AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A ball of mass m moving with a constant velocity strikes against a ball
of same mass at rest. If \( e= \)
coefficient of restitution, then what
will be the ratio of velocity of two balls
after collision?
A \( \frac{1-e}{1+e} \)
в. \( \frac{e-1}{e+1} \)
c. \( \frac{1+e}{1-e} \)
D. \( \frac{2+e}{e-1} \)
Subject: Physics
A pulley fixed to the ceiling carries a string with bodies of masses \( \mathrm{m} \) and \( 3 \mathrm{m} \) attached to its ends. The masses of the
pulley and the string are negligible, friction is absent. The acceleration of
the centre of mass of the system is
\( \mathbf{A} \cdot-g / 4 \)
в. \( g / 4 \)
c. \( g / 5 \)
\( \mathbf{D} \cdot-g / 5 \)
Subject: Maths
If \( \int \frac{2 \sin x+3 \cos x}{3 \sin x+4 \cos x} d x=A \log \)
\( |3 \sin x+4 \cos x|+B x+c, \) then \( A= \)
\( \ldots \ldots \ldots, B=\ldots \ldots \ldots . . \)
A. \( -\frac{1}{25}, \frac{18}{25} \)
8. \( -\frac{1}{5},-\frac{1}{5} \)
c. \( \frac{1}{25}, \frac{18}{25} \)
D. \( \frac{1}{25}, \frac{3}{25} \)
Subject: Maths
Derive the coordinates of the points \( R(x, y, z) \) dividing the line joining the
points \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}, \boldsymbol{z}_{1}\right) \) and \( \boldsymbol{Q}\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}, \boldsymbol{z}_{2}\right) \)
internally in the ratio \( m: n \)
Subject: Chemistry
Identify the type of reaction taking place in \( \boldsymbol{F e}+\boldsymbol{C u S O}_{4} \rightarrow \boldsymbol{C u}+\boldsymbol{F e} \boldsymbol{S O}_{4} \)
A. Redox reaction
B. Displacement reaction
c. Neutralization reaction
D. Precipitation reaction
Subject: Chemistry
Which of the following is used to
prepare \( C l_{2} \) gas at room temperature
from concentrated \( \boldsymbol{H} \boldsymbol{C l} \) ?
This question has multiple correct options
A. \( M n O_{2} \)
в. \( H_{2} \).
c. \( K M n O_{4} \)
\( \mathrm{D} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
Subject: Maths
\( 4 \int \frac{a^{6}+x^{8}}{x} d x \) is equal to
B. \( a^{6} \ln \frac{\sqrt{a^{6}+x^{8}}-a^{3}}{\sqrt{a^{6}+x^{8}}+a^{3}}+c \)
\( I=\sqrt{a^{6}+x^{8}}+\frac{a^{3}}{2} \ln \left|\frac{\sqrt{a^{6}+x^{8}}-a^{3}}{\sqrt{a^{6}+x^{8}}+a^{3}}\right|+c \)
\( ^{\mathrm{D}} a^{6} \ln \frac{\sqrt{a^{6}+x^{8}}+a^{3}}{\sqrt{a^{6}+x^{8}}-a^{3}}+c \)
Subject: Biology
What would be the percentage of thymine (T) and cytosine (C) in a molecule of DNA composed of approximately \( 16.2 \% \) adenine \( (A) \) and 33.4\% guanine (G)?
A . 16.3\% T and 16.3\% C
B. 34.1\% T and 34.1\% C
c. \( 34.1 \% \) T and \( 16.3 \% \) C
D. 16.3\% T and 34.1\% C
E. 33.4\% T and 16.2\% C
Subject: Maths
If \( \boldsymbol{x}=\mathbf{2} \cos ^{-1}\left[\frac{1}{2}\right]+\sin ^{-1}\left[\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}\right]+ \)
\( \tan ^{-1}(\sqrt{3}) \) and \( y= \)
\( \cos \left[\frac{1}{2} \sin ^{-1}\left[\sin \frac{x}{2}\right]\right] \) then which of the
following statements holds good?
A \( \cdot y=\cos \frac{3 \pi}{16} \)
В. \( y=\cos \frac{5 \pi}{16} \)
c. \( x=4 \cos ^{-1} y \)
D. none of these
Subject: Physics
The diagram below shows an aquarium with four typical optical devices submerged in some liquid that has a higher index of refraction than glass.
Each optical device is labeled.
Which of the optical devices will converge light when submerged in this liquid?
A. The concave mirror and the convex lens
B. The convex mirror and the concave lens
c. The concave mirror and the concave lens
D. The convex mirror and the convex lens
E. All of the pictured optical devices converge light under water
Subject: Chemistry
Phosphine, acetylene and ammonia can be formed by treating water with:
A. \( M g_{3} P_{2}, A l_{4} C_{3}, L i_{3} N \)
в. \( C a_{3} P_{2}, C a C_{2}, M g_{3} N_{2} \)
c. \( C a_{3} P_{2}, C a C_{2}, C a C N_{2} \)
D. \( C a_{3} P_{2}, M g_{2} C, N H_{4} N O_{3} \)
Subject: Chemistry
\( \begin{array}{ll}\text { List - I } & \text { List - II } \\ \text { A) Velocity of light } & \text { 1) Energy }\end{array} \) A) Velocity of light
B) Plank's constant Energy particle
2) Energy packet
c) Wavenumber
D)
The correct match is:
\( A \cdot A-2, B-3, C-4, D-5 \)
B. A-1, B-2, C-3. D-4
C. \( A-2, B-4, C-5, D-1 \)
D. A-3, B-4, C-5, D-1,2
Subject: Maths
If \( z=x+i y \) is a complex number such
that \( |z|=\operatorname{Re}(i z)+1, \) then the locus of
\( z \) is
A \( \cdot x^{2}+y^{2}=1 \)
в. \( x^{2}=2 y-1 \)
C \( \cdot y^{2}=2 x-1 \)
D・ \( y^{2}=1-2 x \)
E . \( x^{2}=1-2 y \)
Subject: Chemistry
The correct increasing order of basic
strength for the following compounds is:
\( (\mathbf{I}) \)
(II)
\( (\mathbf{I I I}) \)
\( \mathbf{A} \cdot\|<\| 1<1 \)
B. \( \|I|<|<\| \)
C. \( \|I<\|<1 \)
D. \( \|<I<\| 1 \)
Subject: Physics
The radius of the curved part of the wire
is \( R, \) the linear parts are assumed to be
very long. Find the magnetic induction
of the field at the point \( O \) if a current-
carrying wire has the shape shown in figure above.
\( ^{\mathbf{A}} \cdot B=\frac{\mu_{0}}{4 \pi} \frac{I}{R}\left[1+\frac{3 \pi}{2}\right] \)
в. \( B=\frac{\mu_{0}}{\pi} \frac{I}{R}\left[1+\frac{3 \pi}{2}\right] \)
c. \( _{B}=\frac{\mu_{0}}{2 \pi} \frac{I}{R}\left[1+\frac{3 \pi}{2}\right] \)
D. \( B=0 \)
Subject: Physics
The figure shows the variation of internal energy (U) with the pressure (P)
of 2.0 mole gas in cyclic process abcda.
The temperature of the gas at \( c \) and \( d \) are \( 300 \mathrm{K} \) and \( 500 \mathrm{K} \). Calculate the heat
absorbed by the gas during the process.
\( A \cdot 400 \mathrm{R} \ln 2 \)
B. 200 R \( \ln 2 \)
\( c \cdot 100 \mathrm{R} \ln 2 \)
D. 300 R In 2
Subject: Maths
If \( A \) is a \( 3 \times 3 \) matrix and \( \operatorname{det}(3 A)= \)
\( \boldsymbol{k}\{\boldsymbol{d e t}(\boldsymbol{A})\}, \boldsymbol{k}= \)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 6
c. 1
D. 27
Subject: Maths
If the points \( A \) and \( B \) are (1,2,-1) and
(2,1,-1) respectively, then \( \overrightarrow{A B} \) is
A. \( \hat{i}+\hat{j} \)
в. \( \hat{i}-\hat{j} \)
c. \( 2 \hat{i}+\hat{j}-\hat{k} \)
D. \( \hat{i}+\hat{j}+\hat{k} \)
Subject: Physics
An object is weighed at the North pole by a beam balance and a spring
balance, giving readings of \( W_{B} \) and \( W_{S} \)
respectively. It is again weighed in the same manner at the equator, giving
readings of \( W_{B}^{\prime} \) and \( W_{S}^{\prime} \) respectively. Assume that the acceleration due to
gravity is the same everywhere and that the balances are quite sensitive. This question has multiple correct options
A \( . W_{B}=W_{S} \)
В. \( W_{B}^{\prime}=W_{S}^{\prime} \)
\( \mathbf{c} \cdot W_{B}=W_{B}^{\prime} \)
D. \( W_{S}^{\prime}=W_{S} \)
Subject: Chemistry
Arrange the following compounds in increasing order of their boiling points.
\( (i) C H_{3} C H_{2} C H_{2} C H O \)
\( (i i) C H_{3} C H_{2} C H_{2} C H_{2} O H \)
\( (i i i) C_{2} H_{5} O C_{2} H_{5} \)
\( (i v) C H_{3} C H_{2} C H_{2} C H_{3} \)
A \( \cdot(i)>(i i)>(i i i)>(i v) \)
B. \( (i i)>(i)>(i i i)>(i v) \)
c. \( (i v)>(i)>(i i)>(i i i) \)
D. \( (i i i)>(i)>(i i)>(i v) \)
Subject: Maths
Assertion
\( \int_{-\pi / 4}^{\pi / 4} x^{3} \sin ^{4} x d x \neq 0 \)
Reason
\( \int_{-a}^{a} f(x) d x=0 \) if \( f(-x)=-f(x) \)
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
Subject: Chemistry
\( 0-x y \) lene on ozonolysis will give :
\( A \)
\( \mathrm{CHO} \)
\( \mathrm{I}_{\mathrm{CHO}}^{\mathrm{O}} \mathrm{CH}_{3}-\mathrm{C}-\mathrm{CHO} \)
\( \mathrm{NH} \)
в.
\( \begin{array}{l}\mathrm{CH}_{3}-\mathrm{C}=\mathrm{O} \quad \mathrm{O} \\ \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O}\end{array} \& \mathrm{CH}_{3}-\mathrm{C}-\mathrm{CHO} \)
c.
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O} \)
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O} \)\( \& \mathrm{CHO} \)
\( \mathrm{CHO} \)
\( D \)
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O} \quad \) II
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{O}, \mathrm{CH}_{3}-\mathrm{C}-\mathrm{CHO} \& \underset{\mathrm{CHO}}{\mathrm{I}} \)
Subject: Physics
Five moles of Hydrogen initially at STP compressed acrobatically so that its temperature becomes \( 73 \mathrm{K} \). The increase in internal of the gas in Kilo joules is:
\( (\boldsymbol{R}-\mathbf{8 . 3} \boldsymbol{j} / \boldsymbol{m o l} \boldsymbol{e}-\boldsymbol{K}: \boldsymbol{\gamma}=\mathbf{1 . 4} \) for
A . 80.5
B. 21.55
c. 41.50
D. 65.55
Subject: Chemistry
The pair that contains two \( \boldsymbol{P}-\boldsymbol{H} \)
bonds in each of the oxoacids is:
A. \( H_{3} P O_{2} \) and \( H_{4} P_{2} O_{5} \)
B. \( H_{4} P_{2} O_{5} \) and \( H_{4} P_{2} O_{6} \)
\( \mathrm{c} \cdot H_{3} P O_{3} \) and \( H_{3} P O_{2} \)
D. \( H_{4} P_{2} O_{5} \) and \( H_{3} P O_{3} \)
Subject: Maths
Draw a triangle whose side are
represented by \( \boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=\mathbf{0} \) and \( \boldsymbol{x}+ \)
\( \boldsymbol{y}=\mathbf{3} \) in the Cartesian system Also find
the coordinates of its vertices.
Subject: Maths
Let \( \mathbf{P}\left(\mathbf{x}_{1}, \mathbf{y}_{1}\right) \) be any point on the
cartesian plane then match the
following lists:

LIST - I
A) The distance from \( P \) to \( X- \)
1)
axis
B) The distance from P to Y-
2) | \( y_{1} \mid \) axis
C) The distance from \( P \) to
3) \( \sqrt{x_{1}^{2}+y_{1}^{2}} \)
origin is
4) \( \left|x_{1}\right| \)
\( \mathbf{A} \cdot A-4, B-2, C-1 \)
\( \mathbf{B} \cdot A-2, B-4, C-3 \)
\( \mathbf{c} \cdot A-4, B-2, C-3 \)
D. \( A-2, B-4, C-1 \)
Subject: Physics
Assertion
Potential is work done to bring a point charge from infinity to to required point under the influence of electric field.
Reason
Gravitational potential is analogous to electric potential and have same dimensions.
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
Subject: Physics
Assertion: The induced emf and current
will be same in two identical loops of copper and aluminium, when rotated with same speed in the same magnetic field.
Reason: Mutual induction does not depend on the orientation of the coils.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion and Reason both are false
Subject: Physics
A copper wire \( 3 \mathrm{m} \) long is stretched to increase its length by \( 0.3 \mathrm{cm} \). Find the lateral strain produced in the wire , if poisson's ratio for copper is 0.25
A. \( 5 \times 10^{-4} \)
B. \( 2.5 \times 10^{-4} \)
c \( .5 \times 10^{-3} \)
D. \( 2.5 \times 10^{-3} \)
Subject: Chemistry
Assertion
Pressure, volume and temperature are
all extensive properties.
Reason
Extensive properties depend upon the
amount and nature of the substance.
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
Subject: Physics
Two planets are revolving around the
Earth with velocities \( v_{1}, v_{2} \) and in radii
\( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \) respectively. Then
A \( \cdot v_{1}=v_{2} \)
в. \( v_{1}>v_{2} \)
c. \( v_{1}<v_{2} \)
D. \( \frac{v_{1}}{r_{1}}=\frac{v_{2}}{r_{2}} \)
Subject: Chemistry
Which of the following IUPAC names is
not correctly matched?
\( A \)
cì
B . \( \left(C H_{3}\right)_{2} C=C H C O O H: 3 \) - Methylbut- 2 -enoic acid
c. \( P h C H_{2} C H_{2} C O O H: \) 3-Phenylpropanoic acid
\( D \)
Trinitr
Subject: Maths
The order and degree of the differential equation \( \left(\boldsymbol{y}^{\prime \prime \prime}\right)^{2}+\left(\boldsymbol{y}^{\prime \prime}\right)^{3}-\left(\boldsymbol{y}^{\prime}\right)^{4}+\boldsymbol{y}^{5}= \)
0 is
A. 3 and 2
B. 1 and 2
\( c \cdot 2 \) and 3
D. 1 and 4
E. 3 and 5
Subject: Physics
A car is fitted with a convex side-view
mirror of focal length \( 20 \mathrm{cm} . \) A second
car \( 2.8 \mathrm{m} \) behind the first car is
overtaking the first car at a relative speed of \( 15 \mathrm{m} / \mathrm{s} \). The speed of the image of the second car as seen in the mirror
of the first one is :
A \( \cdot \frac{1}{10} \mathrm{m} / \mathrm{s} \)
в. \( \frac{1}{15} \mathrm{m} / \mathrm{s} \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. \( 15 \mathrm{m} / \mathrm{s} \)
Subject: Physics
If the wavelength of a sound of frequency \( 350 \mathrm{Hz} \) is \( 0.5 \mathrm{m}, \) find the velocity of sound.
A. 700 \( \mathrm{m} s^{-1} \)
B. 175 \( \mathrm{m} \mathrm{s}^{-1} \)
c. \( 17.5 \mathrm{m} s^{-1} \)
D. 70 \( \mathrm{m} s^{-1} \)
Subject: Physics
Regarding linear momentum of a body
a. It is a measure of quantity of motion
contained by the body
b. Change in momentum is the measure
of impulse
c. Impulse and acceleration act in
opposite direction to the change in
momentum
d. In the case of uniform circular motion
the linear momentum is conserved.
\( A \cdot \) a \( \& b \) are true
B. b \& c are true
c. \( c \& \) d are true
D. a, b \& c are ture
Subject: Chemistry
\( \Delta G(H I: g) \equiv+1.7 \quad k J . \) What is the
equilibrium constant at \( 25^{\circ} C \) for
\( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) ? \)
A. 24.0
B. 3.9
c. 2.0
D. 0.5
Subject: Maths
Assertion
For \( \boldsymbol{n} \in \boldsymbol{N},(\boldsymbol{n} !)^{3}<\boldsymbol{n}^{\boldsymbol{n}}\left(\frac{\boldsymbol{n}+\mathbf{1}}{\mathbf{2}}\right)^{2 \boldsymbol{n}} \)
Reason
\( \boldsymbol{n}>\boldsymbol{6},\left(\frac{\boldsymbol{n}}{\boldsymbol{3}}\right)^{\boldsymbol{n}}<\boldsymbol{n} !\left(\frac{\boldsymbol{n}}{2}\right)^{\boldsymbol{n}} \)
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
Subject: Chemistry
What will be the enthalpy of combustion of carbon to produce carbon monoxide on the basis of data given below?
\( \boldsymbol{C}_{(s)}+\boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2(\boldsymbol{g})} \quad \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -393.4 k J \)
\( \boldsymbol{C O}_{(\boldsymbol{g})}+\frac{1}{2} \boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2(\boldsymbol{g})} \quad \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -283.0 k J \)
A \( .+676.4 \mathrm{kJ} \)
B . - 676.4 kJ
c. -110.4 k
D. \( +110.4 \mathrm{kJ} \)
Subject: Maths
Kritika needs to receive completed
surveys from at least 3800 potential
voters in her city. She notices that for
every 5 surveys she sends out, only 1 survey is completed. Last week she
received 1350 completed surveys, and
this week she received 900 completed
surveys. Kritika plans to send out \( s \) additional surveys. Find the inequality which shows all possible for 's' that
would ensure that she received 3800
completed surveys?
A \( . s \geq 1550 \)
B . \( s \geq 2250 \)
\( \mathbf{c} \cdot s \geq 7750 \)
D. \( s \geq 12250 \)
Subject: Chemistry
A sealed gas cylinder is left outside on a
hot, sunny day. What happens to the average speed of the gas molecules and to the pressure of the gas in the cylinder
as the temperature of the gas rises?
Average speed of \( \quad \) Pressure of gas gas molecules \( \quad \) in cylinder
Decreases

Decreases
Decreases

Increases
Increases

Decreases
Increases
\( A \cdot A \)
B. B
\( c \cdot c \)
D. D
Subject: Chemistry
\( 0.25 g \) of an organic compound gave \( 30 \mathrm{cm}^{3} \) of moist nitrogen at \( 288 \mathrm{K} \) and 745mm pressure. Calculate the percentage of nitrogen (aqueous tension at \( 288 \mathrm{K}=12.7 \mathrm{mm} \)
A. 33.6
в. 23.6
c. 13.7
D. 24.5
Subject: Physics
Three planets of same density have
radii \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2} \) and \( \boldsymbol{R}_{3} \) such that \( \boldsymbol{R}_{1}= \)
\( 2 R_{2}=3 R_{3} \) The gravitational field at
their respective surfaces are \( g_{1}, g_{2} \) and
\( g_{3} \) and escape velocities from their
surfaces are \( \boldsymbol{v}_{1}, \boldsymbol{v}_{2} \) and \( \boldsymbol{v}_{3} \) then
This question has multiple correct options
A. \( g_{1} / g_{2}=2 \)
В \( \cdot g_{1} / g_{3}=3 \)
c. \( v_{1} / v_{2}=1 / 4 \)
D. \( v_{1} / v_{3}=3 \)
Subject: Maths
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y} \cos \boldsymbol{x}=\boldsymbol{y}^{\boldsymbol{n}} \sin \boldsymbol{2} \boldsymbol{x} \)
\( \mathbf{A} \cdot \frac{1}{y^{n+1}}=2 \sin x-\frac{2}{1-n}+c e^{(n-1) \sin x} \)
B. \( \frac{1}{y^{n-1}}=2 \sin x+\frac{2}{1-n}+c e^{(n-1) \sin x} x \)
C \( \frac{1}{y^{n-1}}=2 \sin x-\frac{2}{1-n}+c e^{(n-1) \sin x} x \)
D. \( \frac{-1}{y^{n-1}}=2 \sin x-\frac{2}{1-n}+c e^{(n-1) \sin x} x \)
Subject: Physics
A hemispherical glass body of radius 10 \( c m \) and refractive index 1.5 is silvered
on its curved surface. A small air bubble
is \( 6 \mathrm{cm} \) below the flat surface inside it
along the axis. The position of the
image of the air bubble made by the mirror is seen:
A. \( 14 \mathrm{cm} \) below flat surface
B. 20 \( c m \) below flat surface
c. \( 16 \mathrm{cm} \) below flat surface
D. \( 30 \mathrm{cm} \) below flat surface
Subject: Maths
For all real numbers \( a, b \) and positive
integer \( n \) prove that:
\( (a+b)^{n}=^{n} C_{0} a^{n}+^{n} C_{1} a^{n-1} b+^{n} \)
\( C_{1} a^{n-2} b^{2}+\ldots \ldots \ldots .+^{n} C_{n} b^{n} \)
Subject: Physics
A linear object of height \( 10 \mathrm{cm} \) is kept in front of a concave mirror of radius of
curvature \( 15 \mathrm{cm}, \) at a distance of \( 10 \mathrm{cm} \)
The image formed is
A. Magnified and erect
B. Magnified and inverted
c. Diminished and erect
D. Diminished and inverted
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}\}, \) then
\( \boldsymbol{A} \times \boldsymbol{B}= \)
\{(1,2),(1,3),(1,4),(2,2),(2,3),(2,4)\}
If true enter 1 , or else enter 0 .
Subject: Maths
5 students of a class have an average
height \( 150 \mathrm{cm} \) and variance \( 18 \mathrm{cm}^{2} . \) A new student, whose height is \( 156 \mathrm{cm} \)
joined them. The variance \( \left(\operatorname{in} c m^{2}\right) \) of the height of these six students is
A . 22
B. 20
c. 16
D. 18
Subject: Maths
A college teacher has the following
absentee record of 50 students of a
class for the whole year. Find the
median.
\( \begin{array}{lllll}\text { Number } & \mathbf{0}- & \mathbf{4}- & \mathbf{8}- & \mathbf{1 2}- \\ \text { of days } & \mathbf{4} & \mathbf{8} & \mathbf{1 2} & \mathbf{1 6}\end{array} \)
Number
of students
A. 11.66
B. 12.66
c. 13.66
D. 10.66
Subject: Maths
Find the area of the shaded region in fig, where is circular arc of radius \( 6 \mathrm{cm} \) has
been drawn with vertex \( O \) of an
equilateral triangle \( \boldsymbol{O} \boldsymbol{A} \boldsymbol{B} \) of side \( \mathbf{1 2} \boldsymbol{c m} \)
as centre
Subject: Maths
Assertion
\( (A): \overline{G A}+\overline{G B}+\overline{G C}=\overline{0} \) where \( G \) is
the centroid of triangle \( A B C \).
Reason
\( (R): \overline{A B}= \) P.V of \( B- \) P.V of \( A \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Maths
A solid cylinder of glass whose diameter is \( 1.5 \mathrm{m} \) and height \( 1 \mathrm{m} \) is melted an recasted into a sphere then the radius of the sphere is
\( A \cdot 1 m \)
B. 0.75 \( m \)
c. \( 1.25 \mathrm{m} \)
D. \( 1.5 \mathrm{m} \)
Subject: Maths
A line makes the same angle \( \theta \) with
each of the \( x \) and \( z \) -axes. If the angle \( \beta \)
which it makes with \( y \) -axis, is such that \( \sin ^{2} \beta=3 \sin ^{2} \theta, \) then \( \cos ^{2} \theta \) is equal to
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{5} \)
D.
Subject: Biology
Choose the correct answer from the
alternatives given :

If Meselson and Stahls experiment is continued for four generations in bacteria, the ratio of \( N^{15}-N^{15}, N^{14}- \)
\( N^{15}, N^{14}-N^{14} \) containing DNA in the fourth generation would be
A . 1:1:10
B. 1:4:0
c. 0: 1: 3
D. 0:1:7
Subject: Chemistry
What happens when
(i) chlorobenzene is treated with
\( \boldsymbol{C l}_{2} / \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \)
(ii) ethyl chloride is treated with
\( A g N O_{2}, \) and
(iii) 2-bromopentane is treated with alcoholic KOH?
Write the chemical equation in support
of your answer.
Subject: Chemistry
Spin only magnetic moment of the
compound \( \boldsymbol{H} \boldsymbol{g}\left[\boldsymbol{C o}(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})_{4}\right] \) is :
A \( \cdot \sqrt{3} \)
B. \( \sqrt{15} \)
c. \( \sqrt{24} \)
D. \( \sqrt{8} \)
Subject: Maths
Find \( \mathbf{x} \) and \( \mathbf{y} \) if \( \left[\begin{array}{cc}\mathbf{2} \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{y} & \boldsymbol{3} \boldsymbol{y}\end{array}\right]\left[\begin{array}{l}\mathbf{3} \\ \mathbf{2}\end{array}\right]=\left[\begin{array}{c}\mathbf{1} \mathbf{6} \\ \mathbf{9}\end{array}\right] \)
Subject: Physics
Assertion
Projectile motion is called a two dimensional motion, although it takes
place in space.
Reason
In space it takes place in a plane.
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 is incorrect but Reason is correct.
Subject: Maths
Let \( f(x) \) and \( g(x) \) are two functions
which are defined and differentiable for
all \( \boldsymbol{x} \geq \boldsymbol{x}_{0} . \) If \( \boldsymbol{f}\left(\boldsymbol{x}_{0}\right)=\boldsymbol{g}\left(\boldsymbol{x}_{0}\right) \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x})> \)
\( g^{\prime}(x) \) for all \( x>x_{0} \) then
A \( \cdot f(x)<g(x) \) for some \( x>x_{0} \)
B. \( f(x)=g(x) \) for some \( x>x_{0} \)
C. \( f(x)>g(x) \) only for some \( x>x_{0} \)
D. \( f(x)>g(x) \) for all \( x>x_{0} \)
Subject: Maths
In a study of two groups, the following results were obtained
Group
Sample size 20
Sample mean 22
Sample standard deviation 10
Which of the following statements is
correct?
A. Group A is less variable than Group B because Group A's standard deviation is smaller.
B. Group A is less variable than Group B because Group A's sample size is smaller.
C. Group \( A \) is less variable than Group \( B \) because Group A's sample mean is smaller
D. Group A is less variable than Group B because Group A's coefficient of variation is smaller.
Subject: Physics
A person travelled a distance of \( 100 m \)
in 10 seconds. What is the speed of the
person?
A. \( 10 \mathrm{m} / \mathrm{s} \)
в. \( 12 m / s \)
\( \mathbf{c} \cdot 15 m / s \)
D. \( 5 m / s \)
Subject: Maths
The distance of the point (1,-2,3) from the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) measured
parallel to the line. \( \frac{x}{2}=\frac{y}{3}=\frac{z}{-6}, \quad \) is :
\( A \)
B. 6/7
\( c \cdot 7 / 6 \)
D. \( 1 / 6 \)
Subject: Chemistry
The solubility of \( A_{2} X_{5} \) is \( x \) mol \( d m^{-3} \)
Its solubility product is:
A \( \cdot 36 x^{6} \)
В. \( 64 \times 10^{4} x^{7} \)
c. \( 126 x^{7} \)
D. \( 1.25 \times 10^{4} x^{7} \)
Subject: Chemistry
Give the IUPAC name of the complex
compound
\( \left[\boldsymbol{C o}\left(\boldsymbol{N H}_{\boldsymbol{3}}\right)_{\boldsymbol{4}}\left(\boldsymbol{H}_{\boldsymbol{2}} \boldsymbol{O}\right) \boldsymbol{B r}\right]\left(\boldsymbol{N} \boldsymbol{O}_{\boldsymbol{3}}\right)_{\boldsymbol{2}} \)
A. Bromoaquotetraaminecobalt(III) nitrate
B. Bromoaquotetraaminocobalt(III) nitrate
C. Bromoaquatetraaminecobalt(III) nitrate
D. Tetraammineaquabromocobalt(III) nitrate