AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
An alcohol on oxidation gives
\( C H_{3} C O O H \) and \( C H_{3} C H_{2} C O O H . \) The
alcohol is :
A \( \cdot C H_{3} C H_{2} O H \)
в. \( C H_{3} C H(O H) C H_{2} C H_{3} \)
c. \( \left(C H_{3}\right)_{2} C(O H) C H_{2} C H_{3} \)
D. \( C H_{3} C H(O H) C H_{2} C H_{2} C H_{3} \)
Subject: Physics
An object of mass, \( m \) is moving with a constant velocity v. How much work
should be done on the object in order to bring the object to rest?
A \( \cdot-\frac{1}{2} m v^{2} \)
B. \( \frac{1}{2} m v^{2} \)
c. \( -m v^{2} \)
D. \( -\frac{1}{2} m v \)
Subject: Maths
The circumference of a circle is
measured as \( 56 \mathrm{cm} \) with an error 0.02
\( \mathrm{cm} . \) The percentage error in its area is
A \( \cdot \frac{1}{7} \)
в. \( \frac{1}{28} \)
c. \( \frac{1}{14} \)
D. \( \frac{1}{56} \)
Subject: Physics
1 \( g \) mole of an ideal gas at \( S T P \) is subjected to a reversible adiabatic
expansion to double its volume. Find the change in internal energy \( (\gamma=1.4) \)
A. \( 11.695 .5 J \)
в. \( 769.5 J \)
c. \( 1369.5 J \)
D. \( 969.5 J \)
Subject: Physics
The temperature of a gas contained in a closed vessel is increased by \( 2 \mathrm{K} \) when
the pressure is increased by \( 2 \% \). The initial temperature of the gas is :
A. \( 200 k \)
в. 100k
c. \( 200^{\circ} \mathrm{C} \)
D. \( 100^{\circ} \mathrm{C} \)
Subject: Maths
\( \int \sqrt{1+\sin x} d x= \)
A \( \cdot \frac{1}{2}\left(\sin \frac{x}{2}+\cos \frac{x}{2}\right)+c \)
B \( \cdot \frac{1}{2}\left(\sin \frac{x}{2}-\cos \frac{x}{2}\right)+c \)
c. \( 2 \sqrt{1+\sin x}+c \)
D. \( -2 \sqrt{1-\sin x}+c \)
Subject: Chemistry
An open vessel at \( 27^{\circ} \mathrm{C} \) is heated until
\( \left.\frac{2}{5}\right) \) th of the air in it has been expelled. Assuming that the volume of the vessel
remains constant. Which of the
following option is correct?
A. Final temperature is 500 \( \mathrm{K} \)
B. Final volume is 2 times the initial volume
C. Final pressure is 1 atm
D. None of the above
Subject: Chemistry
By which method you can dilute a
concentrated acid properly?
A. Carefully replace unused or excess chemicals into their properly labeled containers from which they came
B. The rule is to add water to the concentrated acid slowly
C. Dispose of chemicals in the proper places following posted procedures. Do not return them to their original containers
D. Flush eyes with water at the eyewash fountain for at least 15 minutes, and then report the accident for further help
E. The rule is to add concentrated acid to water slowly
Subject: Physics
Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as if \( \boldsymbol{v}=\boldsymbol{k}\left(\frac{2 y^{2}}{a^{2}}-\frac{y^{3}}{a^{3}}\right) \) If coefficient of
viscosity for water is \( \eta, \) what will be
shear stress between layers of water at
\( y=a \)
Subject: Chemistry
Standard molar heat of formation of
ethane \( C O_{2} \) and liquid water are -21.1
-94.1 and -68.3 kilo calorie. The value
of standard molar heat of combustion of
ethane will be:
\( \mathbf{A} \cdot-372 \) kcal
B . -272 kcal
c. -172 kcal
D. -472 kcal
Subject: Chemistry
The heat evolved in the combustion of
benzene is given by
\( C_{6} H_{6}(l)+7 \frac{1}{2} O_{2}(g) \rightarrow 3 H_{2} O(l)+ \)
\( \mathbf{6} C O_{2}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{7} \mathbf{8} \mathbf{1} . \mathbf{0} \boldsymbol{K} \boldsymbol{c} \boldsymbol{a} \boldsymbol{l} \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1} \)
When 156 g of \( C_{6} H_{6} \) is burnt in an open container, the amount of heat energy released will be
This question has multiple correct options
A. \( 150.2 \mathrm{kcalmol}^{-1} \)
B . 1562.0 kcalmol-
\( \mathbf{c} \cdot 6528.2 \mathrm{kJmol}^{-1} \)
D. 2448.5 kJmol-
Subject: Physics
The radius of earth is about \( 6400 \mathrm{km} \)
and that ofmars is \( 3200 \mathrm{km} \). The mass
of the earth is 10 times the mass of
mars. An object weight \( 200 \mathrm{N} \) on the surface of earth. Its weight on the
surface of mars will be.
A. 80 N
B. 40 N
\( c . \) 20
\( D \cdot 8 N \)
Subject: Physics
The near point of a myopic eye is \( 15 \mathrm{cm} \) What should be the power of the lens which will enable the eye to read a book
placed at \( 30 \mathrm{cm} ? \)
A. 3.33 dioptre
B. -3.33 dioptre
c. 2.22 dioptre
D. -2.22 dioptre
Subject: Maths
Construct a quadrilateral ABCD, when:
\( \boldsymbol{B C}=\mathbf{7 . 5} \mathrm{cm}, \boldsymbol{A C}=\mathbf{5 . 8} \mathrm{cm}, \boldsymbol{A D}=\mathbf{3 . 6} \)
\( \mathrm{cm} \)
\( C D=4.2 \mathrm{cm} \) and \( A=120^{\circ} \)
Subject: Maths
If the equation of the locus of a point
equidistant from the point \( \left(a_{1}, b_{1}\right) \) and
\( \left(a_{2}, b_{2}\right) \) is \( \left(a_{1}-a_{2}\right) x+\left(b_{1}-b_{2}\right) y+ \)
\( c+0, \) then the value of \( c \) is
A \( \cdot a_{1}^{2}-a_{2}^{2}+b_{1}^{2}-b_{2}^{2} \)
в. \( \sqrt{a_{1}^{2}+b_{1}^{2}-a_{2}^{2}-b_{2}^{2}} \)
c. \( \frac{1}{2}\left(a_{1}^{2}+a_{2}^{2}+b_{1}^{2}+b_{2}^{2}\right. \)
D \( \cdot \frac{1}{2}\left(a_{2}^{2}+b_{2}^{2}-a_{1}^{2}-b_{1}^{2}\right. \)
Subject: Maths
The value of \( x \) satisfying \( \tan \left(\sec ^{-1} x\right)=\sin \left(\cos ^{-1} \frac{1}{\sqrt{5}}\right) \) is
\( ^{A}+\frac{3}{\sqrt{5}} \)
\( ^{\mathrm{B}} \pm \frac{5}{\sqrt{3}} \)
c. \( =\frac{\sqrt{2}}{3} \)
D. \( \pm \frac{3}{5} \)
Subject: Maths
The solution set of the equation \( \sin ^{-1} \sqrt{1-x}+\cos ^{-1} x= \)
\( \cot ^{-1}\left(\frac{\sqrt{1-x^{2}}}{x}\right)-\sin ^{-1} x \)
A \( \cdot[-1,1]-\{0\} \)
B . (0,1]\( \cup\{-1\} \)
c. [-1,0)\( \cup\{1\} \)
D. \{1\}
Subject: Physics
Figure represents two processes, a and
b for a given sample of gas. Let \( \triangle Q_{1} \)
and \( \triangle Q_{2} \) be the heat absorbed by the
systems in the two cases respectively.
Which of the following relations is
correct?
\( \mathbf{A} \cdot \triangle Q_{1}=\triangle Q_{2} \)
B \( \cdot \triangle Q_{1}>\triangle Q_{2} \)
\( \mathbf{c} \cdot \triangle Q_{1} \leq \triangle Q_{2} \)
\( \mathbf{D} \cdot \triangle Q_{1}<\triangle Q_{2} \)
Subject: Chemistry
The freezing point of 0.02 mol fraction of acetic acid in benzene is \( 277.4 K \)
Acetic acid exists partly as a dimer. Calculate the equilibrium constant for dimerization. (approximately)
(Freezing point of \( C_{6} H_{6}=278.4 K \) and
\( \boldsymbol{K}_{f} \) of \( \boldsymbol{C}_{6} \boldsymbol{H}_{6}=\mathbf{5} \boldsymbol{K} \boldsymbol{m}^{-1} \mathbf{)} \)
A . 2.6
в. 3.
c. 4.3
D. 5.8
Subject: Maths
If the circumference (in \( c m \) ) and the
\( \operatorname{area}\left(\operatorname{in} c m^{2}\right) \) of a circle are equal then
find the radius of the circle
A . \( 1 c m \)
в. 2 ст
\( c .3 c m \)
D. \( 4 c m \)
Subject: Physics
yual diape
\( P Q R S^{\prime} \) of dimensions, \( l \times l \) is placed
inside a constant and uniform Magnetic Field \( \vec{B}=B_{0}\left(\frac{1}{\sqrt{2}} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}\right) \) as shown
in the figure such that it's sides are
initially parallel to the \( X \) and \( Y \) axes. Which of the following is the value for the "magnetic flux" associated with the
square loop initially (as in the figure above)?
A \( \cdot \theta_{S}=\frac{B_{0}}{\sqrt{2}} l^{\prime} \)
В . \( \theta_{s}=B_{0} l \)
c. \( \theta_{\mathrm{s}}=0 \)
D. \( \theta_{S}=\sqrt{2} B_{0} l^{2} \)
Subject: Maths
f \( \boldsymbol{y}=(\mathbf{1}+\boldsymbol{x})\left(\mathbf{1}+\boldsymbol{x}^{2}\right)\left(\mathbf{1}+\boldsymbol{x}^{4}\right) \dots(\mathbf{1}+ \)
\( \left.x^{2^{n}}\right), \) then \( \frac{d y}{d x} \) at \( x=0 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. none of these
Subject: Physics
Which of the following gates corresponds to the truth table given below?
\( A B Y \)
\[
\begin{array}{ccc}
1 & 1 & 0 \\
1 & 0 & 1 \\
0 & 1 & 1
\end{array}
\]
\( 0 \quad 0 \quad 1 \)
A. xor
в. ок
c. NAND
D. NOR
Subject: Physics
If a soap bubble, having radius \( r, \) is
charged to a charge density \( \sigma \) and its
increased to \( R \), then \( R \) equals to
\( [T \) is the surface tension]
A \( \cdot R=\frac{9 \varepsilon_{0} T}{\sigma^{2}} \)
в. \( \quad R=\frac{8 \varepsilon_{0} T}{\sigma^{2}} \)
c. \( R=\frac{10 \varepsilon_{0} T}{\sigma^{2}} \)
D. \( R=\frac{11 \varepsilon_{0} T}{\sigma^{2}} \)
Subject: Maths
If \( \vec{b} \) is the vector whose initial point divides the joining \( 5 \hat{i} \) and \( 5 \hat{j} \) in the ratio \( \lambda: 1 \) and terminal point is at origin. If \( |\vec{b}| \leq \sqrt{37}, \) then \( \lambda \in \)
\( ^{\mathbf{A}} \cdot(-\infty,-6] \cup\left[-\frac{1}{6}, \infty\right) \)
B \( \cdot(-\infty,-3) \cup\left[-\frac{1}{4}, \infty\right) \)
\( ^{\mathbf{c}} \cdot(-\infty, 0) \cup\left(\frac{1}{2}, \infty\right) \)
D. \( \left[-6,-\frac{1}{6}\right] \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{A}+\mathbf{2} \boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{0} \\ \mathbf{6} & -\mathbf{3} & \mathbf{3} \\ \mathbf{- 5} & \mathbf{3} & \mathbf{1}\end{array}\right] \) and
\( \mathbf{2} \boldsymbol{A}-\boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{2} & \mathbf{- 1} & \mathbf{5} \\ \mathbf{2} & -\mathbf{1} & \mathbf{6} \\ \mathbf{0} & \mathbf{1} & \mathbf{2}\end{array}\right] \) then Det
\( \operatorname{Tr}(A)-\operatorname{Tr}(B)) \) has the value equal to
\( A \)
B.
\( c \)
\( D \)
Subject: Physics
Acceleration due to gravity at surface of a planet is equal to that at surface of
the earth and density is 1.5 times that of earth. if radius of earth is \( R \), radius of
planet is
A \( \cdot \frac{R}{1.5} \)
в. \( \frac{2}{3} R \)
c. \( \frac{9}{4} R \)
D. \( \frac{4}{9} R \)
Subject: Maths
Let \( M \) and \( N \) be two \( 3 \times 3 \) non-singular
skew-symmetric matrices such that
\( M N=N M . \) If \( P^{T} \) denotes the
transpose of \( P, \) then
\( M^{2} N^{2}\left(M^{T} N\right)^{-1}\left(M N^{-1}\right)^{T} \) is equal to
A \( . M^{2} \)
B. \( -N^{2} \)
c. \( -M^{2} \)
D. \( M N \)
Subject: Chemistry
Which of the following orbitals are
degenerate?

This question has multiple correct options
\( \mathbf{A} \cdot 4 d_{x y}, 3 d_{y z}, 4 d_{y z}, 4 d_{z 2} \)
B. \( 3 d_{y z}, 4 d_{y z} \)
\( \mathbf{c} \cdot 3 d_{x y}, 3 d_{y z} \)
D. \( 4 d_{d y}, 4 d_{d z}, 4 d_{d z}^{2} \)
Subject: Physics
The electric field in a region is radially outwards and has a magnitude \( \boldsymbol{E}=\boldsymbol{K} \boldsymbol{r} \)
The charge contained in a sphere of radius \( a \) is :
A. \( K 4 \pi \varepsilon_{0} a^{2} \)
В \( \cdot \quad K \frac{4}{3} \pi \varepsilon_{0} a^{3} \)
c. \( K 4 \pi \varepsilon_{0} a^{3} \)
D. none of these
Subject: Chemistry
The electronegativity order increases in the order:
A. \( \mathrm{C}, \mathrm{N}, \mathrm{Si}, \mathrm{P} \)
B. \( N, \) Si, \( C, P \)
c. \( \mathrm{si}, \mathrm{P}, \mathrm{C}, \mathrm{N} \)
D. \( P, \) Si, \( N, C \)
Subject: Chemistry
The gas \( A_{2} \) in the left flask is allowed to
react with gas \( B_{2} \) presence in right
flask as \( A_{2}(g)+B_{2}(g) \rightleftharpoons \)
\( 2 A B(g) ; K_{c}=4 \) at \( 27^{\circ} C . \) What is the
concentration of \( A B \) when equilibrium is established?
A. 1.33 м
в. 2.66
\( c .0 .66 \)
\( 0.0 .33 \mathrm{m} \)
Subject: Maths
The measure of an angle is three times the measure of its complement. The angles are:
A \( \cdot 20^{\circ}, 60^{\circ} \)
B. \( 30^{\circ}, 60^{\circ} \)
c. \( 45^{\circ}, 135^{\circ} \)
D . 22.5^, 67.5 \( ^{\circ} \)
Subject: Physics
A particle executes simple harmonic
motion with an amplitude of \( 4 \mathrm{cm} . \) At the mean position the velocity of the particle is \( 10 \mathrm{cm} / \mathrm{s} \). The distance of the particle from the mean position when its speed becomes \( 5 \mathrm{cm} / \mathrm{s} \) is
A \( \cdot \sqrt{3} \mathrm{cm} \)
B. \( \sqrt{5} \mathrm{cm} \)
c. \( \pm 2(\sqrt{3}) \) cm
D. \( 2(\sqrt{5}) \mathrm{cm} \)
Subject: Maths
In the adjoining figure, \( A B C D \) is an
isosceles trapezium. If \( \angle A= \)
\( \mathbf{6 0}^{\circ}, \boldsymbol{D C}=\mathbf{2 0} \boldsymbol{c m} \) and \( \boldsymbol{A} \boldsymbol{D}=\mathbf{1 5} \boldsymbol{c m} \)
find the length of \( \boldsymbol{A B} \)
Subject: Chemistry
Assertion
\( O_{2} \) molecule is diamagnetic while \( C_{2} \)
molecule is paramagnetic in nature
Reason

Bond order of \( O_{2} \) molecule is 1.5 and
that of \( C_{2} \) molecule is 2.5
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
Two moles of \( P C l_{5} \) were heated to
\( 327^{\circ} \mathrm{C} \) in a closed two litre vessel and
when equilibrium was achieved, \( \boldsymbol{P C l}_{5} \)
was found to be \( 40 \% \) disociated into
\( P C l_{3} \) and \( C l_{2} . \) Calcutta the equilibrium
constant \( \left(\boldsymbol{K}_{c}\right) \) for the reaction.
Subject: Maths
Let \( f \) be a continuous function on \( \mathrm{R} \)
satisfying \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \) for all
\( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and \( \boldsymbol{f}(1)=\boldsymbol{4} \) then \( \boldsymbol{f}(\boldsymbol{3}) \) is
equal to
Subject: Physics
Q Type your question.
is earthed. \( C \) is the common center of \( A \)
and \( B . \) Study the following statements.
Which of the following statements are
correct?

The potential at a distance \( r \) from \( C \) where \( a \leq r \leq b, i s \frac{1}{4 \pi \varepsilon_{0}}\left(\frac{Q}{r}\right) \)
i. The potential difference between \( A \) and
\( B \) is \( \frac{1}{4 \pi \varepsilon_{0}} Q\left(\frac{1}{a}-\frac{1}{b}\right) \)
iii. The potential at a distance \( r \) from \( C \) where \( a \leq r \leq b, i s \frac{1}{4 \pi \varepsilon_{0}} Q\left(\frac{1}{a}-\frac{1}{b}\right) \)
A. Only (i) and (ii)
B. Only (ii) and (iii)
c. only (i) and (iii)
Dhe above
Subject: Maths
A mapping from \( N \) to \( N \) is defined as follows
\( \boldsymbol{f}: \boldsymbol{N} \longrightarrow \boldsymbol{N} \)
\( \boldsymbol{f}(\boldsymbol{n})=(\boldsymbol{n}+\mathbf{5})^{2}, \boldsymbol{n} \in \boldsymbol{N} \)
\( (N \) is the set of natural numbers). Then,
A. \( f \) is not one to one
B. \( f \) is onto
c. \( f \) is both one to one and onto
D. \( f \) is one to one but not onto
Subject: Physics
A point object is placed at a distance of \( 12 \mathrm{cm} \) on the axis of a convex lens of
focal length \( 10 \mathrm{cm} . \) On the other side of the lens, a convex mirror is placed at a distance of \( 10 \mathrm{cm} \) from the lens such that the image formed by the combination coincides with the object
itself. The focal length of the convex
mirror is
\( A \cdot 20 \mathrm{cm} \)
B. 25 cm
\( c . \) 30 \( \mathrm{cm} \)
D. 22 cm
Subject: Biology
Complete the following sentence by selecting the correct option. The breathing rhythm is generated in the \( _{--}(i)_{--} \) and is influenced by variation in levels of \( _{--}\left(\text {ii) }_{---} \) in the \right.
blood.
A. (i)medulla \( \left(\text { ii) } C O_{2}\right. \)
B . (i)medulla \( \left(\text { ii) } O_{2}\right. \)
c. (i)frontal lobe
(ii) \( C O_{2} \) and \( O_{2} \)
D. (i)frontal lobe
(ii) \( C O_{2} \)
Subject: Maths
An ellipse has its centre at (1,-1) and semi-major axis \( =8 \) and it passes
through the point \( (1,3) . \) The equation of the ellipse is
A \( \cdot \frac{(x+1)^{2}}{64}+\frac{(y+1)^{2}}{16}=1 \)
в. \( \frac{(x-1)^{2}}{64}+\frac{(y+1)^{2}}{16}=1 \)
c. \( \frac{(x-1)^{2}}{16}+\frac{(y+1)^{2}}{64}=1 \)
D. \( \frac{(x+1)^{2}}{64}+\frac{(y-1)^{2}}{16}=1 \)
Subject: Maths
One pendulum ticks 57 times in 58 seconds and another 608 times in 609
seconds. If they start simultaneously, find the time after which will they tick
together?
A \( \cdot \frac{211}{19} \)
в. \( \frac{1217}{19} s \)
c. \( \frac{1218}{19} s \)
D. \( \frac{1018}{19} s \)
Subject: Physics
The displacement y of a wave traveling in the X-direction is given by \( \boldsymbol{y}= \) \( 10^{-4} \sin \left(600 t-2 x+\frac{\pi}{3}\right) \) metres. where
\( x \) is expressed in metres and \( t \) in
seconds. The speed of the wave motion
\( \operatorname{in} m s^{-1} \) is:
A . 200
в. 300
c. 600
D. 1200
Subject: Physics
The angle made by \( \overrightarrow{\mathrm{j}}+\overrightarrow{\mathrm{k}} \) with \( \mathrm{y} \) -axis is:
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. \( 90^{\circ} \)
Subject: Chemistry
n-Propyl alcohol is obtained on hydrolysis of the adduct obtained by the
reaction of:
A. EtMgX and HCHO
B. MeMgX and \( \left(C H_{2}\right)_{2} O \)
\( \mathrm{C} \cdot \mathrm{EtMgX} \) and \( \mathrm{O}_{2} \)
D. мeMgx and \( C H_{3} C H O \)
Subject: Maths
In Fig. arcs have been drawn of radius
\( 21 \mathrm{cm} \) each with vertices \( A, B, C \) and \( D \)
of the square \( A B C D \) as centres. The
area of the shaded region is
\( \mathbf{A} \cdot 693 \mathrm{cm}^{2} \)
B. \( 346.5 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 2772 \mathrm{cm}^{2} \)
D. \( 1386 \mathrm{cm}^{2} \)
Subject: Chemistry
Formation of a solution from two
components can be considered as:
(i) Pure solvent \( \rightarrow \) separated solvent
molecules, \( \Delta \boldsymbol{H}_{\mathbf{1}} \)
(ii) Pure solvent \( \rightarrow \) separated solute
molecules, \( \Delta \boldsymbol{H}_{2} \)
(ii) Separated solvent and solute
molecules \( \rightarrow \) solution, \( \Delta \boldsymbol{H}_{3} \)

Solution so formed will be ideal if
\( \mathbf{A} \cdot \Delta H_{s o l n .}=\Delta H_{1}+\Delta H_{2}+\Delta H_{3} \)
B. \( \Delta H_{\text {soln.}}=\Delta H_{1}+\Delta H_{2}-\Delta H_{3} \)
C \( . \Delta H_{\text {soln.}}=\Delta H_{1}-\Delta H_{2}-\Delta H_{3} \)
D. \( \Delta H_{\text {soln.}}=\Delta H_{3}-\Delta H_{1}-\Delta H_{2} \)
Subject: Physics
See the diagram. Area of each plate is
\( 2.0 m^{2} \) and \( d=2 \times 10 \times 10^{-3} m . \)
charge of \( 8.85 \times 10^{-8} C \) is given to \( Q \)
Then the potential of \( Q \) becomes:
\( \mathbf{A} \cdot 13 V \)
B. 10v
c. \( 66.7 \mathrm{V} \)
D. \( 8.825 v \)
Subject: Maths
\( \int \frac{d x}{\sqrt{2 e^{x}-1}} \) equals to
A \( \cdot \sec ^{-1} \sqrt{2 e^{x}}+c \)
B・sec-1 \( \left(\sqrt{2} e^{x}\right)+c \)
\( \mathbf{c} \cdot 2 \sec ^{-1}\left(\sqrt{2} e^{x}\right)+c \)
D. \( 2 \sec ^{-1} \sqrt{2 e^{x}}+c \)
Subject: Physics
Assertion
When the electric current in a loop of wire changes, the changing current
creates a changing magnetic field.
Reason
Magnetic field lines of a circular loop of
wire is same as a magnet.
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
The electric potential at the surface of an atomic nucleus \( (z=50) \) of radius
\( 9.0 \times 10^{-13} \mathrm{cm} \) is:
A \( \cdot 9 \times 10^{5} \) volt
B. \( 8 \times 10^{6} \) volt
c. 80 volt
D. 9 volt
Subject: Chemistry
The rate of change in concentration of \( C \) in the reaction \( 2 A+B \rightarrow 2 C+3 D \)
was reported as 1.0 mol litre \( ^{-1} \) sec \( ^{-1} \)
Calculate the reaction rate.
A. 0.05 mol litre \( ^{-1} \) sec \( ^{-1} \)
B. 0.01 mol litre \( ^{-1} \) sec \( ^{-1} \)
c. 0.5 mol litre \( ^{-1} \) sec \( ^{-1} \)
D. 5 mol litre \( ^{-1} \) sec \( ^{-1} \)
Subject: Physics
A block of mass \( 1 \mathrm{Kg} \) is connected with a fixed wall through a light spring of constant \( \mathrm{K}=100 \mathrm{n} / \mathrm{m} . \) The surface are
frictionless. Initially spring is in relaxed position. A horizontal force \( F \) of 50 N is applied on the block. Find the maximum
elongation of the spring.
Subject: Maths
The area bounded by \( \boldsymbol{y}=\mathbf{2}- \) \( |2-x|, y=\frac{3}{|x|} \) is
\( ^{\text {A } \cdot \frac{5-4 \ln 2}{3} . \text { sq.unit }} \)
B. \( \frac{2-\ln 3}{2} . \) sq.unit
c. \( \frac{4-3 \ln 3}{2} \). sq.unit
D. none of these
Subject: Physics
Two persons \( A \) and \( B \) wear glasses of
optical powers (in air) \( P_{1}=+2 D \) and
\( P_{2}=+1 D \) respectively. The glasses
have refractive index \( 1.5 . \) Now they jump into a swimming pool and look at each other. B appears to be present at distance \( 2 m(f r o m A) \) to \( A . A \) appears to
be present at distance \( 1 \mathrm{m} \) (from B) to B,
then
This question has multiple correct options
A. Refractive index of water is 1.2
B. Actual distance between A and B is \( \frac{200}{3} \mathrm{cm} \)
c. Actual distance between A and B is 50 cm
D. Combined power of two glass (when placed in contact in air) is \( +3 D \)
Subject: Physics
A mass m starting from A reaches B of
frictionless track. On reaching B, it pushes the track with a force equal to \( x \)
times its weight, then the applicable relation is :
A \( n=\frac{(5-x)}{2} \)
в. \( h=\frac{x}{2} R \)
\( c \cdot h=R \)
' \( h=\left(\frac{x+1}{2}\right) R \)
Subject: Maths
A spherical iron ball \( 10 \mathrm{cm} \) in radius is
coated with a layer of ice of uniform
thickness that melts at a rate of \( 50 \mathrm{cm}^{3} \)
/min. When the thickness of ice is \( 5 \mathrm{cm} \)
then the rate at which the thickness of
ice decreases, is
\( ^{A} \cdot \frac{1}{18 \pi} \mathrm{cm} / \mathrm{min} \)
B. \( \frac{1}{36 \pi} \mathrm{cm} / \mathrm{min} \)
c. \( \frac{5}{6 \pi} \mathrm{cm} / \mathrm{min} \)
D. \( \frac{1}{54 \pi} \mathrm{cm} / \mathrm{min} \)
Subject: Chemistry
Assertion
The solubility of a solid in a liquid increases with increase of pressure.
Reason

Solubility of gas in a liquid is directly proportional to the pressure of the gas.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Assertion
Frictional force is independent of the
velocity of the body
Reason
Friction is due to surface irregularities.
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
(i) If \( \vec{a} \times \vec{b}=\vec{c} \times \vec{d} \) and \( \vec{a} \times \vec{c}=\vec{b} \times \vec{d} \)
show that \( \vec{a}-\vec{d} \) and \( \vec{b}-\vec{c} \) are paralle
(ii) Find the direction cosines of the line
joining (2,-3,1) and (3,1,-2)
Subject: Maths
\( \int_{0}^{16} \frac{x^{1 / 4} d x}{1+\sqrt{x}} \) is equal to
\( \mathbf{A} \cdot 4 / 3+\tan ^{-1} 2 \)
B. \( 8 / 3+4 \tan ^{-1} 2 \)
\( c \cdot 2 / 3+\tan ^{-1} 2 \)
D. None
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{\sin x-\frac{x}{6}}{6 x}=? \)
A \( \cdot \frac{5}{36} \)
B. \( \frac{2}{360} \)
c. \( \frac{7}{360} \)
D. \( \frac{11}{360} \)
Subject: Maths
If \( \boldsymbol{x}^{\mathbf{3}}-\boldsymbol{a} \boldsymbol{x}^{\mathbf{2}}+\boldsymbol{b} \boldsymbol{x}- \)
\( \boldsymbol{6} \) is exactly divisible by \( \boldsymbol{x}^{2}- \)
\( \mathbf{5 x + 6 . t h e n} \frac{a}{b} \) is
A. an integer
B. an irrational number
\( c \cdot \frac{6}{11} \)
D.
Subject: Physics
A car starts from rest to cover distance
\( s . \) The coefficient of kinetic friction
between the road and tire is \( \mu \). The
minimum time in which the car cover
the distance \( s \) is proportional to
\( A \cdot \mu \)
B. \( \sqrt{\mu} \)
\( c \cdot \frac{1}{\mu} \)
D. \( \frac{1}{\sqrt{\mu}} \)
Subject: Maths
The value of \( \lim _{n \rightarrow \infty}\left(\frac{1}{\sqrt{4 n^{2}-1}}+\frac{1}{\sqrt{4 n^{2}-4}}+\dots+\frac{ }{\sqrt{3}}\right. \)
is.
A \( \cdot \frac{1}{4} \)
B. \( \frac{\pi}{12} \)
c.
D.
Subject: Maths
The limit of the following is \( \lim _{x \rightarrow 3} \frac{\sqrt{1-\cos \left(x^{2}-10+21\right)}}{x-3} \)
\( A \cdot_{-}(2)^{\frac{3}{2}} \)
B・(2)
c. \( (2)^{-\frac{3}{2}} \)
D.