AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Assertion
A light ray is incident on a glass slab.
Some portion of its is reflected and portion of it is reflected and some is refracted. Refracted and reflected rays
are always perpendicular to each other.
Reason

Angle of incidence is equal to angle of
reflection.
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: Maths
Consider the expansion \( \left(x^{2}+\frac{1}{x}\right)^{15} \) Consider the following statements:
1. There are 15 terms in the given expansion.
2. The coefficient of \( x^{12} \) is equal to that
of \( x^{3} \)

Which of the statements is/are correct
\( ? \)
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Chemistry
Consider the process involving gaseous species,
Process \( \mid: C l+e^{-} \rightarrow C l^{-} \)
Process II: \( N a^{+}+e^{-} \rightarrow N a \)
Process III: \( \boldsymbol{S}^{-}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{S}^{2-} \)
Process IV: \( \boldsymbol{K} \rightarrow \boldsymbol{K}^{+}+\boldsymbol{e}^{-} \)
The process in which size of product is
less than reactant?
\( A \)
B. ॥
c. ॥
D. IV
Subject: Physics
The magnetic tield at the centre ot a
circular coil of radius \( r \) is \( \pi \) times that
due to a long straight wire at a distance
r from it, for equal currents. Figure
shows three cases. In all cases the
circular path has radius r and straight
ones are infinitely long. For same
current the \( \mathrm{B} \) field at the centre \( \mathrm{P} \) in
cases 1,2,3 has the ratio:
\( ^{\mathbf{A}} \cdot-\left(\frac{\pi}{4}+\frac{1}{2}\right):\left(\frac{\pi}{2}\right):\left(\frac{3 \pi}{4}-\frac{1}{2}\right) \)
B \( \cdot\left(-\frac{\pi}{2}+1\right):\left(\frac{\pi}{2}+1\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)
\( \mathbf{C} \cdot-\frac{\pi}{2}: \frac{\pi}{2}: \frac{3 \pi}{4} \)
D \( \cdot\left(-\frac{\pi}{2}-1\right):\left(\frac{\pi}{2}-\frac{1}{4}\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)
Subject: Physics
At what temperature will the resistance of a copper wire become three times its value at \( 0^{\circ} \mathrm{C} \) [Temperature coefficient of
resistance for copper \( =4 \times 10^{-3} \) per \( ^{\circ} \mathrm{C} \)
]:
\( \mathbf{A} \cdot 400^{\circ} \mathrm{C} \)
B . \( 450^{\circ} \mathrm{C} \)
c. \( 500^{\circ} \mathrm{C} \)
D. \( 550^{\circ} \mathrm{C} \)
Subject: Chemistry
Among the following the number of
compounds that can react with \( P C l_{5} \) to
give \( P O C l_{3} \) is :
\( \boldsymbol{O}_{2}, \boldsymbol{C} \boldsymbol{O}_{2}, \boldsymbol{S} \boldsymbol{O}_{2}, \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{P}_{4} \boldsymbol{O}_{10} \)
A
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
When \( 1.375 g \) of cupric oxide is reduced on heating in a current of hydrogen, the weight of copper remaining \( 1.098 g . \) In another experiment, \( 1.179 g \) of copper is dissolved in nitric acid and resulting
copper nitrate converted into cupric oxide by ignition. The weight of cupric oxide formed is \( 1.476 g \). This is in agreement with:
A. Law of definite proportion
B. Law of mass conservation
c. Law of momentum conservation
D. None of the above
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{\alpha} \log \boldsymbol{x} \) for \( \boldsymbol{x}>\mathbf{0} \) and \( \boldsymbol{f}(\boldsymbol{x}) \)
follows Rolle's theorem for [0,1] then \( \alpha \)
is :
A . -2
B. -
c. 0
D. \( 1 / 2 \)
Subject: Physics
In Young's double slit experiment, the fringe width is \( \beta . \) If the entire
arrangement is placed in a liquid of refractive index \( \mu, \) the fringe width will become
A. \( \mu \beta \)
в. \( \frac{\beta}{\mu} \)
\( c \cdot \frac{\beta}{\mu+1} \)
D. \( \frac{\beta}{\mu-1} \)
Subject: Maths
Find the order and degree, if defined of
the differential equation
\( \left(\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}\right)^{3}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}+\sin \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\mathbf{1}=\mathbf{0} \)
Subject: Maths
A swimming pool is to be drained for cleaning. If L represents the number of liters of water in the pool t seconds after
the pool has been plugged off to drain and \( L=200(10-t)^{2} . \) What is the
average rate at which the water flows out during the first 5 seconds \( \left(\frac{\text {litres}}{\text {sec}}\right) \)
7
Subject: Physics
A particle of mass \( m \) moves uniformly
with a speed \( v \) along a circle of radius \( r \)
\( A \) and \( B \) are two points on the circle, such that the arc AB subtends an angle
\( \theta \) at the center of the circle. The
magnitude of change in momentum as the particle moves from \( A \) to \( B \) is given by:
A \( \cdot 2 m v \sin \left(\frac{\theta}{2}\right) \)
в. \( 2 m v \cos \left(\frac{\theta}{2}\right) \)
c. zero
D. 2 mvtan\( \left(\frac{\theta}{2}\right) \)
Subject: Chemistry
Which of the following leads to formation of \( 1^{0} \) alcohol?
A \( \cdot C H_{3}-C H=C H_{2} \frac{H_{2} O}{H^{+}} \)
B. \( C H_{3}-C H=C H_{2} \frac{N a B H_{4} / O H^{\circ}}{H g\left(O A c_{2} / T H F\right.} \)
c. \( C H_{3}-C H=C H_{2} \frac{H_{2} Q_{2} / O H^{6}}{B_{2} H_{6} / T H F} \)
D. \( C H_{3}-C \equiv C-C H_{3} \) dil.Haso \( _{\text {di.HgS }} \),
Subject: Maths
Assume that \( P(A)=P(B) . \) Show that
\( A=B \) Is it true that for any sets \( A \) and
\( \boldsymbol{B}, \boldsymbol{P}(\boldsymbol{A}) \cup \boldsymbol{P}(\boldsymbol{B})=\boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) ? \) Justify
Subject: Biology
Match the following and choose the
correct option from below.
A. Cuticle
(i) Guard cells
B. Bulliform cells
(ii) single layer
C. Stomata
(iii) Waxy layer
D. Epidermis
(iv) Empty colourless cell
\( A \cdot A-(\text { iii) }, B-(i v), C-(i), D-(i i) \)
B. A-(i), B-(ii), C-(iii), D-(iv)
C. \( A-(\text { ii }), B-(i i), C-(i v), D-(i) \)
D. A-(iii), B-(ii), C-(i), D-(iv)
Subject: Physics
The potential at a point P due to an electric dipole is \( 1.8 \times 10^{5} V . \) If \( P \) is at a
distance of \( 50 \mathrm{cm} \) apart from the centre O of the dipole and if CP makes an
angle \( 60^{\circ} \) with the positive side of the
axial line of the dipole, what is the moment of the dipole?
A. \( 10 \mathrm{c}-\mathrm{m} \)
B. \( 10^{-3} \mathrm{c}-\mathrm{m} \)
\( c \cdot 10^{-4} c-m \)
D. \( 10^{-5} \mathrm{c}-\mathrm{m} \)
Subject: Physics
According to laws of refraction,
refraction of light at the boundary
between two different regions follow:
A. that the incident ray, the normal at the point of incidence and the refracted ray, all lie in the same plane.
B. that for a given pair of media and given colour of light. the ratio of the sine of angle of incidence to the sine of angle of refraction is constant.
C. both \( A \) and \( B \)
D. neither A nor B
Subject: Maths
Find the altitude of an equilateral triangle of side \( 5 \sqrt{3} c m \)
A \( .7 .5 \mathrm{cm} \)
в. \( 12.5 \mathrm{cm} \)
\( \mathrm{c} .9 .5 \mathrm{cm} \)
D. \( 8.5 \mathrm{cm} \)
Subject: Maths
The equation to the hyperbola of given
transverse axis whose vertex bisects
the distance between the centre and
focus, is given by
A \( \cdot 3 x^{2}-y^{2}=3 a^{2} \)
B . \( x^{2}-3 y^{2}=a^{2} \)
c. \( x^{2}-y^{2}=3 a^{2} \)
D. None of these
Subject: Maths
Prove the following by using the first
principle \( \mathbf{1}+\mathbf{3}+\mathbf{3}^{2}+\ldots \ldots+\mathbf{3}^{n-1}=\frac{\left(\mathbf{3}^{n}-\mathbf{1}\right)}{\mathbf{2}} \)
Subject: Chemistry
Which are true for the reaction: \( A_{2} \rightleftharpoons \)
\( 2 C+D ? \)
This question has multiple correct options
A . If \( \Delta H=0 ; K_{p} \) increases with temperature and dissociation temperature.
B . If \( \Delta H=+v e ; K_{p} \) increases with temperature and dissociation of \( A_{2} \) increases
C . If \( \Delta H=-v e ; K_{p} \) increases with temperature and
dissociation of \( A_{2} \) decreases
D・ \( K_{p}=4 \alpha^{3}\left[\frac{P}{1+2 \alpha}\right]^{2} \)
Subject: Physics
A line source emits a cylindrical expanding wave. If the medium absorbs no energy then the amplitude will vary with distance \( r \) from the source as
proportional to
A \( \cdot r^{-1} \)
B . \( r^{-2} \)
\( c \cdot r^{-1 / 2} \)
\( \mathbf{D} \cdot r^{1 / 2} \)
Subject: Physics
The force on a particle of mass \( 10 g \) is \( (10 \hat{i}+5 \hat{j}) N . \) If it starts from rest, what
would be its position at time \( t=5 s ? \)
A . \( (12500 \hat{i}+6250 \hat{j}) m \)
B. \( (6250 \hat{\imath}+12500 \hat{j}) m \)
c. \( (12500 \hat{i}+12500 \hat{j}) m \)
D. \( (6250 \hat{i}+6250 \hat{j}) m \)
Subject: Physics
A lens is made of flint glass (refractive index \( =1.5 \) ). When the lens is immersed in a liquid of refractive index 1.25, the focal length:
A. Increases to a factor of 1.25
B. Increases to a factor of 2.5
c. Increases to a factor of 1.2
D. Decreases to a factor of 1.2
Subject: Physics
A number of thin prism of prism angle \( A \) and refractive index \( \mu \) are arranged
on periphery of circle such that any light ray entering from one prism move along a regular polygon
A. number of prism used will be \( \frac{4 \pi}{(\mu-1) A} \)
B. If \( A \) is rational, \( \mu \) must be rational
c. if \( A \) is rational, \( \mu \) must be irrational
D. If \( A \) is irrational, \( \mu \) must be irrational
Subject: Chemistry
The reaction \( \boldsymbol{C r}_{2} \boldsymbol{O}_{3}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{l} \rightarrow \boldsymbol{A l}_{2} \boldsymbol{O}_{3}+ \)
\( 2 C r\left(\triangle G^{0}=-421 k J\right) \) is
thermodynamically feasible due to -ve
value of \( \triangle G . \) Why does this reaction not take place at room temperature?
A. Certain amount of activation energy is essential for thermodynamically feasible reactions also.
B. Due to high melting point of chromium oxide the reaction does not take place
c. overall value of \( \triangle G \) for the net reaction becomes positive
D. Molecules of \( C r_{2} O_{3} \) and \( A \) l are not oriented properly
Subject: Physics
Three identical point charges, each of mass \( \mathrm{m} \) and charge \( \mathrm{q}, \) hang from three strings as shown in figure and assume
the system is in equilibrium. The value of \( q \) in terms of \( m, L, \) and is:
A \( \cdot q=\sqrt{(16 / 5) \pi \varepsilon_{0} m g L^{2} \sin ^{2} \theta \tan \theta} \)
в. \( q=\sqrt{(16 / 25) \pi \varepsilon_{0} m g L^{2} s i n^{2} \theta \tan \theta} \)
c. \( q=\sqrt{(15 / 16) \pi \varepsilon_{0} m g L^{2} s i n^{2} \theta \tan \theta} \)
D. none of these
Subject: Physics
A small circular loop of conducting wire
has radius \( a \) and carries current \( I \). It is
placed in a uniform magnetic field \( \boldsymbol{B} \) perpendicular to its plane such that
when rotated slightly about its
diameter and replaced, it starts performing simple harmonic motion of time period \( T . \) If the mass of the loop is
\( m \) then:
\( ^{\mathbf{A}} \cdot_{T}=\sqrt{\frac{2 m}{I B}} \)
в. \( T=\sqrt{\frac{\pi m}{I B}} \)
\( ^{\mathrm{c}} \cdot T=\sqrt{\frac{2 \pi m}{I B}} \)
D \( \cdot T=\sqrt{\frac{\pi m}{2 I B}} \)
Subject: Physics
In an experiment to measure focal length of a concave mirror, the values of focal length in successive observations are \( 17.3 \mathrm{cm}, 17.8 \mathrm{cm}, 18.3 \mathrm{cm}, 18.2 \mathrm{cm} \)
\( 17.9 \mathrm{cm} \) and \( 18.0 \mathrm{cm} . \) Calculate mean
absolute error and percentage error Express the result in a proper way
Subject: Biology
Which of the following is the correct pathway for propagation of cardiac impulse?
A. SA node \( \rightarrow \) AV node \( \rightarrow \) Bundle of His \( \rightarrow \) Purkinje fibers
B. AV node \( \rightarrow \) Bundle of His \( \rightarrow \) SA node \( \rightarrow \) Purkinje fibers
c. sa node \( \rightarrow \) Purkinje fibers \( \rightarrow \) AV node \( \rightarrow \) Bundle of His
D. Purkinje fibers \( \rightarrow \) AV node \( \rightarrow \) SA node \( \rightarrow \) Bundle of Hiss
Subject: Maths
The value of
\( \sin 10^{\circ} \sin 30^{\circ} \sin 50^{\circ} \sin 70^{\circ} \) is:
\( ^{A} \cdot \frac{1}{36} \)
в. \( \frac{1}{32} \)
c. \( \frac{1}{18} \)
D. \( \frac{1}{16} \)
Subject: Chemistry
Which of the following configuration
represents a noble gas?
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 f^{14} 5 s^{2} \)
\( \mathbf{c} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} 5 p^{6} \)
D \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} 5 p^{3} \)
Subject: Chemistry
Find out the EMF of the following cells at \( 25^{0} \mathrm{C} \)
\( p t, B r_{2(l)}\left|B r^{-}(0.010 M)\right|\left|H^{+}(0.030 M)\right| H_{2}(1 a \)
\( \$ \$ 1 \) binom \( \left\{E\{\{0\}\}_{-}\left\{B r_{-}\{2\} / 2 B r^{\wedge}\{-\}\right\}=+1.08\right. \)
\( \left.V, R=8.314 J K^{\wedge}\left\{-\left.1 m o\right|^{\wedge}\{-1\}\right\},\right\} \)
\( \left\{F=96,\left.500 C m o\right|^{\wedge}\{-1\}\right\} \$ \)
A. \( 0.872 v \)
\( v \)
B . -0.872v
c. -1.052v
D. 1.288v
Subject: Physics
Electric field and magnetic field in a region of space is given by \( \vec{E}=E_{o} \hat{j} \) and
\( \vec{B}=B_{o} \hat{j} \cdot A \) particle of specific charge \( \alpha \)
is released from origin with velocity \( \vec{v}=v_{o} \hat{i} \).Then path of particle.
Note- \( \boldsymbol{E}_{\boldsymbol{o}}, \boldsymbol{B}_{\boldsymbol{o}} \) and \( \boldsymbol{v}_{\boldsymbol{o}} \) are constant values
\( A \). is a circle
B. is a helix with uniform pitch
c. is a helix with non-uniform pitch
D. is cycloid
Subject: Maths
Find the slope of a line passing through the following points:
\( \left(a t_{1}^{2}, 2 a t_{1}\right) \) and \( \left(a t_{2}^{2}, 2 a t_{2}\right) \)
A. \( \frac{2}{t_{2}-t_{1}} \)
в. \( \frac{2}{t_{2}+t_{1}} \)
c. \( \frac{1}{t_{2}+t_{1}} \)
D. None of these
Subject: Maths
ff \( \left[\begin{array}{cc}\boldsymbol{x} & \mathbf{2} \\ \mathbf{1 8} & \boldsymbol{x}\end{array}\right]=\left[\begin{array}{cc}\mathbf{6} & \mathbf{2} \\ \mathbf{1 8} & \mathbf{6}\end{array}\right] \) then \( \mathbf{x}= \)
\( A \cdot \pm 6 \)
B. 6
\( c .-5 \)
D.
Subject: Chemistry
A red sol of \( F e(O H)_{3} \) is mixed with an
equivalent amount of yellow sol of
\( A s_{2} S_{3} . \) Which of the following statement is wrong with respect to the resulting solution?
A. A colourless solution
B. Mutual coagulation
C. Precipitation of \( A s_{2} S_{3} \) and \( F e(O H)_{3} \) both
D. Orange solution
Subject: Chemistry
\( \boldsymbol{K}_{p} \) values for, \( \boldsymbol{C}_{2} \boldsymbol{H}_{4}+\boldsymbol{H}_{2} \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{6}, \) is
\( \mathbf{5} \times \mathbf{1 0}^{18} \mathbf{a t m}^{-1} \) and \( \boldsymbol{K}_{p} \) for, \( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+ \)
\[
\boldsymbol{H}_{2} \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{4}, \text { is } \mathbf{5} \times \mathbf{1 0}^{26} \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}^{-1} \text {at } \mathbf{5 0 . ~ I f}
\]
\( \boldsymbol{K}_{\boldsymbol{p}} \) for :
\[
\mathbf{2} \boldsymbol{H}_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{6} \text { is } \boldsymbol{x} \times
\]
\( 10^{45}, \) then \( 10 x \) is
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}(\boldsymbol{B r})-\boldsymbol{C H}_{3} \stackrel{\text {alc. } \boldsymbol{K O H}}{\longrightarrow} \)
\( \boldsymbol{A} \frac{\boldsymbol{H} \boldsymbol{B} \boldsymbol{r}}{\text {peroxide}} \boldsymbol{B} \frac{\boldsymbol{N a I}}{\text {acetone}} \boldsymbol{C} \)
The compound \( C \) is :
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{2}-I \)
B. \( C H_{3}-C H(I)-C H_{3} \)
c. \( C H_{3}-C H I-C H_{2}-I \)
D. \( C H_{3}-C H=C H-I \)
Subject: Physics
A police car moving at \( 22 \mathrm{m} / \mathrm{s} \), chase a motorcyclist. The police man sounds his horn at \( 176 \mathrm{Hz} \), while both of them move
towards a stationary siren of frequency \( 165 \mathrm{Hz} . \) Calculate the speed of the motorcyclist, if he does not observe any beats. (velocity of sound in air \( =330 \) \( \mathrm{m} / \mathrm{s}) \)
\[
\begin{array}{l}
\text { Police car } \\
\hline 176 \mathrm{Hz}^{*} 22 \mathrm{m} / \mathrm{s} \frac{\text { Motorcycle }}{\mathrm{V}} \quad \text { Stationary } \\
\qquad \text { Siren }(165 \mathrm{Hz})
\end{array}
\]
\( A .33 \mathrm{m} / \mathrm{s} \)
B. 22 m/s
c. zero
D. \( 11 \mathrm{m} / \mathrm{s} \)
Subject: Maths
If the distance 's' metres transversed by
a particle in \( t \) seconds is given by \( s= \)
\( t^{3}-3 t^{2}, \) then the velocity of the particle
when the acceleration is zero, in metre/sec is
\( A \cdot 3 \)
B. - -
\( c \cdot-3 \)
D.
Subject: Chemistry
Which is correct relationship?
\( \mathbf{A} \cdot E_{1} \) of \( H=\frac{1}{2} E_{2} \) of \( \mathrm{H} e^{+}=\frac{1}{3} E_{3} \) of \( L i^{+2}= \)
\( \frac{1}{4} E_{4} \) of \( B e^{+3} \)
B \( \cdot E_{1}(H)=E_{2}\left(H e^{+}\right)=E_{3}\left(L i^{+2}\right)=E_{4}\left(B e^{+3}\right) \)
C \( \cdot E_{1}(H)=2 E_{2}\left(H e^{+}\right)=3 E_{3}\left(L i^{+2}\right)=4 E_{4}\left(B e^{+3}\right) \)
D. No relation
Subject: Maths
If universal set \( \boldsymbol{\xi}= \) \( \{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}, \boldsymbol{g}, \boldsymbol{h}\}, \boldsymbol{A}= \)
\( \{b, c, d, e, f\}, B=\{a, b, c, g, h\} \) and
\( \boldsymbol{C}=\{\boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}, \boldsymbol{g}\} \) find \( : \boldsymbol{C}-(\boldsymbol{B} \cap \boldsymbol{A}) \)
Thus find the number of elements in the above set.
Subject: Chemistry
In the Lassaigne's test for the detection of
sulphar, the purple color is due to the
formation of :
\( \mathbf{A} \cdot N a_{4}\left[F e(C N)_{5} N O S\right] \)
B \( \cdot N a_{3}\left[F e(C N)_{5} S\right] \)
\( \mathbf{c} \cdot N a_{2}\left[F e(C N)_{5} N O S\right] \)
D. \( N a_{3}\left[F e(C N)_{6}\right] \)
Subject: Physics
A solenoid of \( 0.4 \mathrm{m} \) length with 500 turns carries a current of \( 3 \mathrm{A} \). A coil of 10
turns and of radius \( 0.01 \mathrm{m} \) carries a
current of 0.4 A. The torque required to hold the coil with its axis at right angle to that of the solenoid in the middle part
of it, is:
A \( \cdot 6 \pi^{2} \times 10^{-7} N m \)
В. \( 3 \pi^{2} \times 10^{-7} \mathrm{Nm} \)
c. \( 9 \pi^{2} \times 10^{-7} N m \)
D. \( 12 \pi^{2} \times 10^{-7} \mathrm{Nm} \)
Subject: Maths
Check if given series is \( A P \) or not? If
they form an \( A P \), find the common
difference \( d \) and write three more terms.
\( \mathbf{3}, \mathbf{3}+\sqrt{\mathbf{2}}, \mathbf{3}+\mathbf{2} \sqrt{\mathbf{2}}, \mathbf{3}+\mathbf{3} \sqrt{\mathbf{2}} \)
Subject: Maths
If \( \int \frac{2^{x}}{\sqrt{1-4^{x}}} d x=k \sin ^{-1} 2^{x}+c, \) then
\( \boldsymbol{k}= \)
\( A \cdot \log 2 \)
в. \( \frac{1}{\log 2} \)
c. \( \frac{1}{2 \log 2} \)
D. \( 2 \log 2 \)
Subject: Physics
A smooth massless wedge is pushed by
a horizontal force \( \boldsymbol{P} \)
\( \mathbf{A} \cdot \) If \( P=0, \) than \( N<m g \cos \theta, ; \mathrm{N}=\mathrm{Normal} \) reaction
received by the block
B. If \( P>0, \) than \( N=m g \cos \theta \)
C. If \( a=0, \) than \( N=m g \cos \theta,= \) acceleration of the wedge.
D. none of these
Subject: Maths
the given statements is true or false.
(P) \( C \) recycled more newspapers than \( D \)
(Q) \( \mathrm{B} \) recycled 80 bunches of newspaper
more than \( \mathbf{A} \)
(R) In all 5 hundred bunches of
newspaper were recycled.
(S) The ascending order of the
newspaper recycled by schools is \( \mathrm{D}, \mathrm{C} \)
\( A, B, E \)
\( \begin{array}{llll}\text { (P) } & \text { (Q) } & \text { (R) } & \text { (S) }\end{array} \)
A. True True False False
B. True True False True
c. False True False True
D. False False True True
Subject: Maths
Let \( t_{r}=\frac{r}{1+r^{2}+r^{4}} \) then, \( \lim _{n \rightarrow \infty} \sum_{r=1}^{n} t_{r} \)
equals
\( A \cdot \frac{1}{4} \)
B. 1
\( c \cdot \frac{1}{2} \)
D. None of these
Subject: Chemistry
Which of the following equations
corresponds to the enthalpy of
combustion at \( 298 K ? \)
\( \mathbf{A} \cdot C_{2} H_{6}(g)+7 / 2 O_{2}(g) \longrightarrow 2 C O_{2}(g)+3 H_{2} O(g) \)
B \( \cdot 2 C_{2} H_{6}(g)+7 O_{2}(g) \longrightarrow 4 C O_{2}(g)+6 H_{2} O(g) \)
\( \mathbf{c} \cdot C_{2} H_{6}(g)+7 / 2 O_{2}(g) \longrightarrow 2 C O_{2}(g)+3 H_{2} O(l) \)
D. \( 2 C_{2} H_{6}(g)+7 O_{2}(g) \longrightarrow 4 C O_{2}(g)+6 H_{2} O(l) \)
Subject: Chemistry
Suppose a gaseous mixture of \( H e, N e, A r, K r \) is irradiated with photons of frequency appropriate to
ionize \( A r . \) What ions will be present in the mixture?
\( \mathbf{A} \cdot A r^{+} \)
в. \( K r^{+} \)
\( \mathrm{c} \cdot \mathrm{He}^{+} \)
D. Both \( A \) and \( B \)
Subject: Maths
Let \( A, B \) are two sets such that \( n(A)= \) \( \mathbf{6}, \boldsymbol{n}(\boldsymbol{B})=\mathbf{8} \) then the maximum number
of elements in \( n(A \cup B) \) is
A. 7
B. 9
c. 14
D. None
Subject: Chemistry
Match the following.
1) Morphine
a) Antipyretic
2) Ibuprofen
b) Narcotic analgesic
3) Paracetamol
c) Tranquilizer
4) Luminal
d) Non-narcotic analgesics
e) Antiseptic
A. \( 1-b, 2-d, 3-a, 4-c \)
B. \( 1-b, 2-c, 3-e, 4-d \)
c. \( 1-d, 2-b, 3-a, 4-e \)
D. \( 1-a, 2-e, 3-b, 4-d \)
Subject: Maths
One litre of water weighs 1 kg. How many cubic millimetres of water will
weigh 0.1 gram?
\( \mathbf{A} \cdot 100 \) cubic \( \mathrm{mm} \)
B. 150 cubic mm.
c. 90 cubic \( \mathrm{mm} \)
D. 80 cubic mm.
Subject: Maths
Find the multiplicative inverse of \( \sqrt{5}+ \)
\( \mathbf{3} i \)
A \( . \sqrt{5}-3 i \)
B. \( \frac{\sqrt{5}-3 i}{14} \)
c. \( -\sqrt{5}+3 i \)
D. \( \frac{-\sqrt{5}+3 i}{14} \)
Subject: Physics
A body cools from \( 80^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 5
minutes. Calculate the time it takes to
cool from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \). The
temperature of the surroundings is
\( \mathbf{2 0}^{\circ} \boldsymbol{C} \)
Subject: Maths
If \( f \) is a differentiable function at a point
'a' and \( f^{\prime}(a) \neq 0 \) then which of the
following is true.
A \( \cdot f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a)-f(a-h)}{h} \)
B. \( \frac{1}{2} f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+2 h)-f(a-h)}{2 h} \)
c. \( f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+2 h)-f(a)}{h} \)
D. none of these
Subject: Physics
A student uses a simple pendulum of
exactly 1 m length to determine \( g \), the
acceleration due to gravity. He uses a
stopwatch with the least count of 1 sec
for this and records 40 seconds for 20
oscillations. For this observation, which
of the following statements is(are)
true?
This question has multiple correct options
A. Error \( \Delta T \) in measuring \( T \), the time period, is 0.05 seconds.
B. Error \( \Delta T \) in measuring \( T \), the time period, is 1 second.
C. Percentage error in the determination of \( g \) is \( 5 \% \)
D. Percentage error in the determination of \( g \) is \( 2.5 \% \)
Subject: Physics
If \( g \) is the acceleration due to gravity on the earth's surface, the gain of the potential energy of an object of mass \( \boldsymbol{m} \)
raised from the surface of the earth to a
height equal to the radius \( R \) of the earth
will be :
A. \( 2 m g R \)
в. \( m g R \)
c. \( \frac{1}{2} m g R \)
D. \( \frac{1}{4} m g R \)
Subject: Chemistry
IUPAC name of given compound is :
A. cyclohexa-3,4-dienylethanone
B. 1-(cyclohexa-2, 3-dienyl)ethanone
c. 2 -(cyclohexa- 2,4 -dienylethanone
D. 1 -(cyclohexa-2, 4 -dienyl)ethanone
Subject: Chemistry
Identify the endothermic and exothermic reaction.
This question has multiple correct options
A. \( H C l+N a O H \rightarrow N a C l+H_{2} O+ \) heat
в. \( 2 K C l O_{3}(s) \triangleq 2 K C l(s)+3 O_{2} \uparrow \)
\( \mathrm{c} \cdot \mathrm{CaO}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}+ \) heat
D. \( \operatorname{CaCO}_{3}(s) \triangleq \operatorname{CaO}(s)+\mathrm{CO}_{2} \uparrow \)