AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Find the mode for the following data:
\( \begin{array}{lllll}\text { class } & 0- & 2- & 4- & 6- \\ \text { interval } & 2 & 4 & 6 & 8\end{array} \)
6 Frequency
A . 5.2
в. 5.3
\( c .5 . \)
D. 5.5
Subject: Maths
f matrix \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{- 2} \\ \mathbf{- 2} & \mathbf{2}\end{array}\right] \) and \( \boldsymbol{A}^{\mathbf{2}}=\boldsymbol{p} \boldsymbol{A} \)
then write the value of \( p \)
Subject: Maths
Construct a quadrilateral \( A B C D, \) when
\( A B=6.3 \mathrm{cm}, B C=C D=4.2 \mathrm{cm} \) and
\( \angle A B C=\angle B C D=90^{\circ} \)
Find the length of side \( A D \) and
\( \boldsymbol{m} \angle \boldsymbol{B} \boldsymbol{A} \boldsymbol{D} \)
A. \( A D=3.5 \mathrm{cm}, 70^{\circ} \)
B. \( A D=4.7 \mathrm{cm}, 65 \)
C . \( A D=4.5 \mathrm{cm}, 70^{\circ} \)
D. \( A D=3.5 \mathrm{cm}, 65 \)
Subject: Chemistry
Each pair forms ideal solution except :
A \( \cdot C_{2} H_{5} B r \) and \( C_{2} H_{5} \)
B . \( C_{6} H_{5} C l \) and \( C_{6} H_{5} B r \)
c. \( C_{6} H_{6} \) and \( C_{6} H_{5} \cdot C H_{3} \)
D. \( C_{2} H_{5} I \) and \( C_{2} H_{5} O H \)
Subject: Maths
The projection of \( \overrightarrow{\boldsymbol{a}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\boldsymbol{2} \hat{\boldsymbol{k}} \) on
\( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \) is:
A \( \cdot \frac{1}{\sqrt{14}} \)
B. \( \frac{2}{\sqrt{14}} \)
c. \( \frac{-1}{\sqrt{14}} \)
D. \( \frac{-2}{\sqrt{14}} \)
Subject: Chemistry
Assertion
Benzene is highly volatile, and most exposure is through inhalation.
Reason
Benzene is soluble in water.
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: Maths
If \( (2+\sin x) \frac{d y}{d x}+(y+1) \cos x=0 \) and
\( y(0)=1, \) then \( y=\left(\frac{\pi}{2}\right) \) is equal to
A \( \cdot \frac{1}{3} \)
B. \( -\frac{2}{3} \)
\( c \cdot-\frac{1}{3} \)
D.
Subject: Physics
A prism of refractive index \( \sqrt{2} \) has
refracting angle \( 60^{\circ} . \) Answer the
following questions In order that a ray suffers minimum deviation it should be incident at an
angle :
A \( .45^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 30^{\circ} \)
D. none
Subject: Physics
A NOR gate and a NAND gate are connected as shown in the figure. Two different sets of inputs are given to this setup. In the first case, the inputs to the gates are \( \boldsymbol{A}=\mathbf{0}, \boldsymbol{B}=\mathbf{0}, \boldsymbol{C}=\mathbf{0} . \) In the
second case, the inputs are \( \boldsymbol{A}=\mathbf{1}, \boldsymbol{B}= \)
\( 0, C=1 . \) The output \( D \) in the first case
and second case respectively are:
A. 0 and 0
B. 0 and 1
c. 1 and 0
D. 1 and 1
Subject: Maths
Using long division method, divide the polynomial \( 4 p^{3}-4 p^{2}+6 p-\frac{5}{2} \) by \( 2 p-1 \)
A \( \cdot 2 p^{2}-p-\frac{5}{2} \)
В \( \cdot 2 p^{2}+p+\frac{5}{2} \)
c. \( _{2 p^{2}-p+\frac{5}{2}} \)
D. None of the above
Subject: Maths
ff \( \alpha, \beta \) are the roots of \( \left|\begin{array}{lll}x & 1 & 2 \\ 0 & 1 & 1 \\ 1 & x & 2\end{array}\right|=0 \)
\( \operatorname{then} \boldsymbol{\alpha}^{\boldsymbol{n}}+\boldsymbol{\beta}^{\boldsymbol{n}}=? \)
A.
в.
\( c \cdot 2 \)
D. 2n
Subject: Chemistry
The important conclusions on the
formation of trihalomethanes are which
of the following?
A. Chlorination of natural waters causes the formation of chloroform and other trihalomethanes because of the
reaction of \( O C l^{-} \) on DOC present in the water
B. Use of both ammonia and chlorine in water treatment
has reduced the level of the trihalomethanes due to
the formation of the chloroamines, which react more slowly than free chlorine
C. Finally, the concentration of the trihalomethanes above \( 100 \mu \) g/l are considered unsafe for drinking water
D. All of the above
Subject: Physics
A satellite is projected with a speed \( \sqrt{\frac{5}{6}} \)
times of its escape speed from the earth's surface. The initial speed of the
satellite is parallel to the surface of the earth. The maximum distance of the
satellite from the center of the earth will
be
A. \( 3 R \)
в. \( 6 R \)
\( c .5 R \)
D. None of these
Subject: Physics
A particle is executing S.H.M. with amplitude A and Time period T. Time
taken by the particle to reach from
extreme position to \( \frac{A}{2} \)
\( A \cdot \frac{T}{6} \)
B・亞
\( c \cdot \frac{T}{3} \)
\( D \cdot \frac{T}{4} \)
Subject: Physics
Sl unit of \( G \) is \( N m^{2} k g^{-2} \) Which of the following can also be used as the Sl unit of G?
A \( \cdot m^{3} k g^{-1} s^{-2} \)
B . \( m^{2} k g^{-2} s^{-1} \)
c. \( m k g^{-1} s^{-1} \)
D. \( m^{3} k g^{-3} s^{-2} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{\theta})=2\left(\sec ^{2} \boldsymbol{\theta}+\cos ^{2} \boldsymbol{\theta}\right), \) then its
value always
A \( \cdot 4>f(\theta)>2 \)
B \( \cdot f(\theta) \geq 4 \)
\( \mathbf{c} \cdot f(\theta)<2 \)
D. \( f(\theta)=2 \)
Subject: Physics
Assertion
A charge, whether stationary or in motion produces a magnetic field around it.
Reason
Moving charges produce only electric field in the surrounding space.
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: Maths
\( \operatorname{Let} g(x)=\lim _{n \rightarrow \infty} \frac{x^{n} f(x)+h(x)+1}{2 x^{n}+3 x+3}, x^{1} 1 \)
and \( g(1)=\lim _{x \rightarrow 1} \frac{\sin ^{2}\left(\pi \cdot 2^{x}\right)}{\ln \left(\sec \left(\pi \cdot 2^{x}\right)\right)} \) be a
continuous function at \( x=1, \) find the
value of \( 4 g(1)+2 f(1)-h(1) . \) Assume
that \( f(x) \) and \( h(x) \) are continuous at
\( \boldsymbol{x}=\mathbf{1} \)
Subject: Physics
A person standing on a train platform listening to the whistle frequency of \( 450 H z \) of the train as it approaches her at a constant speed. As the train approaches the person on the platform, she will hear the frequency (pitch) of the whistle as:
A. Greater than \( 450 H z \) but constant
B. Less than \( 450 H z \) but constant
c. Greater than \( 450 H z \) and steadily increasing
D. Less than \( 450 H z \) and steadily increasing
E. Greater than \( 450 \mathrm{Hz} \) and steadily decreasing
Subject: Physics
A circular current carrying coil has a radius \( R \). The distance from the centre
of the coil on the axis where the
magnetic induction will be \( \left(\frac{1}{8}\right)^{t h} \) of its value at the centre of the coil is
A \( \cdot \frac{R}{\sqrt{3}} \)
в. \( R \sqrt{3} \)
с. \( 2 R \sqrt{3} \)
।
D. \( \left(\frac{2}{\sqrt{3}}\right)^{R} \)
Subject: Physics
Two bodies of masses \( m_{1} \) and \( m_{2} \) are
separated by a distance \( R \). The distance
of the centre of mass of the bodies from
the mass \( m_{1} \) is
A \( \cdot \frac{m_{2} R}{m_{1}+m_{2}} \)
В. \( \frac{m_{1} R}{m_{1}+m_{2}} \)
c. \( \frac{m_{1} m_{2}}{m_{1}+m_{2}} R \)
D. \( \frac{m_{1}+m_{2}}{m_{1}} R \)
Subject: Physics
The oscillations represented by curve 1
in the graph are expressed by equation
\( x= \) Asinwt. The equation for the
oscillations represented by curve 2 is expressed as:
A. \( x=2 A \sin (\omega t-\pi / 2) \)
B. \( x=2 A \sin (\omega t+\pi / 2) \)
c. \( x=-2 \operatorname{Asin}(\omega t-\pi / 2) \)
D. \( x=\operatorname{Asin}(\omega t-\pi / 2) \)
Subject: Maths
Solve :
\( \frac{\mathbf{5}}{\boldsymbol{x}+\boldsymbol{y}}-\frac{\mathbf{2}}{\boldsymbol{x}-\boldsymbol{y}}+\mathbf{1}=\mathbf{0} \)
\( \frac{15}{x+y}+\frac{7}{x-y}-10=0 \)
Subject: Maths
In a town of 10,000 families it was
found that \( 40 \% \) families buy newspaper \( A, 20 \% \) buy newspaper \( B \) and \( 10 \% \) buy newspaper \( C, 5 \% \) families buy \( A \) and \( B \) \( 3 \% \) buy \( B \) and \( C \) and \( 4 \% \) buy \( A \) and \( C . \) If
\( 2 \% \) families buy all three newspapers, find number of families which buy None
of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)
Subject: Physics
An infinitely long time charge having a uniform charge per unit length \( \lambda \) lies at a distance d from a point 0 as shown in Fig. Determine the total electric flux
through the surface of sphere of radius
R centered at 0 resulting from this line charge. Consider both cases where Rd.
\( A \)
B. \( \frac{7 \lambda \sqrt{R^{2}-d^{3}}}{\varepsilon_{0}} \)
c. \( \frac{7 \lambda \sqrt{R^{2}-d^{2}}}{2 \varepsilon_{0}} \)
\( D \)
Subject: Chemistry
Consider the given organometallic compound.
\( (\mathrm{I})\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{H} \boldsymbol{g} \)
(II) \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{Z} \boldsymbol{n} \)
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{M} \boldsymbol{g} \)
\( (\mid V) C H_{3} L i \)
The correct decreasing order of ionic character is :
A. \( I>I I>I I I>I V \)
В. \( I I>I>I I I>I V \)
c. \( I>I I I>I I>I V \)
D. \( I V>I I I>I I>I \)
Subject: Maths
If \( \boldsymbol{x}, \boldsymbol{y} \in(\mathbf{0}, \boldsymbol{3} \boldsymbol{0}) \) such that \( \left[\frac{\boldsymbol{x}}{\mathbf{3}}\right]+\left[\frac{\boldsymbol{3} \boldsymbol{x}}{\mathbf{2}}\right]+ \)
\( \left[\frac{\boldsymbol{y}}{\mathbf{2}}\right]+\left[\frac{\mathbf{3} \boldsymbol{y}}{\boldsymbol{4}}\right]=\frac{\mathbf{1 1} \boldsymbol{x}}{\mathbf{6}}+\frac{\mathbf{5} \boldsymbol{y}}{\boldsymbol{4}}(\text { where }[\mathbf{x}] \)
denote greatest integer \( \leq x \) ) then the
number of ordered pairs \( (x, y) \) is
A . 10
B. 20
\( c \cdot 24 \)
D. 28
Subject: Physics
Maximum velocity of block during
subsequent motion of the system after
release of ball is :
A \( \cdot[g L(1-\cos \theta)]^{1 / 2} \)
B \( \cdot[2 g L(1-\cos \theta)]^{1 / 2} \)
\( \mathbf{c} \cdot[g L(\cos \theta)]^{1 / 2} \)
D. insufficient information
Subject: Maths
If \( \boldsymbol{y}=\log (\sec x+\tan x), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A. \( \sec x-\tan x \)
B. \( \tan x \)
\( c \cdot \sec x \)
D. \( \cos x \)
Subject: Maths
Int he given figure \( l\|\boldsymbol{m}\| \boldsymbol{n} \). If \( \boldsymbol{x}=\boldsymbol{y} \)
and \( a=b, \) then
\( \mathbf{A} \cdot l \| n \)
B. \( l<n \)
c. \( l>n \)
D. \( D \| n \)
Subject: Physics
When a bullet is fired from a gun
a) Kinetic Energy of bullet is more than
that of gun
b) acceleration of bullet is more than
that of gun
c) momentum of bullet is more that of
gun
d) velocity of bullet is more than that of
gun
A. only a \( \& \) b are true
B. only b \& c are true
\( \mathrm{c} \cdot \mathrm{a}, \mathrm{b} \& \mathrm{d} \) are true
D. a, b, c \& d are true
Subject: Physics
The angular frequency for which he detects maximum current in the circuit
is
\( \mathbf{A} \cdot 10^{5} / 7 r a d / s \)
B . \( 10^{4} r a d / s \)
c. \( 10^{5} r a d / s \)
D. \( 10^{4} / 7 r a d / s \)
Subject: Chemistry
How many grams of \( C O_{2} \) are produced by the complete reaction of 100 g \( \mathrm{CaCO}_{3} \) with excess \( \boldsymbol{H C l} \) ?
A .22 g
в. 44 g
c. 79 g
D. \( 110 \mathrm{g} \)
E . 132 g
Subject: Physics
When a metallic wire is stretched with a
tension \( T_{1} \) its length is \( l_{1} \) and with a
tension \( T_{2} \) its length is \( l_{2} \). The original length of the wire is:
A. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
в. \( \frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}} \)
c. \( \sqrt{l_{1} l_{2}} \)
D. \( \frac{l_{1} l_{2}}{2} \)
Subject: Physics
Q Type your question-
connected to a fixed vertical wall and
the other end has a block of mass \( \mathrm{m} \)
initially at rest on a smooth horizontal
surface. The spring is initially in natural length. Now a horizontal force F acts on the block as shown. Then the maximum
extension in spring is equal to the maximum compression in the spring.
Reason

To compress and to expand an ideal unstretched spring by equal amount, same work is to be done on the spring.
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: Physics
Young's modulus of rubber is \( 10^{4} N / m^{2} \)
and area of cross section is \( 2 \mathrm{cm}^{-2} \). If
force of \( 2 \times 10^{5} \) dyn is applied along its
length, then its initial \( l \) becomes.
A . \( 3 l \)
в. \( 4 l \)
\( c \cdot 2 l \)
D. None of these
Subject: Physics
A particle is acted upon by a force given
by \( \boldsymbol{F}=-\boldsymbol{\alpha} \boldsymbol{x}^{3}-\boldsymbol{\beta} \boldsymbol{x}^{4} \) where \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \) are
positive constants. At the point \( x=0 \)
the particle is
A. In stable equilibrium
B. In unstable equilibrium
c. In neutral equilibrium
D. Not in equilibrium
Subject: Maths
\( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\left[1-\tan \left(\frac{x}{2}\right)\right][1-\sin x]}{1+\tan \left(\frac{x}{2}\right)[\pi-2 x]^{3}} \) is
A \( \cdot \infty \)
B.
c. 0
D. \( \frac{1}{32} \)
Subject: Physics
A body falls from rest. In the last second of its fall it covers half of the total
distance. If \( g \) is \( 9.8 m / s^{2}, \) then the total
time of its falls is (in second)?
A . 2
B. \( 2+\sqrt{2} \)
\( c \cdot 4-\sqrt{2} \)
D. 3
Subject: Chemistry
Calculate the e.m.f of the cell in \( \mathbf{V} \)
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}\right|(\mathbf{1} . \mathbf{0} \boldsymbol{a} \boldsymbol{t m}) \mid \boldsymbol{C H}_{3} \boldsymbol{C O O H}(\mathbf{0 . 1} \boldsymbol{M}) \)
\( \boldsymbol{K}_{\boldsymbol{a}}\left(\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}\right)=\mathbf{1 . 8} \times \)
\( \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{B}^{\prime}}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}} . \) if the
value is \( -46 \times 10^{-x}, \) then what is the
value of \( x ? \)
Subject: Physics
A double star is a system of two stars of
masses \( \mathrm{m} \) and \( 2 \mathrm{m}, \) rotating about their centre of mass only under their mutual
gravitational attraction. If \( r \) is the
separation between these two stars
then their time period of rotation about their centre of mass will be proportional
to.
This question has multiple correct options
A \( \cdot \frac{3}{2} \)
B.
c. \( \quad_{m} \frac{1}{2} \)
D. \( _{m^{-}} \frac{1}{2} \)
Subject: Maths
If \( z \) is complex number such that \( z \neq 0 \)
and \( R_{e}(z)=0, \) then
\( \mathbf{A} \cdot \operatorname{Re}\left(z^{2}\right)=0 \)
В. \( \operatorname{Im}\left(z^{2}\right)=0 \)
\( \mathbf{c} \cdot \operatorname{Re}\left(z^{2}\right)=\operatorname{Im}\left(z^{2}\right) \)
D. none of these
Subject: Chemistry
For the reaction: \( \boldsymbol{H}_{2}+\boldsymbol{C l}_{2} \stackrel{\text {sunlight}}{\longrightarrow} \mathbf{2} \boldsymbol{H} \boldsymbol{C l} \)
the order of reaction is :
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
c. 1
D. 3
Subject: Physics
An open pan \( P \) filled with water (density
\( \boldsymbol{\rho}_{\boldsymbol{w}} \boldsymbol{)} \)
is placed on a vertical rod, maintaining
equilibrium. A block of density \( \rho \) is
placed on one side of the pan as shown
in the figure. Water depth is more than
height of the block.
A. Equilibrium will be maintained only if \( \rho<\rho_{w} \)
B. Equilibrium will be maintained only if \( \rho \leq \rho_{w} \)
C. Equilibrium will be maintained for all relations between \( \rho \) and \( \rho_{w} \)
D. Equilibrium will not be maintained in all cases
Subject: Physics
The resistors of resistances \( 2 \Omega, 4 \Omega, 5 \Omega \) are connected in parallel. The total resistance of the combination will be :
A \( \cdot \frac{29}{10} \Omega \)
в. \( \frac{19}{20} \Omega \)
c. \( \frac{10}{20} \Omega \)
D. \( \frac{20}{19} \Omega \)
Subject: Chemistry
The potential of the cell containing two hydrogen electrodes as represented below, is:
\( \boldsymbol{P t}, \boldsymbol{H}_{2(g)}\left|\boldsymbol{H}^{+}\left(\mathbf{1 0}^{-6} \boldsymbol{M}\right) \| \boldsymbol{H}^{+}\left(\mathbf{1 0}^{-4} \boldsymbol{M}\right)\right| \boldsymbol{H} \)
\( \operatorname{at} 298 K \)
A. \( -0.118 V \)
B . \( -0.0591 V \)
c. \( 0.118 V \)
D. \( 0.0591 V \)
Subject: Maths
Integrate w.r.t \( \times \frac{3 x}{1+2 x^{4}} \)
A \( \cdot \frac{3}{\sqrt{2}} \tan ^{-1} \sqrt{2} x^{2}+c \)
B. \( \frac{3}{2 \sqrt{2}} \tan ^{-1} \sqrt{2} x^{2}+c \)
\( \frac{3}{2 \sqrt{2}} \tan ^{-1} 2 x^{2}+c \)
D \( \cdot \frac{3}{\sqrt{2}} \tan ^{-1} x^{2}+c \)
Subject: Physics
Two positively charged particles \( X \) and
\( \boldsymbol{Y} \) are initially far away from each other
and at rest. \( X \) begins to move towards
\( Y \) with some initial velocity. The total
momentum and energy of the system are \( p \) and \( E \).Then:
A. if \( Y \) is fixed, both \( p \) and \( E \) are conserved.
B. if \( Y \) is fixed, \( E \) is conserved, but not \( p \)
c. if both are free to move, \( p \) is conserved but not \( E \)
D. if both are free, \( E \) is conserved, but not \( p \)
Subject: Physics
toppr
Q Type your question
to the other end of the piston, it moves down. If air in the enclosure is cooled
from temperature \( \boldsymbol{T} \) to \( \boldsymbol{T}-\triangle \boldsymbol{T}, \) the
piston moves back to its original
position. Then \( \triangle \boldsymbol{T} / \boldsymbol{T} \) is close to
(Assuming air to be an ideal gas, \( \boldsymbol{g}= \)
\( 10 m / s^{2}, \) atmospheric pressure is \( 10^{5} \)
Pascal)
\( \mathbf{A} \cdot 0.01 \)
B. 0.02
c. 0.04
D. 0.09
Subject: Maths
\( \frac{\tan \theta}{\left(1+\tan ^{2} \theta\right)^{2}}+\frac{\cot \theta}{\left(1+\cot ^{2} \theta\right)^{2}}=\sin \theta \)
\( \cos \theta \quad, \) then \( \theta \) is
\( \mathbf{A} \cdot 2 \pi \)
в. \( \frac{\pi}{56} \)
\( c \cdot \frac{\pi}{2} \)
D.
Subject: Physics
The equation of projectile is \( y=16 x- \)
\( \frac{5 x^{2}}{4} \) Find the horizontal range.
\( \mathbf{A} \cdot R=13.8 m \)
В. \( R=8 m \)
c. \( R=12.8 \mathrm{m} \)
D. \( R=9 m \)
Subject: Maths
The quantity of water that should be added to reduce \( 9 \mathrm{ml} \) lotion containing \( 50 \% \) alcohol to a lotion containing \( 30 \% \)
alcohol is :
A. \( 3 \mathrm{m} \)
B. \( 4 \mathrm{m} \)
\( c \cdot 5 m \)
D. \( 6 \mathrm{m} \)
Subject: Maths
Which of the following functions from \( Z \)
to itself are bijections?
\( \mathbf{A} \cdot f(x)=x^{3} \)
B. \( f(x)=x+2 \)
c. \( f(x)=2 x+1 \)
\( \mathbf{D} \cdot f(x)=X^{2}+x \)
Subject: Maths
ff \( \boldsymbol{y}=\mathbf{8} \boldsymbol{x}^{3}-\boldsymbol{6} \mathbf{0} \boldsymbol{x}^{2}+\mathbf{1 4 4} \boldsymbol{x}+\mathbf{2 7} \) is a
strictly decreasing function in the interval
A. (-5,6)
В \( \cdot(-\infty, 2) \)
c. (5,6)
(年. \( 5,6,6) \)
D. \( (3, \infty) \)
E \( .(2,3) \)
Subject: Physics
A plano convex lens of focal length 30 \( \mathrm{cm} \) has its plane surface silvered. An object is placed \( 40 \mathrm{cm} \) from the lens on
the convex side. The distance of the
image from the lens is:
\( A \cdot 18 \mathrm{cm} \)
B. 24 \( \mathrm{cm} \)
\( c .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Chemistry
\( (\boldsymbol{A}) \boldsymbol{C}_{4} \boldsymbol{H}_{6} \frac{\boldsymbol{H}_{2} / \boldsymbol{P t}}{\longrightarrow}(\boldsymbol{B}) \boldsymbol{C}_{4} \boldsymbol{H}_{8} \frac{\boldsymbol{O}_{3} / \boldsymbol{H}_{2} \boldsymbol{O}}{_{\boldsymbol{}}} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
Hence \( A \) and \( B \) are :
A. \( C H_{3} C \equiv C C H_{3}, C H_{3} C H=C H C H_{3} \)
в. \( C H_{2}=C H C H_{3}=C H_{2}, C H_{3} C H=C H C H_{3} \)
\( ^{c} \cdot \mid, \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{3} \)
D. None of these
Subject: Physics
\( \boldsymbol{E} \) is kinetic energy of a simple harmonic oscillator at its mean
position. The phase angle from mean position at which its kinetic energy is \( \boldsymbol{E} / 2 \) is :
A . \( \pi / 5 \) rad
в. \( \pi / 4 \) rad
c. \( \pi / 3 \) rad
D. None of the above
Subject: Physics
A glass prism of refractive index 1.5 is
placed in water of refractive index 1.33 The minimum value of the angle of the prism so that it will not be possible to
have any emergent ray is :
A \( .150^{\circ} \)
B . \( 125^{\circ} \)
\( c \cdot 165 \)
D. \( 180^{\circ} \)
Subject: Maths
The mean of \( x_{1} \) and \( x_{2} \) is \( M_{1} \) and that of
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \boldsymbol{x}_{3} \ldots . . \boldsymbol{x}_{4} \) is \( \boldsymbol{M}_{2} \)
then the mean of \( a x_{1}, a x_{2}, \frac{x_{3}}{a}, \frac{x_{4}}{a} \) is?
A. \( \frac{a M_{1}+M_{2}}{2} \)
\( ^{\mathbf{B} \cdot} \frac{a M_{1}+\left(\frac{M_{2}}{a}\right)}{2} \)
c. \( \frac{1}{2 a}\left[\left(a^{2}-1\right) M_{1}+M_{2}\right] \)
D \( \cdot \frac{1}{2 a}\left[\left(a^{2}-1\right) M_{1}+2 M_{2}\right] \)
Subject: Physics
An elevator carrying a charge of \( 0.5 C \) is
moving down with a velocity of \( 5 \times \) \( 10^{3} m s^{-1} . \) The elevator is \( 4 m \) from the
bottom and \( 3 m \) horizontally form \( P \) as
shown in figure. What magnetic field (in
\( \mu T \) ) does it produce at point \( P ? \)
Subject: Physics
The gas mixture constists of 3 moles of oxygen and 5 moles of argon at temperature \( T . \) Considering only
translational and rotational modes, the
total internal energy of the system is:
A . \( 12 R T \)
в. \( 20 R T \)
c. \( 15 R T \)
D. \( 4 R T \)
Subject: Maths
If \( f(x) \) is a differentiable function,
\( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq \mathbf{2}, \) for all \( \boldsymbol{x} \in \boldsymbol{R}, \boldsymbol{f}(\mathbf{1})=\mathbf{2} \)
then possible value of \( f(3) \) are This question has multiple correct options
A. 5
B. 6
\( c \cdot 7 \)
D.
Subject: Maths
The value of \( \cos ^{2} 10^{\circ}- \)
\( \cos 10^{\circ} \cos 50^{\circ}+\cos ^{2} 50^{\circ} \) is?
A \( \cdot \frac{3}{2}\left(1+\cos 20^{\circ}\right) \)
в. \( \frac{3}{4} \)
c. \( \frac{3}{4}+\cos 20^{\circ} \)
D. \( \frac{3}{2} \)
Subject: Chemistry
Assertion
Refining of zinc is done by distillation
under reduced pressure.
Reason

Zinc is a transition metal.
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
Which of the following has an optical isomer?
\( \mathbf{A} \cdot\left[\mathrm{CO}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}\right]^{+} \)
B . \( \left[\mathrm{CO}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\right]^{2-} \)
\( \mathbf{c} \cdot\left[\mathrm{CO}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}(\mathrm{en})\right]^{3+} \)
D \( \cdot\left[\mathrm{CO}(\mathrm{en})_{2}\left(\mathrm{NH}_{3}\right)_{2}\right]^{3+} \)
Subject: Physics
The tables show the resistance values
for three different resistors and the
currents through each resistor.
What is the ranking of the power
dissipated by each resistor, greatest
first?
\( \begin{array}{lc}\text { Current 1 } & \mathbf{2 I} \\ \text { Resistance 1 } & R \\ \text { Current 2 } & I \\ \text { Resistance 2 } & 2 R \\ \text { Current 3 } & I \\ \text { Resistance 3 } & 4 R\end{array} \)
A \( .3,2, \) and 1 tie
\( \mathbf{B} \cdot 3,2,1 \)
\( c \)
1,2,3
D. 1 and 3 tie, 2
E . All tie
Subject: Chemistry
In which pairs do both species have the same number of unpaired electrons in \( \mathrm{p} \)
orbitals?
10 and \( C l^{+} \)
2. \( F^{+} \) and \( G a^{-} \)
3. \( \mathrm{N} \) and \( \boldsymbol{K} \boldsymbol{r}^{\boldsymbol{3}+} \)
A. 1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct
Subject: Maths
The value of \( \int \frac{d x}{\sqrt{2 x-x^{2}}} \) is
\( A \cdot \sin ^{-1}(x)+c \)
B \( \cdot \sin ^{-1}(x-1)+c \)
\( \mathbf{c} \cdot \sin ^{-1}(1+x)+c \)
D. \( -\sqrt{2 x-x^{2}}+c \)