AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A light body moving at some speed collides with a heavier body. Which of
the following statements is true?
I. Heavier body applies a greater impulse on the lighter body.
II. The lighter body experiences a greater change of momentum.
III. Acceleration of the lighter body will
be more than the acceleration of the
heavier body.
A. I and II only
B. II only
C. III only
D. II and III only
E . ।, II, and III
Subject: Physics
Assertion
The coil in the resistance boxes are
made by doubling the wire.
Reason
Thick wire is required in resistance box.
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
Natural rubber or raw rubber consists of
basic material latex which is a
dispersion of isoprene. During the treatment, this isoprene forms a high molecular weight polymer of isoprene. Natural rubber can be obtained from
five hundred different species of plants. Consider the following properties of
rubber,
(i) Tensile strength of vulcanized rubber is almost ten times more than raw
rubber.
(ii) The elasticity of the raw rubber is very high. Choose the correct option.
A \( \cdot \) (i) is true (ii) is false.
B. (i) is false (ii) is true.
c. Both (i) and (ii) are true.
D. Both (i) and (ii) are false.
Subject: Physics
Steam at \( 100^{\circ} \mathrm{C} \) is passed into \( 1.1 \mathrm{kg} \) of water contained in a calorimeter of
water equivalent \( 0.02 \mathrm{kg} \) at \( 15^{\circ} \mathrm{C} \) till the temperature of the calorimeter and its
contents rises to \( 80^{\circ} \mathrm{C} \). The mass of the
steam condensed in kilograms is
A. 0.130
B. 0.065
c. 0.260
D. 0.135
Subject: Maths
\( \mathrm{f} \mathrm{A}=\left[\begin{array}{cc}1 & 3 \\ 3 & 2 \\ 2 & 5\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}-1 & -2 \\ 0 & 5 \\ 3 & 1\end{array}\right] \).Find the
matrices D such that \( \boldsymbol{A}+\boldsymbol{B}-\boldsymbol{D}=\boldsymbol{O} \)
e. zero matrices
Subject: Chemistry
In the reaction, \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}, \) if \( \mathbf{2} \)
moles of \( A, 3.0 \) moles of \( B \) and 2.0 moles of \( C \) are placed in a \( 2 L \) flask and the
equilibrium concentration of \( \mathrm{C} \) is 0.5 mol \( / L . \) The equilibrium constant
\( \left(K_{c}\right) \) for the reaction is:
\( \mathbf{A} \cdot 0.073 \)
B. 0.1470
c. 0.0500
D. 0.0080
Subject: Chemistry
\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2}, \boldsymbol{G} \boldsymbol{e} \boldsymbol{O}_{2}, \boldsymbol{S} \boldsymbol{n} \boldsymbol{O} \) and \( \boldsymbol{P b O} \) are
respectively:
A. acidic, amphoteric, acidic, basic
B. acidic, amphoteric, amphoteric, acidicç
c. acidic, basic, amphoteric, basic
D. acidic, amphoteric, amphoteric, basic
Subject: Chemistry
Molar conductivities of oxalate, \( \boldsymbol{K}^{+} \) and
\( N a^{+} \) ions at infinite dilution are 148.2 \( \mathbf{5 0 . 1 , 7 3 . 5} S \mathrm{cm}^{2} \) mol \( ^{-1} \) respectively.
Then, equivalent conductivity at infinite dilution for sodium-potassium oxalate \( \left[\left(\boldsymbol{C O O}^{-}\right)_{2} \boldsymbol{N} \boldsymbol{a}^{+} \boldsymbol{K}^{+}\right] \) will be:
A. \( 271.8 \mathrm{S} \mathrm{cm}^{2} \) eq \( ^{-1} \)
В. \( 67.95 \mathrm{S} \mathrm{cm}^{2} \mathrm{eq}^{-1} \)
c. \( 543.6 S \mathrm{cm}^{2} e q^{-1} \)
D. \( 135.9 S \mathrm{cm}^{2} e q^{-1} \)
Subject: Physics
Equations of a stationary wave and a travelling wave are \( \boldsymbol{y}_{1}= \)
\( \mathbf{1} \sin (\boldsymbol{k} \boldsymbol{x}) \cos (\boldsymbol{\omega} \boldsymbol{t}) \) and \( \boldsymbol{y}_{2}=\boldsymbol{a} \sin (\boldsymbol{\omega} \boldsymbol{t}- \)
\( k x \). The phase difference between two
points \( x_{1}=\frac{\pi}{3 k} \) and \( x_{2}=\frac{3 \pi}{2 k} \) is \( \phi_{1} \) for
the first wave and \( \phi_{2} \) for the second wave.The ratio \( \frac{\phi_{1}}{\phi_{2}} \) is
A.
B. 5/6
\( c \cdot 3 / 4 \)
D. 6/7
Subject: Chemistry
In kjeldahl's method of estimation of nitrogen, nitrogen is quantitatively converted to ammonium sulphate. It is
the treated with the standard solution
of alkali. The nitrogen which is present is estimated as:
A . \( N_{2} \) gas
B. \( N O_{2} \) gas
C. \( N H_{3} \) gas
D. \( \left(N H_{4}\right)_{2} S O_{4} \)
Subject: Physics
A constant torque acting on a uniform circular wheel changes its angular
momentum from \( A_{0} \) to \( 4 A_{0} \) in 4 sec. The
magnitude of this torque is:
\( \mathbf{A} \cdot 4 A_{0} \)
в. \( A_{0} \)
c. \( \frac{3}{4} A_{0} \)
D. \( 12 A_{0} \)
Subject: Chemistry
Assertion
\( P H \) of a buffer solution does not
change on dilution.
Reason
On dilution, the ratio of concentration of salt and acid (or base) remains
unchanged.
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
Match the column
\( \begin{array}{lllll}\text { Sr.No } & \text { a } & \text { b } & \text { c } & \\ \text { (i) } & + & + & \text { (1) Commensalism } \\ \text { (ii) } & + & - & \text { (2) Competition } \\ \text { (iii) } & - & - & \text { (3) Parasitism } \\ \text { (iv) } & + & \text { 0 } & \text { (4) mutualism }\end{array} \)
\( A \)
\( (i) 1,(i i) 2,(i i i) 3,(i v) 4 \)
B. \( (i) 2,(i i) 3,(i i i) 1,(i v) \)
C . \( (i) 4,(i i) 3,(i i i) 2,(i v) 1 \)
\( D \)
\( (i) 3,(i i) 2,(i i i) 1,(i v) \)
Subject: Physics
An ideal gas is enclosed in a cylinder with a movable piston on top of it. The
piston has a mass of \( 8000 g \) and an
area of \( 5.00 \mathrm{cm}^{2} \) and is free to slide up
and down, keeping the pressure of the gas constant. How much work is done
on the gas as the temperature of 0.200 mol of the gas is raised from
\( \mathbf{2 0 . 0 ^ { \circ }} \boldsymbol{C} \) to \( \mathbf{3 0 0 ^ { \circ }} \boldsymbol{C} \) ?
A. \( -466 J \)
в. -233.5
с. 233 .
D. \( 0 . J \)
Subject: Maths
Derivative of \( \tan ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right) \) with
respect to \( \sin ^{-1}\left(3 x-4 x^{3}\right) \) is
A \( \cdot \frac{1}{\sqrt{1-x^{2}}} \)
в. \( \frac{3}{\sqrt{1-x^{2}}} \)
\( c .3 \)
D.
Subject: Physics
If weight of an object in air \( W_{a} \) is
\( (10.0 \pm 0.1) g \) and its weight in water
\( W_{L} \) is \( (5.00 \pm 0.2) g, \) then percentage
error in its relative density is? \( \left(\text { Relativedensity }=\frac{W_{a}}{W_{a}-W_{L}}\right) \)
A . \( 2 \% \)
B. \( 5 \% \)
c. \( 7 \% \)
D. \( 1.5 \% \)
Subject: Chemistry
Arrange the following in decreasing order of their basic strength:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2}, \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{N} \boldsymbol{H}, \boldsymbol{\lambda} \)
Subject: Chemistry
Which of the following molecule have zero dipole moment?
\( (a) C_{6} H_{6}(b) X e F_{2} \)
\( (c) S O_{2} \)
\( (d) S F_{4}(e) \)
\( \boldsymbol{S} \boldsymbol{F}_{\boldsymbol{6}} \)
\( A \cdot(b) \) and \( (d) \)
B. (a), (b) and (e)
c. (a) and (e)
D. (c) and (d)
Subject: Physics
In a double-slit experiment, at a certain point on the screen the path difference
between the two interfering waves is \( \frac{1}{8} t h \) of a wavelength. The ratio of the
intensity of light at that point to that at the centre of a bright fringe is:
\( \mathbf{A} \cdot 0.672 \)
B. 0.853
c. 0.760
D. 0.568
Subject: Maths
\( \int \frac{2^{x}}{\sqrt{1-4^{x}}} d x=K \sin ^{-1}\left(2^{x}\right)+C, \) then
the value of \( K \) is equal to
A \( . e n 2 \)
B. \( \frac{1}{2} \ell 2 \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\ell n^{2}} \)
Subject: Maths
We number both the rows and the
columns of an \( 8 \times 8 \) chess-board with
the numbers 1 to \( 8 . A \) number of grains are placed onto each square, in such a way that the number of grains on a certain square equals the product of its row and column numbers. How many
grains are there on the entire chessboard?
A . 1296
B. 1096
\( c .2490 \)
D. 1156
Subject: Maths
If \( (0, b, 0) \) is the centroid of the triangle
formed by the points (4,2,-3) \( (a,-5,1) \) and \( (2,-6,2) . \) If \( a, b \) are the
roots of the quadratic equation \( x^{2}+ \)
\( \boldsymbol{p} \boldsymbol{x}+\boldsymbol{q}=\mathbf{0}, \) then \( \boldsymbol{p}, \boldsymbol{q} \) are
A .9,18
в. -9,-18
c. 3,-18
D. -3,18
Subject: Chemistry
Which of the following facts about the complex \( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \) is wrong?
A. The complex involves \( d^{2} s p^{3} \) hybridisation and is octahedral in shape
B. The complex is paramagnetic
c. The complex is an outer orbital complex.
D. The complex gives white precipitate with silver nitrate solution.
Subject: Chemistry
Which of the following is correct electron dot structure of oxygen?
\( A \)
\[
\therefore \dot{0}: \therefore \dot{0}:
\]
в.
\[
\therefore \dot{0}: \stackrel{\because}{0}:
\]
\( c \)
\[
\therefore 0:: 0:
\]
D.
\[
\therefore \dot{0}:: \dot{0}
\]
Subject: Physics
A mass \( \mathrm{m} \) is suspended form a sensitive spring balance kept in a satellite. The reading of the balance is
\( W_{1} \) when the satellite is in an orbit of
radius \( \mathrm{R} \) and is \( W_{2} \) when it is in an orbit
of radius \( 2 \mathrm{R} \). Then
A. \( W_{1}>W_{2} \)
в. \( W_{1}<W_{2} \)
c. \( W_{1}=W_{2} \)
D. cannot be predicted
Subject: Maths
If \( A \) and \( B \) are square matrices of order
n' such that \( A^{2}-B^{2}=(A-B)(A+ \)
\( B \) ), then which of the following will be
true?
A. Either of A or B is zero matrix
в. \( A=B \)
c. \( A B=B A \)
D. Either of A or B is an identity matrix
Subject: Physics
\( \boldsymbol{n} \) identical cells, each of internal
resistance \( (r) \) are first connected in
parallel and then connected in series \( \operatorname{across} \) a resistance \( (\boldsymbol{R}) . \) If the
current through \( R \) is same in both the
cases then:
A. \( R=r / 2 \)
в. \( r=R / 2 \)
c. \( R=r \)
\( \mathbf{D} \cdot r=0 \)
Subject: Chemistry
A gas occupies a volume of \( 250 \mathrm{ml} \) at
\( 745 \mathrm{mm} \mathrm{Hg} \) and \( 25^{\circ} \mathrm{C} . \) What additional pressure is required to reduce the gas volume to \( 200 \mathrm{ml} \) at the same time?
\( \mathbf{A} \cdot 180.25 \mathrm{mm} \)
B. \( 200.9 \mathrm{mm} \)
c. \( 186.25 \mathrm{mm} \)
D. \( 189.4 \mathrm{mm} \)
Subject: Chemistry
(i) Write IUPAC name of \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{N H}_{2} \)
(ii) Arrange the following amines in the order of their increasing basic strength in aqueous solution.
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{N}_{1}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{H}_{1} \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{N} \boldsymbol{H}_{2} \)
Subject: Maths
\( \cos ^{-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right\}= \)
A \( \cdot \frac{23 \pi}{20 \pi} \)
B. \( \frac{7 \pi}{10} \)
\( c \cdot \frac{7 \pi}{20} \)
D. \( \frac{17 \pi}{20 \pi} \)
Subject: Maths
Let \( A \) be a \( 3 \times 3 \) matrix such that \( a_{11}= \)
\( a_{33}=2 \) and all the other \( a_{i j}=1 . \) Let
\( \boldsymbol{A}^{-1}=\boldsymbol{x} \boldsymbol{A}^{2}+\boldsymbol{y} \boldsymbol{A}-\boldsymbol{z} \boldsymbol{I}, \) then find the
value of \( (x+y+z) \) where \( I \) is a unit of
matrix of order 3
A . -9
B. 9
c. 1
D. -
Subject: Chemistry
Sulfide ion in alkaline solution reacts
with solid sulfux to form polysulfide ions having formules \( S_{2}^{-2}, S_{3}^{2-}, S_{4}^{2-} \) and so on. The equilibrium constant for the formation of \( S_{2}^{2-} \) is \( 12\left(K_{5}\right) \& \) for the formulation of \( S_{3}^{2-} \) is \( 132\left(K_{2}\right), \) both
from \( \mathrm{S} \) and \( S^{2-} . \) What is the equilibrium content for the formation of \( S_{3}^{2-} \) from \( S_{2}^{2-} \) and \( s ? \)
A. 11
в. 12
\( c \cdot 132 \)
D. None of these
Subject: Chemistry
A 1.00 molal aqueous solution of
trichloroacetic acid \( \left(C C l_{3} C O O H\right) \) is
heated to its boiling point. The solution
has the boiling point of \( 100.8^{\circ} \mathrm{C} \).
Determine the van 't Hoff factor for
trichloroacetic acid. \( \left(K_{b} \text { for water } 0.512 \mathrm{K}\right. \)
\( \left.\operatorname{kg} M o l^{-1}\right) \)
Define the following terms:
(i) Mole fraction
(ii) Isotonic solutions
(iii) Van 't Hoff factor
(iv) Ideal solution
Subject: Maths
If \( \sum_{k=0}^{100} i^{k}=x+i y, \) then the values of \( x \) and y are
A. \( x=-1, y=0 \)
B. \( x=1, y=1 \)
c. \( x=1, y=0 \)
D. \( x=0, y=1 \)
Subject: Maths
Let \( \boldsymbol{f}:[\mathbf{0}, \boldsymbol{4} \boldsymbol{\pi}] \rightarrow[\mathbf{0}, \boldsymbol{\pi}] \) be defined by
\( f(x)=\cos ^{-1}(\cos x) . \) The number of
points \( \boldsymbol{x} \in[\mathbf{0}, \mathbf{4} \boldsymbol{\pi}] \) satisfying the
equation \( f(x)=\frac{10-x}{10} \) is
Subject: Maths
Evaluate the following integral by expressing them as a limit of a sum. \( \int_{1}^{2}(3 x-2) d x \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{5}{2} \)
D. \( \frac{7}{2} \)
Subject: Maths
Find \( \boldsymbol{A}^{\boldsymbol{T}}: \)
\( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{4} & \mathbf{3} & \mathbf{- 1} \\ \mathbf{6} & \mathbf{8} & \mathbf{- 3} \\ \mathbf{4} & \mathbf{1} & \mathbf{3}\end{array}\right] \)
Subject: Physics
Consider the following two statements \( A \) and \( B \) and identify the correct answer.
A) When the length of a wire is doubled, the Young's modulus of the wire is also doubled
B) For elastic bodies Poisson's ratio is \( + \)
Ve and for inelastic bodies Poissons
ratio is -Ve
A. Both A \& B are true
B. A is true but B is false
c. \( A \) is true but \( B \) is true
D. Both A \& B are false
Subject: Maths
\( \boldsymbol{l} \boldsymbol{t}_{n \rightarrow \infty}\left[\frac{\mathbf{1}}{\boldsymbol{n a}}+\frac{\mathbf{1}}{\boldsymbol{n a}+\mathbf{1}} \frac{\mathbf{1}}{\boldsymbol{n a}+\mathbf{2}} \cdots \cdots+\frac{\mathbf{1}}{\boldsymbol{n b}}\right] \)
\( ^{\mathrm{A}} \cdot \log \left(\frac{b}{a}\right) \)
B. \( \log \left(\frac{a}{b}\right) \)
\( c \cdot \log a \)
D. \( \log b \)
Subject: Maths
\( \frac{7 x^{3}+3 x^{2}-x+1}{x+1}=\left(a x^{2}+b x+c\right) \)
\( \frac{2}{x+1} \) then \( a= \)
A . 3
B. 7
\( c \cdot 1 \)
D.
Subject: Maths
If \( f(x)=\left|x^{2}-4 x+3\right|, \) then \( f^{\prime}(x) \) is
A. \( 2 x-4 \) for \( 1<x<3 \)
B. \( 4-2 x \) for \( 1<x<3 \)
c. \( 2 x-4 \) for \( 1 \leq x \leq 3 \)
D. \( 4-2 x \)
Subject: Chemistry
The number of moles of \( K M n O_{4} \) that will be needed to react completely with
one mole of ferrour oxalate \( F e\left(C_{2} O_{4}\right) \) in acidic solution is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D.
Subject: Physics
Match the columns:
\( \begin{array}{ll}\text { । } & \text { II } \\ \text { 1. Mass } & \text { a. } m / s^{2} \\ \text { 2. Weight } & \text { b. kilogram } \\ \text { 3. Gravitational acceleration } & \text { c. } N m^{2} k g^{-2} \\ \text {4. Gravitational constant } & \text { d. Newton }\end{array} \)
A. \( 1-a, 2-b, 3-c, 4-d \)
B. \( 1-b, 2-a, 3-d, 4-c \)
c. \( 1-b, 2-d, 3-c, 4-a \)
D. \( 1-b, 2-d, 3-a, 4-c \)
Subject: Physics
A long straight conductor, carrying a
current \( i, \) is bent to form an almost
complete circular loop of radius \( r \) as
shown. The magnetic field at the centre
of the loop:
A \( \cdot \) has magnitude \( \frac{\mu_{0} i}{r}\left(1-\frac{1}{\pi}\right) \)
B. has magnitude \( \frac{\mu_{0} i}{r}\left(1+\frac{1}{\pi}\right) \)
c. has magnitude \( \frac{\mu_{0} i}{2 r}\left(1-\frac{1}{\pi}\right) \)
D. has magnitude \( \frac{\mu_{0} i}{2 r}\left(1+\frac{1}{\pi}\right) \)
Subject: Maths
By Rolles theorem for \( f(x)=(x- \)
\( a)^{m}(x-b)^{n} \) on \( [a, b] ; m, n \) being
positive integer. Find the value of \( c \) which lies between \( a \)
\& b.
A \( \cdot c=\frac{m b+n a}{m+n} \)
в. \( c=\frac{m b-n a}{m+n} \)
c. \( _{c}=\frac{n b+m a}{m+n} \)
D. \( c=\frac{n b-m a}{m+n} \)
Subject: Physics
Velocity of a particle of mass \( 2 \mathrm{kg} \) changes from \( \overrightarrow{\boldsymbol{v}}_{1}=-2 \widehat{\boldsymbol{i}}-\widehat{\boldsymbol{2}} \hat{\boldsymbol{j}} \boldsymbol{m} / \boldsymbol{s} \) to
\( \overrightarrow{\boldsymbol{v}}_{2}=(\widehat{\boldsymbol{i}}-\widehat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} \) after colliding with a
plane surface
This question has multiple correct options
A. the angle made by the plane surface with the positive \( x \) -axis is \( 90^{\circ}+\tan ^{-1}\left(\frac{1}{3}\right) \)
B. the angle made by the plane surface with the positive x-axis is \( \tan ^{-1}\left(\frac{1}{3}\right) \)
C. the direction of change in momentum makes an angle \( \tan ^{-1}\left(\frac{1}{3}\right) \) with the positive \( x \) -axis.
D. the direction of the change in momentum makes an angle \( 90^{\circ}+\tan ^{-1}\left(\frac{1}{3}\right) \) with the plane surface.
Subject: Physics
Two moving coil meters, \( M_{1} \) and \( M_{2} \)
have the following particulars:
\( \boldsymbol{R}_{1}=\mathbf{1 0} \boldsymbol{\Omega}, \boldsymbol{N}_{\mathbf{1}}=\mathbf{3 0} \)
\( \boldsymbol{A}_{\mathbf{1}}=\mathbf{3 . 6} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{m}^{\mathbf{2}}, \boldsymbol{B}_{\mathbf{1}}=\mathbf{0 . 2 5} \boldsymbol{T} \)
\( \boldsymbol{R}_{2}=\mathbf{1 4} \boldsymbol{\Omega}, \boldsymbol{N}_{2}=\boldsymbol{4} \boldsymbol{2} \)
\( \boldsymbol{A}_{2}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{3}}, \boldsymbol{B}_{\mathbf{2}}=\mathbf{0 . 5 0} \boldsymbol{T} \)
(The spring constants are identical for the two meters).Determine the ratio
of (a) current sensitivity and
(b) voltage
sensitivity of \( M_{2} \) and \( M_{1} \)
Subject: Chemistry
The bond dissociation energies of
\( X_{2}, Y_{2} \) and \( X Y \) are in the ratio of 1
\( 0.5: 1 . \Delta H \) for the formation of \( X Y \) is
\( -200 k J m o l^{-1} . \) The bond dissociation
energy of \( \boldsymbol{X}_{2} \) will be:
В. 200 kJ mol-
c. \( 400 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 100 k J mol\( ^{-} \)
Subject: Maths
If \( a+b+c+d+e+f=12 \) then the
maximum value of \( a b+b c+c d+d e+ \)
\( e f+f a \) is \( (a, b, c, d, e, f \) are non
negative real numbers)
A . 36
B . 24
c. 30
D. none of these
Subject: Physics
A sphere of mass \( m \) and radius \( r \) is
pushed onto the fixed horizontal surface such that it rolls without
slipping from the beginning. The
minimum speed v of its mass centre at
the bottom so that it rolls completely around the loop of radius \( (\boldsymbol{R}+\boldsymbol{r}) \)
without leaving the track in between is \( \operatorname{given} \operatorname{as} v=\sqrt{\frac{x}{7} g R} \) Find \( x \)
Subject: Biology
Assertion
Alveoli are the primary sites for
exchange of gases.
Reason
All factors in our body are favourable for
the diffusion of \( O_{2} \) from alveoli to
tissues and that of \( \mathrm{CO}_{2} \) from tissues to
alveoli.
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
If in the ground state an atom has seven valence electrons, which of the following is the correct electronic configuration of the atom in the ground state?
A \( .3 s^{1} 3 p^{6} \)
В. \( 3 s^{6} 3 p^{\text {। }} \)
c. \( 3 s^{1} 3 p^{4} 3 d^{2} \)
D. \( 3 s^{3} 3 p^{4} 3 d^{1} \)
E \( .3 s^{2} 3 p^{5} \)
Subject: Maths
If \( A \) and \( B \) are square matrices of order \( n \)
\( x \) n such that \( A^{2}-B^{2}= \)
\( (A-B)(A+B), \) then of the following
will always be true?
\( A \cdot A=B \)
c. either of A or B is a zero matrix
D. either of A or B is an identify matrix
Subject: Physics
I wo plane mırrors or lengtn \( \boldsymbol{L} \) are
separated by distance \( L \) and a man \( M_{2} \)
is standing at distance \( L \) from the
connecting line of mirrors as shown in
figure. A man \( M_{1} \) is walking in a
straight line at distance \( 2 L \) parallel to
mirrors at speed \( u, \) then \( \operatorname{man} M_{2} \) at 0
will be able to see image of \( M_{1} \) for time
\( A \cdot \frac{4 L}{u} \)
B. \( \frac{3 L}{u} \)
\( c \cdot \frac{6 L}{u} \)
D. \( \frac{9 L}{_{n}} \)
Subject: Maths
Let \( A=\{0,1,2,3\} \) and define a relation \( R \)
as follows
\( R=\{(0,0),(0,1),(0,3),(1,0),(1,1),(2,2) \)
(3,0),(3,3)\}
Is \( \mathrm{R} \) reflexive, symmetric and transitive
\( ? \)
Subject: Physics
The vertical section of a road over a
canal bridge in the direction of its length is in the form of circle of radius \( 8.9 m . \) Then the greatest speed at which the car can cross this bridge without losing contact with the road at its
highest point, the centre of gravity of the car being at a height \( h=1.1 m \)
from the ground (Take \( \left.g=10 m / s e c^{2}\right) \)
A. \( 5 \mathrm{m} / \mathrm{sec} \)
в. \( 10 \mathrm{m} / \mathrm{sec} \)
c. \( 15 \mathrm{m} / \mathrm{sec} \)
D. \( 20 \mathrm{m} / \mathrm{sec} \)
Subject: Physics
State the Krichhoff's law of electric
network. In the figure shown \( \boldsymbol{P}= \) \( 2 \mathrm{ohms} Q=4 \mathrm{ohms}, R=4 \mathrm{ohms} \) and
\( S=2 \) ohms. Resistance between \( C \) and
\( D \) is 1 ohms. Find the current through
each resistance
Subject: Physics
A hammer weighing \( 3 \mathrm{kg}, \) moving with a velocity of \( 10 \mathrm{m} / \mathrm{s}, \) strikes against the head of a spike and drives it into a block of wood. If the hammer comes to
rest in 0.025 s, the impulse associated with the spike will be :
\( A \cdot \) 30 Ns
B. -30Ns
c. 15 Ns
D. -15 Ns
Subject: Chemistry
The product obtained at anode when \( \mathbf{5 0 \%} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{S O}_{\mathbf{4}} \) aqueous solution is
electrolysed using platinum electrodes is :
A. \( H_{2} S O_{3} \)
B. \( H_{2} S_{2} O_{8} \)
\( c \cdot O_{2} \)
D. \( H_{2} \)
Subject: Physics
A point charge \( q \) is brought from infinity(slowly so that the heat developed in the shell is negligible) and is placed at the centre of a conducting
neutral spherical shell of inner radius a and outer radius \( b \), then work done by
external agent is:
\( A \cdot O \)
B. \( \frac{k q^{2}}{2 b} \)
c. \( \frac{k q^{2}}{2 b}-\frac{k q^{2}}{2 a} \)
D. \( \frac{k q^{2}}{2 a}-\frac{k q^{2}}{2 b} \)
Subject: Chemistry
Which of the following ions or molecules has a nonzero dipole moment?
A \( \cdot C O_{2} \)
в. \( N O_{3}^{-} \)
\( \mathbf{c} \cdot P O_{4}^{3-} \)
D. \( S O_{2} \)
E \( . S O_{4}^{2} \)
Subject: Maths
Multiply: \( \left(4 x^{4}-3 x^{2}-7 x+8\right) \) by
\( \left(5 x^{2}-2 x-3\right) \)
Answer: \( 20 x^{6}-8 x^{5}-27 x^{4}-29 x^{3}+ \)
\( 63 x^{2}+5 x-24 \)
A. True
B. False
Subject: Physics
One of the rectangular components of a force of \( 50 \mathrm{N} \) is \( 30 \mathrm{N} \). The other
rectangular component will be :
A. \( 40 \mathrm{N} \)
B. 30 N
\( c . \) 35 \( \mathrm{N} \)
D. 45 N
Subject: Physics
If the angle of projection is \( 60^{\circ}, \) the height of the projectile when it has travelled a distance \( \frac{3 R}{4} \) is \( (R \) is the range)
A \( \cdot \frac{3 \sqrt{3} R}{16} \)
в. \( \frac{2}{3} R \)
c. \( \frac{\sqrt{3} R}{16} \)
D. \( \frac{4}{5} R \)
Subject: Maths
What should be added to \( 5 x^{2}+2 x y+ \)
\( y^{2} \) to get \( 3 x^{2}+4 x y ? \)
A. \( -2 x^{2}+2 x y-y^{2} \)
B . \( x^{2}+2 y-y^{2} \)
C \( .-2 x^{2}+2 y-x y^{2} \)
D. \( x^{2}+2 x y-y^{2} \)
Subject: Maths
The value of \( ^{n} C_{0}+3 \times^{n} C_{1}+9 \times^{n} \)
\( \boldsymbol{C}_{2}+\ldots+\boldsymbol{3}^{n} \times^{n} \boldsymbol{C}_{n} \)
A \( \cdot 2^{n} \)
B. \( 3^{n} \)
\( c \cdot 4^{n} \)
D. \( 5^{n} \)