If \( \boldsymbol{A}=\mathbf{6 0}^{\circ} \) and \( \boldsymbol{B}=\mathbf{3 0}^{\boldsymbol{o}}, \) verify that
\( \tan (\boldsymbol{A}+\boldsymbol{B})=\frac{\tan \boldsymbol{A}+\tan \boldsymbol{B}}{1-\tan \boldsymbol{A} \tan \boldsymbol{B}} \)


If \( X \) is normally distributed with mean 6 and standard deviation \( 5, \) find:
(i) \( \boldsymbol{P}[\mathbf{0} \leq \boldsymbol{X} \leq \mathbf{8}] \)
(ii) \( \boldsymbol{P}(|\boldsymbol{X}-\mathbf{6}|<\mathbf{1 0}) \)
Here \( \boldsymbol{P}(\mathbf{0}<\boldsymbol{Z}<\mathbf{1} . \mathbf{2})=\mathbf{0 . 3 8 4 9} \)
\( \boldsymbol{P}(\mathbf{0}<Z<\mathbf{0 . 4})=\mathbf{0 . 1 5 5 4} \)
\( \boldsymbol{P}(\mathbf{0}<\boldsymbol{Z}<\mathbf{2})=\mathbf{0 . 4 7 7 2} \)


Find the degree of given polynomial:
\( 4 x^{3}-1 \)


What is menopause and menarche?


In which of the following pyrenoids are
present?
A. Marchantia
B. Riccia
c. Anthoceros
D. All of the above


Protons and \( \alpha \) -particles of equal
momenta enter a uniform magnetic field normally. The radii of their orbits will have the ratio
\( A \)
B. 2
c. 0.5
\( D \)


If \( x y- \) plane and \( y z- \) plane divides the line segment joining \( A(2,4,5) \) and \( B(3,5,-4) \) in the ratio \( a: b \) and \( p: q \) respectively then value of \( \left(\frac{a}{b}+\frac{p}{q}\right) \) may be
A \( \cdot \frac{23}{12} \)
в. \( \frac{7}{5} \)
\( c \cdot \frac{7}{12} \)
D. \( \frac{21}{10} \)


Which reagent, when mixed with ammonium sulfate and then heated,
liberates ammonia?
A. aqueous bromine
B. dilute hydrochloric acid
c. limewater
D. potassium dichormate
(VI) in acidic solution


Expand: \( (\boldsymbol{p}+\boldsymbol{q}-\boldsymbol{2} \boldsymbol{r})^{2} \)


If the \( 2^{n d} \) term of an AP is 13 and the \( 5^{t h} \)
term is 25 what is its \( 7^{t h} \) term?


The pH of the solution after Expt. 2 is:
A . 2.8
в. 4.7
\( c .5 . \)
D. 7.0


CuT, LNG-20 and Cu7 are examples of
A. Contraceptive pills
B. Surgical methods of sterilization
C. Assisted reproductive technology
D. Intrauterine device
E. Monoclonal antibodies


Hydroponic is a subset of what type of culture?
A. Hydroculture
B. Solid medium culture
c. xeroculture
D. Tissue culture


The coefficient of friction between two
surfaces is 0.2. The angle of friction is
\( A \cdot \sin ^{-1}(0.2) \)
\( B \cdot \cos ^{-1}(0.2) \)
\( c \cdot \tan ^{-1}(0.1) \)
D. \( \cot ^{-1}(5) \)


Which one is not a cofactor?
A . Co-enzyme
B. Apoenzyme
c. Prosthetic group
D. Metal ions


\( \tan ^{-1} x+2 \cot ^{-1} x=\frac{2 \pi}{3}, \) then the
value of \( x \) is-
A \( \cdot \sqrt{2} \)
B. 3
\( c \cdot \sqrt{3} \)
D. \( \frac{\sqrt{3}-1}{\sqrt{3}+1} \)


Find the exponent of 10 in \( ^{75} C_{25} \)


How many monochloro products can be formed when n-butane is subjected to
monochlorination?


Find the angle between \( \vec{a}+\vec{b}+\vec{c} \) and \( \vec{a}+\vec{b}-\vec{c} \)
A \( \cdot \cos ^{-1}\left(\frac{8}{\sqrt{57}}\right) \)
B. \( \cos ^{-1}\left(\frac{9}{\sqrt{75}}\right) \)
\( ^{\mathbf{C}} \cdot \cos ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)
D. \( \cos ^{-1}\left(\frac{-7}{\sqrt{85}}\right) \)


\( \lim _{x \rightarrow 0} \frac{\sin x^{n}}{(\sin x)^{m}}(m<n) \) is equal to
A . 1
B.
c. \( \frac{n}{m} \)
D. None of he above


In the preparation of \( C a O \) from \( C a C O_{3} \)
using the equilibrium \( C a C O_{3}(s) \rightleftharpoons \) \( \boldsymbol{C a O}(s)+\boldsymbol{C O}_{2}(\boldsymbol{g}) \boldsymbol{K}_{p} \) is expressed as:
\( \log \boldsymbol{K}_{p}=\mathbf{7 . 2 8 2}-\frac{\mathbf{8 5 0 0}}{\boldsymbol{T}} \)
for complete decomposition of \( C a C O_{3} \)
the temperature in celsius to be used is:
A . 1167
в. 894
c. 8500
D. 850


Which of the following is not dielectric materials?
A. Silicon dioxide
B. Silicon nitride
c. Titanium oxide
D. None of the above


Cyclic succession is
A. Pattern of vegetation change in which a small number of species tend to replace each other over time in the absence of large-scale disturbance
B. Pattern of vegetation change in which large number of species tend to replace each other over time
C. Pattern of vegetation change
D. Pattern of succession change


The approximate change in the volume of a cube of side \( x \) metres caused by
increasing the side by \( 3 \% \) is :
B. \( 0.6 x^{3} m^{3} \)
D. \( 0.9 x^{3} m^{3} \)


Find the sum of the following arithmetic progressions:
\( 1,3,5,7, \dots . \) to 12 terms


If \( \bar{a}, \bar{b} \) and \( \bar{c} \) are non-zero non collinear vectors and \( \theta(\neq 0, \pi) \) is the angle between \( \bar{b} \) and \( \bar{c} \) if \( (\bar{a} \times \bar{b}) \times \bar{c}=\frac{1}{2}|\bar{b}| \bar{c} \mid \bar{a} \)
then \( \sin \theta= \)
A \( \cdot \sqrt{\frac{2}{3}} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{4 \sqrt{2}}{3} \)
D. \( \frac{2 \sqrt{2}}{3} \)


The correct IUPAC name of the following
alkane is ?
A. 3,6 -diethyl-2-methyloctane
B. 5-iso-propyl-3-ethyloctane
C. 5-ethyl-5-iso-propyloctane
D. 3-iso-propyl-6-ethyloctane


If \( \mathbf{A}+\left|\begin{array}{cc}\mathbf{4} & \mathbf{2} \\ \mathbf{1} & \mathbf{3}\end{array}\right|=\left|\begin{array}{cc}\mathbf{6} & \mathbf{9} \\ \mathbf{1} & \mathbf{4}\end{array}\right| \) then \( \mathbf{A}= \)
\( \mathbf{A} \cdot\left|\begin{array}{ll}2 & 7 \\ 0 & 1\end{array}\right| \)
\( \mathbf{B} \cdot\left|\begin{array}{ll}0 & 1 \\ 2 & 7\end{array}\right| \)
\( \mathbf{C} \cdot\left|\begin{array}{ll}1 & 0 \\ 2 & 7\end{array}\right| \)
\( \mathbf{D} \cdot\left|\begin{array}{ll}2 & 1 \\ 0 & 7\end{array}\right| \)


The range of a random variable \( \boldsymbol{X} \) is
\{0,1,2\} and given that \( P(X=0)= \)
\( \mathbf{3 c}^{3}, \quad \boldsymbol{P}(\boldsymbol{X}=\mathbf{1})=\mathbf{4 c}- \)
\( \mathbf{1 0 c}^{2}, \quad \boldsymbol{P}(\boldsymbol{X}=\mathbf{2})=\mathbf{5} c-\mathbf{1}, \) find (i)
the value of \( c \)
(ii) \( \boldsymbol{P}(\boldsymbol{X}<\mathbf{1}), \quad \boldsymbol{P}(1<\boldsymbol{X} \leq \)
2) \( , \quad P(0<X \leq 3) \)


The frequency of radiation emitted
when the electron falls from \( n=4 \) to
\( \boldsymbol{n}=\mathbf{1} \) in a hydrogen atom will be (Given
ionisation energy of \( \boldsymbol{H}=\mathbf{2 . 1 8} \times \)
\( 10^{-18} J a t o m^{-1} \) and \( h=6.626 \times \)
\( \left.10^{-34} J-s\right) \)
\( \mathbf{A} \cdot 1.54 \times 10^{15} s^{-1} \)
В. \( 1.03 \times 10^{15} s^{-1} \)
C \( .3 .08 \times 10^{15} s^{-1} \)
D. \( 2 \times 10^{15} s^{-1} \)


Which of the following statement is
incorrect?
A. Amylose is water soluble component of starch
B. Amylopectin is water insoluble component of starch
C. \( \alpha \) -D Glucose units are present in amylose and amylopectin
D. None of these


Recently, sodium naphthalenide
\( \left.C_{10} H_{8} N a\right) \) has been used as reductant
in complex formation. \( C_{10} H_{8} N a \) is :
This question has multiple correct options
A. paramagnetic
B. deep-green in colour
c. diamagnetic
D. colourless


What should be subtracted from \( 2 a+ \)
\( 6 b-5 \) to get \( -3 a+2 b+3 ? \)
A. \( 5+4 b-8 \)
в. \( 5 a+4 b-8 \)
c. \( 5 a+4 a b-8 \)
D. \( 5 a+4 b-10 \)


Which of the following cause green house effect?
(i) Deforestation
(ii) Emission of gases from factories
(iii) Melting of polar ice
A. Only (i) and (ii)
B. Only (i) and (iii)
c. only (ii) and (ii)
D. (i), (ii) and (iii)


The combination of oxygen with haemoglobin is called as
A. Oxidation
B. Oxyhaemoglobin
c. Reduction
D. None of the above


\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is treated with marble, it
releases which
A \( \cdot C O_{2}, \) turns lime water milky
B. \( H_{2} \), burns with a pop sound
c. \( O_{2} \), rekindles a burning spirit
D. none of the above


You are given a tissue with its potential
for differentiation in an artificial
culture. Which of the following pairs of
hormones would you add to the medium to secure shoots as well as roots?
A. Auxin and abscisic acid
B. Gibberllin and abscisic acid
c. IAA and gibberellin
D. Auxin and cytokinin


Two conducting plates \( A \) and \( B \) are placed parallel to each other at a small
distance between them. Plate A is given
a charge \( q_{1} \) and plate \( B \) is given a
charge \( \boldsymbol{q}_{2} . \) Then :

This question has multiple correct options
A. the outer surfaces of \( A \) and \( B \) (not facing each other) get no charge
B. the inner surfaces of \( A \) and \( B \) (facing each other) get al the charge
C. the inner surfaces of \( A \) and \( B \) (facing each other) get equal and opposite charge of magnitude \( \left|\frac{q_{1}-q_{1}}{2}\right| \)
D. the outer surfaces of \( A \) and \( B \) (not facing each other) get charge of the same polarity and of magnitude
\( \frac{q_{1}+q_{2}}{2} \)
2


Two marks on a glass rod \( 10 \mathrm{cm} \) apart are found to increase their distance by \( 0.08 \mathrm{mm} \) when the rod is heated from
\( 0^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \). A flask made of the same
glass as that of rod measures a volume
of \( 100 \mathrm{cc} \) at \( 0^{\circ} \mathrm{C} \). The volume it
measures at \( 100^{\circ} \mathrm{C} \) in cc is
A . 100.24
B. 100.12
c. 100.36
D. 100.48


Match Column-I with Column-II.


Identify the substance in each of the following pairs of samples that has the
higher entropy?
(A) \( B r_{2}(l) \) or \( B r_{2}(g) \)
(B) \( C_{2} H_{6}(g) \) or
\( \boldsymbol{C}_{3} \boldsymbol{H}_{8}(\boldsymbol{g}) \)
(C) \( M g O(s) \) or \( N a C l(s) \)
(D) \( K O H(s) \)
or \( \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{q}) \)


State the following statement is True or
False
The area (in sq. units) of the triangle formed by the points with polar coordinates (1,0)\( \left(2, \frac{\pi}{3}\right) \) and \( \left(3, \frac{2 \pi}{3}\right) \)
is \( \frac{5 \sqrt{3}}{4} \)
A. True
B. False


A spherical refractive surface of radius
\( 10 \mathrm{cm} \) separates two media of
refractive indices \( \mu=1 \) and \( \mu=3 / 2 \)
respectively. A point object P starts
from rest at \( t=0 \) with an acceleration
\( 2 \mathrm{cms}^{-2} . \) Find the speed of image at \( t=1 \mathrm{s} \)
A \( \cdot 2 c m s^{-1} \)
B. \( 6 \mathrm{cms}^{-1} \)
\( \mathbf{c} \cdot 3.7 \mathrm{cms}^{-1} \)
D. none of these


About alkali metal - liquid \( \boldsymbol{N} \boldsymbol{H}_{3} \)
solution which of the following statement is not true?
A. Blue colour due to ammoniated electrons
B. Blue colour changes to bronze on dilution due to formation of metal clusters
c. with increse in concentration of alkali metals paramagnetic nature decreases due to electron electron combination
D. on heating blue colour becomes colourless due to formation of metal amide and \( H_{2} \) gas


Evaluate \( 8.5 \times 9.5 \) using suitable
standard identity.


Find the coordinates of the foci, the
vertices, the length of major axis, the
minor axis, the eccentricity and the length of the latus rectum of the ellipse \( \frac{x^{2}}{36}+\frac{y^{2}}{16}=1 \)


Zinc corrodes in
\( \mathbf{A} \cdot 2 M \) alkaline solution
B. 2 \( M \) acid solution
C. \( 2 M \) neutral salt solution
D. all of the above


The wavelength range of thermal
radiation is
A. from \( 4000 \AA \) to 7000 ,
B. from 7700 A to \( 4 \times 10^{6} \) A
c. from \( 10^{6} \AA \) to \( 10^{8} \AA \)
D. from \( 4 \times 10^{-12} \AA \) to \( 4 \times 10^{8} \AA \)


f \( \tan \theta+\sin \theta=m \) and \( \tan \theta-\sin \theta= \)
\( n, \) then prove that \( m^{2}-n^{2}=4 \sqrt{m n} \)


A player tosses two fair coins. He wins Rs. \( 5 /- \) if two heads occur, \( R s .2 /- \) if one head occurs and \( R s .1 /- \) if no head
occurs. Then his expected gain is
A \( \cdot \) Rs. \( \frac{8}{3} \)
в. \( \operatorname{Rs} . \frac{7}{3} \)
c. \( R s .2 .5 \)
D. Rs.1.5


What is the basic difference between a
real image and a virtual image?
A. Real image are the image that can be obtained on a screen whereas virtual image cannot be obtained on the screen
B. Virtual image can be obtained on a screen while real images cannot be obtained on a screen
C. Virtual images are formed only in refraction not in reflection while real image can be formed in both
D. Virtual images are formed only in reflection while real image are also only found in refraction


When a certain weight is suspended from a long uniform wire, its length increases by \( 1 \mathrm{cm} \). If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the
increase in length will be
\( \mathbf{A} \cdot 0.5 \mathrm{cm} \)
B. \( 2 c m \)
\( c .4 c m \)
D. 8 cm


For all real numbers \( b \) and \( c \) such that
the product of \( c \) and 3 is \( b \), the
expression which represents the sum of \( c \) and 3 in terms of \( b \) is
B. \( 3 b+3 \)
\( c \cdot 3(b+3) \)
D. \( \frac{b+3}{3} \)
E \( \cdot \frac{b}{3}+3 \)


The velocity of a particle at an instant is \( 10 \mathrm{m} / \mathrm{s} . \) After 3 sec its velocity will
become \( 16 \mathrm{m} / \mathrm{s} \). The velocity at \( 2 \mathrm{sec} \) before the given instant, will be?
\( \mathbf{A} \cdot 6 \mathrm{m} / \mathrm{s} \)
B. \( 4 \mathrm{m} / \mathrm{s} \)
c. \( 2 \mathrm{m} / \mathrm{s} \)
D. \( 1 \mathrm{m} / \mathrm{s} \)


An external force \( F \) acts horizontally on
a box of mass \( m \) at a height \( h \). If the
\( C M \) of the box is situated at a height \( c \)
find the:
minimum value of \( F \) so as to topple the
box
\( ^{A} \cdot \frac{m g b}{2 h} \)
в. \( \frac{m g b}{b} \)
\( c \cdot \frac{m g b}{3 b} \)
D. \( \frac{m g b}{4 b} \)


Identify the correct increasing order of the stability of the following alkenes,
I.cis-2-butene;
II.trans-2-butene;
III. isobutene:
A. \( I I<I I I<I \)
в. \( I<I I I<I I \)
c. \( I<I I<I I I \)
D. \( I I I<I I<I \)


Let \( 0(0,0), P(3,4), Q(6,0) \) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR,PQR, OQR are of equal area. The coordinates of \( \mathrm{R} \) are
\( ^{\mathrm{A}} \cdot\left(\frac{4}{3}, 3\right) \)
в. \( \left(3, \frac{2}{3}\right) \)
c. \( \left(3, \frac{4}{3}\right) \)
D \( \cdot\left(\frac{4}{3}, \frac{2}{3}\right) \)


Assertion
A reaction cannot become fast by itself unless a catalyst is added.
Reason
A catalyst always increases the speed
of a reaction.
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


If the binary operation on the set of integers \( Z, \) defined by \( a \times b=a+3 b^{2} \)
then find the value of \( 8 \times 3 \)


The sum of first 9 terms of an AP is 81
and the sum of its first 20 terms is 400 .
Find the first term and the common
difference of the AP.


ldentify \( \boldsymbol{B} \)


If \( f(x)=\sin ^{-1}\left(\frac{2 \times 3^{x}}{1+9^{x}}\right), \) then \( f^{\prime}\left(-\frac{1}{2}\right) \)
\( ^{\mathrm{A}} \cdot \frac{-\sqrt{3}}{2} \log _{e} \sqrt{3} \)
B. \( \frac{\sqrt{3}}{2} \log _{e} \sqrt{3} \)
c. \( -\sqrt{3} \log _{e} 3 \)
D. \( \sqrt{3} \log _{e} 3 \)


If \( f: R \rightarrow R \) such that \( f(x+y)-K x y= \)
\( f(x)+2 y^{2} \) for all \( x, y \in R \) and \( f(1)= \)
\( 2, f(2)=8 \) then \( f(20)-f(10) \)
A. 600
в. 300
c. 60
D. 200


In a particular season, some birds in our surrounding migrate from long distances. How do they know their way?


Tangent is drawn from (1,0) to \( y=e^{x} \)
then the area bounded between the
coordinate axes and the tangent is
equal to -
A \( \cdot \frac{e}{2} \)
B. \( e \)
\( ^{c} \cdot \frac{e^{2}}{2} \)
\( \mathbf{D} \cdot e^{2} \)


The latent heat of vaporization is than the latent heat of
fusion. Fill in the gap.
A. Greater
B. Smaller
c. same
D. None


Roots of quadratic equation \( 5 x^{2}- \) \( 22 x-15=0 \) are
A \( \cdot_{-5,} \frac{-3}{5} \)
в. \( _{5,} \frac{3}{5} \)
c. \( _{5}, \frac{-3}{5} \)
D. None of these


Four letters mailed today each have a
probability of arriving in two days or sooner equal to \( \frac{2}{3} . \) Calculate the probability that exactly two of the four letters will arrive in two days or sooner.
\( \mathbf{A} \cdot \frac{4}{81} \)
B. \( \frac{16}{81} \)
c. \( \frac{6}{27} \)
D. \( \frac{8}{27} \)
E \( \cdot \frac{4}{9} \)


A die is thrown. Let \( A \) be the event that
the number obtained is greater than 3
Let \( \mathrm{B} \) be the event that the number
obtained is less than 5. Then \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)
is
A . 1
B. \( \frac{2}{5} \)
c. \( \frac{3}{5} \)
D.


A wire suspended vertically from one of its ends is stretched by attaching a weight of \( 200 \mathrm{N} \) to the lower end. The weight stretches the wire by 1 mm. Then the energy stored in the wire is
A . 0.1
B. 0.2
c. 10
D. 20


Let \( f(x)=\left\{\begin{array}{cc}-2, & -3 \leq x \leq 0 \\ x-2, & x<x \leq 3\end{array} \) and \right.
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(|\boldsymbol{x}|)+\mid \boldsymbol{f}(\boldsymbol{x}) \)
Which of the following statements are correct?
1. \( g(x) \) is continuous at \( x=0 \)
2. \( g(x) \) is continuous at \( x=2 \)
3. \( g(x) \) is continuous at \( x=-1 \)
Select the correct answer using the code given below
A. 1 and 2 only
B. 2 and 3 only
c. 1 and 3 only
D. 1,2 and 3


State whether the statement is true or
false :
In the electron dot structure, the
valence shell electron is represented by
cross or dot.


Prove the \( \boldsymbol{A}(-\mathbf{5}, \mathbf{4}), \boldsymbol{B}(-\mathbf{1},-\mathbf{2}), \boldsymbol{C}(\mathbf{5}, \mathbf{2}) \)
are the vertices of \( n \) isosceles right
angled triangle?


The Y of a material having a cross sectional area of \( 1 \mathrm{cm}^{2} \) is \( 2 \times 10^{12} \)
dynes/cm \( ^{2} \). The force required to double the length of the wire is:
A \( \cdot 1 \times 10^{12} \) dynes
B. 2 x 10 \( ^{12} \) dynes
c. \( 0.5 \times 10^{12} \) dynes
D. \( 4 \times 10^{12} \) dynes


Th direction of magnetic lines of force of
a bar magnet is:
A. from south to north pole
B. from north to south pole
c. across the bar magnet
D. from south to north pole inside the magnet and from north to south pole outside the magnet


Draw the diagram of electromagnetic
wave


Which of the following cannot undergo
\( E 2 \) reaction?
\( A \)
B.
\( c \)
D.


The \( K_{a}-X \) ray of Molybdenum has a
wavelength of \( 71 \times 10^{-12} \) m. If the
energy of a Molybdenum atom with \( \mathrm{K} \) electron removed is \( 23.32 K e V \), then
the energy of Molybdenum atom when
an L-electron removed is:
\( \left(h c=12.42 \times 10^{-7} e V\right) \)
A \( .40 .82 \mathrm{KeV} \)
в. \( 23.32 \mathrm{KeV} \)
\( \mathbf{c} .5 .82 \mathrm{KeV} \)
D. \( 17.5 \mathrm{KeV} \)


The normal to the curve \( 2 x^{2}+y^{2}=12 \)
at the point (2,2) cuts the curve again
at
\( ^{\mathbf{A}} \cdot\left(-\frac{22}{9},-\frac{2}{9}\right) \)
в. \( \left(\frac{22}{9}, \frac{2}{9}\right) \)
c. (-2,-2)
D. none of these


A cricket ball of mass 150 gram moving with a velocity of \( 12 \mathrm{m} / \mathrm{s} \) strikes against the bat. It rebounces with a velocity of \( 20 \mathrm{m} / \mathrm{s} . \) The ball remains in touch with the batfor 0.01 second. The average force
applied by the bat on the ball is
A. 840 Newton
B. 480 Newton
c. 804 Newton
D. 408 Newton


n identical waves each of intensity \( 1_{0} \) interfere with each other. The ratio of
maximum intensities if the
interference is (i) coherent and (ii) incoherent is:
\( \mathbf{A} \cdot n^{2} \)
B.
c. \( \frac{1}{n^{2}} \)
D.


Match the correct pairs of isomers with their examples.
A)Ionisation \( \left.P t\left(N H_{3}\right)_{2} C l_{2}\right]\left[P t\left(N H_{3}\right)_{4}\right] \)
\( \left[P t C l_{4}\right. \)
B) Linkage \( \left[C r\left(N H_{3}\right)_{6}\right]\left[C o(C N)_{6}\right] \& \)
\( \left[C o\left(N H_{3}\right)_{6}\left[C r(C N)_{6}\right]\right. \)
C)Coordination \( \left[\operatorname{Co}\left(N H_{3}\right)_{5}\left(N O_{2}\right)\right] C l_{2} \& \)
\( \left[\operatorname{Co}\left(N H_{3}\right)_{5}(O N O)\right] C l_{2} \)
DPolymerisation \( \left[\mathrm{Co}\left(\mathrm{SO}_{4}\right)\left(\mathrm{NH}_{3}\right)_{5}\right] \mathrm{Br} \& \)
\( \left[\operatorname{Col} \operatorname{Br}\left(N H_{3}\right)_{5}\right] S O_{4} \)
\( A \cdot A->a, B->b, C->c, D \rightarrow d \)
B. \( A->b, B->a, C->d, D \rightarrow C \)
\( c \cdot A->d, B->c, C->b, D \rightarrow a \)
D. \( A->d, B->b, C->c, D \rightarrow a \)


Identify the wrong statement about
Mars.
A. It is called the red planet
B. It is the last inner planet
c. It takes 687 days to complete one revolution around the sun
D. It has 3 moons


If liquids \( A \) and \( B \) form an ideal solution,
then :
A. the entropy of mixing will be zero
B. the Gibbs free energy of mixing will be zero
C. the Gibbs free energy as well as the entropy of mixing both will be zero
D. the enthalpy of mixing will be zero


Vitamin E is also called:
A. Cyanocobalamin
B. Tocopherol
c. Lactoflavin
D. Ascorbic acid


Find the middle term in the expansion of \( (5 x-7 y)^{7} \)


A factor of \( \left(3 x^{4}-12 y^{4}\right) \) is
\( A \cdot 3 \)
B. \( x^{2}-2 y^{2} \)
c. \( x^{2}+2 y^{2} \)
D. All of these


Calculate the heat energy required to convert completely \( 10 \mathrm{kg} \) of water at \( 50^{\circ} \mathrm{C} \) into steam at \( 100^{\circ} \mathrm{C} \), given that the
specific heat capacity of water is \( 4200 J /\left(k g^{\circ} C\right) \) and the specific latent heat of vaporisation of water is
\( 2260 k J / k g \)
A. 30451 KJ
B. 60562 KJ
c. 72103 KJ
D. 24700 KJ


Differentiate with respect to \( x \) :
\( \mathbf{3}^{e^{x}} \)


If four numbers are in A.P. such that
their sum is 60 and the greatest
number is 4 times the least, then the
numbers are
A . 5,10,15.20
B. 4,10,16,22
c. 3,7,11,15
D. None of these


According to Dalton, atoms combine in ratio to form compounds.


If the \( 10^{t h} \) term of an A.P. is 52 and the
\( 17^{t h} \) term is 20 more than the \( 13^{t h} \) term,
find the A.P.


What is the absolute value of the difference
between the roots of \( x^{2}+6 x+5=0 ? \)


Find the value of \( x+y \) from the
following equation:
\( \mathbf{2}\left[\begin{array}{cc}\boldsymbol{x} & \mathbf{5} \\ \mathbf{7} & \boldsymbol{y}-\mathbf{3}\end{array}\right]+\left[\begin{array}{cc}\mathbf{3} & \mathbf{- 4} \\ \mathbf{1} & \mathbf{2}\end{array}\right]=\left[\begin{array}{cc}\mathbf{7} & \mathbf{6} \\ \mathbf{1 5} & \mathbf{1 4}\end{array}\right] \)


Which two of the following aldohexoses
give the same osazone derivative?
A. I and IV
B. I and III
c. Il and III
D. III and IV


\( 0.2 g \) of fine animal charcoal is mixed
with half litre of acetic acid \( (2 M) \)
solution and shaken for 30 minutes?
A. Concentration remains same
B. Concentration increases
c. concentration of the solution decreases
D. None of above


Which of the following pairs will form the most stable ionic bond?
A. \( N a \) and \( C l \)
B. \( M g \) and \( F \)
c. \( L i \) and \( F \)
D. \( N a \) and \( F \)


The curved surface area of a
hemisphere of diameter 2 r is
\( \begin{array}{l}\text { A } 2 \pi r^{2} \\ ^{2}+2 r r^{2} \\ ^{2}\end{array}^{2} \)
В. \( 3 \pi r^{2} \)
\( \mathbf{c} \cdot 4 \pi r^{2} \)
D. \( 8 \pi r^{2} \)


How does algal bloom destroy the quality of a fresh water body? Explain.


The distance from the surface of the
earth at which above and below the
surface acceleration due to gravity is
same will be
\( ^{\mathrm{A}} \cdot_{h}=\frac{\sqrt{5}-1}{2} R \)
B. \( h=\frac{\sqrt{3}-1}{2} R \)
c. \( h=\frac{\sqrt{3}-1}{3} R \)
D. None of these


A planet is revolving in an elliptical orbit around the sun. Its closest
distance from the sun is \( r \) and the
farthest distance is \( R \). If the velocity of
the planet nearest to the sun be \( v \) and
that farthest away from the sun be \( \boldsymbol{V} \)
then \( \boldsymbol{v} / \boldsymbol{V} \) is :
A \( \cdot \frac{R^{2}}{r^{2}} \)
B. \( \frac{r^{2}}{R^{2}} \)
\( \mathbf{c} \cdot \frac{R}{r} \)
D. \( \frac{r}{R} \)


A reversible reaction is carried out at
\( 500 \mathrm{K} \) where its equilibrium constant is unity. If \( \Delta H \) at \( 500 \mathrm{K} \) is \( 4.0 k J, \) the
value of \( \Delta S^{o} \) is


Mark the correct option
A. The state of motion of an object is described by its speed only
B. Many a time application of force does not result in a change in the state of motion of an object
C. By sitting on a bicycle seat force is applied to the spring fixed to the seat of a bicycle
D. All of the above


Assertion
Degree of hydrolysis and \( p H \) of a salt
\( \operatorname{say} N H_{4} C N \) is independent of
concentration of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C} \boldsymbol{N} \)
Reason
The solution of \( N H_{4} C N \) in water has
\( \boldsymbol{p} \boldsymbol{H} \) slightly greater than \( \mathbf{7} \)
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


\( |\vec{a}+\vec{b}|^{2}-|\vec{a}-\vec{b}|^{2} \) is equal to
\( \mathbf{A} \cdot 4|\vec{a}||\vec{b}| \sin (\theta) \)
B . \( 4|\vec{a}||\vec{a}| \sin (\theta) \)
\( \mathbf{c} \cdot \mathbf{4}|\vec{a}||\vec{b}| \cos (\theta) \)
\( \mathbf{D} \cdot \mathbf{4}|\vec{a}||\vec{b}| \tan (\theta) \)


Which of the following fluorides of xenon is impossible?
A. \( X e F_{2} \)
в. \( X e F_{3} \)
c. \( x e F_{4} \)
D. \( X e F_{6} \)


The molecular weights of \( O_{2} \) and \( N_{2} \) are
32 and 28 respectively. At \( 15^{0} \mathrm{C} \), the
pressure of \( 1 \mathrm{gm} \mathrm{O}_{2} \) will be the same as
that of \( 1 \mathrm{gm} N_{2} \) in the same bottle at the temperature:
A. \( -21^{0} \mathrm{C} \)
B. \( -13^{0} \mathrm{C} \)
\( \mathrm{c} \cdot 15^{\circ} \mathrm{C} \)
D. \( 56.4^{0} \mathrm{V} \)


The earliest man-like primate was
A. Ramapithecus
B. Australopithecus
c. Homo habitue
D. Homo erectus


The curve satisfying \( \frac{\mathbf{d}^{2} \boldsymbol{y}}{\mathbf{d} \boldsymbol{x}^{2}}-\mathbf{4} \boldsymbol{y}^{\prime}=\mathbf{0} \) and
passing through (1,0) is:
A \( \cdot y=x e^{4 x} \)
B . \( y=a e^{4 x} \)
c. \( y=e^{4 x}-e^{4} \)
D・ \( y=a\left(e^{4 x}-e^{4}\right) \)


Which of the following is true about
Fischer Projection?
A. The vertical lines are oriented away from you and the horizontal lines are oriented toward you.
B. The vertical lines are oriented towards you and the horizontal lines are oriented away from you.
C. Both the horizontal and vertical lines are oriented away from you.
D. Both the horizontal and vertical lines are oriented
towards you.


Which of the following alkaline earth metal sulphates has hydration enthalpy higher than the lattice enthalpy?
A \( \cdot \operatorname{CaSO}_{4} \)
в. \( B e S O_{4} \)
c. \( B a S O_{4} \)
D. \( \operatorname{sr} \operatorname{sO} 4 \)


If the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left(a^{2}-3 a+2\right) \cos \frac{x}{2}+(a-1) x \)
possesses critical points, then \( a \) belongs to the interval
\( \mathbf{A} \cdot(-\infty, 0) \cup(4, \infty) \)
B . \( (-\infty, 0] \cup[4, \infty) \)
\( \mathbf{c} \cdot(-\infty, 0] \cup\{1\} \cup[4, \infty) \)
D. None of these


If \( P \) is a point on a circle with centre \( C \) then the line drawn through \( P \) and perpendicular to CP is the tangent to the circle at the point \( P \)
A. True
B. False
c. Either
D. Neither


Which of the following is synthetic sweetener?
A. Saccharin
B. Aspartame
c. Dulcin
D. All of the above


The breakdown field for air is about \( 2 x \)
\( \mathbf{1 0}^{6} \) volt/m. Therefore, the maximum
charge that can be placed on a sphere of diameter \( 10 \mathrm{cm} \) is
A \( .2 .0 \times 10^{-4} \mathrm{c} \)
В. \( 5.6 \times 10^{-7} \mathrm{c} \)
c. \( 5.6 \times 10^{-2} \mathrm{c} \)
D . \( 2.0 \times 10^{2} \mathrm{c} \)


If the standard internal energy change for the reaction \( O F_{2}(g)+H_{2} O(g) \longrightarrow \)
\( O_{2}(g)+2 H F(g), \) at \( 298 \mathrm{K} \) is \( x k J \)
[Given standard enthalpies of formation
in \( k J m o l^{-1} \) are \( O F_{2}(g)= \)
\( +20 ; H_{2} O(g)=-250 \) and \( H F(g)= \)
\( -270 . \)
Then \( -100 x \) is


If \( \vec{a}+\vec{b}+\vec{c}=0,|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7 \)
then the angle between \( \vec{a} \& \vec{b} \) is?
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{2 \pi}{3} \)
\( c \cdot \frac{5 \pi}{3} \)
D.


toppr
Q Type your question
\( A \)
B.
\( c \)
\( D \)


Lymph does not contain
A. Red blood cells
B. White blood cells
c. Platelets
D. Both A and C


The mobility of hole in a semiconductor depend on
A. Electric field
B. Potential difference
c. current
D. Mass


\( A B C \) is an isosceles triangle such that
\( A B=A C . D \) is the mid point of \( A C . A \)
circle is drawn taking \( B D \) as diameter which intersects \( A B \) at point \( E \).then
\( \boldsymbol{A C}=\mathbf{3 A E} \)
A. True
B. False


A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) The maximum height to which it rises.
\( (i i) \) The total time it takes to return to
the surface of the earth.


Two identical helium filled balloon \( \boldsymbol{A} \)
and \( B \mathrm{m} \) fastened to a weight of \( 5 g \) by
threads floats in equilibrium as shown
in fig. Calculate the charge on each
balloons, assuming that they carry
equal charges


Any point on the \( x \) -axis is of the form
\( \mathbf{A} \cdot(x, y) \)
в. \( (0, y) \)
c. \( (x, 0) \)
D. \( (x, x) \)


Consider the Newmann projection
formula of most stable conformation of
3-hydroxybutanal. It is stable due to:
This question has multiple correct options
A. minimum torsional strain
B. intramolecular H bonding
C. its being in the anti conformation
D. all of these


Give an account on the classes reptilia
and aves.


A woman weighing \( 63 \mathrm{kg} \) eats plum cake whose energy content is 9800 calories. If all this energy could be utilized by her, she can ascend a height of
A. \( 1 m \)
B. \( 66 m \)
\( c \cdot 100 m \)
D. \( 42 m \)


Let \( S \) be the infinite sum given by \( S= \) \( \sum_{n=0}^{\infty} \frac{a_{n}}{10^{2 n}}, \) where \( \left(a_{n}\right)_{n \geq 0} \) is a sequence
defined by \( a_{0}=a_{1}=1 \) and \( a_{j}= \)
\( 20 a_{j-1} \) for \( j \geq 2 . \) If \( S \) is expressed in the form \( \frac{a}{b}, \) where \( a, b \) are coprime positive
integers, than \( a \) equals.
A . 60
B. 75
c. 80
D. 81


\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\boldsymbol{x}-1) \) in the interval \( [\mathbf{1}, \mathbf{2}] \) if
\( \boldsymbol{f}^{\prime}(\boldsymbol{c})=\boldsymbol{f}(1) . \) Find \( c \)


Focal length of a convex lens is \( 10 \mathrm{cm} \) When the object is moved from \( 15 \mathrm{cm} \) to
\( 25 \mathrm{cm}, \) the magnitude of linear magnification
A. will increase
B. will decrease
c. will first increase then decrease
D. will first decrease then increase


Find \( (-32)-(-50) \)


A proton and ana - particle
accelerated through same voltage.The ratio of their de-broglie wavelength will
be:
A .1: 2
B . \( 2 \sqrt{2}: 1 \)
c. \( \sqrt{2}: 1 \)
D. 2: 1


Let \( f \) be any continuously differentiable function on \( [a, b] \) and twice
differentiable on \( (a, b) \) such that
\( \boldsymbol{f}(\boldsymbol{a})=\boldsymbol{f}^{\prime}(\boldsymbol{a})=\mathbf{0} \) and \( \boldsymbol{f}(\boldsymbol{b})=\mathbf{0} . \) Then
This question has multiple correct options
A \( \cdot f^{\prime \prime}(a)=0 \)
B. \( f^{\prime}(x)=0 \) for some \( x \in(a, b) \)
C \( . f^{\prime \prime}(x) \neq 0 \) for some \( x \in(a, b) \)
D. \( f^{\prime \prime \prime}(x)=0 \) for some \( x \in(a, b) \)


Current of 10 ampere and 2 ampere are passed through two parallel wires A and
B, respectively in opposite directions. If the wire \( A \) is infinitely long and the length of the wire \( \mathrm{B} \) is \( 2 \mathrm{m} \), the force on the conductor \( B \) which is situated at 10
\( \mathrm{cm} \) distance from A will be
\( \mathbf{A} \cdot 8 \times 10^{-5} N \)
B \( \cdot 4 \times 10^{-5} N \)
c. \( 8 \pi \times 10^{-7} N \)
D. \( 4 \pi \times 10^{-7} N \)


A small object of mass \( m, \) on the end of
a light cord, is held horizontally at a distance \( r \) from a fixed support as
shown. The object is then released. What is the tension in the cord when the
object is at the lowest point of its
swing?
A. \( m g / 2 \)
в. \( m g \)
\( \mathbf{c} \cdot 2 m g \)
D. \( 3 m g \)


Two particles, A and B having equal charges, after being accelerated through the same potential difference enter into a region of uniform magnetic field and the particles describe circular
paths of radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) respectively.
The ratio of the masses of \( A \) and \( B \) is:
\( \mathbf{A} \cdot \sqrt{R_{1} / R_{2}} \)
в. \( R_{1} / R_{2} \)
c. \( \left(R_{1} / R_{2}\right)^{2} \)
\( \mathbf{D} \cdot\left(R_{2} / R_{1}\right)^{2} \)


A system consists of two identical
small balls of mass 2 kg each
connected to the two ends of a 1 m long light rod. The system is rotating about a fixed axis through the centre of the rod and perpendicular to it at angular speed of 9 rad/s. An impulsive force of
average magnitude \( 10 N \) acts on one of the masses in the direction of its
velocity for \( 0.20 s . \) Calculate the new
angular velocity of the system.


A long straight wire in the horizontal
plane carries a current of \( 50 A \) in north
to south direction. Given the magnitude
and direction of \( B \) at a point 2.5 m east
of the wire.
A \( \cdot 2 \times 10^{-6} T, \) south
B . \( 3 \times 10^{-6} T \), down
c. \( 4 \times 10^{-6} T, \) up
D. \( 6 T \), north


What is heavy water?
\( \mathbf{A} \cdot H_{2} O^{18} \)
B. \( D_{2} \),
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}^{1} \)
D. \$\$H_\{2]


Excretion of wastes produced during photosynthesis in plants takes place through
A. Roots
B. Stomata.
c. stem
D. Both A and B


Simplify:
\( (a+b+c)^{2}+(a-b+c)^{2} \)


Which is used to produce smoke
screen?
A. Calcium phosphide
B. zinc sulphate
c. sodium carbonate
D. zinc phosphide


The decomposition of a beam of white light into its constituent colours is known as:
A. Scattering
B. Dissemination
c. Dispersion
D. Angular dispersion


The largest subunit of prokaryotic ribosomes is
A . 30s
B. 40S
\( c .50 s \)
D. 60 s


In the \( X e F_{4} \) molecule, the \( X e \) atom is
in the:
A \( \cdot s p^{2} \) -hybridisation state
B. \( s p^{3} \) -hybridisation state
c. \( s p^{2} d \) -hybridized state
D. \( s p^{3} d^{2} \) -hybridized state


Enthalpy of the system is given as:
\( \mathbf{A} \cdot H+P V \)
в. \( U+P V \)
c. \( U-P V \)
\( \mathbf{D} \cdot H-P V \)


n the given figure, which of the
following is a line of symmetry?
A. Line A
B. Line B
c. Line A and B
D. Line


What is the range of the data:
\( \mathbf{4 8}, \mathbf{6 5}, \mathbf{2 7}, \mathbf{2 3}, \mathbf{4 4}, \mathbf{4 1}, \mathbf{2 5}, \mathbf{7 0}, \mathbf{4 9} ? \)


The mean of 8 numbers is 25 if each
number is multiplied by 2 the new mean will be
A . 12.5
B. 25
c. 40
D. 50


is the stored carbohydrates in animals.
A. Cellulose
B. Glycogen
c. starch
D. Glucose
E . Fructose


If \( y=\frac{x^{2}}{2}+\frac{1}{2} \times \sqrt{x^{2}+1}, \) then \( 2 y= \)
\( x y^{\prime}, \) where \( y^{\prime} \) denotes the derivative of \( y \)
w.r.t. \( \boldsymbol{x} \)
A. True
B. False


Factorise \( \$ \$ 5 x^{\wedge} 2 y-15 x y^{\wedge} 2 \$ \)
A \( .2 x y(2 x-15 y) \)
в. \( 5 y(x-15 y) \)
c. \( 5 x y(x-3 y) \)
D. \( x y(5 x-3 y) \)


What is the action of acidified
potassium dichromate on acetaldehyde?


A capacitance of \( \left(\frac{10^{-3}}{2 \pi}\right) F \) and an inductance of \( \left[\frac{100}{\pi}\right] m H \) and \( a \) resistance of \( 10 \Omega \) are connected in
series with an AC voltage source of \( 220 V, 50 H z . \) The phase angle of the circuit is
A . \( 60^{\circ} \)
B. \( 30^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


\( n \) moles of an ideal gas undergoes a
process \( A \rightarrow B \) as shown in the figure.
Maximum temperature of the gas
during the process is:
A \( \cdot \frac{3 P_{o} V_{o}}{2 n R} \)
B. \( \frac{9 P_{o} V_{o}}{4 n R} \)
c. \( \frac{9 P_{o} V_{o}}{2 n R} \)
D. \( \frac{9 P_{o} V_{o}}{n R} \)


An emulsifier is a substance which:
A. stabilises the emulsion
B. homogenises the emulsion
c. coagulates the emulsion
D. accelerates the dispersion of liquid in liquid


Rewrite the following rational numbers in the simplest form:
\( \frac{-44}{72} \)


A research satellite of mass \( 200 \mathrm{kg} \) circles the earth in an orbit of average radius \( \frac{3 R}{2}, \) where \( R \) is the radius of the earth. Assuming the gravitational pull on a mass \( 1 \mathrm{kg} \) on earth's surface to be
\( 10 \mathrm{N}, \) the pull on this satellite will be:
A . \( 860 \mathrm{N} \)
B. 889 N
c. \( 827 \mathrm{N} \)
D. 798 N


How do chlorofluorocarbons (CFSs)
enter the atmosphere and how do they affect humans? Explain.


In system called the star system we have 1 star kilogram \( =10^{20} k g .1 \)
starmeter \( =10^{8} m, 1 \) starsecond \( = \)
\( 10^{3} \)second then calculate the value of
1 joule in this system.
A \( \cdot 10^{-30} \) star joule
B . \( 10^{-27} \) star joule
C \( .10^{-32} \) star joule
D. None of these


Which of the following is tertiary alcohol?
A. Ethyl alcohol
B. Isopropyl alcohol
c. Neopentyl alcohol
D. 2-methyl 2-propanol


In the following, which is the cube of odd natural number: 8,64,216,343
A . 343
B. 64
\( c \cdot 216 \)
D. 8


A charge of \( 5 \mu \mathrm{C} \) is placed at the center
of a square \( A B C D \) of side \( 10 \mathrm{cm} . \) Find the work done (in \( \mu \) ) in moving a charge of
\( 1 \mu C \) from \( A \) to \( B \)


Glycolysis cannot occur in absence of
A. \( C a \)
в. \( M n \)
c. \( M g \)
D. \( C o \)


When two waves of almost equal
frequency \( n_{1} \) and \( n_{2} \) are produced simultaneously, then the times interval between successive maxima is
A \( \cdot \frac{1}{n_{1}+n_{2}} \)
в. \( \frac{1}{n_{1}}+\frac{1}{n_{2}} \)
c. \( \frac{1}{n_{1}}-\frac{1}{n_{2}} \)
D. \( \frac{1}{n_{1}-n_{2}} \)


The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of
energy?
A. Yes
B. No
c. Yes, at certain instants
D. None of the above


Expand the following binomial \( \left(1-\frac{1}{x}\right)^{10} \)


Reverberation means
A. persistence of sound when intensity of sound from the source is increased
B. persistence of sound when intensity of sound from the source is decreased
C . persistence of sound even when source is turned off
D. persistence of sound when source is moved away


The common oxidation state shown by Europium in their compounds is:
\( A \cdot+1 \)
\( B \cdot+3 \)
\( c \cdot+5 \)
\( D \cdot+6 \)


Two solids \( A \) and \( B \) float in water. It is
observed that \( A \) floats with half of its
volume immersed and B floats with \( 2 / 3 \) of its volume immersed. The ratio of
their densities is
A .4: 3
B. 3:4
\( c \cdot 2: 3 \)
D. 3:2


Find the value of
\( a \) for which the function \( f \) defined by
\( f(x)=\left\{\begin{array}{ll}a \sin \frac{\pi}{2}(x+1) & , x \leq 0 \\ \frac{\tan x-\sin x}{x^{3}} & , x>0\end{array}\right. \)
continuous at \( x=0 \)


Which of the following oxides dissolves in water to form a strongly acidic
solution?
\( \mathbf{A} \cdot N a_{2} O \)
в. \( C a O \)
c. \( A l_{2} O_{3} \)
D. ZnO
E. \( S O_{3} \)


Identify the term or substance based on the descriptions given below:
Hydrocarbon containing a triple bond used for welding purposes.


A bullet of mass 125 gm leaves a rifle with a velocity of \( 500 m s^{-1} \). The rifle
recoils with a velocity of \( 5 m s^{-1} \). Find
the mass of the rifle.
\( A \cdot 100 \mathrm{kg} \)
B. 12.5 kgg
\( c \cdot 1.25 \mathrm{kg} \)
D. 125 kg


Which of the following statement is
incorrect about xenon trioxide?
A. It can be prepared by hydrolysis of \( X e F_{4} \)
B. It can be prepared by hydrolysis of \( X e F_{6} \)
C. It is a non volatile solid.
D. It's aqueous is slightly basic.


One girl student uses the liquid compound to remove nail paint from her nail. The liquid compound removes the nail paint from her nail. Give the name of this compound.
A . Acetic acid
B. Formalin
c. Ethanol
D. Propanone


From a group of 2 men and 3 women two persons are selected. Describe the
sample space of the experiment. If \( \boldsymbol{E} \) is
the event in which one man and one
woman are selected, then which are the
cases favourable to \( \boldsymbol{E} \) ?


The maximum probability of finding
electron in the \( d_{x y} \) orbital is:
A. along with \( x \) - axis
B. along the \( y \) -axis
c. at an angle of 45 from the \( x \) and \( y \) axis
D. at an angle of 90 from the \( x \) and \( y \) axis


A stone falls freely from rest from a height \( h \) and it travels a distance \( \frac{9 h}{25} \) in the last second. The value of h is :
A . \( 145 \mathrm{m} \)
B. 100 \( m \)
c. \( 122.5 \mathrm{m} \)
D. 200 m


A particle is moving in a circle of radius \( 4 \mathrm{cm} \) with constant speed of \( 1 \mathrm{cm} / \mathrm{s} \) Find the time period of the particle.


A 0.004 M solution of \( N a_{2} S O_{4} \) is
isotonic with a \( 0.010 \mathrm{M} \) solution of
glucose at same temperature. The apparent degree of dissociation of
\( N a_{2} S O_{4} \) is:
A . \( 25 \% \)
B. \( 50 \% \)
c. \( 75 \% \)
D. \( 85 \% \)


In an unbiased \( n \) -p junction electrons diffuse from n-region to p- region because
A. electrons travel across the junction due to potential difference
B. electrons concentration in n region is more as compared to that in p-region
c. holes in p-region attract them.
D. only electrons move from n- to p- region and not the vice-versa.


Two thick plates having same charges (same charge density \( \sigma \) ) are placed side by side. Consider the case of infinite plate. Find the difference between the electric field present
between the plate and remaining space of the plate, \( (\varepsilon=\text { permittivity }) \)
A \( \cdot \frac{\sigma}{\varepsilon} \)
в. \( 2 \frac{\sigma}{\varepsilon} \)
c. \( \frac{\sigma}{2 \varepsilon} \)
D.


What is the maximum capacity of a normal human eye to see small objects?
A. 10,000 micrometer
B. 10 micrometer
c. 100 micrometer
D. 1000 micrometer


The strongest fundamental force in nature is
A. Electromagnetic force
B. Strong nuclear force
c. weak nuclear force
D. gravitational force


Prove that, \( \left(^{2 n} C_{1}\right)^{2}+2 \cdot\left(^{2 n} C_{1}\right)^{2}+ \)
3. \( \left(^{2 n} C_{3}\right)^{2}+\ldots .+2 n .\left(^{2 n} C_{2 n}\right)^{2}= \)
\( \frac{(4 n-1) !}{\{(2 n-1) !\}^{2}} \)


The figure shows a source (a battery) with an emf \( E \) of \( 12 V \) with an internal
resistance \( r \) of \( 2 \Omega \) and an external
resistance of \( 4 \Omega \) is added to complete the circuit. What are the voltmeter and
ammeter readings?


A battery of \( 10 \mathrm{V} \) and internal resistance
\( 0.5 \Omega \) is connected across a variable
resistance R. The value of \( R \) for which
the power delivered in its maximum state, is equal to :-
A \( .0 .5 \Omega \)
в. \( 1 \Omega \)
c. \( 1.5 \Omega \)
D. \( 2.0 \Omega \)


Calcium superphosphate, sodium
nitrate and ammonium sulphate are
used:
A. in refrigerators
B. air conditioners
c. to increase the yield of fruits, vegetables and other crops
D. invertors


Can you draw a triangle which has exactly three lines of symmetry? Sketch a rough figure.


Write the function of the following part of human eye.
Cornea.


The two p orbitals are deflected by an angle of:
A \( \cdot 45^{\circ} \)
B . \( 180^{\circ} \)
\( c .90^{\circ} \)
D. \( 120^{\circ} \)


Suicide bags of cells are
A. Endoplasmic reticulum
B. Lysosome
c. Golgi bodies
D. Vacuoles


Write the formula of the compound of
iodine which is obtained when
conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) oxidises \( \boldsymbol{I}_{2} \)


Drying of a shirt in the sun is an
example of changes.


Which of the following is a fat soluble vitamin?
\( A \cdot \) Vitamin A
B. Vitamin C
c. Pyridoxine
D. Vitamin B - complex


a. Both (A) and (B) are resolvable.


A source of constant potential
difference is connected across a
conductor having irregular cross-
section as shown in figure. Then :-
A. Electric field intensity at \( P \) is greater than at \( Q \).
B. Rate of electric current crossing per unit area of cross section at \( P \) is less than that at \( Q \)
C. The rate of generation of heat per unit length at \( P \) is greater than that at \( Q \).
D. Mean kinetic energy of free electron at \( P \) is greater than that at \( Q \)


Dobereiner classified elements into
groups based on their properties. The number of elements in each group is


Assertion
STATEMENT 1 (Assertion)- Absolute
value of H cannot be determined
Reason
STATEMENT 2 (Reason)- \( \Delta \boldsymbol{H}_{(g)}= \)
\( \boldsymbol{\Delta} \boldsymbol{E}_{(\boldsymbol{g})}+\boldsymbol{\Delta} \boldsymbol{n}_{(g)} \boldsymbol{R} \boldsymbol{T} \)
A. Statement 1 is True, statement 2 is True; statement 2 is a correct explanation for statement 1
B. Statement 1 is True, statement 2 is True; statement 2 is not a correct explanation for statement 1
c. Statement 1 is True, statement 2 is False.
D. Statement 1 is False, statement 2 is True


Many metals, like, chromium, molybdenum, cobalt and nickel become inert (chemically unreactive) on adding concentrated:
A. barium sulphate
B. nitric acid
c. caustic soda
D. a solution of bromine in water


toppr
Q Type your question
totally reflected internally and is "trapped" within the rod even if it is curved, provided the curvature is not
too great. the rod. is something referred to as a light pipe. A bundle of fine fiber will behave in the same way and has the
advantage of being flexible. The study of the properties of such a bundle is an active field of research known as fiber
optics. A bundle may consist of thousand of individual fibers, each of the order of
0.002 to \( 0.01 \mathrm{mm} \) in diameter. If the fiber
can be assembled in the bundle so that
the relative positions of the ends are the same at both ends, the bundle can transmit an image as shown in Fig.(b) Bundles several km in length have been
made. Device using fiber optics are finding a wide range of applications in medical science. The interior of lungs
and other passage in the human body can be viewed by insertion of a fiber bundle that can be enclosed in a
hypodermic needle for the study of
tissues and blood vessels far beneath
the skin. Despite the enormous technical difficulties of manufacturing fiber-optic components, such system promise to become an extremely important class of optical systems.
(1) what are the losses in fiber optic?
this question has multiple correct options
A. Brillouin zone and Raman scattering
B. polarisation
c. evanscent field
D. diffraction


Chipko-Andolan (Hug the trees movement) is the well known example of conservation of which form of nature?
A. Jungle
B. water
c. coal
D. Petroleum


\( \mathbf{A} \cdot-62.7 k J m o l^{-1} \)
\( \mathbf{B} \cdot-31.4 k J m o l^{-1} \)
\( \mathbf{c} \cdot-15.7 k J m o l^{-1} \)
D. \( -3.14 k J \) mol\( ^{-1} \)


\( 3 x^{2}-x-4 \)


phytohormone is responsible for cell elongation and
differentiation of shoots and roots.


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) of the following implicit
functions \( : \boldsymbol{y}^{3}-\boldsymbol{3} \boldsymbol{y}^{2} \boldsymbol{x}=\boldsymbol{x}^{3}+\boldsymbol{3} \boldsymbol{x}^{2} \boldsymbol{y} \)


What are the essential components of an oscillator? Draw its block diagram?


Solve the given equation by the method
of Completion of Squares: \( x^{2}+4 x+ \)
\( \mathbf{4}=\mathbf{0} ? \)
\( A \cdot 2 \)
B. -
\( c \cdot 4 \)
D. -4


Which of the following phenomena helps in the degradation of complex substances of food into simpler ones?
A. Digestion
B. Ingestion
c. Excretion
D. Assimilation


Solve : \( \left(3 x-\frac{1}{2 y}\right)\left(3 x+\frac{1}{2 y}\right) \)


In an electric bell a flat \( \ldots \). spring brings the armature back to its original position.


The time taken by block to sliding downward from the smooth surface of
an angle \( 45^{\circ}, \) the time taken by block
kept on same type of rough surface is 'n times. Then what is the coefficient of
friction between block and surface?
A \( \cdot\left(1-\frac{1}{n^{2}}\right)^{\frac{1}{2}} \)
B. \( \left(\frac{1}{1-n^{2}}\right)^{\frac{1}{2}} \)
c. \( \left(1-\frac{1}{n^{2}}\right) \)
\( D \cdot\left(\frac{1}{1-n^{2}}\right) \)


A coin is tossed \( 2 n \) times. The chance
that the number of times one gets head is not equal to the number of times one
gets tail is
A \( \cdot \frac{(2 n) !}{(n ! !)^{2}} \cdot\left(\frac{1}{2}\right)^{2} n \)
B. \( _{1-} \frac{(2 n) !}{(n !)^{2}} \)
c. \( _{1-} \frac{(2 n) !}{(n !)^{2}} \cdot \frac{1}{4^{n}} \)
D. none of these


For a cubical block, error in
measurement of sides is \( \pm 1 \% \) and
error in measurement of mass is \( \pm 2 \% \)
then maximum possible error in density is
A . 1\%
B. 5\%
c. अ\%
D. 7\%


The freezing point of a 0.05 molal solution of a non-electrolyte in water is:
\( \mathbf{A} \cdot-0.093^{\circ} \mathrm{C} \)
B . \( 1.86^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 0.93^{\circ} \mathrm{C} \)
D. \( 0.093^{\circ} \mathrm{C} \)


How does ozone react with the
following?
(i) \( C_{2} H_{4} \)
(ii) Moist \( \boldsymbol{I}^{-} \)
(iii) \( \boldsymbol{H} \boldsymbol{g} \)
(iv) \( \boldsymbol{A} \boldsymbol{g} \)


Find the difference of :
\( \frac{1}{12} \) and \( \frac{3}{4} \)


\( (1+i)^{-1} \)
A \( \cdot \frac{1+i}{2} \)
B. \( \frac{1-i}{2} \)
\( \mathbf{C} \cdot 1+i \)
D. \( 1-i \)


Nursing infants of mothers living near hazardous waste sites may be exposed to PAHs through their mother's milk.
A. True
B. False


Which of two elements among the following will display the most similar chemical properties?
A. Aluminum and calcium
B. Nickel and phosphorus
c. chlorine and sulfur
D. Carbon and sulfur
E. Lithium and potassium


If \( \boldsymbol{\alpha}=\cos 10^{\circ}-\sin 10^{\circ}, \beta=\cos 45^{\circ}- \)
\( \sin 45^{\circ}, \gamma=\cos 70^{\circ}-\sin 70^{\circ} \) then the
descending order of \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) is
\( \mathbf{A} \cdot \alpha, \beta, \gamma \)
в. \( \gamma, \beta, \alpha \)
c. \( \alpha, \gamma, \beta \)
\( \mathbf{D} \cdot \beta, \alpha, \gamma \)


Describe briefly with the help of a circuit diagram, how the flow of current
carriers in a \( \boldsymbol{p}-\boldsymbol{n}-\boldsymbol{p} \) transistor is
regulated with emitter-base junction forward biased and base-collector
junction reverse biased.


What type of chemical reaction takes place when i) limestone is heated?
ii) a magnesium ribbon is burnt in air?


Six identical particles each of mass \( \boldsymbol{m} \)
are arranged at the corners of a regular hexagon of side length \( L \). If the mass of one of the particle is doubled, the shift in the centre of mass is:
A.
в. \( \frac{6 \mathrm{L}}{7} \)
\( c \cdot \frac{L}{7} \)
D. \( \frac{\mathrm{L}}{\sqrt{3}} \)


Let
\( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y})=\left|\begin{array}{lll}\boldsymbol{y}-\boldsymbol{x}^{2} & \boldsymbol{x}-\boldsymbol{y}^{2} & \boldsymbol{x} \boldsymbol{y}-\mathbf{1} \\ \boldsymbol{x}-\boldsymbol{y}^{2} & \boldsymbol{x} \boldsymbol{y}-\mathbf{1} & \boldsymbol{y}-\boldsymbol{x}^{2} \\ \boldsymbol{x} \boldsymbol{y}-\mathbf{1} & \boldsymbol{y}-\boldsymbol{x}^{2} & \boldsymbol{x}-\boldsymbol{y}^{2}\end{array}\right| \)
find \( \boldsymbol{f}(\boldsymbol{2}, \boldsymbol{2}) \)


Colours of rainbow are in VIBGYOR
sequence:
A . True
B. False


A charge \( 10 n C \) is situated in a medium
of relative permittivity 10. The potential due to this charge at a distance of \( 0.1 m \)
is :
\( \mathbf{A} \cdot 900 V \)
в. \( 90 V \)
\( c .9 V \)
D. \( 0.09 V \)


Which of the following bonds has maximum bond length?
A . C-O
B. C-H
c. \( c-c \)
D. C-N


The densities of two substances are in
the ratio 1: 2 and their specific heat in
the ratio \( 2: 3 . \) Compare their thermal capacities if their volumes are in the ratio 3: 4


An organic compound must contain:
A. carbon
B. hydrogen
c. oxygen
D. silicon


Of the isomeric hexanes, the isomers
that give the minimum and the maximum number of monochloro
derivatives are respectively:
A. 2,3- dimethylbutane and n- hexane
B. 3- -methylpentane and 2,3- dimethylbutane
c. 2,2 - dimethylbutane and
2 - methylpentane
D. 2,3 - dimethylbutane and
2 - methylpentane
E. 2-methylpentane and 2,2-dimethylbutane


Preeti reached the metro station and
found that the escalator was not
working. She walked up the stationary
escalator in time \( t_{1} . \) On other days, if
she remains stationary on the moving
escalator, then the escalator takes her
up in time \( t_{2} . \) The time taken by her
walk up on the moving escalator will be:
\( \mathbf{A} \cdot t_{1}-t_{2} \)
B. \( \frac{t_{1}+t_{2}}{2} \)
\( \mathbf{C} \cdot \frac{t_{1} t_{2}}{t_{2}-t_{1}} \)
D. \( \frac{t_{1} t_{2}}{t_{2}+t_{1}} \)


Which of the following reaction(s) gives a gem-dichloride?
This question has multiple correct options
A. \( C H_{3} C H O \) and \( P C l_{5} \)
в. \( C H_{3} C O C H_{3} \) and \( P C l_{5} \)
c. \( C H_{2}=C H_{2} \) and \( C l_{2} \)
D. \( C H_{2}=C H C l \) and \( H C l \)


Prickles of rose are
A. Modified leaves
B. Modified stipules
C. Exogenous in origin
D. Endogenous in origin


A mixture of \( S O_{3}, S O_{2} \) and \( O_{2} \) gases is
maintained in a \( 10 L \) flask at a
temperature at which the equilibrium constant for the reaction is 100 and the
reaction is, \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g) \)
(i) If the number of moles of \( S O_{2} \) and
\( S O_{3} \) in the flask are equal, how many
moles of \( \boldsymbol{O}_{2} \) are present?
(ii) If the number of moles of \( S O_{3} \) in the
flask is twice the number of moles of
\( S O_{2}, \) how many moles of oxygen are
present?


Which of the following is an ideal fuel?
A. coal
B. LPG
c. Petrol
D. None of these


The Lanthanoid contraction refers to:
A. valence electrons of the Lanthanide series
B. ionic radius of the series
C . the density of the series
D. nuclear mass of the series


\( E C \) of \( G d(64) \) is written as:
A \( \cdot[X e]_{54} 4 f^{7} 5 d^{1} 6 s^{2} \)
В \( \cdot[X e]_{54} 4 f^{8} 8 s^{2} \)
\( \mathbf{c} \cdot[X e]_{54} 4 f^{9} 6 s^{1} \)
D. \( [X e]_{54} 4 f^{10} \)


Which of the following properties can be assigned to water?
I. It has a permanent dipole moment attributed to its molecular structure.
Il. It is a very good conductor of
electricity.
III. It has its polar covalent bonds with hydrogen on opposite sides of the oxygen atom, so that the molecule is
linear
A. I only
B. III only
c. I and II only
D. II and III only
E . I, II and III


If \( n=4 m+3, m \) is an integer, then \( i^{n} \)
is equal to:
A . \( -i \)
B.
\( c . i \)
D. -


Determine the length of the chord common to the circles \( x^{2}+y^{2}= \)
\( 64 a n d x^{2}+y^{2}-16 x=0 \)
A \( \cdot 2 \sqrt{3} \)
B. \( 4 \sqrt{3} \)
\( c \cdot 6 \sqrt{3} \)
D. \( 8 \sqrt{3} \)


\( \int 3^{x} \cos 5 x d x= \)
A. \( \frac{3^{x}}{(\log 3)^{2}+25}[(\log 3) \cdot \cos 5 x-5 \sin 5 x]+c \)
B. \( \frac{3^{x}}{(\log 3)^{2}+25}[(\log 3) \cdot \cos 5 x+5 \sin 5 x]+c \)
C. \( \frac{3^{x}}{(\log 3)^{2}+25}[5 \cos 5 x-(\log 3) \cdot \sin 5 x]+c \)
D. \( \frac{3^{x}}{(\log 3)^{2}+25}[5 \cos 5 x+(\log 3) \cdot \sin 5 x]+c \)


Match the terms to these definitions.
Trypanosoma, euglenoid, formaminiferan, isogamy, plankton, plasmodial slime mold, Protista, pseudopod, sporozoan, trichocyst, Dinoflagellate Includes all unicellular eukaryotic
organisms.


Choose the wrong statements from the following.

Two spheres made of the same material have the same diameter. One sphere is
hollow and the other is solid. If they are
heated through the same range of
temperature, Then:
This question has multiple correct options
A. Both spheres will expand equally.
B. Hollow sphere will expand more than solid one
c. solid sphere will expand more than hollow one
D. Solid sphere will expand three times that of hollow sphere


Identity the acid which gives \( C O \) and
\( C O_{2} \) on reaction with \( H_{2} S O_{4} \)
A. Oxalic acid
B. Formic acid
c. Nitric acid
D. Hydrochloric acid


The ignition temperature of an ideal fuel should
A. Lowest
B. Highest
c. Neither too high nor too low
D. None of the above


The initial velocity of a particle \( (\operatorname{at} t=0 \)
is \( u \) and the acceleration by \( f \) of
particle at time \( t \) is given \( \boldsymbol{f}=\boldsymbol{a t} . \) Where
\( a \) is a constant which of the following
relation for velocity \( v \) of particle after time \( t \) is turn
A \( \cdot v=u+a t^{2} \)
B. \( v=u+\frac{a t^{2}}{2} \)
c. \( v=u+a t \)
D. \( v=u \)


A sinusoidal voltage of peak value \( 293 \mathrm{V} \) and frequency \( 50 \mathrm{Hz} \) is applied to a series LCR circuit in which \( \mathrm{R}=6 \Omega, \mathrm{L} \)
\( =25 \mathrm{mH} \) and \( \mathrm{C}=750 \mu \mathrm{F} \). The impedance
of the circuit is:
A. \( 7.0 \Omega \)
B. \( 8.9 \Omega \)
\( c \cdot 9.9 \Omega \)
D. 10.0 \( \Omega \)


Which law of Newton defines an 'inertial
frame of reference'?
A. First law of motion
B. Second law of motion
c. Third law of motion
D. Law of gravitation


Clouds are colloidal dispersions of :
A. water in air
B. air in water
C. air in solid
D. solid in air


The boiling point of a compound is raised by increase in:
A. intermolecular hydrogen bonding
B. high volatility
c. intramolecular hydrogen bonding
D. non-polarity


A velocity - time graph is shown above
in figure (i) and (ii) find the
acceleration and displacement


Vector \( \underset{A}{A} \) has a magnitude of 6 units and is in the direction of \( +x a x i s . \) Vector
\( \vec{B} \) has a magnitude of 4units lies in
the \( x \) -y plane making an angle of \( 30^{\circ} \) with \( +x-a x i s . \) Find the vector
product \( \underset{A}{A} \times \frac{ }{B} \)


Column 1
a) A linear S.H.M
e) \( \frac{d^{2} \Theta}{d t^{2}}=\frac{c}{\Theta} \)
b) Angular S.H.M
f) \( \frac{d^{2} x}{d t^{2}}+ \)
\( \frac{\boldsymbol{R}}{\boldsymbol{m}} \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{M} \boldsymbol{t}}+\boldsymbol{x} \boldsymbol{w}^{2}=\frac{\boldsymbol{F}}{\boldsymbol{m}} \cos \boldsymbol{\theta} \)
c) Damped harmonic
motion
g) \( \frac{d^{2} x}{d t^{2}}- \)
\( \frac{k}{m} x=0 \)
d) forced oscillation
h) \( m \frac{d^{2} x}{d t^{2}}+ \)
\( R \frac{d n}{d t}+m x \omega^{2}=0 \)
A. a-e, \( b-h, c-g, d-f \)
B. \( a-f, b-g, c-e, d-h \)
\( c \cdot a-g, b-e, c-h, d-f \)
D. a-g, b-h, c-e, d-f


A wire mesh consisting of very small squares is viewed at a distance of \( 8 \mathrm{cm} \) through a magnifying converging lens of focal length \( 10 \mathrm{cm}, \) kept close to the eye. The magnification produced by the lens is.
A. 5
B. 8
\( c \cdot 10 \)
D. 20


\( \sum_{i=l}^{n}\left(x_{i}-a\right)= \)
\( ^{\mathrm{A}} \cdot \sum_{i=l}^{n} x_{i}-n a \)
В. \( _{n a-\sum_{n}^{i=l} x_{i}} \)
c. \( _{n a-\sum_{n}^{i=l} x_{i}+n a} \)
D. None of these


If \( D \) is any point on the side \( B C \) of \( \Delta A B C \) such that \( \Delta A D B \) and \( \Delta A D C \)
are equal in area, then
A. AD is the median
B. AD is the altitude
c. AD is an angle bisector
D. AD is any line


According to Watson-Crick model hydrogen bonding in a double-stranded
DNA occurs between.
A. Adenine and guanine
B. Adenine and thymine.
c. cytosine and adenine.
D. Guanine and thymine.


\( 2 S O_{2}(g)+O_{2}(g) \leftrightharpoons 2 S O_{3}(g) \)
Given that the equilirbium constant for
the reaction above has a value of 278 at
a particular temperature, what is the value of equilibrium constant for the following reaction at same temperature?
\( \boldsymbol{S O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
A \( \cdot 1.3 \times 10^{-5} \)
B . \( 1.8 \times 10^{-3} \)
c. \( 3.6 \times 10^{-3} \)
D. \( 6 \times 10^{-2} \)


If \( \boldsymbol{I}=\int_{0}^{1} \frac{\boldsymbol{e}^{t}}{\mathbf{1}+\boldsymbol{t}} \) dt, then \( \boldsymbol{p}= \)
\( \int_{0}^{1} e^{t} \log (1+t) d t= \)
\( A \)
B. \( 2 I \)
c. \( e \log 2-I \)
D. none


Two long straight wires of length \( l \) lie parallel to one another and carry currents opposite to one another of
magnitudes \( i_{1} \) and \( i_{2} \) respectively.
The force experienced by each of the straight wires is \( (r \) is the distance of
their separation)
A . repulsive and equal to \( \left(\mu_{0} / 2 \pi\right)\left(i_{1} i_{2} l / r\right) \)
B. attractive and equal to ( \( \left.\mu_{0} / 2 \pi\right)\left(i_{1} i_{2} l^{2} / r\right) \)
c. repulsive and equal to \( \left(\mu_{0} / 2 \pi\right)\left(i_{1} i_{2} l^{2} / r\right) \)
D. attractive and equal to \( \left(\mu_{0} / 2 \pi\right)\left(i_{1} i_{2} l / r\right) \)


If \( \cos \Theta_{1}+\cos \Theta_{2}+\cos \Theta_{3}=3, \) find
\( \sin \Theta_{1}+\sin \Theta_{2}+\sin \Theta_{3} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


The excitation energy of a hydrogen like ion to first excited state is \( 40.8 \mathrm{eV} \). The
energy needed to remove the electron
from the ion the ground state is
A. 54.4 ev
B. 62.6 ev
c. \( 72.6 \mathrm{ev} \)
D. 58.6 ev.


The shortest possible time required by
the boat to cross the river will be:-
A. 125 sec
B. 250 sec
C . 500 sec
D. \( \frac{250}{\sqrt{3}} \) sec


The external pressure exerted on the fluid is transmitted uniformly. Is the statement True or false
A. True
B. False


Which of the following is not true about
feasibility?
A. It cannot be determined in a graphical solution of an LPP
B. It is independent of the objective function
C. It implies that there must be a convex region satisfying all the constraints
D. Extreme points of the convex region gives the optimum solution.


In which of the following case(s), the
angular momentum is conserved?
This question has multiple correct options
A. The planet Neptune moves in elliptical orbit around the sun with sun at one focus
B. A solid sphere rolling on an inclined plane
C. An electron revolving around the nucleus in an elliptical orbit
D. An \( \alpha \) particle approaching a heavy nucleus from sufficient distance.


Assertion: \( P_{2} O_{3} \) is more basic than
\( N_{2} O_{3} \)
Reason: Metallic nature of the oxides
increases down the group.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. Assertion is true and Reason is false
D. Assertion is false but Reason is true


If \( p, q, r \) are positive and are in A.P., then the roots of the quadratic equation
\( p x^{2}+q x+r=0 \) are real for
A \( \cdot\left|\frac{r}{p}-7\right| \geq 4 \sqrt{3} \)
В \( \cdot\left|\frac{p}{r}-7\right|<4 \sqrt{3} \)
c. all \( p \) and \( r \)
D. no \( p \) and \( r \)


Find the distance of the point (2,3,5) from the \( x y- \) plane


If the displacement of a particle varies
with time as \( \sqrt{x}=t+7, \) which of the
following statements is(are) true?
This question has multiple correct options
A. Velocity of the particle is inversely proportional to \( t \).
B. Velocity of the particle is proportional to \( t \)
C. Velocity of the particle is proportional to \( \sqrt{t} \)
D. The particle moves with a constant accelera


Assertion
According to Mendeleev's periodic law;
The properties of elements are the
periodic a function of their atomic
numbers.
Reason
Mendeleev's periodic law could explain
the phenomenon of anomalous pairs.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In uniform electric field, \( \boldsymbol{E}=\mathbf{1 0} \boldsymbol{N} \boldsymbol{C}^{-1} \)
as shown in figure.
Find. \( (\mathrm{i}) \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}} \)
(ii) \( V_{B}-V_{C} \)
A . -10,20
B. 30,50
\( c .-20,30 \)
D. 40,50


\( \int \frac{\cos ^{2} x}{\sin ^{4} x} d x \)
A. \( -\frac{1}{3} \tan ^{3} x \)
B. \( \frac{1}{3} \cot ^{3} x \)
C. \( -\frac{1}{3} \cot ^{3} x \)
D. \( \frac{1}{3} \tan ^{3} x \)


The phenomenon of electromagnetic
induction is
A. the process of charging a sphere
B. the process of producing magnetic field in a coil
C. the process of producing induced current in a coil whenever there is a relative motion between the coil
and the magnet
D. the process of producing cooling effect


\( 2 n \) boys are randomly divided into two
subgroups containing \( n \) boys each. The
probability that the two tallest boys are in different groups is
A \( . n /(2 n-1) \)
B. \( (n-1) /(2 n-1) \)
c. \( (n-1) / 4 n^{2} \)
D. None of these


Assertion
All \( \boldsymbol{F}-\boldsymbol{S}-\boldsymbol{F} \) angles in \( \boldsymbol{S} \boldsymbol{F}_{4} \) is greater
than \( 90^{\circ} \) but lesser than \( 180^{\circ} \)
Reason
The lone pair-bond pair repulsion is stronger than bond pair-bond pair repulsion.
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 wire is bent into the shape of a
square, then the area enclosed by the square is \( 81 \mathrm{cm}^{2} \). When the same wire
is bent into a semi-circular shape, then the area enclosed by the semi circle will be
\( \mathbf{A} \cdot 81 c m^{2} \)
B. \( 44 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 77 c m^{2} \)
D. \( 154 c m^{2} \)


The sex of a child is determined by the
A. Chromosome of the father
B. Chromosome of the mother
c. Rh factor of the parents
D. Blood group of the father


The standard electrode potential \( \boldsymbol{E}_{l_{2} / r}^{o}, \quad \boldsymbol{E}_{B r^{-} / B r_{2}}^{0} \quad \) and \( \quad \boldsymbol{E}_{\boldsymbol{F} e / F e^{2+}}^{0} \) are
respectively \( +0.54 \mathrm{V},-1.09 \mathrm{V} \) and \( 0.44 \mathrm{V} . \) On
the basis of above data which of the
following process is non spontaneous?
\( \mathbf{A} \cdot B r_{2}+2 I^{1} \rightarrow 2 B r+I_{2} \)
B. \( F e+B r_{2} \longrightarrow F e^{2+}+2 B r \)
C. \( F e+I_{2} \longrightarrow F e^{2+}+2 I^{-} \)
D. \( I_{2}+B r \longrightarrow 2 I^{-}+B r_{2} \)


A light ray is incident perpendicular to
one face of a \( 90^{0} \) prism and is totally intemally reflected at the glass-air
interface. If the angle of reflection is \( 45^{\circ} \)
we conclude that the refractive index n
4
B \( . n>\sqrt{2} \)
\( c \cdot n>\frac{1}{\sqrt{2}} \)
D. \( n<\sqrt{2} \)


Simplify using associative property :
\( \frac{-8}{9} \times\left(\frac{27}{32} \times \frac{-8}{21}\right) \)
A \( \cdot \frac{2}{7} \)
B. \( \frac{-2}{7} \)
\( c \cdot \frac{-8}{21} \)
D. \( \frac{-3}{4} \)


Match the Column I with Column II.
Column I
(Physical
quantity) Column II
(Dimensional
formula) (Dimensio
formula)
(A) Premittivity
of free
space
\( (p) \)
\( \left[M^{0} L^{0} T^{-1}\right] \)
(В) \( \left[M L^{3} T^{-3} A^{-2}\right] \)
(C) \( \begin{array}{ll}\text { Radiant flux } & \text { (q) } \\ \text { Resistivity } & \text { (r) } \\ \text { Hubble } & \text { (s) } \\ \text { constant } & \text { (s) }\end{array} \) \( \left[\mathrm{M} \mathrm{L}^{2} \mathrm{T}^{-3}\right] \) A
(D) (s) \( \quad\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
\( A \cdot A-p, B-q, C-r, D-s \)
B. \( A-q, B-p, C-s, D-r \)
C. \( A-s, B-r, C-q, D-p \)
\( D \cdot A-r, B-s, C-q, D-p \)


What two metals are often used in
electrochemical cells?
A. zinc and copper
B. Zinc and sulfur
c. carbon and copper
D. zinc and carbon
E. Sulfur and copper


A d-block element has total spin value
of \( +3 . \) Then, the spin only magnetic moment of the element is
approximately:
A. 2.83 В.M.
B. 3.87 В.М.
c. 5.9 в.М
D. 6.93 В.М.


Purification of alumina takes place by
A. Bosch process
B. Hall's process
c. Hoope's process
D. Quartation process


Sol is a type of a colloidal in which:
A. solid is dispersed in liquid
B. liquid is dispersed in solid
C . gas is dispersed in liquid
D. solid is dispersed in solid


If the ordered pairs \( (a-3, a+2 b) \) and
\( (3 a-1,3) \) are equal, find the value of
\( a+b \)


It is possible to write down the
electronic configuration of an atom if we know its atomic numbers.Why this
is so?


If \( \mathbf{A} \) and \( \mathbf{B} \) are two square matrices
such that \( \mathbf{B}=-\mathbf{A}^{-1} \mathbf{B} \mathbf{A} \) then \( (\mathbf{A}+ \)
\( \mathbf{B})^{2}= \)
A . 0
B. \( A^{2}+B^{2} \)
c. \( A^{2}+2 A B+B^{2} \)
D. \( A+B \)


The volatility of \( H F \) is low because of:
A. its low polarizability
B. the weak dispersion interaction between the molecules
c. its small molecular mass
D. its strong hydrogen bonding


Find the interaction force of two coils
with magnetic moments \( \boldsymbol{p}_{1 m}=\mathbf{4 . 0} \boldsymbol{m} \boldsymbol{A} \)
\( -m^{2} \) and \( p_{2 m}=6.0 m A-m^{2} \) and
collinear axes if the separation between the coils is equal to \( l=20 \mathrm{cm} \) which
exceeds considerably their linear dimensions.
A . 9
B. 5
c. 8
D. 10


\( \cos ^{-1}\left[\cos \left(\left(-\frac{17}{15}\right) \pi\right)\right] \) is equal to
A \( \cdot \frac{17 \pi}{15} \)
в. \( \frac{13 \pi}{15} \)
\( c \cdot \frac{3 \pi}{15} \)
D. \( -\frac{17 \pi}{15} \)


||\( \vec{a}|=3,| \vec{b}|=4,| \vec{c} \mid=5, \vec{a} \perp(\vec{b}+ \)
\( \vec{c}), \vec{b} \perp(\vec{c}+\vec{a}) \) and \( \vec{c} \perp(\vec{a}+\vec{b}) \) then
\( \sqrt{2}|\vec{a}+\vec{b}+\vec{c}| \) is equal to


Find the values of \( x \) for which the angle between the vectors \( \vec{a}=x \hat{i}-3 \hat{j}-1 \hat{k} \) and \( \vec{b}=2 x \hat{i}+x \hat{j}-1 \hat{k} \) is acute and
the angle between the vector b and \( y- \) axis is obtuse.
\( \mathbf{A} \cdot x<0 \)
B . \( x>0 \)
c. \( _{x}<\frac{1}{2} \)
D. \( x>\frac{1}{2} \)


What will be the ratio of temperatures of sun and moon if the wavelengths of their maximum emission radiations
rates are \( 140 A^{\circ} \) and \( 4200 A^{\circ} \)
respectively:
\( \mathbf{A} \cdot 1: 30 \)
B. 30: 1
c. 42: 14
D. 14: 42


The sequence \( \boldsymbol{S}=\boldsymbol{i}+\boldsymbol{2} \boldsymbol{i}^{2}+\boldsymbol{3} \boldsymbol{i}^{3}+\ldots \ldots \)
upto 100 times simplifies to where \( i= \) \( \sqrt{-1} \)
A. \( 50(1-i) \)
B . 25
c. \( 25(1+i) \)
D. \( 100(1-i) \)


One natural source of atmospheric \( C O_{2} \)
is precipitation reaction such as the precipitation of silicates in the oceans:
\( M g^{2+}(a q)+S i O_{2}(\text {dispersed})+ \)
\( 2 H C O_{3}(a q) \rightarrow M g S i O_{3}(s)+ \)
\( \mathbf{2} C O_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
How many grams of magnesium silicate would be precipitated during
the formation of 100 L of \( C O_{2} \) at \( 30^{\circ} C \)
and 775 torr?
\( (M g=24, S i=28, C=12, O=16) \)
A \( .102 g \)
в. \( 410 g \)
c. \( 205 g \)
D. \( 51 g \)


Solve \( \frac{\mathbf{3}}{\mathbf{1 1}}+\boldsymbol{x}=\frac{\mathbf{9}}{\mathbf{1 1}} \) for the value of \( \boldsymbol{x} \)


Who arranged elements his periodic table, based upon atomic weight:
A. Thomson
B. Mendeleev
c. Lavoisier
D. sir Humphrey Davy


Which of the following is correct?
\( \boldsymbol{S} \boldsymbol{O}_{3}+\boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \rightarrow \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C} \)
Reddish Acidic Neutral
Brown Oxide compound
Coloured
Substance
A. B can act as bleaching agent
B. A can be starch iodide test
c. \( B \) can oxidise \( C l \)
D. A oxidises Hypo to \( S_{4} O_{6}^{2} \)


A piece of wire of resistance \( \boldsymbol{R} \) is cut
into five equal parts out of which four of them are connected to forms a square
\( A B C D . \) The fifth one is connected
diagonally across \( B D . \) If a battery is
connected across \( A C, \) what would be
the equivalent resistance in the circuit?
A. \( R / 25 \)
в. \( 4 R / 5 \)
c. \( R / 5 \)
D. \( 2 R / 5 \)


Choose the Correct answer from
alternative given. The phenomena which is not explained by Huygen's construction of wavefront.
A. reflection
B. diffraction
c. refraction
D. origin of spectra


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 \( \cdot \frac{1}{r\left(v_{a}+v_{b}\right)} \)
B. \( \frac{v_{a} \sin \theta_{a}+v_{b} \sin \theta_{b}}{r} \) in the anticlockwise direction
c. \( \frac{v_{a} \sin \theta_{a}-v_{b} \sin \theta_{b}}{r} \) in the clockwise direction
D \( \frac{1}{r\left(v_{a}-v_{b}\right)} \)


\( \operatorname{Let}\left(a_{1}, a_{2}, a_{3}, \dots, a_{2011}\right) \) be a
permutation (that is a rearrangement) of the numbers \( 1,2,3, \ldots, 2011 . \) Show
that there exist two numbers \( j, k \) such that \( 1 \leq j<k \leq 2011 \) and \( \left|a_{j}-j\right|= \)
\( \left|\boldsymbol{a}_{\boldsymbol{k}}-\boldsymbol{k}\right| \)
A. 20101005
B. 2011 1006
c. 20111005
D. 2011 1010


The number of chromosomes in a
somatic cell, of a diploid organism (with original of 10 pairs), after DNA replication and before mitosis would be
A . 10
B. 20
c. 30
D. 40
E . 50


Class of enzymes contained in Iysosome
A. Lyases
B. Ligases
c. Hydrolases
D. Transferases


A toy car travels in a horizontal circle of
radius \( 2 a, \) kept on the track by a radial elastic string of unstretched length a. The period of rotation is T. Now the car
is speeded up until it is moving in a circle of radius 3 a. Assuming that the string obeys Hooke's law then the new period will be
A \( \cdot \sqrt{\frac{4}{3}} T \)
B \( \cdot \frac{3^{2}}{3^{3}} T \)
c. \( \sqrt{\frac{3}{2}} T \)
D. \( \frac{3}{4} T \)


Excretion of bile pigments in the urine
indicates
A. Anaemia
B. Diabetes
c. Rickets
D. Jaundice


A point moves such that its displacement as a function of time is given by \( x^{3}=t^{3}+1 . \) Its acceleration as
a function of time \( t \) will be:
A \( \cdot \frac{2}{x^{5}} \)
B. \( \frac{2 t}{x^{3}} \)
\( c \cdot \frac{2 t}{x^{4}} \)
D. \( \frac{2 t^{2}}{x^{5}} \)


Which of the following is correct?
A. \( \% \) abundance of \( B^{10}=\% \) abundance of \( B^{11} \)
B. \( \% \) abundance of \( B^{10}>\% \) abundance of \( B^{11} \)
C. \( \% \) abundance of \( B^{10}<\% \) abundance of \( B^{11} \)
D. none of the above


The receptors for non-steroid peptide hormones are on the :
A. plasma membrane
B. nuclear envelope
c. DNA receptor complex
D. peptide chain


Volume and surface area of a solid
hemisphere are numerically equal then what is the diameter of hemisphere?


\( B r C H_{2}-C H_{2}-C H=O \) and
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\underset{\mid \boldsymbol{B} \boldsymbol{r}}{\boldsymbol{C}}=\boldsymbol{O} \) are :
A. Functional isomers
B. Position isomers
c. chain isomers
D. Metamers


A storage battery takes \( t_{0} \) time when
DC current \( I_{0} \) is used to charge it. Find
the time taken if a half wave rectifier is
used with \( A C \) mains and effective
current is \( \boldsymbol{I}_{0} \)
A \( \cdot t_{0} \pi \)
в. \( \frac{2 t_{0}}{\pi} \)
c. \( \frac{\pi t_{0}}{2} \)
D. \( t \)


A \( 2 V \) battery, a \( 990 \Omega \) resistor and a
potentiometer of \( 2 m \) length,all are connected in series of the resistance of
potentiometer wire is \( 10 \Omega \), then the potential gradient of the potentiometer wire is
A \( \cdot 0.05 V m^{-1} \)
B \( .0 .5 V m^{-1} \)
c. \( 0.01 V m^{-1} \)
D. \( 0.001 V m^{-1} \)


\( \boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{H}^{+}+\boldsymbol{O} \boldsymbol{H}^{-} \)
The above reaction is dissociation or
ionization?
A. Dissociation
B. Ionization
c. Both dissociation and ionization together
D. None of these


If emf induced in a coil is \( 2 V \) by
changing the current in it from \( 8 A \) to
\( 6 A \) in \( 2 \times 10^{-3} s, \) then the coefficient of
self induction is
A \( \cdot 2 \times 10^{-3} H \)
в. \( 10^{-3} H \)
c. \( 0.5 \times 10^{-3} H \)
D. \( 4 \times 10^{-3} H \)


An electron \( \left(\operatorname{mass}=9.1 \times 10^{-31}\right. \)
charge \( \left.=-1.6 \times 10^{-19} \mathrm{C}\right) \) experiences
no deflection if subjected to an electric field of \( 3.2 \times 10^{5} V / m \) and a magnetic
field of \( 2.0 \times 10^{-3} \mathrm{Wb} / \mathrm{m}^{2} . \) Both the
fields are normal to the path of electron and to each other. Ifthe electric field is
removed, then the electron will revolve in an orbit of radius:
A . \( 45 \mathrm{m} \)
в. 4.5 т
c. \( 0.45 m \)
D. \( 0.045 \mathrm{m} \)


Which of the following reactions is/ are
not intermolecular redox reaction?
This question has multiple correct options
\( \mathbf{A} \cdot P b O_{2}+H_{2} O \rightarrow P b O+H_{2} O_{2} \)
B \( \cdot 2 K C l O_{3} \rightarrow 2 K C l+3 O_{2} \)
\( \mathbf{C} \cdot\left(N H_{4}\right)_{2} C r_{2} O_{7} \rightarrow N_{2}+C r_{2} O_{3}+4 H_{2} O \)
D. \( N H_{4} N O_{2} \rightarrow N_{2}+2 H_{2} O \)


\( M \) and \( N \) are midpoints of \( A B \) and \( A C \)
respectively \( \boldsymbol{A} \boldsymbol{M}=\mathbf{3} \mathbf{c m}, \boldsymbol{A} \boldsymbol{N}=\mathbf{5} \) cm
and \( M N=7 \) cm. Find \( B C \)
A. \( 14 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
D. \( 7 \mathrm{cm} \)


Which of the reactants act as oxidant or
reductant if any:
\( 2 I^{-}+H_{2} O_{2} \rightarrow 2 O H^{-}+I_{2} \)
\( \mathbf{A} \cdot H_{2} O_{2} \)
B . \( I^{-} \)
c. Both of these
D. None of these


If the compression factor of a gas is
more than unity at \( S T P \), then the value
of \( V_{m} \) is:
A . greater than \( 22.4 d m^{3} \)
B. lesser than \( 22.4 d m^{3} \)
c. equal to \( 22.4 d m^{3} \)
D. dependent on its molecular mass


Find the mean and variance for the
following frequency distrubution
\( \begin{array}{lllll}\text { classes } & \begin{array}{l}0- \\ 10\end{array} & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}\text { 20- } \\ \text { 30 }\end{array} & \begin{array}{l}\text { 30 } \\ 40\end{array}\end{array} \)
Frequencies 5 8 3.
15


\( \sin ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right)+ \)
\( \cos ^{-1}\left(\sin \left(\cos ^{-1} x\right)\right) \) is equal to
\( A \cdot \frac{\pi}{2} \)
B.
\( c \cdot \frac{3 \pi}{4} \)
D.


Explain the principle on which a fire extinguisher works.


A reaction takes place in three steps;
the rate constants are \( K_{1}, K_{2} \) and \( K_{3} \)
respectively. The overall rate constant \( \boldsymbol{K}=\frac{\boldsymbol{K}_{\mathbf{1}}^{\mathbf{3} / \mathbf{2}} \boldsymbol{K}_{\mathbf{3}}^{\mathbf{2} / \mathbf{3}}}{\boldsymbol{K}_{\mathbf{2}}^{\mathbf{1} / \mathbf{4}}} . \) If activation energy of
each steps are 50,500 and \( 90 k J \) respectively, then overall activation energy of the reaction is:
A . 10
в. 270
\( c \cdot 300 \)
D. 620


\( \ln \operatorname{an} A P, \) if \( d=-2, n=5 \) and \( a_{n}=0 \)
then the value of \( a \) is
A . 10
B. 5
\( c \cdot-8 \)
D. 8


The magnitude of the earths magnetic
field at a place is \( B_{0} \) and the angle of
dip is \( \delta . A \) horizontal conductor of length
lying along the magnetic north-south moves eastwards with a velocity \( v . \) The emf induced across the conductor is:
A . zero
B. \( B_{0} v l \sin \delta \)
c. \( B_{0} l v \)
D. \( B_{0} l \cos \delta \)


Crus cerebri is found in
A. Hind brain
B. Fore brain
c. Mid brain
D. spinal cord


The approximate value of quantum number \( n \) for the circular orbit of
hydrogen 0.0001 mm diameter is
A. 1000
B. 60
c. 10000
D. 31


In a Young's double slit experiment, a
slab of thickness \( 1.2 \mu m \) and refractive
index 1.5 is placed in front of one slit
and another slab of thickness t and
refractive index 2.5 is placed in front of
the second slit. If the position of the central fringe remains unaltered, then
the thickness is
A. \( 0.4 \mu m \)
B. \( 0.8 \mu m \)
c. \( 1.2 \mu m \)
D. \( 0.72 \mu m \)


The graph of \( \ln \left(R / R_{0}\right) \) versus \( \ln A \)
\( (R=\text { radius of a nucleus and } A=\mathrm{its} \)
mass number) is then
A. a straight line
B. a parabola
c. an ellipse
D. none of them


For a satellite moving in an orbit around the earth, the ratio of K.E to P.E is:
A \( -\frac{1}{2} \)
B. \( -\frac{1}{\sqrt{2}} \)
\( c \cdot 2 \)
D. \( \sqrt{2} \)


Find the value of \( \boldsymbol{y} \) if \( \mathbf{1}+\mathbf{4}+\mathbf{7}+\mathbf{1 0}+ \)
\( \ldots .+y=287 \)


Atomic mass of an element is:
A. actual mass of one atom of the element
B. relative mass of an atom of the element
C . average mass of an atom of different atoms of the element
D. always a whole number


A projectile fired from the top of a \( 40 m \) high cliff with an initial speed of \( 50 m / s \) at an unknown angle. Find its speed when it hits the ground. \( (g= \) \( \left.10 m / s^{2}\right) \)


A simple camera with a converging lens of \( 60 \mathrm{mm} \) focal length is focused on very far objects. To focus the camera on a nearby object \( 1.5 \mathrm{m} \) away, the distance between the film and lens will have to
be
A. decreased by \( 2.5 \mathrm{mm} \)
B. increased by 2.5 mm
c. kept fixed as before, but aperture increased by a factor of 2.5
D. kept fixed as before, but aperture decreased by a factor of 2.5


Who was the first to classify the elements into metals and non-metals?
A. Meyer
B. Mendeleev
C. Lavoisier
D. None of the above


a) Write Haworth structure of "Lactose"
b) i) What are non-essential amino acids?
ii) Write Zwitter ionic structure of
"glycine".
c) Name the nitrogenous base present in RNA but not in DNA.


Find the heat radiated per second by a body of surface area \( 12 \mathrm{cm}^{2} \) kept in
thermal equilibrium in a room at
temperature \( 20^{\circ} \mathrm{C} \). The emissivity of the
surface is 0.8 and \( \sigma=6 x \)
\( 10^{-8} W m^{-2} K^{-4} \)
A . 4.2
B . 0.42
c. 0.042
D. 42


Copper of fixed volume 'v; is drawn into wire of length 'I. When this wore is subjected to a constant force 'F', the
extension produced in the wire is ' \( \Delta l \) Which of the following graphs is a straight line?
A \( \cdot \Delta l \) versus \( \frac{1}{i} \)
B. \( \Delta l \) versus \( l^{2} \)
c. \( \Delta l \) versus \( \frac{1}{l^{2}} \)
D. \( \Delta l \) versus \( l \)


Reduction of aldehydes and ketones into hydrocarbons using zinc amalgam and conc. HCl is called
A . Cope reduction
B. Dow reduction
c. Wolf-kishner reduction
D. Clemmensen reduction


Two simple harmonic motions are
represented by the equations.
\( \boldsymbol{y}_{1}=\mathbf{1 0} \sin \frac{\pi}{4}(\mathbf{1 2} \boldsymbol{t}+\boldsymbol{I}), \boldsymbol{y}_{2}= \)
\( \mathbf{5}(\sin 3 p t+\sqrt{3} \cos 3 p t) \)
The ratio of their amplitudes is
A . 1: 1
B. 1: 2
\( c .3: 2 \)
D. 2: 3


A comparison of the plots of the magnitude of acceleration - time graph and displacement - time graph for a particle executing SHM with angular velocity 2 rad/s reveals
A. Both the curves overlap exactly with their magnitudes
B. The curve appear complementary to each other
C. The time periods calculated using these plots are identical
D. The time period calculated in both the plots are different


Which of the following is true
This question has multiple correct options
\( \mathbf{A} \cdot(3+\sqrt{-5})(3-\sqrt{-5})=14 \)
B \( \cdot(-2+\sqrt{-3})(-3+2 \sqrt{-3})=-7 \sqrt{3} i \)
\( \mathbf{c} \cdot(2+3 i)^{2}=(-5+12 i) \)
D. \( (\sqrt{5}-7 i)^{2}=-44-14 \sqrt{5} i \)


An electron is revolving around a proton in a circular orbit of diameter 1 A. If it
produces a magnetic field of \( 14 w b / m^{2} \) at the proton, then its angular velocity will be about
A. \( 8.75 \times 10^{16} \) rad/s
B. \( 10^{10} \) rad/s
\( \mathbf{c} \cdot 4 \times 10^{15} \mathrm{rad} / \mathrm{s} \)
D. \( 10^{15} \) rad/s


Let \( \boldsymbol{f}: \mathbb{N} \rightarrow \mathbb{N} \) be defined by \( \boldsymbol{f}(\boldsymbol{n})= \)
\( \left\{\begin{array}{ll}\frac{n+1}{2}, & \text { if } n \text { is odd } \\ \frac{n}{2}, & \text { if } n \text { is even }\end{array} n \in \mathbb{N}\right. \)
State whether the function \( f \) is
bijective. Justify your answer.


A body of mass \( m \) is hauled from the
Earth's surface by applying a force \( \overrightarrow{\boldsymbol{F}} \) varying with the height of ascent \( y \) as \( \vec{F}=2(a y-1) m g, \) where \( a \) is a positive
constant. Find the work performed by
this force \( W \) and the increment in the
body's potential energy \( \Delta U \) in the gravitational field of the Earth over the
first half of the ascent.
A. \( W=\frac{3 m g}{4 a}, \Delta U=\frac{m g}{2 a} \)
в. \( W=\frac{3 m g}{a}, \Delta U=\frac{m g}{2 a} \)
c. \( _{W}=\frac{3 m g}{4 a}, \Delta U=\frac{m g}{a} \)
D. \( W=\frac{3 m g}{4 a}, \Delta U=\frac{m g}{3 a} \)


Any unit which can be obtained by the combination of one or more
fundamental units is called
A. Fundamental unit
B. Scale
c. Derived unit
D. standard unit


Which of the following structures are
ring chain isomer of each other?
\( A \)
B.
\( c \)
Methylcyclopropane
D.


Watson and Crick are known for their
discovery that DNA
A. Is a single stranded helix
B. Contains deoxyribose only
c. Is a double stranded helì
D. synthesizes rRNA


Assertion
The relation \( \boldsymbol{R} \) given by
\( \boldsymbol{R}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{4}, \mathbf{2}),(\mathbf{2}, \mathbf{4}),(\mathbf{2}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\} \)
on a set \( A=\{1,2,3,4\} \) is not
symmetric.
Reason
For symmetric relation \( \boldsymbol{R}=\boldsymbol{R}^{-1} \)
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. Both Assertion and Reason are incorrect


A long, thin metal wire is suspended
from a fixed support and hangs
vertically. Masses are suspended from
its lower end.

The load on the lower end is increased
from zero and then decreased again
back to zero.
The diagram shows the force-extension
graph produced
Where on the graph would the elastic limit be found?
A. anywhere between point \( R \) and point \( S \)
B. just beyond point \( S \)
c. exactly at point \( S \)
D. exactly at point \( T \)


\( \frac{1}{2}-\frac{1}{2^{2} \cdot 2}+\frac{1}{2^{3} \cdot 3}-\frac{1}{2^{4} \cdot 4}+\ldots \infty= \)
A \( . \log 2 \)
B. \( \log 3 \)
\( \mathrm{c} \cdot \log \frac{3}{2} \)
D. \( \log _{3} \frac{2}{3} \)


The set of all solution of the inequality \( (1 / 2)^{x^{2}-2 x}<1 / 4 \) contains the set:
\( A \cdot(-\infty, 0) \)
B \( \cdot(-\infty, 1) \)
\( \mathbf{c} \cdot(1, \infty) \)
D \cdot \( (3, \infty) \)


\( \operatorname{Let} g(x)=\frac{f(x)}{x+1} \) where \( f(x) \) is
differentiable on [0,5] such that
\( \boldsymbol{f}(\mathbf{0})=\mathbf{4}, \boldsymbol{f}(\mathbf{5})=-1 . \) There exists \( \boldsymbol{c} \in \)
(0,5) such that \( g^{\prime}(c) \) is ?
\( A \cdot-\frac{1}{6} \)
B. \( \frac{1}{6} \)
c. \( -\frac{5}{6} \)
D. -


\( N a^{+} \) secreting from the kidney are highly affected by the hormone
A. cortisol
B. ADH
c. Aldosteron
D. Progesteron


Identify, the correct sequence of the cell cycle events.
I. Nuclear membrane dissolves
I. Cell size increases
III. Two daughter cells form
IV. DNA replicates
A . I, IV, Il and III
B. I, IV, III and II
c. ॥, ।, IV and III
D. II, IV, I and III
E. IV, II, III and


In the fig the bar is uniform and
weighting \( 500 N \). How large must \( W \) be
f \( T_{1} \) and \( T_{2} \) are to equal?
\( A \cdot 500 N \)
3. \( 300 N \)
\( c .750 N \)
D. \( 1500 N \)


What was the percentage increase in
production of fertilizers in 2002
compared to that in \( 1995 ? \)
enlilizers b
A . 320\%
B. 300\%
c. 220\%
D . 200\%


Which of the following statements is
false?
A. Oxygenated blood is pumped to all other parts of the body from left ventricle.
B. Gaseous exchange in the alveoli happens through capillaries.
C. Blood-from the right side of the heart enters into left side through right auricle and left auricle.
D. Lungs oxygenate the deoxygenated blood.


The sensitivity of a voltmeter of 1000 ohms is \( 1 \mathrm{mV} / \) div When a resistance of
\( 99,000 \Omega \) is connected in series, its sensitivity becomes:
A. 1 Volt / div
B. 10 Volt / div
c. 1.1 volt / div
D. 0.1 volt / div


The following displacement - time graph shows the posiitions of a body at
different times. Calculate the velocity of
the body as it moves from
(i) \( A-B \)
(ii) \( B-C \)
\( (\text { iii) } C-D \)


Two balls of same mass are released
simultaneously from heights h \( \& 2 \mathrm{h} \) from the ground level. The balls collide
with the floor \( \& \) sticks to it. Then the
velocity-time graph of centre of mass of the two balls is best represented by:


What is the formula of the compound
cesium trichlorofluoro iodate(III)?
\( \mathbf{A} \cdot\left[\operatorname{Cr}\left(N H_{3}\right)_{5} C l\right] S O_{4} \)
\( \mathbf{B} \cdot \operatorname{Cs}\left[I C l_{3} F\right] \)
\( \mathbf{c} \cdot \operatorname{Cs}\left[I C l_{2} F\right] \)
D. None of the above


Alkene can be produced by:
A. dehydration of alcohols
B. dehydrohalogenation of alkyl halides
C. dehalogenation of haloalkanes
D. all of above


The real part of \( (1-\cos \theta+2 i \sin \theta)^{-1} \)
is?
A \( \cdot \frac{1}{3+5 \cos \theta} \)
в. \( \frac{1}{5-3 \cos \theta} \)
c. \( \frac{1}{3-5 \cos \theta} \)
D. \( \frac{1}{5+3 \cos \theta} \)


The process of change in position of an object over time is called
A . rest
B. stationary
c. motion
D. none of the above


\( 2 N O C l(g) \leftrightharpoons 2 N O(g)+C l_{2}(g) \)
For the above reaction, which of the
following expressions gives the equilibrium constant?
\( ^{\text {A. }} \frac{[N O C l]}{[N O]\left[C l_{2}\right]} \)
\( ^{\mathrm{B}} \cdot \frac{[N O]\left[C l_{2}\right]}{[N O C l]} \)
c. \( \frac{[N O C l]^{2}}{[N O]^{2}\left[C l_{2}\right]} \)
D. \( \frac{[N O]^{2}\left[C l_{2}\right]}{[N O C l]^{2}} \)
E \( \frac{[N O C l]^{2}}{[N O]^{2}\left[C l_{2}\right]^{2}} \)


\( d \)
\( c \)
\( \% \)


\( \operatorname{Det}\left\{\begin{array}{lll}2 & 45 & 55 \\ 1 & 29 & 32 \\ 3 & 68 & 87\end{array}\right\}=\dots \dots \)
A . 45
B. 64
\( c \cdot 54 \)
D. 32


Solve :
\( \mathbf{2} \boldsymbol{y}=-\boldsymbol{x}+\mathbf{1} \)


Assertion: Alcohols on dehydration can produce ether as well as alkene under different conditions.
Reason: Dehydration of alcohol proceeds through the formation of carbonium ion.
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


A sudden large jump between the values of second and third ionization
energies of an element would be associated with the
electronic configuration of:
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{1} \)
B . \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{1} \)
C \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{2} \)
D. \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} \)


The Young's modulus of a wire of length
\( \boldsymbol{L} \) and radius \( \boldsymbol{r} \) is \( \boldsymbol{Y} \boldsymbol{N} / \boldsymbol{m}^{2} . \) The length
and radius are reduced to \( \frac{L}{6} \) and \( \frac{r}{6} \) then its Young's modulus is :
\( A \cdot 6 Y \)
в. \( \frac{Y}{6} \)
\( c \cdot Y \)
D. \( 3 Y \)


Find the point of inflexion of \( \boldsymbol{f}(\boldsymbol{x})= \) \( 3 x^{4}-4 x^{3} \) and hence draw the graph of
\( \boldsymbol{f}(\boldsymbol{x}) \)


tood
E


The initial velocity of a particle is \( u \) (at
\( t=0 \) ) and the acceleration \( a \) is given by
\( \boldsymbol{f} \boldsymbol{t} \)
Which of the following relations is
valid?
A \( \cdot v=u+f t^{2} \)
B . \( v=u+f t^{2} / 2 \)
\( \mathbf{c} \cdot v=u+f t \)
D. \( v=u \)


Find the number of molecule(s) is/are having zero dipole moment and linear shape from the following:
\( \boldsymbol{C l} \boldsymbol{F}_{3}, \boldsymbol{I}_{3}^{-}, \boldsymbol{C O}_{2}, \boldsymbol{H} \boldsymbol{g} \boldsymbol{C l}_{2}, \boldsymbol{I} \boldsymbol{C l}_{2}^{-}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2} \)


Assertion
A glass ball is dropped on concrete floor can easily get broken compared if it is dropped wooden floor.
Reason
On concrete floor glass ball will take
less time to come to 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. Both Assertion and Reason are incorrect


150 is what percent of \( 30 ? \)
\( A \cdot 5 \% \)
B . \( 20 \% \)
c. \( 50 \% \)
D. \( 200 \% \)
E . \( 500 \% \)


The radius of a circular disc is given as
\( 24 c m \) with a maximum error in
measurement of \( 0.02 \mathrm{cm} . \) Estimate the
maximum error in the calculated area
of the disc and compute the relative error by using differentials.


Solve:
\( \left(\frac{x^{a}}{x^{b}}\right)^{a+b-c}\left(\frac{x^{b}}{x^{c}}\right)^{b+c-a}\left(\frac{x^{c}}{x^{a}}\right)^{c+a-b}= \)


Two \( 2 \mathrm{m} \) long parallel wires are placed in vacuum at a distance \( 0.2 \mathrm{m} \). If
current \( 0.2 \mathrm{A} \) flows in both the wires in
the same direction, calculate the force acting per unit length between them.


Chemotaxonomy does not deal with
A. Chemical nature of protiens
B. DNA sequences
c. Aromatic compounds found in plants
D. Chromosome number


Statement \( 1: \sim(\mathbf{p} \leftrightarrow \sim \mathbf{q}) \) is equivalent
to \( \mathbf{p} \leftrightarrow \mathbf{q} \)
Statement \( 2: \sim(\mathbf{p} \leftrightarrow \sim q) \) is a
tautology
A. Both Statement 1 and Statement 2 are true and
Statement 2 is a correct explanation for statement 1
B. Both Statement 1and Statement 2 are true and Statement 2 is not a correct explanation for Statement
1
C. Statement 1 is true but statement 2 is false
D. Statement 1 is false but Statement 2 is true


Write the general outer electronic configuration of \( s, p, d \) and \( f \) block elements.


Meeta saves Rs. 400 from her salary. If
this is \( 10 \% \) of her salary. What is her salary?
A. Rs7000
B. Rs6000
c. Rs 4000
D. Rs5000


Which of the following reactions is not correct for the formation of acid rain?
A. \( N_{2}+O_{2} \rightarrow 2 N O \)
в. \( 2 N O+O_{2} \rightarrow 2 N O_{2} \)
c. \( H_{2} O+2 N O_{2} \rightarrow H N O_{2}+H N O_{3} \)
D. \( N O+O_{2} \rightarrow N O_{2} \)


Woolen clothes keep the body warm
because the wool:
A. decreases the temperature of the body
B. is a good conductor of heat
C. increases the temperature of the body
D. is a bad conductor of heat


Find the midpoint between the coordinates \( (\mathbf{9}, \mathbf{3}) \) and \( (\mathbf{1}, \mathbf{1}) \)
\( \mathbf{A} \cdot(5,2) \)
B \( \cdot(3,2) \)
\( \mathbf{c} \cdot(5,1) \)
D \( \cdot(3,1) \)


Which of the following compounds
favours \( \boldsymbol{S}_{N} \) 2 mechanism?
A. \( C H_{3}-C H_{2}-B r \)
в. \( C H_{3}-O-C H_{2} B r \)
\( \mathbf{c} \cdot C_{6} H_{5}-C O-C H_{2} B r \)
D. \( C H_{3}-C\left(C H_{3}\right)_{2} C H_{2} B r \)


Increase of temperature due to
scattering of energy is by ozone, \( \mathrm{CO}_{2} \) and water vapour, is known as
A. Radioactivity
B. Ozone effect
c. solar reaction
D. Greenhouse effect


What is the velocity of vertically projected body at its maximum height
\( (h) ? \)
A \( \cdot \sqrt{2 g h} \)
B. zero
c. \( \frac{h^{2}}{g} \)
D. \( \sqrt{\frac{2 h}{g}} \)


The number of integer solutions \( (x, y, z) \) of \( x y z=18 \) is
A . 48
B. 64
c. 72
D. 81


AB is a potentiometer wire of length 100
\( \mathrm{cm} \) and resistance 10 ohms. It is
connected in series with a resistance
\( \mathrm{R}=40 \) ohms and a battery of e.m.f. \( 2 \mathrm{V} \)
and negligible internal resistance. If a
source of unknown e.m.f. E is balanced
by \( 40 \mathrm{cm} \) length of the potentiometer
wire, the value of E is :-
A. \( 0.8 \mathrm{V} \)
B. \( 1.6 v \)
c. \( 0.08 \mathrm{v} \)
D. 0.16 v


Find the forward \( \Delta_{r} U^{\circ} \) at \( 300 K \) for the
reaction \( 4 H C l(g)+O_{2}(g) \rightarrow \)
\( 2 C l_{2}(g)+2 H_{2} O(g) \) Assume all gases
are ideal. Given \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \)
\( 2 H C l(g) \Delta_{r} H_{300}^{\circ}=-184.5 k J / m o l \)
\( \mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
\( \boldsymbol{\Delta}_{r} \boldsymbol{H}_{300}^{\circ}=-\mathbf{4 8 3 k J} / \) mol (Use \( \mathrm{R}=\mathbf{8 . 3} \)
J/mole)
A . 111.5 kJ/mole
B. -109.01 kJ/mole
c. -111.5 kJ/mole
D. None


Define the term refractive index of a
medium in terms of velocity of light.


If \( a, b, c \) are in G.P., then
A \( \cdot a^{2}, b^{2}, c^{2} \) are in G.P.
B . \( a^{2}(b+c), c^{2}(a+b), b^{2}(a+c) \) are in G.P.
c. \( \frac{a}{b+c}, \frac{b}{c+a}, \frac{c}{a+b} \) are in G.P
D. None of the above.


Malonic acid and succinic acid are
distinguish by:
A. heating
в. \( \operatorname{NaH} \mathrm{CO}_{3} \)
c. both \( A \) and \( B \)
D. None of these


Molar heat capacity of water (liquid) in equilibrium with water vapour at
constant pressure is:
A. zero
B . \( \infty \)
c. 75.48 J mol \( ^{-1} \mathrm{k}^{-1} \)
D. 40.45 J mol \( ^{-1} \mathrm{K}^{-1} \)


For the following congruent triangles, find the pairs of corresponding angles.


The conversion of vinyl allyl ether to
pent-4-enol follows a certain kinetics.
The following plot is obtained for such a
reaction.
A . zer
B.
\( c \)
2


The net force exerted by fluid on moving
plate is
A. \( 0.6 N \) backwards
B. \( 0.6 N \) forward
c. \( 0.2 N \) backwards
D. \( 0.2 N \) forward


Length of silk thread produced by one cocoon is
A. \( 300-400 \) metres
B. 600 - 900 metres
c. \( 200-300 \) metres
D. less than 200 meters


The dimensions of strain is:
A. \( L \)
B \( \cdot L^{2} \)
c. It is dimensionless
D. \( M L^{2} T^{-2} \)


If \( \boldsymbol{E}^{o}_{\boldsymbol{F} e^{2+} / \boldsymbol{F} e}=\boldsymbol{x}_{1} \boldsymbol{V} \) and \( \boldsymbol{E}^{o}_{\boldsymbol{F} e^{3+} / \boldsymbol{F} e^{2+}}= \)
\( \boldsymbol{x}_{2} \boldsymbol{V}, \) then \( \boldsymbol{E}^{o} \boldsymbol{F e}^{3+} / \boldsymbol{F} e \) will be :
A \( \cdot\left(2 x_{1}+x_{2}\right) V \)
В . \( \left(3 x_{2}-x_{1}\right) V \)
\( \mathbf{c} \cdot\left(2 x_{1}+x_{2}\right) / 3 V \)
\( \mathbf{D} \cdot\left(x_{1}+2 x_{2}\right) / 3 V \)


Which of the following is true about the number \( 0.66 \overline{66} ? \)
A. It is a rational number
B. It is an irrational number
c. It is correctly gridded as ".66"
D. It is equivalent to \( \frac{67}{100} \)
E. None of the above


For the given circuit, the natural
frequency is given by :
\( \mathbf{A} \cdot \frac{1}{2 \pi} \sqrt{L C} \)
B. \( \frac{1}{2 \pi \sqrt{L C}} \)
\( c \cdot \sqrt{\frac{l}{C}} \overline{\underline{l}} \)
D. \( \sqrt{\frac{c}{L}} \)


Evaluate \( \int_{0}^{\infty} \frac{x^{2}+1}{x^{4}+7 x^{2}+1} d x \)
\( A \)
в. \( \frac{\pi}{2} \)
c.
D.


The number of integral values of \( \boldsymbol{m}, \) for
which the roots of \( x^{2}-2 m x+m^{2}- \)
\( \mathbf{1}=\mathbf{0} \) will between \( -\mathbf{2} \) and \( \mathbf{4} \) is :
A .2
B. 0
\( c .3 \)
D.


Which of the following is an example of a broad spectrum antibiotic? This question has multiple correct options
A. Penicillin G
B. Chloramphenicol
c. streptomycin
D. Ampicillin