AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
In addition to carbon monoxide \( (C O) \)
and carbon dioxide \( \left(C O_{2}\right), \) there is a third compound of carbon called carbon
sub-oxide. If a \( 2.500 g \) sample of carbon
sub-oxide contains \( 1.32 g \) of \( C \) and \( 1.18 g \) of \( O, \) using the law of multiple proportions, a possible formula of carbon sub-oxide can be deduced. What
is the number of carbon atoms in such
a formula?
Subject: Physics
Relation to another coordinate system
\( \mathbf{S}_{2} \) (denoted by double primes) having an acceleration \( -\overline{\mathbf{g}}, \) and coincident with
the original coordinate system \( \mathbf{S}_{0} \) at
\( \mathbf{t}=\mathbf{0}, \) the equation of the object
becomes
A \( \cdot 0=-\mathrm{m} \overline{\mathrm{g}}-\mathrm{b} \overline{\mathrm{v}}^{\prime \prime} \)
B. \( m\left(\frac{d \vec{v}^{\prime \prime}}{d t}\right)=0 \)
\( ^{\mathrm{c}} m\left(\frac{d \overrightarrow{v^{\prime \prime}}}{d t}\right)=-b v^{\vec{\eta}}-b g t \)
\( ^{\mathrm{D}} \cdot_{m}\left(\frac{d \overrightarrow{v^{\prime \prime}}}{d t}\right)=-b v^{\vec{\eta}}+b g t \)
Subject: Chemistry
Arrange \( A g F, A g C l, A g B r \) and \( A g l \) in the increasing order of solubility in water.
A \( . A g B r<A g I<A g C l<A g F \)
в. \( A g I<A g B r<A g C l<A g F \)
c. \( A g I<A g C l<A g B r<A g F \)
D. None of the above
Subject: Maths
The family of curves represented by \( \frac{d y_{1}}{d x}=\frac{x^{2}+x+1}{y^{2}+y+1} \) and the family
represented by \( \frac{\boldsymbol{d} \boldsymbol{y}_{2}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\boldsymbol{y}^{2}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}}=\mathbf{0} \)
A. touch each other
B. orthogonal to each other
c. identical
D. intersect at an angle of \( \frac{\pi}{4} \)
Subject: Maths
If \( y=\sin ^{-1} \frac{1}{2}(\sqrt{1+x}+\sqrt{1-x}) \) then
\( y^{\prime}= \)
A. \( \frac{1}{2 \sqrt{1-x^{2}}} \)
B. \( \frac{-1}{2 \sqrt{1-x^{2}}} \)
c. \( \frac{1}{2 \sqrt{1+x^{2}}} \)
D. \( \frac{-1}{2 \sqrt{1+x^{2}}} \)
Subject: Physics
A copper ball of radius \( r \) is moving with
a uniform velocity \( v \) in the mustard oil
and the dragging force acting on the ball is \( F . \) The dragging force on the
copper ball of radius \( 2 r \) with uniform
velocity \( 2 v \) in the mustard oil is
A. \( F \)
в. \( 2 F \)
c. \( 4 F \)
D. \( 8 F \)
Subject: Maths
If \( f \) be a continuous function on \( [\mathbf{0}, \mathbf{1}] \)
differentiable in (0,1) such that
\( f(1)=0, \) then there exists some \( c \in \)
(0,1) such that
A \( \cdot c f^{\prime}(c)-f(c)=0 \)
B. \( f^{\prime}(c)+c f(c)=0 \)
c. \( f^{\prime}(c)-c f(c)=0 \)
D. \( c f^{\prime}(c)+f(c)=0 \)
Subject: Physics
A particle moves in the \( x-y \) plane. Its
motion is given by equations \( x=\sin 2 t \)
and \( y=(1-\cos 2 t) . \) The distance
travelled by the particle during time \( \boldsymbol{t}=\boldsymbol{2} \boldsymbol{s} \) is
\( \mathbf{A} \cdot 1 m \)
в. \( 6 m \)
c. \( 4 m \)
D. \( 8 m \)
Subject: Maths
If \( 4 i+7 j+8 k, 2 i+7 j+7 k \) and \( 3 i+ \)
\( 5 j+7 k \) are the position vectors of the
vertices \( A, B \) and \( C \) respectively of triangle \( A B C . \) The position vector of the point where the bisector of angle \( \boldsymbol{A} \)
meets \( B C \).
A \( \cdot \frac{1}{3}(5 j+12 k) \)
B. \( \frac{1}{3}(6 i+13 j+18 k) \)
c. \( \frac{2}{3}(6 i+8 j+6 k) \)
D \( \cdot \frac{2}{3}(-6 i-8 j-6 k) \)
Subject: Physics
A mass of \( 10 k g \) is suspended by a rope
of length \( 4 m, \) from the ceiling. A force \( F \) is applied horizontally at the mid-point of the rope such that the top half of the
rope makes an angle of \( 45^{\circ} \) with the
vertical. Then F equals: (Take \( \boldsymbol{g}= \)
\( 10 m s^{-2} \) and the rope to be massless)
A . \( 70 N \)
B. \( 75 N \)
c. \( 100 N \)
D. \( 90 N \)
Subject: Physics
Two particles \( X \) and \( Y \) having equal
charges after being accelerated thorough the same potential difference enter a region of uniform magnetic field and describe circular paths of radius
\( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) respectively. the ratio of
mass of \( X \) to that of \( Y \) is
\( \mathbf{A} \cdot \sqrt{R_{1} / R_{2}} \)
в. \( R_{2} / R_{1} \)
c. \( \left(R_{1} / R_{2}\right)^{2} \)
D. \( R_{1} / R_{2} \)
Subject: Maths
If \( \vec{b} \) and \( \vec{c} \) are the position vectors of the points \( \mathrm{B} \) and \( \mathrm{C} \) respectively, then the position vector of the point D such that \( \overrightarrow{B D}=4 \overrightarrow{B C} \) is
A \( \cdot 4(\vec{c}-\vec{b}) \)
в. \( -4(\vec{c}-\vec{b}) \)
c. \( 4 \vec{c}-3 \vec{b} \)
D \( \cdot 4 \vec{c}+3 \vec{b} \)
Subject: Chemistry
The first transition state in the overall
exothermic addition of HBr to propane
resembles the
intermediate (carbocation). Choose the
best phrase to complete the following
statement
The second transition states (for
addition of \( B r^{-} \) to the carbocation):
A. resembles the final product
B. resembles the 2-propyl cation
c. resembles propene
D. has all carbons almost entirely sp \( ^{3} \) hybridized
Subject: Chemistry
Select the coloured and paramagnetic ions.
A \( \cdot C u^{+}, Z n^{2+}, C a^{2+} \)
B \( \cdot S c^{3+}, T i^{4+}, V^{5+} \)
c. \( C u^{2+}, C r^{+}, M n^{2+} \)
D. \( N i^{2+}, C u^{+}, H g^{2+} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\int_{0}^{x}(\cos (\sin t)+\cos (\cos t) d t \)
then \( f(x+\pi) \) is?
\( \mathbf{A} \cdot=f(\pi)+2 f\left(\frac{\pi}{2}\right) \)
B. \( =f(\pi)+6 f\left(\frac{\pi}{6}\right) \)
\( \mathbf{c} \cdot=f(\pi)+9 f\left(\frac{\pi}{11}\right) \)
\( \mathbf{D} \cdot=f(\pi)+10 f\left(\frac{\pi}{3}\right) \)
Subject: Physics
Q Type your question-
\( 65 k m h^{-1} . \) When they reach the crossroad, one of the cars turns towards
town \( Q \) whereas the other continues
forward towards town \( R \). Both continue
to move with the same speed of
\( 65 k m h^{-1} \)
Which of the following options is correct for given statements?
(i) Both cars have the same velocities
even if the car turns towards town \( Q \)
(ii) Two bodies have same velocities if
they are moving with same speed in different directions.
A. Both (i) and (ii) are correct and (ii) is the correct explanation of (i)
B. Both (I) and (ii) are correct but (ii) is not the correct explanation of (i
c. only (i) is correct
D. Neither (i) nor (ii) is correct
Subject: Maths
The remainder when \( f(x)=3 x^{4}+ \)
\( 2 x^{3}-\frac{x^{2}}{3}-\frac{x}{9}+\frac{2}{27} \) is divided by
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}+\frac{\boldsymbol{2}}{\boldsymbol{3}} \) is
\( A \)
B. 1
c. 0
D. -
Subject: Maths
Equation of the plane passing through a point with position vector \( 3 \hat{i}-3 \hat{j}+\hat{k} \)
\& normal to the line joining the points with position vectors \( 3 \hat{i}+4 \hat{j}-\hat{k} \& \) \( \mathbf{2} \hat{\mathbf{i}}-\hat{\boldsymbol{j}}=\mathbf{5} \hat{\boldsymbol{k}} \) is
\( \mathbf{A} \cdot \bar{r} \cdot(-\hat{i}-5 \hat{j}+6 \hat{k})+18=0 \)
B \( \cdot \bar{r} \cdot(\hat{i}-5 \hat{j}+6 \hat{k})=22 \)
c. \( \bar{r} .(\hat{i}+5 \hat{j}-6 \hat{k})+18=0 \)
D \( \cdot \bar{r} .(-\hat{i}+5 \hat{j}+6 \hat{k})+12=0 \)
Subject: Physics
A wire bent as shown in Fig is oriented
along yz plane. Find the magnetic field
at \( P \) and \( P_{1} \)
A \( \cdot \frac{\mu_{0} I}{4 a}, \frac{\mu_{0} I}{2 \pi x_{x}} \)
B. \( \frac{\mu I}{4 a}, \frac{\mu I}{2 \pi\left(x^{2}+a^{2}\right)} \)
C. \( \frac{\mu_{0} I}{4 a}, \frac{\mu_{0} I}{2 \pi a\left(x^{2}+a^{2}\right)} \)
D. none of thes
Subject: Chemistry
What is the mass of \( 6.022 \times 10^{23} \)
molecules of \( \boldsymbol{N} \boldsymbol{H}_{3} \) ?
A. \( 45.06 g \)
в. \( 19.06 g \)
c. \( 17.04 g \)
D. \( 31.02 g \)
Subject: Chemistry
Consider the following graph and mark
the correct statement.
A. Chemical equilibrium in the reaction. \( H_{2}+I_{2} \rightleftharpoons 2 H I \) can be attained from either directions
3. Equilibrium can be obtained when \( H_{2} \) and \( I_{2} \) are mixed
an open vessel
C. The concentrations of \( H_{2} \) and \( I_{2} \) keep decreasing while concentration of \( H I \) keeps increasing with time.
D. We can find out equilibrium concentration of \( H_{2} \) and
\( I_{2} \) from the given graph
Subject: Maths
Find the value of \( x \) in given figure if
\( \boldsymbol{A B} \| \boldsymbol{C D} \)
\( x \) is the exterior angle of \( \angle P Q R \)
A \( .275^{\circ} \)
B . \( 280^{\circ} \)
\( \mathbf{c} \cdot 285^{\circ} \)
D. \( 295^{\circ} \)
Subject: Physics
A cube of side \( 10 \mathrm{cm} \) encloses a charge
of \( 0.1 \mu C \) at its centre.What is the
number of lines of force through each
face of the cube
A \( \cdot 1.13 \times 10^{11} \)
В. \( 1.13 \times 10^{6} \)
c. \( 1.13 \times 10^{23} \)
D. 1883
Subject: Chemistry
An element forms two oxides \( \boldsymbol{X} \boldsymbol{O}, \boldsymbol{X} \boldsymbol{O}_{2} \)
The oxide \( X O \) is neutral, insoluble in water and burns with blue flame. It is
poisonous. \( X O_{2} \) is acidic in nature.
Soluble in water and extinguishes fire.
(i) Identify the \( x \)
(ii) write reaction of \( X O_{2} \) with water.
(iii) What happens when \( X O_{2} \) is passed in lime water
Subject: Chemistry
Acid rain is caused due to increase
in concentration of (in atmosphere)
A. \( S O_{2} \) and \( N O_{2} \)
B. \( \operatorname{coand} C O_{2} \)
c. \( \operatorname{coand} S O_{3} \)
\( \mathrm{D} \cdot O_{3} \) and dust
Subject: Maths
If \( a=\hat{i}+\hat{j}, b=2 \hat{j}-\hat{k} \) and \( r \times a= \)
\( \boldsymbol{b} \times \boldsymbol{a}, \boldsymbol{r} \times \boldsymbol{b}=\boldsymbol{a} \times \boldsymbol{b}, \) then a unit vector
in the direction of \( r \) is?
A \( \cdot \frac{1}{\sqrt{11}}(\hat{i}+3 \hat{j}-\hat{k}) \)
B. \( \frac{1}{\sqrt{11}}(\hat{i}-3 \hat{j}+\hat{k}) \)
c. \( \frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k}) \)
D. None of these
Subject: Chemistry
An inorganic white crystalline compound A has a rock salt structure. A
on reaction with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and
\( M n O_{2}, \) evolves a pungent smelling, greenish - yellow gas B. Compound A gives white ppt. of \( \mathbf{C} \) with \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \)
solution. Compounds \( (A),(B) \) and \( (C) \) will be respectively;
A \( . \) NaCl \( , C l_{2}, \) AgCl
в. \( \operatorname{NaBr}, \operatorname{Br}_{2}, \) Na Вт
c. \( N a C l, C l_{2}, A g_{2} S O_{4} \)
D. \( N a_{z} C O_{3}, C O_{2}, A g_{2} C O_{3} \)
Subject: Maths
Suppose \( f \) and \( g \) both are linear function
with \( f(x)=-2 x+1 \) and \( f(g(x))= \)
\( 6 x-7 \) then slope of line \( y=g(x) \) is
\( \mathbf{A} \cdot \mathbf{3} \)
B. -3
\( c \cdot 6 \)
D. - 2
Subject: Chemistry
What is the major product (s) when 2
methyl-2-butene reacts with (i) \( O_{3} \) (ii)
\[
Z n / C H_{3} C O O H(a q) ?
\]
A. \( I+I I \)
B. \( I I+I I I \)
c. \( I I I+I V \)
D. II
Subject: Chemistry
\( N a^{+}, M g^{2+}, A l^{3+} \) and \( S i^{4+} \) are
isoelectronic ions. Their ionic size
follows the order:
A \( \cdot N a^{+}<M g^{2+}<A l^{3+}<S i^{4+} \)
B. \( N a^{+}>M g^{2+}<A l^{3+}>s i^{4+} \)
C. \( N a^{+}<M g^{2+}>A l^{3+}>S i^{4+} \)
D. \( N a^{+}>M g^{2+}>A l^{3+}>S i^{4+} \)
Subject: Maths
ABCD is a parallelogram \( P \) and \( R \) are two points on AB such that the area of parallelogram ABCD is 8 times the are
of \( \Delta D P R \) If \( P R=5 c m \) then \( C D \) is equal
to
\( A \cdot 10 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .20 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)
Subject: Physics
Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of \( 444 m / s \) in 1.83 seconds, then what is the distance that the sled travels? \( (\text { in } m) \)
\( \mathbf{A} \cdot 406 m \)
в. \( 40 m \)
\( c .46 m \)
D. \( 506 m \)
Subject: Physics
The depression produced at the end of a
\( 50 c m \) long cantilever on applying a load is 15 mm. The depression produced at a
distance of \( 30 \mathrm{cm} \) from the rigid end will
be
A. 3.24 \( \mathrm{mm} \)
B. 1.62 \( \mathrm{mm} \)
c. \( 6.48 \mathrm{mm} \)
D. 12.96 mm
Subject: Chemistry
What is the wavelength of light emitted when the electron in hydrogen atom undergoes transition from the energy
level with \( n=4 \) to energy level \( n=2 ? \)
\( \left(\operatorname{given} R_{n}=109678 c m^{-1}\right) \)
A. 786 nm
B. 486 nm
c. \( 586 \mathrm{nm} \)
D. 986 nm
Subject: Maths
In a \( \triangle A B C, \) perpendicular \( A D \) from \( A \) on \( B C \) meets \( B C \) at \( D . \) If \( B D=8 \mathrm{cm} \)
\( D C=2 \mathrm{cm} \) and \( A D=4 \mathrm{cm}, \) then
A. \( \triangle A B C \) is isosceles
B. \( \triangle A B C \) is equilateral
c. \( A C=2 A B \)
D. \( \triangle A B C \) is right angled at \( A \)
Subject: Chemistry
Few quantities with their units are listed below. Mark the units which are
not correctly matched.
(i) Density \( : \operatorname{kg} m^{-3} \)
(ii) Velocity of light \( : \mathrm{m} s^{-1} \)
(iii) Planck's constant \( : \boldsymbol{J}^{-1} \boldsymbol{s}^{-1} \)
(iv) Acceleration : \( \mathrm{m} \boldsymbol{s}^{-2} \)
(v) Force : \( \mathrm{kg} \) m
A. (ii) and (iv)
B. (i) and (iii)
c. (iii) and (v)
D. (iv) and (v)
Subject: Maths
If \( I=\int \sec ^{2} x \operatorname{cosec}^{4} x d x=A \cot ^{3} x+ \)
\( B \tan x+C \cot x+D \) then
This question has multiple correct options
A \( \cdot A=-\frac{1}{3} \)
в. \( B=2 \)
c. \( C=-2 \)
D. none of these
Subject: Physics
Which of the following are correct?
This question has multiple correct options
A. An astronaut going from the earth to the Moon will experience weightlessness once.
B. When a thin uniform spherical shell gradually shrinks maintaining its shape, the gravitational potential at its centre decreases
C. In the case of a spherical shell, the plot of \( V \) versus \( r \) is continuous.
D. In the case of a spherical shell, the plot gravitational field intensity \( I \) versus \( r \) is continuous
Subject: Physics
A planar coil of area \( 7 \mathrm{m}^{2} \) carrying an anti-clockwise current 2 A is placed in an extemal magnetic field \( \vec{B}=(0.2 \hat{i}+ \) \( 0.2 \hat{j}-0.3 \hat{k}), \) such that the normal to the plane is along the \( \operatorname{line}(3 \hat{i}-5 \hat{j}+ \)
4 \( \hat{k} \) ). Select correct statements from the
following. ( Consider Normal of the coil and Magnetic moment vectors to be in the same direction
This question has multiple correct options
A. The potential energy of the coil in the given orientation is 6.4
B. The angle between the normal (positive) to the coil and the external magnetic field is \( \cos ^{-1}(0.57) \)
c. The potential energy of the coil in the given orientation is 3.2
D. The magnitude of magnetic moment of the coil is about \( 14 A m^{2} \)
Subject: Maths
If the major axis of an ellipse is three times the minor axis, then its
eccentricity is equal to
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{\sqrt{3}} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{2 \sqrt{2}}{3} \)
E \( \frac{2}{3 \sqrt{2}} \)
Subject: Physics
Let \( A, B \) and \( C \) are unit vectors
suppose \( A . B=A . C=0 \) and angle between \( B \) and \( C \) is \( \frac{\pi}{6} \) then
A \( . A=\pm 2(B \times C) \)
B. \( A=\pm \sqrt{2}(B \times C) \)
c. \( A=\pm 3(B \times C) \)
D. \( A=\pm \sqrt{3}(B \times C) \)
Subject: Chemistry
What would be the ionisation constant
\( \left(\boldsymbol{K}_{\boldsymbol{a}}\right) \) of \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} ? \)
A \( \cdot 2 \times 10^{-5} \)
B \( \cdot 10^{-5} \)
C \( .2 \times 10^{-6} \)
D. \( 5 \times 10^{-6} \)
Subject: Maths
This question has four choices \( (A),(B) \)
(C) and (D) out of which ONE or MORE
are correct.
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}} \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \sqrt{x^{2}+2 x}-x, \) then
This question has multiple correct options
A \( \cdot \lim _{x \rightarrow \infty} g(x)=1 \)
B. \( \lim _{x \rightarrow-\infty} f(x)=1 \)
c. \( \lim _{x \rightarrow-\infty} f(x)=-1 \)
D. \( \lim _{x \rightarrow \infty} g(x)=-1 \)
Subject: Chemistry
A 3.4 g sample of \( \mathrm{H}_{2} \mathrm{O}_{2} \) solution containing \( x \% \mathrm{H}_{2} \mathrm{O}_{2} \) by mass requires \( \mathrm{x} \)
\( \mathrm{ml} \) of a \( \mathrm{KMnO}_{4} \) solution for complete oxidation under acidic condition. The
molarity of \( \mathrm{KMnO}_{4} \) solution is :
\( A \)
B. 0.5
\( c \cdot 0.4 \)
D. 0.2
Subject: Chemistry
aqueous \( N a O H+P_{4}(w h i t e) \longrightarrow \)
\( \boldsymbol{P H}_{3}+\boldsymbol{X} . \) Compound \( \mathbf{X} \) is:
A. \( N a H_{2} P O_{2} \)
в. \( N a_{2} H P O_{4} \)
c. \( N a_{2} C O_{3} \)
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)
Subject: Chemistry
Match the polymers given in column
with monomers in column II and mark
the appropriate choice.
\( \rightarrow(\text { iv }) \)
(B) (ii) (iii)
\( A \cdot(A) \)
\( - \)
\( (C) \rightarrow(i),(D) \) \( \rightarrow \)
B. (iii) \( \rightarrow(\text { iv }) \) \( \rightarrow \) (ii) \( (A) \rightarrow(i) \) (B) \( \rightarrow \)
\( (C) \)
(D)
\( c \)
\( (A) \rightarrow(i v) \)
(B) \( \rightarrow \) (i)
\( (C) \rightarrow(i i),(D) \) \( \rightarrow \) (iii)
\( D \cdot(A) \)
\( \rightarrow \) (ii)
\( \mathrm{R} \)
v)
C) \( \rightarrow \) (iii)
\( (D) \rightarrow(i) \)
Subject: Maths
In the equation \( y=k x+3, k \) is a
constant. If \( \boldsymbol{y}=\mathbf{1 7} \) when \( \boldsymbol{x}=\mathbf{2}, \) what is
the value of \( \boldsymbol{y} \) when \( \boldsymbol{x}=\mathbf{4} ? \)
A . 34
B. 31
c. 14
D. 11
\( E .7 \)
Subject: Physics
A rectangular loop PQRS made from a
uniform wire has length a, width b and mass m. It is free to rotate about the
\( \operatorname{arm} \mathrm{PQ}, \) which remains hinged along a horizontal line taken as the y-axis. Take the vertically upward direction as the zaxis. A uniform magnetic field \( \vec{B}= \) \( (3 \hat{i}+4 \hat{k}) B_{0} \) exists in the region. The
loop is held in the \( x \) -y plane and a current I is passed through it. The loop is now released and is found to stay in
the horizontal position in equilibrium. Find the magnetic force on the arm RS.
Subject: Maths
Find the value of the determinant:
\[
\left|\begin{array}{ccc}
\cos (\theta+\phi) & -\sin (\theta+\phi) & \cos 2 \phi \\
\sin \theta & \cos \theta & \sin \phi \\
-\cos \theta & \sin \theta & \cos \phi
\end{array}\right|
\]
Subject: Maths
Say true or false.
A.M. of any \( n \) positive numbers
\( a_{1}, a_{2}, a_{3}, \dots, a_{n} \) is \( A \) then \( A= \)
\( \frac{\boldsymbol{a}_{1}+\boldsymbol{a}_{2}+\ldots .+\boldsymbol{a}_{\boldsymbol{n}}}{\boldsymbol{n}} \)
A . True
B. False
Subject: Physics
Assertion
A light-year is a distance that light
travels with velocity of \( 3 \times 10^{8} m s^{-1} \) in
one year.
Reason
Light year is the unit for measuring time.
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
When a body of mass \( 1.0 \mathrm{kg} \) is suspended from a certain light spring hanging vertically, its length increases by \( 5 \mathrm{cm} . \) By suspending \( 2.0 \mathrm{kg} \) block to the spring and if the block is pulled through \( 10 \mathrm{cm} \) and released, the
maximum velocity in it in \( m / s \) is
A . 0.5
B. 1
c. 2
D. 4
Subject: Chemistry
The formula of the hydride of nitrogen
that is acidic in nature is :
A . \( \mathrm{NH}_{3} \)
в. \( \mathrm{HN}_{3} \)
c. \( \mathrm{N}_{2} \mathrm{H}_{4} \)
D. \( \mathrm{NH}_{2} \mathrm{OH} \)
Subject: Physics
In YDSE using monochromatic visible light, the distance between the plane of slits and the screen is \( 1.7 m . \) At point \( P \)
on the screen which is directly in front of the upper slit, maximum path is observed. Now, the screen is moved
\( 50 c m \) closer to the plane of slits. Point
\( P \) now lies between third and fourth
minima above the central maxima and
the intensity at \( P \) is one-fourth of the maximum intensity on the screen. Find the wavelength of light if the separation of slits is \( 2 m m \)
A. \( 2.9 \times 10^{-7} \mathrm{m} \)
В. \( 3.9 \times 10^{-7} \mathrm{m} \)
c. \( 5.9 \times 10^{-7} m \)
D. \( 6.9 \times 10^{-7} \) т
Subject: Maths
Consider the principle diagonal
elements of \( B \) as \( \left(b_{1}, b_{2}, b_{3}\right) \) such that
\( b_{1}>b_{2}>b_{3}, \) then the value of \( \lambda \) for
which \( b_{1}, b_{2},\left(b_{3} \lambda\right) \) are in \( G . P \)
\( A \cdot 3 \)
B.
c. \( -\frac{1}{3} \)
D. \( \frac{81}{91} \)
Subject: Maths
Without doing any actual division, find which of the following rational numbers have terminating decimal representation:
(i) \( \frac{7}{16} \)
(ii) \( \frac{23}{125} \)
(iii) \( \frac{\mathbf{9}}{\mathbf{1 4}} \)
(iv) \( \frac{32}{45} \)
\( (v) \frac{43}{50} \)
(vi) \( \frac{17}{40} \)
(vii) \( \frac{61}{75}(\text { viii }) \frac{123}{250} \)
A \( . \) (i), (iii), (v), (vi) and (vii)
B. (i), (ii), (v), (vi) and (viii)
C . (i), (iii), (v), (vi) and (viii)
D. (i), (ii), (v), (vi) and (vii)
Subject: Maths
Solve the following pair of linear (simultaneous) equations by the method of elimination:
\( 8 x+5 y=9 \)
\( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{4} \)
A. \( x=1 \) and \( y=-2 \)
B. \( x=1 \) and \( y=-5 \)
c. \( x=3 \) and \( y=6 \)
D. \( x=-2 \) and \( y=5 \)
Subject: Physics
In an oscillating \( L-C \) circuit in which
\( C=4.00 \mu F, \) the maximum potential
across the capacitor during the oscillations is \( 1.50 V \) and the maximum
current through the inductor is \( 50.0 m A \)
How much time does the charge on the capacitor take to rise from zero to its maximum value?
A. \( 0.238 \mathrm{ms} \)
B. \( 0.788 \mathrm{ms} \)
c. \( 0.488 \mathrm{ms} \)
D. \( 0.188 \mathrm{ms} \)
Subject: Maths
\( \int e^{x} \sqrt{1+e^{x}} d x= \)
A \( \cdot\left(1+e^{x}\right)^{\frac{3}{2}}+c \)
B \( \cdot \frac{2}{3}\left(1-e^{x}\right)^{3 / 2}+c \)
\( \mathbf{c} \cdot\left(1-e^{x}\right)^{3 / 2}+c \)
D. \( \frac{2}{3}\left(1+e^{x}\right)^{3 / 2}+c \)
Subject: Physics
A quarter cylinder of radius \( \boldsymbol{R} \) and
refractive index 1.5 is placed on a table.
A point object \( P \) is kept at a distance of
\( m R \) from it. The value of \( ^{\prime} m^{\prime} \) for which a
ray from P will emerge parallel to the
table, as shown in figure, is
\( A \cdot 4 / 3 \)
B. \( 3 / 4 \)
\( c \cdot 3 / 2 \)
D. \( 2 / 3 \)
Subject: Maths
If \( f(x)=\left\{\begin{array}{cc}x^{2} \sin \frac{1}{x} & x \neq 0 \\ 0 & x=0\end{array} \) then R.H.D \right.
is
\( \mathbf{A} \cdot \mathbf{1} \)
B . -
\( c \)
D. None
Subject: Physics
Two spheres of masses \( 1 \mathrm{kg} \) and \( 2 \mathrm{kg} \) are moving with velocities of \( 10 \mathrm{m} / \mathrm{s} \) and 5 \( \mathrm{m} / \mathrm{s} \) respectively in the same direction. After the collision the velocity of the lighter sphere decreases by \( 4 \mathrm{m} / \mathrm{s} \). Find the velocity of the heavier sphere after collision and calculate the coefficient of
restitution.
Subject: Maths
Let \( z, \omega \) be complex numbers such that
\( \vec{z}+i \vec{\omega}=0 \) and \( A r g(z \omega)=\pi \) then
\( A r g(z)= \)
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{5 \pi}{4} \)
c. \( \frac{3 \pi}{4} \)
D.
Subject: Physics
A square metal wire loop of side \( 10 \mathrm{cm} \)
and of resistance \( 2 \Omega \) moves with
constant velocity in the presence of a uniform magnetic field of induction \( 4 \mathrm{T} \)
perpendicular and into the plane of the loop. The loop is connected to a network
of resistance as shown in the Figure. If
the loop should have a steady current of \( 2 \mathrm{mA} \), the speed of the loop must be (in \( \left.\mathrm{cm} \mathrm{s}^{-1}\right): \)
4
B.
\( c \)
)
Subject: Chemistry
Two samples of HI each of 5 g was taken separately in two vessels of volume 5 lit and 10 lit respectively at
\( 27^{\circ} \mathrm{C} . \) The extent of dissociation of \( \mathrm{HI} \)
will be:
A. More in 5 litre vessel
B. More in 10 litre vessel
c. Equal in both vessels
D. Can't be predicted