. In a similar spin condition
D. Equally shared in between the two


If a body is projected with speed
greater than escape speed \( v_{e} \) from the surface of earth, find its speed in interstellar space.


Which of the following methods is suitable for preventing an iron vessel from rusting?
A. Applying grease
B. Applying paint
C. Applying a coating of zinc
D. All of the above


Consider the diagram of the trajectory
of a thrown tomato. At what point is the
potential energy greatest?


Fill in the blanks: The graph of line \( x+2 \) \( =0 \) is parallel to \( \ldots \ldots . . . . \) axis.


Assertion
Acini of pancreas release three major
enzymes and Islet of Langerhans two important hormones.
Reason
Pancreas, the second largest gland is a heterocrine gland.
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


Which of the following overlapping results non-bonding molecular orbitals, if z-axis is considered as internuclear
axis?
A \( \cdot p_{z}+p_{z} \)
B . \( p_{y}+p_{y} \)
c. \( p_{x}+s \)
D. \( p_{y}+s \)


f \( A=\{1,2,3\} \) and \( B=\{3,4\} \) and
\( \boldsymbol{C}=\{\mathbf{1}, \mathbf{3}, \mathbf{5}\} . \) Find \( \boldsymbol{A} \times(\boldsymbol{B} \cup \boldsymbol{C}) \)


Find \( \boldsymbol{X} \) and \( \boldsymbol{Y}, \) if \( \boldsymbol{2}\left[\begin{array}{ll}\mathbf{1} & \boldsymbol{3} \\ \boldsymbol{0} & \boldsymbol{x}\end{array}\right]+\left[\begin{array}{ll}\boldsymbol{y} & \boldsymbol{0} \\ \boldsymbol{1} & \boldsymbol{2}\end{array}\right]= \)
\( \left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right] \)


A scientist say that the efficiency of his
heat engine which operates at source
temperature \( 127^{\circ} \mathrm{C} \) and sink
temperature \( 27^{\circ} C \) is \( 26 \% \), then
A. It is impossible
B. It is possible but less probable
C. It is quite probable
D. Data are incomplete


Typical 'lubb-dup' sounds heard in heart
beat are due to
A. closing of bicuspid and tricuspid valves
B. closing of semilunar valves
c. Blood under pressure through aorta
D. closure of bicuspid-tricuspid valves followed by semilunar valves


Height at which they collide is
A . \( 58.8 \mathrm{m} \)
B. \( 111.5 \mathrm{m} \)
\( c .117 .6 m \)
D. 122.5m


In the system of equations \( \frac{12}{x+y}+ \) \( \frac{8}{x-y}=8 \) and \( \frac{27}{x+y}-\frac{12}{x-y}=3, \) the
values of \( x \) and \( y \) will be
A \( \cdot \frac{5}{3} \) and \( \frac{1}{3} \)
B. \( \frac{5}{2} \) and \( \frac{1}{2} \)
c. 2 and \( \frac{1}{3} \)
D. \( \frac{5}{4} \) and \( \frac{1}{4} \)


Mirage is found due to
A. Refraction of light
B. Total internal reflection
C . Reflection of light
D. All


Ten students collected the following amounts (in rupees) for an orphanage:
250,450,500,750,300,650,200,350
500,560
Find their mean and median.


Solve the differential equation : \( \boldsymbol{y}+ \)
\( \boldsymbol{x} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}=\boldsymbol{x}-\boldsymbol{y} \frac{d \boldsymbol{y}}{d \boldsymbol{x} \boldsymbol{x}} \)


Assertion
If the matrices \( A, B,(A+B) \) are
nonsingular, then \( \left[\boldsymbol{A}(\boldsymbol{A}+\boldsymbol{B})^{-1} \boldsymbol{B}\right]^{-1}= \)
\( \boldsymbol{B}^{-1}+\boldsymbol{A}^{-1} \)
Reason
\( \left[\boldsymbol{A}(\boldsymbol{A}+\boldsymbol{B})^{-1} \boldsymbol{B}\right]^{-1}=\left[\boldsymbol{A}\left(\boldsymbol{A}^{-1}+\right.\right. \)
\( \left.\left.\boldsymbol{B}^{-1}\right) \boldsymbol{B}\right]^{-1}=\left[\left(\boldsymbol{I}+\boldsymbol{A} \boldsymbol{B}^{-1}\right) \boldsymbol{B}\right]^{-1}= \)
\( \left[\left(\boldsymbol{B}+\boldsymbol{A B}^{-1} \boldsymbol{B}\right)\right]^{-1}=[(\boldsymbol{B}+ \)
\( \boldsymbol{A I})]^{-1}=[(\boldsymbol{B}+\mathbf{1})]^{-1}=\boldsymbol{B}^{-1}+\boldsymbol{A}^{-1} \)
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. Assertion is incorrect but Reason is correct


A car moves with a speed of \( 40 \mathrm{km} / \mathrm{h} \) for
15 minutes and then with a speed of 60 \( \mathrm{km} / \mathrm{h} \) for the next 15 minutes. The total
distance covered by the car is :
A . 35
B. 25
\( c \cdot 45 \)
D. 66


Name spectral series of hydrogen which lies in the ultraviolet region of
electromagnetic spectrum


Select the correct options about the solubility of the following species in
\( \boldsymbol{H}_{2} \boldsymbol{O} \) and \( \boldsymbol{N} \boldsymbol{H}_{3}(\mathbf{a q}) \)
\( A g F, A g C N, A g C l, A g l, C a F_{2}, C a C l_{2} \)
This question has multiple correct options
A \( . A g F \) and \( C a C l_{2} \) are soluble in \( H_{2} O \)
B. \( A g C N \) and \( A g C l \) are soluble in \( N H_{3} \)
c. \( A g I \) and \( C a F_{2} \) are soluble in \( H_{2} O \) and \( N H_{3} \) (aq) both
D. None of these


Select the correct order of Lewis basic
strength for exocyclic carbonyl oxygen.
\( \mathbf{A} \)
B.
\( C \)
\( D \)


Name the instruments for which more
than one part is responsible for the production of sound.
\( A \). Tabla
B. Violin
c. Guitar
D. All of the above


f'o' is the centre of the circle ; \( 0 L=4 \)
\( \mathrm{cm}, \mathrm{AB}=6 \mathrm{cm} \) and \( \mathrm{OM}=3 \mathrm{cm}, \) then \( \mathrm{CD} \)
\( A \cdot 4 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


If \( y=e^{a \sin ^{-1} x} \) then prove that
\( \left(1-x^{2}\right) y_{2}-x y_{1}-a^{2} y=0, \) where \( y_{1} \)
and \( y_{2} \) are first and second order
derivatives of \( y \) respectively.


Justify the following statements on the basis of external features:
(i) Underground parts of a plant are not always roots.
(ii) Flower is a modified shoot


Temporary hardness can be removed by mixing water with slaked lime, this process is known as


In the adjoin figure, \( A B C \) is an isocules triangle with \( A B=A C \& L M \) is
parallel to \( B C . \) If \( \angle A=50^{\circ}, \) find \( \angle L M C \)


The de-brogile wavelength of an electron in the ground state of hydrogen atom is:
\( [\boldsymbol{K} . \boldsymbol{E} .=\mathbf{1 3 . 6} e \boldsymbol{V} ; \mathbf{1} e \boldsymbol{V}=\mathbf{1 . 6 0 2} \times \)
\( \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{J} \)
A. \( 33.28 n m \)
B. \( 3.328 n m \)
\( \mathbf{c} .0 .3328 n m \)
D. \( 0.0332 n m \)


The conducting sphere of radii \( r_{1} \) and \( r_{2} \) are at the same potential. What is the ratio of their charges?
B . \( r_{2}: r_{1} \)
C \( \cdot r_{1}^{2}: r_{2}^{2} \)
D \( \cdot r_{2}^{2}: r_{1}^{2} \)


A particle is in SHM. Then the graph of its acceleration as a function of
displacement is a
A . circle
B. hyperbola
c. straight line with negative slope
D. straight line with positive slope


This conversion can be achieved by :
A \( \cdot \operatorname{NaNH}_{2}, C H_{3} C H O \)
B. \( \operatorname{NaNH}_{2}, C H_{3}-C H_{2}-C H_{2}-B r \)
c. КОН\( , \)СН\( _{3}- \)СН\( _{2}- \)Вг
D.


Convex lenses correct
A. Presbyopia
B. Myopia
c. Hypermetropia
D. Glaucoma


Assertion
Linear momentum of a body changes even when it is moving uniformly in a
circle.
Reason
In uniform circular motion velocity
remains constant.
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


Metallic tin and conc.\( H N O_{3} \) reacts to
form:
A. metastannic acid.
B. stannic nitrate
c. stannous nitrite
D. stannous acid


\( \mathbf{A} \)
\( 4 \Omega(\text { or } 4 \text { ohm }) \) wire and \( a 2 \Omega \) (or 2
ohm)wire are connected in parallel. \( \mathbf{A} \)
current of \( 3 A \) passes through the wires. How much current passes through the 2
\( \Omega(\text { or } 2 \text { ohm }) \) wire?
\( A \cdot 2 A \)
B. 4A
\( c \cdot 6 A \)
D. 8A


The sum of the length, breadth and
height of a cuboid is \( 38 \mathrm{cm} \) the length of
its diagonal is \( 22 \mathrm{cm} . \) Find the surface area of the cuboid.


The oxidation states of nitrogen in
\( \mathbf{N H}_{4} \mathbf{N} \mathbf{O}_{3} \) are :
A. -3,+5
B. -4,+5
\( c_{1}+3,+5 \)
\( D \cdot+3,-5 \)


Differentiate between heat capacity and
specific heat capacity


\[
\begin{array}{c}
\operatorname{Let}\left|\begin{array}{ccc}
a^{2}+1 & a b & a c \\
a b & b^{2}+1 & b c \\
a c & b c & c^{2}+1
\end{array}\right|=k+ \\
a^{2}+b^{2}+c^{2}
\end{array}
\]
then \( 4 k \) is


A gas is at \( 10 P a \) pressure with a
volume \( 8 m^{3} . \) When \( 100 J \) of heat is
supplied to the gas, it expands to \( 10 m^{3} \) at constant pressure. The change in its internal energy is :
A . \( 80 J \)
В. \( -80 J \)
c. \( 20 J \)
D. \( -20 J \)


Electrons with de Broglie wavelength \( \lambda \) are bombarded on a metal target. It is found that photons are emitted from the metal target. The minimum wavelength of emitted photons is \( [\mathrm{m}= \) mass of eletron]


rove: \( (\overrightarrow{\boldsymbol{A}}-\overrightarrow{\boldsymbol{B}}) \times(\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}})=2(\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}) \)


A closed hollow insulated cylinder is
filled with gas at \( 0^{0} \mathrm{C} \) and also contains
an insulated piston of negligible weight and negligible thickness at the the middle point. The gas at one side of the piston is heated to \( 100^{\circ} \mathrm{C} \). If the
piston moves \( 5 \mathrm{cm} \), the length of the hollow cylinder is
A. \( 13.65 \mathrm{cm} \)
B. 27.3 cm
c. \( 64.6 \mathrm{cm} \)
D. \( 54.6 \mathrm{cm} \)


Prove that \( 25^{n}-20^{n}-8^{n}+3^{n} \) is
divisible by 5


Calculate the angular \( \& \) Linear speed of tip of 2 nd hand of a clock a length \( 7 \mathrm{cm} \)


\( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \) and \( \boldsymbol{B}=\{\mathbf{5}, \mathbf{7}, \boldsymbol{9}\} . \) The
relation from \( B \) to \( A \) is
This question has multiple correct options
A \( \cdot\{(a, 5),(a, 7),(b, 7),(c, 9)\} \)
B . \{(5,7),(9,9),(7,5)\}
c. \( \{(5, a),(5, b),(5, c)\} \)
D \cdot \( \{(5, b),(7, c),(7, a),(9, b)\} \)


Oxides of the various metals are
converted into metal by heating but not in :
A. \( A g_{2} O \)
в. \( C u O \)
c. \( H g O \)
D. All of these


Coefficient of restitution depends upon,
A. The relative velocities of approach and separation
B. The masses of the colliding bodies
C. the materials of the colliding bodies
D. all the above


The sum of the series \( \frac{2}{3 !}+\frac{4}{5 !}+\frac{6}{7 !}+\ldots \)
\( \infty=\frac{a}{e} . \) Find \( (a+3)^{2} \)


ff \( \quad A=\tan ^{-1}\left(\frac{x \sqrt{3}}{2 k-x}\right) \) and \( B= \)
\( \tan ^{-1}\left(\frac{2 x-k}{k \sqrt{3}}\right) . \) Then, \( A-B \) is equal
to
A \( \cdot \frac{\pi}{2} \)
в.
c.
D. None of these


Find out which of the following sequences are arithmetic progressions. For those which are arithmetic
progressions, find out the common
difference.
\( -225,-425,-625,-825, \dots \)


Fullerene is an allotrope of carbon which is similar to a football. It has 60
carbon atoms joined together and no other element in it. There are various
types of fullerenes. \( C_{60}, C_{70}, C_{74} \) and \( C_{75} \)
are the members of the fullerene family.
But \( C_{60} \) (pronounced as \( C \) sixty) is the most stable and most studied form
of fullerenes. What do you think is the
nature of the bond which is
joining these atoms together?
A. lonic
B. Covalent
c. Hydrogen
D. Polar covalent


Sex determination by chromosomes in human and Drosophila is through.
A. \( x x-x y \)
B. XX-XO
c. zz-zw
D. Both A and E


Balance the following reaction.
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{P b C l}_{2}(\boldsymbol{a q}) \longrightarrow \boldsymbol{P b}(\boldsymbol{s})+ \)
\( Z n C l_{2}(a q) \)
\( \mathbf{A} \cdot Z n(s)+P b C l_{2}(a q) \longrightarrow P b(s)+Z n C l_{2}(a q) \)
B \( \cdot 2 Z n(s)+P b C l_{2}(a q) \longrightarrow P b(s)+2 Z n C l_{2}(a q) \)
\( \mathbf{c} \cdot Z n(s)+2 P b C l_{2}(a q) \longrightarrow P b(s)+Z n C l_{2}(a q) \)
D \( \cdot Z n(s)+2 P b C l_{2}(a q) \longrightarrow P b(s)+2 Z n C l_{2}(a q) \)


How many half-lives does Carbon10 undergo in 2 minutes and 32 seconds? Given the half-life of Carbon-
10 is about 19 seconds.
A. 8 half-lives
B. 7 half-lives
c. 6 half-lives
D. 5 half-lives
E. 4 half-lives


Let \( A(\vec{a}), B(\vec{b}), C(\vec{c}) \) be the vertices of the triangle \( A B C \) and let \( D E F \) be the
mid points of the sides \( B C, C A, A B \)
respectively. If \( \boldsymbol{P} \) divides the median
\( A D \) in the ratio 2: 1 then the position
vector of \( \boldsymbol{P} \) is
A . 0
B \( \cdot \vec{a}+\vec{b}+\vec{c} \)
\( \overbrace{3}^{\text {c. }} \frac{\vec{a}+\vec{b}+\vec{c}}{3} \)
\( \frac{2 \vec{a}+\vec{b}+\vec{c}}{3} \)


Impurities found in ores are called:
A. mud
B. gangue
c. electrolyte
D. none of the above


\( \mathrm{CaOCl}_{2} \) (bleaching powder) has two types of chlorine with different
oxidation numbers. The sum of both the
oxidation numbers is


A stream line body with relative density
\( d_{1} \) falls into air from a height \( h_{1} \) on the
surface of a liquid of relative density \( \boldsymbol{d}_{2} \)
where \( d_{2} \) is greater than \( d_{1} \). The time of immersion of the body into the liquid will be
\( A \)
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)} \times \frac{d_{1}}{d_{2}-d_{1}}
\]
в.
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)}
\]
\( c \)
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)} \times \frac{d_{1}}{d_{2}}
\]
D.
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)} \times \frac{d_{2}}{d_{1}}
\]


The half life period of a radioactive element is 50 days. The activity of the
substance gets reduced to \( 1 / 8 \) of the original value in:
A. 50 days
B . 100 days
c. 25 days
D. 150 days


Gases mix at the molecular level. In an
experiment, oxygen molecules were added to hydrogen molecules. This on burning became a substance that had both oxygen and hydrogen. What is this product?
A. Mixture
B. Compound
c. Both a mixture as well as a compound
D. Solution


Jamila started noticing some kind of reddish brown particles around a photo frame, which is an old one. Why it could have happened and what is it?


Show that
\( \tan 36^{\circ} \tan 17^{\circ} \tan 54^{\circ} \tan 73^{\circ}=1 \)


Which of the following does not cause a depletion in the water table of a place?
A. Constructing factories and houses
B. Making concrete roads and floors
c. Deforestation
D. None of these


A convex lens makes a real image \( 4 \mathrm{cm} \) long on a screen.When the lens is
shifted to a new position without disturbing object or the screen, we again get a real image on the screen which is \( 9 \mathrm{cm} \) long. The length of the
object must be :
A . \( 2.25 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c .6 .50 \mathrm{cm} \)
D. \( 36 \mathrm{cm} \)


\( X e F_{6} \) exists as \( \left[X e F_{4}\right]^{+2}\left[2 H F_{2}\right]^{-} \) in
\( \boldsymbol{H} \boldsymbol{F} \)
A. True
B. False


In an astronomical telescope of
refracting type:
A. Eyepiece has greater focal length
B. Objective has greater focal length
C. Objective and eyepiece have equal focal length
D. Eyepiece has greater aperture than the objective


Shown in the figure are the velocity
time graphs of the two particles \( P_{1}, \) and
\( P_{2} \) Which of the following statements
about their relative motion is
true? Magnitude of their relative
velocity:
A. is zero
B. is non zero constant
c. continuously decreases
D. continuously increases


The 17 th term of the series \( 3+7+11+15 \)
+ ............ is:
\( A \cdot 63 \)
B. 65
\( c \cdot 67 \)
D. 69


If the two analytes present in the sample are of similar chemical type. Choose the correct chromatographic technique for separation.
A. Adsorption chromatography
B. Gel chromatography
c. Partition chromatography
D. None of these


The mineral of aluminium which does
not contain oxygen is:
A. bauxite
B. diaspore
c. gibsite
D. cryolite


The \( 4 t h \) term from the end in the
expansion of \( \left(\frac{x^{3}}{2}-\frac{2}{x^{2}}\right)^{7} \) is
A . \( 35 x \)
B. \( 70 x^{2} \)
\( c \cdot 35 x^{2} \)
D. \( 70 x \)


Identify \( \mathrm{W}, \mathrm{X}, \mathrm{Y}, \) and \( \mathrm{Z} \) respectively in the given reactions. \( \boldsymbol{C a C O}_{3} \stackrel{\triangle}{\rightarrow} \boldsymbol{W}+\boldsymbol{X} \)
\( \boldsymbol{W}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{Y} \)
\( \boldsymbol{Y}+\boldsymbol{Z} \rightarrow \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{C a C O}_{3} \)
A. \( C a O, C O_{2}, C a C O_{3}, N a_{2} C O_{3} \)
в. \( C O_{2}, \) Са\( (O H)_{2}, C a(H C O)_{3}, N a H C O_{3} \)
c. \( C a O, C O_{2}, C a(O H)_{2}, N a_{2} C O_{3} \)
D. \( C O_{2}, C a O, H_{2} C O_{3}, N a_{2} C O_{3} \)


State whether the following statements are True or False. Rewrite the false
statements correctly. Transpiration is the loss of water from the roots of the plant.
A. True
B. False


What is Lenz's law?


Under similar conditions, which of the
following gas will have same value of
\( \mu_{r m s} \) as \( C O_{2} ? \)
A. \( N O \)
в. \( C_{3} H_{8} \)
\( c \cdot c o \)
D. \( N_{2} \)


Which of the following statement is not
true?
A. The resistance of intrinsic semiconductors decreases with increase to temperature
B. Doping pure Si with trivalent impurities gives p-type semiconductor
c. The majority carriers in n-type semiconductors are holes
D. A p-njunction can act as a semiconductor diode


A thin rod of length \( \frac{f}{3} \) lies along the axis of a concave mirror of focal length \( \boldsymbol{f} \)
One end of its image touches at end of the rod. The length of the image is :
\( A \cdot f \)
в. \( \frac{f}{2} \)
c. \( 2 f \)
D. \( \frac{f}{4} \)


Which among the following is best lubricant?
A. Solids
B. Liquids
c. Gases
D. Both B and C


Find the locus of the point equidistant from (-1,2) and (3,0)


Fill in the blanks:
The relation between the angle of
incidence and angle of reflection is given by


The value of \( \int \frac{d x}{\sqrt{8+3 x-x^{2}}} \) is equal to
A \( \cdot \frac{2}{3} \sin ^{-1}\left(\frac{2 x-3}{\sqrt{41}}\right)+C \)
B. \( \frac{3}{2} \sin ^{-1}\left(\frac{2 x-3}{\sqrt{41}}\right)+C \)
c. \( \frac{1}{\sqrt{41}} \sin ^{-1}\left(\frac{2 x-3}{\sqrt{41}}\right)+C \)
D. \( \sin ^{-1}\left(\frac{2 x-3}{\sqrt{41}}\right)+C \)


Which of the following reproduces only
inside a host cell?
A. Bacteria
B. Virus
c. Protist
D. Fungus


Select correct statement(s).
This question has multiple correct options
\( \mathbf{A} \cdot^{131} I \) is used for the treatment of thyroid cancer
B. \( ^{59} \) Co cannot be used for treatment of cancer
C. \( ^{33} P \) is used for treatment of cancer
D. Excessive use of radioactive elements cause cancer


A dilute ferrous sulphate solution was
gradually added to the beaker
containing acidified potassium
permanganate solution. The light purple colour of the solution fades and finally disappears. Which of the following is the correct explanation for the observation?
\( \mathbf{A} \cdot K M n O_{4} \) is an oxidising agent, it oxidises \( F e S O_{4} \)
B. \( F e S O_{4} \) acts as an oxidising agent and oxidises \( K M n O_{4} \)
C. The colour disappears due to dilution; no reaction is involved
D. \( K M n O_{4} \) is an unstable compound and decomposes in presence of \( F e S O_{4} \) to a colourless compound


Time taken by a \( 836 W \) heater to heat
one litre of water from \( 10^{0} C \) to \( 40^{0} C \) is:
A . \( 50 s \)
B. 100 s
c. \( 150 s \)
D. 200


n figure 2 , if \( D E \| B C \), then the value
of \( x \) is equal to
\( A \cdot 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 7 c m \)
D. \( 4.7 \mathrm{cm} \)


State any two possible sources of errors in meter bridge experiment.


Calculate the arc length for the given
diagram.
A . 1.23 in
B . 2.23 in
c. 4.23 in
D. 5.23 in


Value based questions. How quickly do you think-a steroid hormone can start to exert its effect?


What is the approximate peak value of an alternating current producing four times the heat produced per seconds by a steady current of \( 2 \mathrm{A} \) in a resistor?
A \( .2 .8 \mathrm{A} \)
в. 4.0 А
c. 5.6 A
D. 8.0 A


Prove that \( (1 \times 2 \times 5)+(2 \times 3 \times 7)+ \)
\( (3 \times 4 \times 9)+\ldots . \) is
\( \frac{n(n+1)(n+2)(3 n+7)}{6} \)


What is the nitrogenous waste produced by amphibian larvae and by the adult animals different?


The percentage error in the surface area of a cube with edge \( x \mathrm{cm}, \) when the edge is increased by \( 11 \% \) is
A . 11
B . 22
c. 10
D. 44


What effect does the presence of ANF
have on the body?
A. It increases the production of renin
B. It increases the excretion of sodium and water
C. It stimulates the production of aldosterone
D. It stimulates the production of angiotensin


When an elastic material with Young's
modulus \( ^{\prime} Y^{\prime} \) is subjected to a
stretching stress \( ^{\prime} S^{\prime}, \) then the elastic
energy stored per unit volume is:
\( ^{A} \cdot \frac{S^{2}}{2 Y} \)
B. \( \frac{Y S^{2}}{2} \)
c. \( \frac{s}{2 Y} \)
D. \( \frac{Y S}{2} \)


Matrix A shows the weight of four boys and four girls in kg at the beginning of a diet programme to lose weight. Matrix B shows the corresponding weights after
the diet programme. \( \boldsymbol{A}=\left[\begin{array}{llll}\mathbf{3 5} & \mathbf{4 0} & \mathbf{2 8} & \mathbf{4 5} \\ \mathbf{4 2} & \mathbf{3 8} & \mathbf{4 1} & \mathbf{3 0}\end{array}\right] \underset{\mathbf{G i r l s}}{\mathbf{B o y s}}, \mathbf{B}= \)
\( \left[\begin{array}{cccc}\mathbf{3 2} & \mathbf{3 5} & \mathbf{2 7} & \mathbf{4 1} \\ \mathbf{4 0} & \mathbf{3 0} & \mathbf{3 4} & \mathbf{2 7}\end{array}\right] \begin{array}{c}\boldsymbol{B} \mathbf{o y s} \\ \text {Girls}\end{array} \)
Find the weight loss of the Boys and Girls.


In double decomposition reaction are exchanged


In triangle \( A B C, D \) and \( E \) are mid-
points of sides \( A B \) and \( B C \)
respectively. Also, \( \boldsymbol{F} \) is a point in side
\( A C \) so that \( D F \) is parallel to \( B C \)
Find the perimeter of parallelogram
\( D B E F, \) if \( A B=10 \mathrm{cm}, B C=8 \cdot 4 \mathrm{cm} \)
and \( A C=12 \mathrm{cm} \)
A \( .28 .7 \mathrm{cm} \)
в. \( 22.5 \mathrm{cm} \)
c. \( 18.4 \mathrm{cm} \)
D. \( 18.5 \mathrm{cm} \)


A block of \( 1 k g \) is stopped against a wall
by applying a force \( F \) perpendicular to
the wall. If \( \mu=0.2 \) then minimum value
of \( \boldsymbol{F} \) will be :
\( \begin{array}{ll}\text { A } & \text { N }\end{array} \)
в. \( 49 N \)
\( \mathbf{c} .98 N \)
D. \( 490 N \)


The number of real solution of the
equation \( \tan ^{-1} \sqrt{x^{2}-3 x+2}+ \)
\( \cos ^{-1} \sqrt{4 x-x^{2}-3}=\pi \) is
\( A \)
B. 2
\( c \cdot c \)
D. infinite


For the reaction at \( 298 K \)
\( \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C}(\boldsymbol{g})+\boldsymbol{D}(\boldsymbol{g}) \)
\( \Delta H^{o}=29.8 k c a l ; \Delta S^{o}=0.1 k c a l / K \)
Calculate \( \Delta G^{o} \) and \( K \)
A. \( \Delta G^{o}=0 ; K=1 \)
В. \( \Delta G^{o}=1 ; K=e \)
c. \( \Delta G^{o}=2 ; K=e^{2} \)
D. None of these


Draw a well labelled diagram of
Euglena.


Which of the following compounds has DBE equal to benzene?
\( A \)
B.
\( c \)
D. All the above


Which one of the following sets of vitamins is fat soluble?
A \( . C, D, B_{6}, B_{12} \)
в. \( A, D, E, K \)
c. \( A, D, B_{1}, B_{2} \)
D. \( D, B_{1}, B_{2}, E \)


A wire carrying a current of \( 100 A \) is bent into the form of a circle of radius
5cm. The flux density at the centre of
the coil is \( _{-}-_{-}-_{-}-_{-} W b / m^{2} \)
\begin{tabular}{l}
A \( \cdot 12.57 \times 10^{-5} \) \\
\hline
\end{tabular}
B . \( 125.7 \times 10^{-5} \)
c. \( 1.257 \times 10^{-5} \)
D. \( 1257 \times 10^{-5} \)


Instead of using biomass directly as fuel, it is always advantageous to use biogas produced from biomass.
a) What do you mean by biomass?
b) What are the advantages of using biogas as fuel?


A particle is executing \( S H M \) and its velocity \( v \) is related to its position \( (x) \)
as \( y^{2}+a x^{2}=b, \) where a and b are
positive constants. The frequency of oscillation of particle is
\( ^{A} \cdot \frac{1}{2 \pi} \sqrt{\frac{b}{a}} \)
B. \( \frac{\sqrt{a}}{2 \pi} \)
\( c \cdot \frac{\sqrt{b}}{2 \pi} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{a}{b}} \)


What is an equation?
A. A statement in which the values of two mathematical
expressions are equal
B. An expression that computes the values of variables.
C. A mathematical expression.
D. None of these


Factors responsible for base strength comparison of amines in aqueous solution?
A. Availability of Ione pair on nitrogen
B. Lone pair donating power of nitrogen
c. Stability of conjugate acid formed by solvation through H-bonding.
D. All of the above


Why is adsorption always exothermic?


\( 2 K_{2} C r_{2} O_{7}+8 H_{2} S O_{4} \rightarrow 2 K_{2} S O_{4}+ \)
\( 2 C r_{2}\left(S O_{4}\right)_{3}+8 H_{2} O+3 O_{2} \)
Is the above reaction correct?
A. True
B. False


The IUPAC name of the given compound
is:
A. Propylbenzene
B. Benzyl propane
c. 3 -propyl benzene
D. None of these


Convert:
Ethanoic acid to methylamine.


ASSERTION (A):Hyugens' theory failed to explain polarization

REASON (R): According to Hyugens' theory light is longitudinal wave
A. A is correct, R is correct and it is the correct explanation
B. A is correct, R is correct but it is not a correct explanation
c. A is correct, R is wrong
D. A is wrong, R is correct


Amylopectin is composed of:
\( \mathbf{A} \cdot \alpha-D- \) glucose \( , C_{1}-C_{4} \) and \( C_{1}-C_{6} \) linkages
B. \( \alpha-D- \) glucose, \( C_{1}-C_{4} \) and \( C_{2}-C_{6} \) linkages
\( \mathbf{c} \cdot \beta-D- \) glucose, \( C_{1}-C_{4} \) and \( C_{2}-C_{6} \) linkages
D. \( \beta-D- \) glucose, \( C_{1}-C_{4} \) and \( C_{1}-C_{6} \) linkages


An urn contains 3 white and 6 red balls.
Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also find mean and
variance of the distribution


Which of the following statement is true about the relation between electric field
and potential?
A. Electric field in the direction in which the potential decreases steepest
B. Magnitude of electric field is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at that point.
C. In the region of strong electric field, equipotentia
D. Both the statements
(a) and
(b) are correct.


A force acts on a \( 30 \mathrm{gm} \) particle in such a way that the position of the particle as a function of time is given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}- \)
\( 4 t^{2}+t^{3}, \) where \( x \) is in metres and \( t \) is in
seconds. The work done during the first
4 second is?
A .5 .28
B. 450mJ
c. \( 490 \mathrm{mJ} \)
D. 530 mJ


When a lead storage battery is discharged, then:
\( A \cdot \mathrm{SO}_{2} \) is evolved
B. lead is formed
c. lead sulphate is consumed
D. sulphuric acid is consumed


Which statement is correct for
compositae?
A. 5-lobed stamens
B. Syngenesious stamens
c. Basal ovule
D. Ligulate ray florets


The shift of the interference pattern on
the screen when the slit is displayed by
\( \boldsymbol{S l}=\mathbf{1} \boldsymbol{m} \boldsymbol{m} \) along the arc of radius \( \boldsymbol{r} \)
with centre at 0
\( A \cdot 4 m m \)
B. \( 6 m m \)
\( c .10 m m \)
D. \( 13 m m \)


The \( 7^{t h} \) term of an \( A P \) is 32 and its \( 13^{t h} \)
term is 62 find first 5 terms of the \( A P \)


\( \lim _{h \rightarrow 0}\left\{\frac{1}{h^{3} \sqrt{8+h}}-\frac{1}{2 h}\right\}= \)
A \( \cdot \frac{-1}{12} \)
B. \( \frac{-4}{3} \)
\( c \cdot \frac{-16}{3} \)
D. \( \frac{-1}{48} \)


Which or the rollowıng grapns given
below is impossible?
\( A \)
B.
\( \mathbf{c} \)
D.


A metal is irradiated with light of
wavelength \( 600 n m . \) Given that the work
function of the metal is \( 1.0 e V \), the de
Broglie wavelength of the ejected electron is close to:
A \( \cdot 6.6 \times 10^{-7} \mathrm{m} \)
в. \( 8.9 \times 10^{-11} \) \( _{m} \)
c. \( 1.3 \times 10^{-9} m \)
D. \( 6.6 \times 10^{-13} \) и


The time taken by a particle performing
S.H.M. to pass from point \( \boldsymbol{A} \) to \( \boldsymbol{B} \) where its velocities are same is 2 seconds.
After another 2 seconds it returns to \( \mathrm{B} \)
The time period of oscillation is (in seconds):
A .2
B. 4
\( c \cdot 6 \)
\( D \)


Gases like
and \( ------ \) are generated in a biogas
plant.
A. Methane \( \left(C H_{4}\right),\left(C O_{2}\right), \) Hydrogen \( \left(H_{2}\right) \) and \( H_{2} S \)
B. Sulphuric acid, \( \left(C O_{2}\right) \), Hydrogen \( \left(H_{2}\right) \) and \( H_{2} S \)
C. Methane \( \left(C H_{4}\right), \) Oxygen, Hydrogen \( \left(H_{2}\right) \) and \( H_{2} S \)
D. methane \( \left(C H_{4}\right), C O_{2}, \) Sulphuric acid and \( H_{2} S \)


Two capillary tubes of the same material but of different radii are
dipped in a liquid. The heights to which the liquid rises in the two tubes are
\( 2.2 c m \) and \( 6.6 c m . \) The ratio of radii of
the tubes will be
A . 1: 9
B. 1: 3
c. 9: 1
D. 3: 1


If at any instant of time the
displacement of a harmonic oscillator is \( 0.02 \mathrm{m} \) and its acceleration is \( 2 \mathrm{ms}^{-2} \)
its angular frequency at that instant will be
A. \( 0.1 \mathrm{rads}^{-1} \)
B. \( 1 \mathrm{rads}^{-1} \)
\( \mathbf{c} \cdot 10 \mathrm{rads}^{-1} \)
D. \( 100 \mathrm{rads}^{-1} \)


How many of the following reactions goes almost all the way to completion?
\( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) ; K_{c}=2.7 \times \)
\( \mathbf{1 0}^{-18} \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \)


If the mass of proton \( =1.008 a . m . u \)
and mass of neutron \( =1.009 a . m . u \)
then binding energy per nucleon for \( _{4} B e^{9}(\text { mass }=9.012 a m u) \) would be:
A . 40.065 Mev
B. \( 60.44 \mathrm{MeV} \)
c. 67.2 Mev
D. 6.72 Mev


Which of the following is NOT a constant polynomial?
A \( \cdot p(y)=y^{\circ} \)
В . \( p(x)=x^{o} \)
c. \( p(y)=\frac{y}{y} \)
D. \( p(x)=y x \)


Aquatic species are more comfortable
in cold water because of:
A. as the temperature decreases, the solubility of dissolved oxygen increases
B. as the temperature increases, the solubility of dissolved oxygen increases.
c. as the temperature increases, the solubility of dissolved oxygen decreases
D. none of the above


Identify the shape of this histogram.
A. Symmetric
B. Skewed right
C. Skewed left
D. Rotational


In the formatioin of octahedral complex
ligands approach towards
and orbital of
central metal
\( \mathbf{A} \cdot d_{z^{2}}, d_{x^{2}-y^{2}} \)
B . \( d_{x^{2}-y^{2}}, d_{x y} \)
\( \mathbf{c} \cdot d_{x y}, d_{y z} \)
D. \( d_{z^{2}}, d_{x z} \)


If \( y=\sqrt{x+\sqrt{x+\sqrt{x}}}+\ldots . \infty, \) then
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A. \( \frac{1}{y^{2}-1} \)
в. \( \frac{1}{2 y+1} \)
c. \( \frac{2 y}{y^{2}-1} \)
D. \( \frac{1}{2 y-1} \)


Which of the following could be true
from the figure.
A. Motion with a variable retardation
B. May be a car approaching its destination
c. Motion with decreasing velocity over the time
D. All the above


Evaluate: \( \int \cot x \log \sin x d x \)
A \( \cdot(\log \sin x)^{2} \)
B \( \cdot \frac{1}{2}(\log \sin x) \)
c. \( \frac{1}{2}(\log \operatorname{cosec} x)^{2} \)
D. \( \frac{1}{2}(\log \sin x)^{2} \)


Weak base is
A. \( N a O H \)
в. КОН
c. \( N H_{4} O H \)
D. \( N a_{2} O \)


Consider driving in a car at 65 MPH while drinking a cup of coffee. Which of the following would be traveling at the greatest speed?
A. The car, coffee and you are traveling at the same velocity
B. The coffee is traveling with the greatest velocity assuming it has the least mass
c. The car is the only object with velocity, as the other objects are within the car
D. None of the objects have velocity, as they are all traveling together
E. As velocity is a function of speed and direction, this question cannot be answered


In a car lift, compressed air exerts a force \( F \) on a small piston having a radius of \( 5 \mathrm{cm} . \) This pressure is transmitted to a second piston of
radius \( 15 \mathrm{cm} . \) If the mass of the car to
be lifted is \( 1350 k g \), what is \( F ? \)
A . \( 1.5 \times 10^{3} N \)
В. \( 2.5 \times 10^{3} N \)
c. \( 3.5 \times 10^{3} N \)
D. \( 4.5 \times 10^{3} N \)


Let \( m_{p} \) be the mass of proton, \( m_{n} \) the
mass of a neutron, \( M_{1} \) the mass of a
\( _{10}^{20} N e \) nucleus, and \( M_{2} \) the mass of a
\( _{20}^{40} C a \) nucleus. Then This question has multiple correct options
A. \( M_{2}=2 M_{1} \)
В . \( M_{2}>2 M_{1} \)
c. \( M_{2}<2 M_{1} \)
D. \( M_{1}<10\left(m_{p}+m_{p}\right) \)


The oxides of nitrogen contain \( 63.65 \% \) \( 46.69 \% \) and \( 30.46 \% \) of nitrogen by weight, respectively. This
data illustrates the law of:
A. constant proportions
B. multiple proportions
c. reciprocal proportions
D. conservation of mass


For \( a>0 \) the value of \( \int_{-\pi}^{\pi} \frac{\sin ^{2} x}{1+a^{x}} d x \)
A \( \cdot \frac{\pi}{2} \)
B. \( \pi \)
c. \( \frac{a \pi}{2} \)
D. \( a \pi \)


\( \mathbf{f}\left[\begin{array}{cc}\boldsymbol{x}+\mathbf{3} & \mathbf{4} \\ \boldsymbol{y}-\mathbf{4} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right]=\left[\begin{array}{ll}\mathbf{5} & \mathbf{4} \\ \mathbf{3} & \mathbf{9}\end{array}\right], \) find \( \boldsymbol{x} \) and
\( \boldsymbol{y} \)


Let \( \vec{p} \) and \( \vec{q} \) be the position vectors of \( \boldsymbol{P} \)
and \( Q \) respectively with respect to \( O \) and \( |\vec{p}|=p,|\vec{q}|=q . R, S \) divide \( P, Q \)
Internally and externally in the ratio 2:
3 respectively. If \( O R \) and \( O S \) are
perpendicular, then
\( \mathbf{A} \cdot 9 p^{2}=4 q^{2} \)
B. \( 4 p^{2}=9 q^{2} \)
c. \( 9 p=4 q \)
D. \( 4 p=9 q \)


0
primary sludge and activated sludge
and select the incorrect ones.
\( \begin{array}{lll} & \text { Primary Sludge } & \text { Activated sludge } \\ \text { (i) } & \begin{array}{l}\text { It is sludge } \\ \text { formed during } \\ \text { primary sewage } \\ \text { treatment. }\end{array} & \begin{array}{l}\text { It is sludge formed } \\ \text { during secondary } \\ \text { sewage treatment. }\end{array} \\ \text { (ii) } & \begin{array}{l}\text { It possesses flocs } \\ \text { of decomposer } \\ \text { microbes. }\end{array} & \begin{array}{l}\text { It does not possess } \\ \text { flocs of }\end{array} \\ \text { (iii) } & \begin{array}{l}\text { decomposer } \\ \text { microbes. }\end{array} \\ \text { (iv) } & \begin{array}{l}\text { It does not } \\ \text { require aeration. }\end{array} & \begin{array}{l}\text { Formation of } \\ \text { activated sludge } \\ \text { requires aeration. }\end{array} \\ \begin{array}{l}\text { A lotof } \\ \text { decomposition } \\ \text { occurs during } \\ \text { formation of } \\ \text { primary sludge. }\end{array} & \begin{array}{l}\text { Very little } \\ \text { decomposition } \\ \text { occurs during } \\ \text { formation of } \\ \text { activated sludge. }\end{array}\end{array} \)
A. (i) and (ii)
B. (ii) and (iv)
\( y(i v) \)
c. only
D. (ii) and (iii)


How does Ozone react with the
following?
(i) \( P b S \)
(ii) \( C_{2} H_{4} \)
(iii) \( \boldsymbol{A} \boldsymbol{g} \)
(iv) \( \boldsymbol{H} \boldsymbol{g} \)


The atmospheric pressure at the surface of the earth is about:
A \( \cdot 10^{2} N m^{-2} \)
B . \( 10^{5} \mathrm{Nm}^{-2} \)
D. \( 10^{-5} N m^{-2} \)


Light year is a measurement of
A. Speed of aeroplanes
B. Speed of light
c. Stellar distances
D. speed of rockets


The half life period of a first order reaction is 20 minutes. The time
required for the concentration of the
reactant to change from \( 0.16 M \) to
\( \mathbf{0 . 0 2} \boldsymbol{M} \) is:
\( \mathbf{A} .80 \) minutes
B. 60 minutes
c. 40 minutes
D. 20 minutes


Statement I: Aniline on reaction with
\( \mathrm{NaNO}_{2} / \mathrm{HCl} \) at \( 0^{\circ} \mathrm{C} \) followed by
coupling with \( \beta \) -naphthol gives a dark blue coloured precipitate. Statement II: The colour of the
compound formed in the reaction of
aniline with \( \mathrm{NaNO}_{2} / \mathrm{HCl} \) at \( 0^{\circ} \mathrm{C} \)
followed by coupling with \( \beta \) -naphthol.
A. Statement I and statement II are true and statement is the correct explanation of statement
B. Statement I and statement II are true and state is not the correct explanation of statement
c. statementl is true and the statement ll is false
D. statement I is false and the statement II is true


Symbol for steradian is


Assertion
All molecules of an ideal gas move with
the same speed.
Reason
There is no attraction between the
molecules in an ideal gas.
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. Assertion is incorrect but Reason is correct


The ligand called \( \pi \) -acid is:
A \( . C O \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{C}_{2} \mathrm{O}_{4}^{2-} \)
D. ethylene diamine


The value of \( \sqrt[3]{5 \times 25} \) is
A. 5
B. 25
\( c \cdot 1 \)
D. 125


Which of the following characteristics can be related to cardiac muscles?
A. They are striated.
B. They are involuntary muscles.
c. They are less prone to fatigue.
D. All of the above


As the nuclear charge increases from neon to calcium, the orbital energies:
A. increase
B. increase very rapidly
c. increase very slowly
D. fall


The compounds are:
A . Constitutional isomers
B. Enantiomers
C. Diastereomers
D. None of these


Which of the following compounds has highest boiling point?
A. Propan-1-ol
B. n-Butane
c. chloroethane
D. Propanal


If \( 2 \tan h^{-1} x=\log y, \) then the value of \( y \)
in the terms of \( x \) is
A \( .2 x \)
в. \( \frac{2 x}{1-x^{2}} \)
c. \( x^{2} \)
D. \( \left(\frac{1+x}{1-x}\right) \)


The longest chord passes through a centre of a circle is


A conductor of length \( x \) and diameter \( x \)
has a resistance \( x \). The resistivity of the
material is:
A \( \cdot \pi x^{3} / 4 \)
B . \( \pi x^{2} \)
c. \( \pi x^{2} / 4 \)
D. \( \pi x / 2 \)


Aqueous solutions of magnesium
chloride and silver nitrate are mixed to
form solid silver chloride and aqueous
magnesium nitrate.The balanced net ionic equation contains which of the
following terms?
\( \mathbf{A} \cdot A g_{(a q)}^{+} \)
B. \( M g_{(a q)}^{2+} \)
c. \( N O_{3(a q)}^{-} \)
D. \( 2 N O_{3(a q)}^{-} \)
E \( .3 A g C l_{s} \)


An angle is such that the ratio between its complementary and supplementary angles is \( 1: 4 . \) Then the angle measure
is?
A \( \cdot 45^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 75^{\circ} \)
D. \( 90^{\circ} \)


A metal conductor of length 1 m rotates
vertically about one of its ends at angular velocity 5 radians per second. If
the horizontal component of earths
magnetic field is \( 0.2 \times 10^{-4} T, \) then the
e.m.f. developed between the two ends of
the conductor is
A. depends on the nature of the metal used
B. depends on the intensity of the radiation
c. depends both on the intensity of the radiation and the metal used
D. is the same for all metal and independent of the intensity of the radiation.


Two fractions are equivalent, if their cross multiplications are
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. equal
D. not equal


Statement 1: Iron is an element.
Statement 2: It cannot be broken into
smaller units and retain its physical and chemical properties.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1
c. statement 1 is correct but statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


Double helix model of DNA was
proposed by
A. Nirenberg
B. Komberg
c. Holley and Nirenberg
D. watson and Crick


The gap between two myelin sheath is known as
A. Nodes of Ranvier
B. Synaptic cleft
c. Schwann cells
D. Synaptic knob
E. Neural plate


\( X e O_{4} \) shows maximum oxidation state
\( (+8) . \) If \( X e \) reacts with fluorine atom
the maximum oxidation state shown by
\( \boldsymbol{X} \boldsymbol{e} \) is :


\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{3} / \mathbf{8} ; \boldsymbol{P}(\boldsymbol{B})=\mathbf{1} / \mathbf{2} ; \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
\( \mathbf{5} / \mathbf{8}, \) which of the following do/does hold
good? This question has multiple correct options
A \( \cdot P\left(A^{C} / B\right)=2 P\left(A / B^{C}\right) \)
B . \( P(B)=P\left(A^{C} / B\right) \)
C \( \cdot 15 P\left(A^{C} / B^{C}\right)=8 P\left(B / A^{C}\right) \)
D \( \cdot P\left(A / B^{C}\right)=(A \cap B) \)


An aeroplane is flying in a horizontal direction with a velocity \( 600 \mathrm{km} / \mathrm{h} \) at
height of 1960 m. When it is vertically above the point \( A \) on the ground, a body is dropped from it. The body strikes the ground at point B. Calculate the distance AB.


Assertion
If the potential difference applied to an electron is made 4 times, the de Broglie wavelength associate halved.
Reason
On making a potential difference 4 times, velocity is doubled and hence \( \lambda \) is halved.

Read the above assertion and reason
and choose the correct option regarding
¡t.
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


Which of the compounds shown will react with dimethyl malonate in the presence of methoxide ion to give a compound, which on treatment with aqueous acid and gentle heating will decarboxylate to form butanoic acid?
A. \( C H_{2} C H C H_{2} \) СООН
в. \( C H_{3} C H_{2} B r \)
c. \( C H_{3} C H_{2} C O C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} B r \)


Two particles \( A \) and \( B \) are moving as
shown in the figure. At this moment
of time, the angular speed of A with
respect to B is:
A \( \cdot \frac{v_{a}+v_{b}}{r} \)
в. \( \frac{v_{a}-v_{b}}{r} \)
\( \frac{v_{a} \sin \theta-v_{b} \sin \theta}{r} \) in anticlockwise direction
D. \( \frac{v_{a} \sin \theta+v_{b} \sin \theta}{r} \) in anticlockwise direction


The structure of a protein can be denatured by heat.
A. True
B. False


is a force that
resists the movement of a solid object
through a fluid.
A. Thrust
B. Magnetic force
C. Fluid friction
D. None of these


Steam is passed into 22 gm of water at \( 20^{\circ} \mathrm{C} . \) The mass of water that will be
present when the water acquires a
temperature of \( 90^{\circ} \mathrm{C} \) (Latent heat of
steam is 540 cal/g j is
A. \( 24.83 \mathrm{gm} \)
B. 24 gm
c. \( 36.6 \mathrm{gm} \)
D. 30 gm


The value of \( \alpha \) of a transistor is \( 0.9 . \) The
change in the collector current
corresponding to a change of 4 m \( A \) in
the base current in a common
emitter arrangement is
\( \mathbf{A} .36 \mathrm{mA} \)
в. 72 тА
\( c .18 m A \)
D. 54 m


A large tank is filled with water to a height H. A small hole is made at the
base of the tank. It takes 71 time to
decrease the height of water to \( \frac{H}{\eta}(\eta> \)
1) and \( T_{2} \) time to take out the rest of 11
water. If \( T_{1}=T_{2} \) then the value of \( \eta \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8


Can phosphorus with outer electronic configuration \( 3 s^{2} 3 p^{3} \) form \( P H_{5} ? \)


Find the vertical height through which a
body of mass \( 0.5 k g \) is lifted if the
energy spent in doing so is \( 1.0 J \)
Consider \( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \)
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
c. \( 20 \mathrm{cm} \)
D. \( 50 \mathrm{cm} \)


Assertion
In a two-body collision, the momenta of
the particles are equal and opposite to one another, before as well as after the
collision when measured in the centre
of mass frame.
Reason
The momentum of the system is zero from the centre of mass frame.
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


ff \( x \) follows the Binomial distribution
with parameters \( n=6 \) and \( p \) and
\( \mathbf{9} P(X=4)=P(X=2), \) then \( p \) is
A \( \cdot \frac{1}{4} \)
B.
\( c \cdot \frac{1}{2} \)
D. \( \frac{2}{3} \)


A line passing through the points \( (a, 2 a) \) and (-2,3) is perpendicular to the line \( 4 x+3 y+5=0, \) find the value
of a.


\( \int \frac{1}{(2 x+1) \sqrt{x^{2}-x-2}} d x= \)
A. \( -\frac{1}{\sqrt{5}} \sin ^{-1} \frac{7+4 x}{3(2 x+1)}+c \)
B. \( -\frac{1}{\sqrt{5}} \cos \frac{7+4 x}{3(2 x+1)}+c \)
c. \( -\frac{1}{\sqrt{5}} \sinh ^{-1} \frac{7+4 x}{3(2 x+1)}+c \)
D. \( -\frac{1}{\sqrt{5}} \cosh ^{-1} \frac{7+4 x}{3(2 x+1)}+c \)


A particle of mass \( m_{1} \) collides elastically with a stationary particle of
\( \operatorname{mass} \boldsymbol{m}_{2}\left(\boldsymbol{m}_{1}>\boldsymbol{m}_{2}\right) . \) The maximum
angle through which the striking particle may deviate as a result of the collision is given as \( \sin \theta_{1 \max }=\frac{x m_{2}}{m_{1}} \)
Find \( \boldsymbol{x} \)


\( O \) is the centre of the circle with radius
\( 5 \mathrm{cm} . \) Chords \( A B \) and \( C D \) are parallel.
\( A B=6 \mathrm{cm} \) and \( C D=8 \mathrm{cm} . \) If \( P Q \) is
distance between \( A B \) and \( C D \), then the
length of \( \boldsymbol{P Q} \) is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c \cdot 7 \mathrm{cm} \)
D. \( 7 \sqrt{2} \mathrm{cm} \)


Write two points of differences between arteries and veins.


Let \( \left[\varepsilon_{0}\right] \) denote the dimensional formula of the permittivity of vacuum. If \( \boldsymbol{M}= \) mass, \( \boldsymbol{L}= \) length, \( \boldsymbol{T}= \) time and \( \boldsymbol{A}= \)
electric current, then:
\( \mathbf{A} \cdot\left[\varepsilon_{0}\right]=\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
B . \( \left[\varepsilon_{0}\right]=\left[M^{-1} L^{2} T^{-1} A^{-2}\right] \)
\( \mathbf{c} \cdot\left[\varepsilon_{0}\right]=\left[M^{-1} L^{2} T^{-1} A\right] \)
\( \mathbf{D} \cdot\left[\varepsilon_{0}\right]=\left[M^{-1} L^{-3} T^{2} A\right] \)


The potential energy of a particle varies
with height \( h \) from a fixed point as \( \boldsymbol{E}= \) \( \left(\frac{\boldsymbol{P} \sqrt{\boldsymbol{h}}}{\boldsymbol{h}+\boldsymbol{Q}}\right) \) where, \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) are
constants. The dimensions of \( P Q \) are
A \( \cdot\left[M L^{2} T^{-2}\right] \)
B. \( \left[M^{3 / 2} L^{3 / 2} T^{-2}\right. \)
C . \( \left[M L^{7 / 2} T^{-2}\right] \)
D \cdot \( \left[M L^{3 / 2} T^{-2}\right. \)


A beam of unpolarised light passes through a tourmaline crystal \( A \) and
then through another such crystal \( B \)
oriented so that the principal plane is
parallel to \( A \). The intensity of emergent
light is \( I . \) If \( A \) now rotated by \( 45^{\circ} \) in a
plane perpendicular to direction of the incident ray. The emergent light will have intensity.
A \( \cdot \frac{I}{2} \)
B. \( \frac{I}{\sqrt{2}} \)
c. \( I \)
D. \( \frac{I}{4} \)


Consider the letters of the word
INTERMEDIATE. Number of words formed
by using all the letters of the given
words are


Find the values of \( \alpha \& \beta \) for which the
following system of linear equations has infinite number of solution.
\( 2 x+3 y=7 \)
\( 2 \alpha x+(\alpha+\beta) y=28 \)


\( \mathbf{A} \cdot C H_{2} C l_{2} \)
\( \mathbf{B} \cdot K_{2} S O_{4} \)
\( \mathbf{c} \cdot B e C l_{2} \)
D. \( S O_{2} \)


Which one of the following options
correctly represents a thermodynamic
process that is used as a correction in
the determination of the speed of sound
in an ideal gas?
A \( \cdot(I)(i i)(Q) \)
c. \( (I V)(i i)(R) \)
D. \( (I I I)(i v)(R \)


The simplified value of \( \frac{1-i}{1+i} \) is:
\( \mathbf{A} \cdot i \)
B. \( -i \)
\( c .1 \)
D. \( -2 i \)


The emf of the battery in a thermocouple is doubled. The rate of
heat generation at one of the junctions will
A. remains unchanged
B. becomes half
c. becomes double
D. becomes four times


A very long straight wire carries a
current \( I . \) At the instant when a charge
\( +Q \) at point \( P \) has velocity \( \vec{v}, \) as shown in figure, the force on charge is
A. along OY
B. opposite to OY
c. along ox
D. opposite to OX


Bessemerization is carried out for:
I. Fe
II. Cu
III. \( A \)
IV. \( A g \)
A . ।, ॥
в. ॥, III
c. ॥ा, । v
D. I, III


The value of \( \lim _{x \rightarrow 2} \frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2} \) is
equal to?
A. \( \frac{1}{8 \sqrt{3}} \)
в. \( \frac{1}{\sqrt{3}} \)
c. \( 8 \sqrt{3} \)
D. \( \sqrt{3} \)


Which of the following shows the bending of light from rarer (R) into denser (D) medium?
\( A \)
в.
c.
D.


Water infiltration will be slowest in
A. Black cotton soil
B. Sandy soil
c. Red soil
D. Loamy soil


A line passes through the point (6,-7,-1) and \( (2,-3,1) . \) if the angle \( \alpha \) which the line makes with the positive
direction of \( x \) -axis is acute, the
direction cosines of the line are,
A \( .2 / 3,-2 / 3,-1 / 3 \)
в. \( 2 / 3,2 / 3,-1 / 3 \)
c. \( 2 / 3,-2 / 3,1 / 3 \)
D. \( 2 / 3,2 / 3,1 / 3 \)


The saturation temperature for 20.7 g of CuSO4 soluble in water is


The value of \( 2 x^{4}+5 x^{3}+7 x^{2}-x+41 \)
when \( \boldsymbol{x}=-\boldsymbol{2}-\sqrt{\mathbf{3} \boldsymbol{i}} \) is:
A . -
B. 4
\( c \cdot-6 \)
D. 6


A parallelogram is cut by two sets of \( \boldsymbol{m} \)
lines parallel to its sides. Find the
number of parallelograms then formed.


Sporangiospores of Mucor are
A. Haploid
B. Diploid
c. Triploid
D. Polyploid


I : Number of partial fractions of \( \frac{x^{3}+x^{2}+1}{x^{4}+x^{2}+1} \) is 4
II : Number of partial fractions of \( \frac{3 x+5}{(x-1)^{2}\left(x^{2}+1\right)^{3}} \) is 5
Which of the above statement is true.
A. onlyı
B. Only II
c. Both I and II
D. Neither I nor II


Match the following.
\begin{tabular}{llll}
(a) & Protein & (i) & SER \\
(b) & Lipid & (ii) & Golgi body \\
(c) & Glycoprotein & (iii) & Lysosome \\
(d) & Hydrolytic enzyme & (iv) & RER \\
\hline
\end{tabular}
\( A \cdot a-i, b-i i, c-i i i, d-i v \)
B. a-iv, b-ii, c-i, d-iii
c. a-iv, b-i, c-ii, d-iii
D. a-i, b-iii, c-ii, d-iv


Most of the alpha particles go straight through the foil if it is passed through a thin metal foil. This is due to the reason
that:
A. alpha particles are much heavier than electrons
B. alpha particles are positively charged
c. most part of the atom is empty
D. alpha particles move with the high velocity


To use Boyle's Law, which of the
following needs to remain constant?
A. Temperature and number of moles of a gas
B. Temperature and pressure
C. Pressure and number of moles of a gas
D. Pressure and volume
E. Temperature and volume


Which of the following is more reactive towards nucleophilic addition
reactions?
A. \( C H_{3} C O C H_{3} \)
в. НСНО
c. \( C H_{3} C H O \)
D. \( C_{2} H_{5} C H O \)


When \( H_{2} O_{2} \) mixed with \( N H_{3} \) is applied
to hair, the colour of the hair changes
to :
A. silvery
B. ivory white
c. golden yellow
D. brown


Find the expansion of \( (\boldsymbol{a}-\boldsymbol{2} \boldsymbol{x})^{\boldsymbol{7}} \)


The sum of first 5 odd numbers is called
A. term
B. constant
c. series
D. sequence


The price of a scooter is \( R s .14000 . \) If it
depreciates by \( 2 \% \) of its value at the beginning of each year. Find the sale value after 4 years.
A . \( R s 1213.154 \)
в. \( R s 12000.154 \)
c. \( R s 12913.154 \)
D. None of these


Prove that:
\( \frac{\sin A+\sin 3 A+\sin 5 A+\sin 7 A}{\cos A+\cos 3 A+\cos 5 A \cos 7 A}= \)
\( \tan 4 A \)


Which of the following is a tridentate ligand?
A \( . E D T A^{4-} \)
B. \( (C O O)_{2}^{2} \)
c. \( \operatorname{dien} \)
D. \( N O_{2} \)


Two capacitors of \( 0.5 \mu F \) and \( 1 \mu F \) are connected in parallel across a battery. If the charge on \( 0.5 \mu F \) is \( 50 \mu C \), the charge
on the other capacitor is :
A. \( 100 \mu C \)
B. \( 50 \mu C \)
c. \( 25 \mu C \)
D. zero


Find the \( z- \) score that corresponds to
the \( 65^{t h} \) percentille of the standard Normal curve.


Ammonium chloride used in dry cell
acts as
A. Catalyst
B. Electrolyte
C. Polariser
D. Both (1) and (3)


In figure, when an ideal voltmeter is
connected across \( 4000 \omega \) resistance, it
reads \( 30 \mathrm{V} \). If the voltmeter is connected
\( \operatorname{across} 3000 \omega \) resistance, it will read
\( A \cdot 20 V \)
B. 22.5
\( c \cdot 35 v \)
D. \( 40 \mathrm{V} \)


Phosphoglyceraldehyde and dihydroxy acetone phosphate are
A. Isomers
B. Polymers
c. Tautomers
D. Synonyms


Assertion
STATEMENT-1: The current density \( \overrightarrow{\boldsymbol{J}} \) at any point in ohmic resistor is in direction of electric field \( \overrightarrow{\boldsymbol{E}} \) at that point.
Reason
STATEMENT-2:A point charge when released from rest in a region having only electrostatic field always moves along electric lines of force.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


Match the compounds in column I with
their
characteristics/test(s)/reagents(s)/ste reochemistry given in column II Matching can be one or more than one.


In the following sequence the product \( D \) \( \mathrm{is}: C H \equiv C H \frac{H B r}{\longrightarrow} A \quad \stackrel{H B r}{\longrightarrow} \)
\( \boldsymbol{B} \quad \stackrel{a l c . K O H}{\longrightarrow} \boldsymbol{C} \stackrel{N a N H_{2}}{\longrightarrow} \quad \boldsymbol{D} \)
A. ethanol
B. ethane
c. ethyne
D. ethanal


If \( p H \) of any solution is equal to zero, then solution will be:
A . acidic
B. basic
c. neutral
D. none of these


Ratio of initial active nuclei of the two
different samples is 2 ratio 3 . Their half lives are 1 and 2 respectively. Ratio of
active nuclei at the end of 6 hours will
be
A . 1: 1
B. 1: 12
c. 4: 3
D. 3: 4


One litre of \( C O_{2} \) is passes over hot coke. After one hour volume becomes
1.4 4 Itres. Composition of product is:
A. 0.6 litre \( C O_{2} \)
B. 0.8 litre \( C O_{2} \)
c. 0.6 litre \( C O_{2} \) and 0.8 litre co
D. None of these


The element, with atomic number 118 will be
A . Alkali
B. Noble gas
c. Lanthanide
D. Transition element


Two electrons separated by a distance \( r \)
experiences a force \( F \) between them.
The force between a proton and a single joined helium atom separated by a
distance \( 2 r \) is
A \( .4 F \)
в. \( 2 F \)
c. \( F / 2 \)
D. \( F / 4 \)


On a horizontal frictionless frozen lake,
a girl \( (36 \mathrm{kg}) \) and a box \( (9 \mathrm{kg}) \) are connected to each other by means of a rope. Initially they are 20 m apart. The girl exerts a horizontal force on the box, pulling it towards her. How far has the girl traveled when she meets the box?
A . 10
B. since there is no friction, the girl will not move
\( c \cdot 16 m \)
D. \( 4 \mathrm{m} \)


Which amongst the following is not an alkaline earth metal?
\( A \cdot \) Mg
B. Ba
\( c . F r \)
D. sr


Latus rectum of a parabola is a \( \ldots \ldots . . \) line
segment with respect to the axis of the parabola through the focus whose endpoints lie on the parabola.
A. perpendicular
B. parallel
c. tilted
D. None of these


The ratio between the acceleration to
the displacement of a particle in S.H.M.
is \( 4 \pi^{2} . \) The time period of S.H.M. is:
A . 1 s
B. 2
\( c \cdot 2 \pi s \)
D. \( \pi / 2 \mathrm{s} \)


What is meant by imperfect sheilding of
\( e^{-} \) by the nucleus?


What would be the freezing point of a
solution that has 684 grams of sucrose
\( (1 \mathrm{mol}=342 \mathrm{g}) \) dissolved in 2,000
grams of water (1 mole= 18 grams)?
B. \( -0.93^{\circ} \mathrm{C} \) or \( 272.07 \mathrm{K} \)
\( \mathbf{c} .-1.39^{\circ} \mathrm{C} \) or \( 271.61 \mathrm{K} \)
D. \( -2.48^{\circ} \mathrm{C} \) or \( 270.52 \mathrm{K} \)
E. \( -3.72^{\circ} \mathrm{C} \) or \( 269.28 \mathrm{S} \)


\( N H_{3}+H_{2} O \longrightarrow(C)+(D)( \) both oxy
acid)
A \( \cdot(c): H N O_{2} ; \quad(D): H N O_{2} \)
B \( \cdot(\mathrm{C}): H_{2} N O_{3} ; \quad \) (D) \( : H N O_{3} \)
C \( \cdot(\mathrm{C}): H N O_{2} ; \quad(\mathrm{D}): H N O_{3} \)
D. None of these


The energy required to brake one mole
of \( C l-C l \) bonds in \( C l_{2} \) is
\( 242 k j m o l^{-1} . \) The longest wavelength
of light capable of breaking single \( C l \)
\( C l \) bond is:
\( \left(c=3 \times 10^{8} m s^{-} 1 \text { and } N_{A}=6.02 \times\right. \)
\( \left.10^{23} m o l^{-1}\right) \)
A . \( 494 n m \)
В. 594 пт
\( c .640 n m \)
D. 700 nm


Let \( p, q, r \epsilon R^{+} \) and \( 27 p q r \geq(p+q+r)^{3} \)
and \( 3 p+4 q+5 r=12 \) then \( p^{3}+q^{4}+ \)
\( r^{5} \) is equal to
\( A \cdot 3 \)
B. 6
\( c \cdot 2 \)
\( D \)


Heavy water is used as a:
A. fuel in engines
B. semiconductor
c. moderator in nuclear reactors
D. insulator in steam engines


A resistance \( (R=12 \Omega), \) an inductor
\( \boldsymbol{L}=\mathbf{2} \boldsymbol{H}) \) and a capacitor \( (\boldsymbol{C}=\mathbf{5} \boldsymbol{\mu} \boldsymbol{F}) \)
are connected to an AC generator of
frequency \( 50 H z . \) Which of the following statement is correct?
A. At resonance, the circuit impedance is zero
B. At resonance, the circuit impedance is \( 12 \Omega \)
c. At resonance, the frequency of the circuit is \( 1 / 2 \pi \)
D. The inductive reactance is less than the capacitive reactance


The area of a circle is the measurement
of the region enclosed by its
A . radius
B. centre
c. circumference
D. area


Domain of \( \sin (\cos \theta) \) is \( \ldots \ldots \)
A \( \cdot\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)
в. \( R \)
c. \( [0 . \pi] \)
D \cdot [-1,1]


Name the two different categories of microbes naturally occurring in sewage water. Explain their role in cleaning sewage water into usable water


Very short answer type:
List two characters of pollen grains that
favour anemophily in plants.


Choose the correct answers from the
alternatives given. In which of the following groups would you place, a plant which produces spores and embryos but lacks seeds and
vascular tissue?
A. Bryophytes
B. Pteridophytes
c. Gymnosperms
D. Algae


Endosperm in gymnosperms is
A. Haploid and developed after fertilization
B. Haploid and developed before fertilization
C. Triploid and developed before fertilization
D. Triploid and developed after fertilization


\( \# \)
\( * \)
\( k \)
\( k \)


Example of fossil energy is :
A. Alcohol
B. Hydrogen
c. Petrol
D. Gobar gas


Steps in non-cyclic photophosphorylation include passage of electrons along
\( A \cdot F R S \longrightarrow F D \longrightarrow C y t b_{6} \longrightarrow \) Cyt \( f \longrightarrow P C \longrightarrow \) Chl a
в. сhl a \( \rightarrow \) cyt \( b_{6} \longrightarrow \) Cyt \( f \longrightarrow \mathrm{PC} \longrightarrow \mathrm{PS} \) । \( \longrightarrow \mathrm{FRS} \longrightarrow \)
\( F D \)
c. chl a \( \rightarrow \mathrm{PQ} \longrightarrow \mathrm{cyt} b_{6} \longrightarrow \mathrm{cyt} \mathrm{f} \longrightarrow \mathrm{PC} \rightarrow \mathrm{PS} 1 \rightarrow \)
FRS \( \rightarrow \) FD
D. PQ \( \rightarrow \) Cyt \( b_{6} \rightarrow \) Cyt \( f \longrightarrow P C \longrightarrow P S 1 \longrightarrow F R S \longrightarrow F D \)


A mass \( m \) is moving with a constant velocity along a line parallel to x-axis. Its angular momentum with respect to origin on z-axis is
A. zero
B. Remain constant
c. Goes on increasing
D. Goes on decreasing


The probability of the simultaneous occurrence of two events \( A \) and \( B \) is \( p \). If
the probability that exactly one of \( A, B \)
occurs is \( \boldsymbol{q} \), then This question has multiple correct options
A \( \cdot P\left(A^{\prime}\right)+P\left(B^{\prime}\right)=2+2 q-p \)
B . \( P\left(A^{\prime}\right)+P\left(B^{\prime}\right)=2-2 p-q \)
c. \( P(A \cap B \mid A \cup B)=\frac{p}{p+q} \)
D . \( P\left(A^{\prime} \cap B^{\prime}\right)=1-p-q \)


A non-zero vector \( \vec{a} \) is parallel to the line
of intersection of the plane determined by the vectors \( \hat{i}, \hat{i}+\hat{j} \) and the plane determined by the vectors \( \hat{i}-\hat{j}, \hat{i}+\hat{k} \) The angle between \( \vec{a} \) and \( \hat{i}-2 \hat{j}+2 \hat{k} \) is
A.
в.
c.
D. \( \frac{\pi}{2} \)


Transparent front part of eye is:
A . pupil
B. cornea
\( c \). iris
D. retina


Name the following
(1) Thte non-sublimable solid from a
mxiture of iodine and potassion nitrate
(2) The heavier liquid component from mercury and water
(3) The lower boiling point component from methyl alcohol and water.
(4) The compound containing one atom of sulphur and two atoms of oxygen
(5) An acid whose formula is \( \boldsymbol{H}_{\mathbf{2}} \boldsymbol{C} \boldsymbol{O}_{3} \)


Correct balanced equation from the
following reactions is:
\( \mathbf{A} \cdot 2 B a C l_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+H C l \)
B \( \cdot B a C l_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+2 H C l \)
\( \mathbf{c} \cdot 3 B a C l_{2}+H_{2} S O_{4} \rightarrow 4 B a S O_{4}+2 H C l \)
D. \( B a C l_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+H C l \)


If \( a, b, c \) and \( d \) are in \( G . P . \) show that \( \left(a^{2}+b^{2}+c^{2}\right)\left(b^{2}+c^{2}+d^{2}\right)= \)
\( (a b+b c+c d)^{2} \)


A string of length \( 1 \mathrm{m} \) and linear mass density \( 0.01 \mathrm{kg} / \mathrm{m} \) is stretched to a tension of 100 N. When both ends of the
string are fixed, the three lowest
frequencies for standing wave are \( \boldsymbol{n}_{1}, \boldsymbol{n}_{2} \) and \( \boldsymbol{n}_{3} . \) Then
A \( \cdot n_{3}=5 n_{1}=f_{3}=125 \mathrm{H} \)
B . \( f_{3}=5 f_{1}=n_{2}=125 \mathrm{Hz} \)
C \( . f_{3}=n_{2}=3 f_{1}=150 \mathrm{Hz} \)
D. \( n_{2}=\frac{f_{1}+f_{2}}{2}=75 \mathrm{Hz} \)


The value of specific heat depends on
A. Nature of the material
B. amount of work done externally due to expansion of the substance caused by raising the temperature
c. both (a) and (b)
D. none of these


Because of the lanthanide contraction
A. \( z r \) and \( Y \) have about the same radius
B. Zr and Nb have similar oxidation states
C. \( \mathrm{Zr} \) and \( \mathrm{Hf} \) have about the same radius
D. zrand zn have the same oxidation states


When a ball of mass 5 kg hits a bat with a velocity of \( 3 \mathrm{m} / \mathrm{s}, \) in a positive direction and it moves back with a
velocity of \( 4 \mathrm{m} / \mathrm{s}, \) find the impulse in \( \mathrm{S} \) units.
A. 5
B . 15
\( c \cdot 25 \)
D. 35


The reaction \( \boldsymbol{C O}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{C O C l}_{2} \)
proceeds in a closed vessel at a constant temp. The reactants are taken
in equimolar proportion at a pressure of atm. when the equilibrium sets in \( 50 \% \)
of initial amount of CO remains. The
pressure of equilibrium mixture is :
A. 0.5 atm
B. 0.75 atm
c. 1 atm
D. 1.5 atm


Assertion
Silver may be prepared by using silver
coins; in this process, coins are treated
with \( H N O_{3} \) and then treated with \( H C l \)
to get \( A g C l, \) but directly coins are not
treated with \( \boldsymbol{H} \boldsymbol{C l} \)
Reason
HCl is not a good oxidizing agent.
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


A dice is thrown twice. A success is an
even number on each throw. Find the
probability distribution of the number
of successes.


The order of reactivity of some interhalogens is as follows:
\( \boldsymbol{C I F}_{3}>\boldsymbol{B r F}_{3}>\boldsymbol{I F}_{7}>\boldsymbol{B r F}_{5}>\boldsymbol{B r F} \)


Evaluate: \( \lim _{x \rightarrow 0} \frac{(1+x)^{4}-1}{(1+x)^{3}-1} \)
A \( \cdot-\frac{4}{3} \)
B.
\( c \cdot \frac{4}{3} \)
D.


n \( 6(2 a-1)+8=14 \);the value of ' \( a \) ' is
A . -1
в. \( _{3} \frac{1}{12} \)
c. \( _{1} \frac{1}{12} \)
D. +1


The line joining the points \( \left(x_{1}, y_{1}\right) \) and
\( \left(x_{2}, y_{2}\right) \) subtends a right angle
This question has multiple correct options
\( \mathbf{A} \cdot \) at the point (1,-1) if \( x_{1} x_{2}+y_{1} y_{2}+2=x_{1}-y_{1}+x_{2}- \)
\( y_{2} \)
B. at the point (-1,1) if \( x_{1} x_{2}+y_{1} y_{2}+2=y_{1}-x_{1}+y_{2}- \)
\( x_{2} \)
C \( . \) at the point (1,1) if \( x_{1} x_{2}+y_{1} y_{2}+2=x_{1}+y_{1}+x_{2}+ \)
\( y_{2} \)
D. at the point (-1,-1) if \( x_{1} x_{2}+y_{1} y_{2}+2=x_{1}+y_{1}+ \)
\( x_{2}+y_{2} \)


If \( A \) and \( B \) are two mutually exclusive
events, then This question has multiple correct options
A \( . P(A) \leq P(\bar{B}) \)
в. \( P(A)>P(B) \)
c. \( P(B) \leq P(\bar{A}) \)
\( D(A)<P(B) \)


Assertion
An alternative definition of a reversible
process is a process that, after it has
taken place, can be reversed and, when
reversed, causes no change in either the
system or its surroundings.
Reason
By making no changes to system or surrounding we make sure that no no change in entropy has taken place.
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


\( \mathrm{Zn}+\mathrm{NaOH} \rightarrow \)


For the numbers in the list, write down
(a) the range
(b) the mode
(c) the median


Find the value of \( x \) for which \( \left(\frac{4}{9}\right)^{x} \times \)
\( \left(\frac{4}{9}\right)^{-7}=\left(\frac{4}{9}\right)^{2 x+1} \)


Let \( A \) and \( B \) be two events such that
\( P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4} \) and
\( P(\bar{A})=\frac{1}{4}, \) where \( \bar{A} \) stands for the
complement of the event A. Then the
events \( A \) and \( B \) are?
A. Independent but not equally likely
B. Independent and equally likely
c. Mutually exclusive and independent
D. Equally likely but not independent


is taken in through the tiny pores present on the surface of the leaves
A. Carbon dioxide
B. Nitrogen
c. oxygen
D. None of these


The value of a car depreciates every year at the rate of \( 10 \% \) on its value at the
beginning of the year. If the present value of the car is Rs 52,488 its worth
four years ago was
\( \mathbf{A} \cdot R s 68.232 \)
B. \( R s 68.234 \)
\( \mathbf{c} . R s 69.862 \)
D. \( R s 80,000 \)


A man' \( A^{\prime} \) stands at the position shown
in the figure and a second man \( ^{\prime} B^{\prime} \)
approaches the mirror along the line perpendicular to it which passes through its centre. AT the moment when
\( A^{\prime} \) and \( ^{\prime} B^{\prime} \) first sec each other in the
mirror, the distance of \( B \) from the mirror is:


Which one of the following is a polyamide polymer?
A. Terylene
B. Nylon-6
c. Buna- -
D. Bakelite


A closed conical vessel is filled with
water fully and is placed with its vertex down. The water is let out at a constant
speed. After 21 minutes, it was found that the height of the water column is half of the original height. How much more time in minutes does it empty the
vessel?
A . 21
B. 14
\( c \cdot 7 \)
D. 3


Three point particles of masses \( 1.0 k g \)
\( 1.5 k g \) and \( 2.5 k g \) are placed at three corners of a right angle triangle of sides
4.0 \( c m, 3.0 c m \) and \( 5.0 c m \) as shown in
the figure. The centre of mass of the
system is at a point :
A. \( 1.5 \mathrm{cm} \) right and \( 1.2 \mathrm{cm} \) above \( 1 \mathrm{kg} \) mass
B. \( 2.0 \mathrm{cm} \) right and \( 0.9 \mathrm{cm} \) above \( 1 \mathrm{kg} \) mass
c. \( 0.6 \mathrm{cm} \) right and \( 2.0 \mathrm{cm} \) above \( 1 \mathrm{kg} \) mass
D. \( 0.9 \mathrm{cm} \) right and \( 2.0 \mathrm{cm} \) above \( 1 \mathrm{kg} \) mass


\( (\sim p \wedge q) \wedge q \) is
A. a tautology
B. a contradiction
C. neither a tautology nor a contradiction
D. none of these


Molecules whose mirror image is nonsuperimposable over them are known as chiral. Which of the following molecules is chiral in nature?
A. 2 - Bromobutane
B. 1 - Bromobutane
c. 2 - Bromopropane
D. 2 - Bromopropan-2-ol


If the traces of the matrices \( A \) and \( B \) are
20 and \( 8, \) then trace of \( \mathbf{A}+\mathbf{B}= \)
A . 28
B. 20
\( c \cdot-8 \)
D. 12


\( \left|\begin{array}{ccc}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & \boldsymbol{1}\end{array}\right|=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3}\end{array}\right| \) then the
two triangles whose vertices are \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right) \) and
\( \left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right),\left(a_{3}, b_{3}\right) \) are
A. congruent
B. similar
c. equal in areas
D. right angled triangles


Largest ovule is present in
A . Cycas
B. Pinus
c. wolffia
D. Rafflesia


If the equation \( \sin ^{-1}\left(x^{2}+x+1\right)+ \)
\( \cos ^{-1}(\lambda x+1)=\frac{\pi}{2} \) has exactly two
solutions, then \( \lambda \) can not have the
integral value(s) This question has multiple correct options
A . -1
B. 0
c. 1
D. 2


Magnesium is present in:
A. ascorbic acid
B. vitamin B \( _{12} \)
c. chlorophyll
D. haemoglobin


The properties of hydrides of oxygen family members that decrease down
the group are :
This question has multiple correct options
A. bond angle
B. covalent nature
c. thermal stability
D. dissociation constant


A chord of a circle of radius \( 12 \mathrm{cm} \)
subtends an angle of \( 120^{0} \) at the centre.
Find the area of the corresponding segment


If the vector \( \vec{b} \) is colllinear with the vector \( \overrightarrow{\boldsymbol{a}}=(2 \sqrt{\mathbf{2}},-\mathbf{1}, \mathbf{4}) \) and \( |\overrightarrow{\boldsymbol{b}}|=\mathbf{1 0} \)
then:
\( \mathbf{A} \cdot \vec{a}+\vec{b}=0 \)
B . \( \vec{a}+2 \vec{b}=0 \)


The stable nucleus that has a radius
\( 1 / 3 \) that \( O s^{189} \) is
\( \mathbf{A} \cdot_{3} L i^{7} \)
B \( \cdot_{2} \mathrm{He}^{4} \)
\( \mathbf{c} \cdot_{5} B^{10} \)
\( \mathrm{D} \cdot_{6} C^{12} \)


A uniform rod of mass \( \mathrm{m} \) and length Lis
suspended with two massless strings as shown in the figure. If the rod is at
rest in a horizontal position the ratio of
tension in the two strings \( T_{1} / T_{2} \) is
\( A \cdot 1: \)
B. 1: 2
\( c \cdot 2: 1 \)
\( D \)


Which of one of the following burns in the air giving a gaseous oxide? (at room temp.)
A. Hydrogen
B. Sodium
c. sulphur
D. Helium


You are given n identical wires, each of resistance R When these are connected
in parallel, the equivalent resistance is
X. When these will be connected in
series, then the equivalent resistance will be
A \( \cdot X / n^{2} \)
в. \( n^{2} X \)
\( c \cdot x / n \)
D. nx


Which one of the following reactions of
Xenon compounds is not feasible?
\( \mathbf{A} \cdot X e O_{3}+6 H F \rightarrow X e F_{6}+3 H_{2} O \)
B. \( 3 X e F_{4}+6 H_{2} O \rightarrow 2 X e+X e O_{3}+12 H F+1.5 O_{2} \)
\( \mathbf{c} \cdot 2 X e F_{2}+2 H_{2} O \rightarrow 2 X e+4 H F+O_{2} \)
\( \mathbf{D} \cdot X e F_{6}+R b F \rightarrow R b\left[X e F_{7}\right] \)


Formula of coloumbs inverse square
law is (using electric charges), assume \( k=\frac{1}{4 \pi \epsilon_{0}} \)
A. \( F=q_{1} q_{2} d^{2} \cdot K \)
B. \( F=\frac{q_{1} q_{2}}{K d^{2}} \)
\( ^{\mathrm{c}} \cdot_{F}=\frac{\sqrt{K} q_{1} q_{2}}{d^{2}} \)
D. None of these


If \( \frac{\mathbf{d} \boldsymbol{y}}{\mathbf{d} \boldsymbol{x}}=\frac{\boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x}+\boldsymbol{y}} \) and \( \boldsymbol{y}(1)=\mathbf{1} \) then \( \boldsymbol{y}(\boldsymbol{2}) \)
equals
\( \mathbf{A} \cdot \mathbf{5} \)
B. \( 2 \pm \sqrt{10} \)
c. \( 2 \pm \sqrt{12} \)
D. \( -2 \pm \sqrt{10} \)


Visible light passing through a circular hole forms a diffraction disc of radius
\( 0.1 \mathrm{mm} \) on a screen. If \( \mathrm{X} \) -ray is passed through the same set up, the radius of the diffraction disc will be
A . zero
B. < 0.1 \( m m \)
\( c .0 .1 \mathrm{mm} \)
D. > 0.1 \( m m \)


Evaluate; \( \int_{0}^{\pi / 2} \log \sin 2 x d x \)


\( P C l_{3} \) is a precursor to which type of chemical compounds?
A. organophosphorus compounds
B. Organonitrogen compounds
c. organolithium compounds
D. Organo compounds


What is meant by Oxime? Give an example of reaction(with mechanism) showing its formation.


How many significant figures does 0.8900 g have in it?
A .2
B. 3
\( c \cdot 4 \)
D.


Which of the following is not a state function?
A. Temperature
c. work
D. volume


The relative positions of the stars in the
night sky
A. are absolutely fixed and therefore we can name constellations with certainty.
B. change appreciably over about four thousand years, which is why the ancient. Egyptians named different constellations than those of today
C . are changing, but very slowly such that appreciable change cannot be observed even over several centuries or even several thousand years.
D. appear to change because the sun moves among them over the course of a year.


DNA in the offsprings is contributed by
A. Male parent
B. Female parent
C. Both male and female parent equally
D. None of the above


How do you bring about the following conversion?
Acetylene to Oxalic acid


Assertion
Generally, covalent compounds are gases, liquids or soft solids at room temperature.
Reason
Between covalent compounds Vander
Waal's forces of attraction exists.
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. Assertion is incorrect but Reason is correct


If a deposit of Rs 1000 earns simple interest of Rs 250 in 3 years, how much interest would a deposit of Rs 3600 earn
in 3 years with the same rate of interest?


State whether the given statement is
true or false:
Fluid friction is more than solid friction.
A. True
B. False


Find the value of \( k \) for which the given
equations has real and equal roots:
(i) \( (k-12) x^{2}+2(k-12) x+2=0 \)
(ii) \( k^{2} x^{2}-2(k-1) x+4=0 \)


Autotrophic organism include
A. Green plants and sulphur bacteria
B. Green plants and all the bacteria
C. Bacteria and virus
D. Bacteria and fungi


toppr \( t \)
Q Type your question
\( B \)
\( c \)
\( D \)


One of the reaction that takes place to
producing steel from iron ore is the reduction of iron(III) oxide by carbon
monoxde to give iron metal and \( C O_{2} \) \( \boldsymbol{F} \boldsymbol{e} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{0 . 2 6 5} \)
What are the equilibrium partial
pressures of \( C O \) and \( C O_{2} \) at \( 1050 K \) if
the initial partial pressures are: \( \boldsymbol{p}_{C O}= \)
1.4 atm and \( p_{C O_{2}}=0.80 a t m ? \)


Assertion
When a bus starts suddenly, a person standing in it falls backwards.
Reason
It is due to inertia of rest.
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. Assertion is incorrect but Reason is correct


If you factorise \( 4 p^{2}-(q+r)^{2} \) the
factors are
A \( \cdot(2 p+q-r) \)
в. \( (2 p-q-r) \)
c. \( (2 p+q+r) \)
D. Both B \& C


Time when ball again meets the lift:
A \( \cdot \frac{5}{3} s \)
в. \( \frac{4}{3} s \)
c. \( \frac{3}{4} \)
D. \( \frac{3}{5} s \)


The 4 th term of a G.P is square of its
second term, and the first term is -3 Determine its 7 th term.


The electric potential due to charges \( 2 q \)
and \( -3 q, \) fixed at points \( (4 m, 0,0) \) and
\( (9 m, 0,0) \) respectively, is zero on:
A \( \cdot \) a spherical surface \( x^{2}+y^{2}+z^{2}=36 \)
B. a parabola \( y^{2}=36 z \)
c. an ellipsoidal \( \frac{x^{2}}{16}+\frac{y^{2}}{81}+z^{2}=1 \)
D. a spherical surface \( (x-4)^{2}+y^{2}+z^{2}=81 \)


.has the same properties of that of a rhombus but not a rectangle.
A. Square
B. Parallelogram
c. Trapezium
D. Kite


When zinc is added to \( C u S O_{4} \) solution,
copper is precipitated because :
A \( \cdot C u^{+2} \) is reduced
B. \( C u^{+2} \) is oxidised
c. \( C u S O_{4} \) is ionized
D. \( C u S O_{4} \) is hydrolysed


Find the numerical value of \( e \) which
satisfies \( 6 e(e+3)=3 e(2 e+4)+5 \)
A \( \cdot \frac{5}{6} \)
B. \( \frac{3}{4} \)
c. \( \frac{9}{8} \)
D. \( \frac{10}{3} \)


Evaluate: \( \int_{1}^{2} \log x d x \)
A. \( 2 \log 2-1 \)
B. \( \log 2-1 \)
c. \( 2 \log 2+1 \)
D. \( \log 2-2 \)


What is meant by superconductivity?


EM waves are
A. Longitudinal waves
B. Transverse waves
c. Both
D. None


For which of the following reactions the equilibrium mixture will contain an appreciable concentration of both reactants and products.
(a) \( C l_{2}(g) \rightleftharpoons 2 C l(g) ; K_{c}=6.4 \times 10^{39} \)
(b) \( C l_{2}(g)+2 N O(g) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{O} \boldsymbol{C l}(\boldsymbol{g}) ; \boldsymbol{K}_{c}=\mathbf{3 . 7} \times \mathbf{1 0}^{8} \)
(c) \( C l_{2}(g)+2 N O_{2}(g) \rightleftharpoons \)
\( \mathbf{2} N \boldsymbol{O}_{2} \boldsymbol{C l}(\boldsymbol{g}) ; \boldsymbol{K}_{c}=\mathbf{1 . 8} \)
\( A \)
B.
\( c \)
D. None of these


Read the following statements and
answer as true or false.

Metals occur in nature only as free
elements.
A. True
B. False


Write the molecular and structural
formulae of:
Dithionous acid.


Which of the following does not contain \( O-O \) bond?
This question has multiple correct options
\( A \cdot S_{2} O_{8}^{2-} \)
B. \( S_{4} O_{6}^{2-} \)
\( \mathbf{c} \cdot S O_{5}^{2-} \)
D. \( S_{2} O_{7}^{2} \)


A sphere of radius \( r \) has a volume density of charge \( \rho=k r . \) Find the
electric field intensity at the surface of
the sphere.
A. \( \frac{4 \pi k R^{4}}{3 \epsilon_{0}} \)
в. \( \frac{k R}{3 \epsilon_{0}} \)
c. \( \frac{4 \pi k R}{\epsilon_{0}} \)
D. \( \frac{k R^{2}}{4 \epsilon_{0}} \)


Show that the function \( \boldsymbol{f}: \boldsymbol{R}-\{\boldsymbol{3}\} \rightarrow \)
\( R-\{1\} \) given by \( f(x)=\frac{x-2}{x-3} \) is a
bijection.


Two coils of self inductances \( 6 m H \) and
\( 8 m H \) are connected in series and are
adjusted for highest co-efficient of coupling. Equivalent self inductance \( L \)
for the assembly is approximately
\( \mathbf{A} \cdot 50 m H \)
в. \( 36 m H \)
\( \mathrm{c} \cdot 28 m H \)
D. \( 18 m H \)