AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The surface area of the drop is:
Spherical drop
\( \mathbf{A} \cdot 4 \pi R^{2} \)
\( \mathbf{B} \cdot 4 \pi\left(9 t^{2} R^{4}\right)^{1 / 3} \)
\( \mathbf{C} \cdot 4 \pi\left(9 t^{4} R^{2}\right)^{1 / 3} \)
D. \( 4 \pi R(t+R) \)
Subject: Physics
The maximum intensity in Young's
double slit experiment is \( I_{0} . \) Distance
between the slits is \( d=5 \lambda \), where \( \lambda \) is
the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the
slits on a screen at a distance \( D=10 d \)
\( ? \)
A \( . I_{0} \)
в. \( I_{0} / 4 \)
c. \( _{\overline{4}_{l_{0}}^{I_{0}}} \)
D. \( I_{0} / 2 \)
Subject: Maths
For any two complex numbers \( z_{1} \) and \( z_{2} \)
prove that \( \operatorname{Re}\left(z_{1} z_{2}\right)=\operatorname{Re} z_{1} \operatorname{Re} z_{2} \)
\( \operatorname{Im} z_{1} \operatorname{Im} z_{2} \)
Subject: Maths
Find the area of a quadrilateral \( \boldsymbol{P Q R S} \)
in which \( \angle Q P S=\angle S Q R= \)
\( 90^{\circ}, P Q=12 \mathrm{cm}, P S=9 \mathrm{cm}, Q R= \)
\( 8 c m \) and \( S R=17 \mathrm{cm} \)
Subject: Maths
The complex number \( x+i y \) whose
modulus is unity, \( y \neq 0, \) can be represented as \( \boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}=\frac{\boldsymbol{a}+\boldsymbol{i}}{\boldsymbol{a}-\boldsymbol{i}}, \) where \( \boldsymbol{a} \)
is real number.
A . True
B. False
Subject: Chemistry
Assertion
\( P b_{3} O_{4} \) react with \( H N O_{3} \) and form
\( P b O_{2} \)
Reason
Lead is stable in +4 oxidation state.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) such that \( \boldsymbol{A} \boldsymbol{X}=\boldsymbol{I}, \) then
find \( \boldsymbol{X} \)
Subject: Physics
Assertion
A charge \( q \) is placed inside the square of side b. The flux associated with the
square is independent of side length.
Reason

Gauss's law is independent of size of
the Gaussian surface.
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
The Henry law constant for dissolution of a gas in an aqueous medium is \( 3 \times \) \( 10^{2} \) atm. At what partial pressure of the
gas (in atm), the molality of gas in aqueous solution will be \( \frac{5}{9} M ? \)
A . 2.2 M
в. 9 м
\( c .3 \) м
D. none
Subject: Chemistry
The solution of \( H_{2} O_{2} \) can be stored for a
long time at room temperature. However, bubbles of oxygen form as soon as a drop of bromine is added. The role of bromine for the reaction
\( 2 H_{2} O_{2}(a q) \rightarrow 2 H_{2} O(l)+O_{2}(g) \) is :
This question has multiple correct options
A. to act as a positive catalyst
B. to form an intermediate \( \left(B r^{-}\right) \) on reacting with \( H_{2} O_{2} \) following reduction of bromine and then to show oxidation of \( B r^{-} \) to \( B r_{2} \) by \( H_{2} O_{2} \)
c. to act as heterogeneous catalyst
D. to act as negative catalyst
Subject: Physics
What type of lens from the following would you have in your magnifying lens to read a page in small print?
A. A convex lens of focal length \( 80 \mathrm{cm} \)
B. A concave lens of focal length 80 cm
c. A concave lens of focal length \( 4 \mathrm{cm} \)
D. A convex lens of focal length of \( 4 \mathrm{cm} \)
Subject: Chemistry
\( \operatorname{Both}\left[N i(\mathbf{C O})_{4}\right] \) and \( \left[N i(C N)_{4}\right]^{2-} \) are
diamagnetic. The hybridization of nickel in these complexes, respectively, are:
\( \mathbf{A} \cdot \mathbf{s p}^{3}, \mathbf{s p}^{3} \)
\( \mathbf{B} \cdot \mathbf{s p}^{3}, \mathrm{dsp}^{2} \)
\( \mathbf{c} \cdot \mathrm{d} \mathbf{s} \mathrm{p}^{2}, \mathrm{sp}^{3} \)
D. \( \operatorname{dsp}^{2}, \operatorname{dsp}^{2} \)
Subject: Chemistry
Which of the following electron transition in hydrogen atom will require the largest amount of energy?
A. from \( n=1 \) to \( n=2 \)
B. from \( n=2 \) to \( n=3 \)
\( c . \) from \( n=\infty \) to \( n=1 \)
D. from \( n=3 \) to \( n=5 \)
Subject: Chemistry
Which among the following has highest boiling point?
A. \( C H_{3} C H_{2} C H_{2} C H_{2} C l \)
в. \( \left(C H_{3}\right)_{2} C H C H_{2} C l \)
c. \( \left(C H_{3}\right)_{3} C-C l \)
D. None of the above
Subject: Maths
Let \( A \) and \( B \) be two events such that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \geq \mathbf{3} / \mathbf{4} \) and \( \mathbf{1} / \mathbf{8} \leq \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B}) \leq \mathbf{3} / \mathbf{8} \)
Statement
1: \( \boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B}) \geq \mathbf{7} / \mathbf{8} \)
statement
2: \( \boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B}) \leq 11 / 8 \)
A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1
B. Both the statements are TRUE and STATEMENT 2 is not the correct explanation of STATEMENT
c. STATEMENT1 is TRUE and STATEMENT 2 is FALSE
D. STATEMENT1 is FALSE and STATEMENT 2 is TRUE
Subject: Chemistry
Homologue of \( \boldsymbol{C}_{3} \boldsymbol{H}_{4} \) is :
A \( \cdot C_{4} H_{6} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C H_{3} O H \)
D. \( H C H O \)
Subject: Physics
If \( n \) balls hit elastically and normally on a surface per unit time and all the balls are of mass \( m \) moving with the same
velocity \( u, \) then force on the surface is:
\( \mathbf{A} \cdot m \times u \times n \)
В . \( 2 \times m \times u \times n \)
c. \( \frac{1}{2} \times m u^{2} n \)
D. \( m u^{2} n \)
Subject: Maths
\( \lim _{n \rightarrow \infty}\left[\frac{1}{n^{2}} \sec ^{2} \frac{1}{n^{2}}+\frac{2}{n^{2}} \sec ^{2} \frac{4}{n^{2}}+\frac{3}{n^{2}} \sec ^{2}\right. \)
equals
A \( \cdot \frac{1}{2} \operatorname{cosec} 1 \)
B. \( \frac{1}{2} \) sec
c. \( \frac{1}{2} \tan 1 \)
D. \( \tan 1 \)
Subject: Maths
Assertion
Consider the polynomial function \( f(x)=\frac{x^{7}}{7}-\frac{x^{6}}{6}+\frac{x^{5}}{5}-\frac{x^{4}}{4}+\frac{x^{3}}{3}- \)
\( \frac{x^{2}}{2}+x . \) The equation \( f(x)=0 \) cannot
have two or more roots.
Reason
Rolle's theorem is not applicable for \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) on any interval \( [\boldsymbol{a}, \boldsymbol{b}], \) where
\( \boldsymbol{a}, \boldsymbol{b} \boldsymbol{\epsilon} \boldsymbol{R} \)
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
A inductance capacitance circuit is in
the state of resonance. if the \( C=0.1 \mu F \)
and \( \boldsymbol{L}=\mathbf{0 . 2 5} \) Henry. Neglecting ohmic resistance of circuit what is the
frequency of oscillations
A. \( 1007 \mathrm{Hz} \)
в. \( 100 \mathrm{Hz} \)
\( \mathrm{c} .109 \mathrm{Hz} \)
D. \( 500 H z \)
Subject: Maths
A die is rolled so that the probability of
face \( i \) is proportional to \( i,\{i= \) \( 1,2, \dots .6\} . \) The probability of an even number occurring when the die is rolled
is
\( A \cdot \frac{7}{4} \)
B. \( \frac{4}{7} \)
\( c \cdot \frac{5}{7} \)
D. None of these
Subject: Chemistry
When a brown compound of \( \mathrm{Mn}(\mathrm{A}) \) is treated with \( H C l, \) it gives a gas B. The
gas B taken in excess reacts with \( N H_{3} \) to give an explosive compound C. The compounds \( A, B \) and \( C \) are :
A. \( A=M n O_{2}, B=C l_{2}, C=N C l_{3} \)
В. \( A=M n O, B=C l_{2}, C=N H_{4} C l \)
c. \( A=M n_{3} O_{4}, B=C l_{2}, C=N C l_{3} \)
D. \( A=M n O_{3}, B=C l_{2}, C=N C l_{2} \)
Subject: Chemistry
The order of decreasing \( \boldsymbol{S}_{N} \mathbf{1} \) reactivities of the halides:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C l} \quad \boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H} \boldsymbol{C H} \boldsymbol{C l C H}_{3} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H C l C} \)
\( \boldsymbol{I} \)
\( \boldsymbol{I} \)
A. \( I>I I>I I I \)
в. \( I I>I>I I I \)
c. \( I I>I I I>I \)
D. \( I I I>I I>I \)
Subject: Maths
In the figure above, point \( \mathrm{B} \) lies on \( \overline{\boldsymbol{A} C} \).
Find a possible value of \( \boldsymbol{X}, \) if \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
are integers.
A \( .30^{\circ} \)
B. \( 35^{\circ} \)
\( c \cdot 40^{\circ} \)
\( D .50 \)
E. 55
Subject: Physics
One end of a lagged cylindrical metal rod of length \( 31.4 \mathrm{cm} \) and radius \( 2 \mathrm{cm} \)
is kept in contact with ice at \( 0^{\circ} \mathrm{c} \) and
the other end in water at \( 100^{\circ} \mathrm{C} \). Find
the rate of melting of ice per minute. \( \boldsymbol{L}=\mathbf{8 0} \boldsymbol{c a l} / \boldsymbol{g}, \boldsymbol{k}=\mathbf{1 0}^{\mathbf{5}} \) S.I. units \( (\mathbf{7 . 5} \boldsymbol{g}) \)
Subject: Maths
Given the perimeter of rhombus is 40 \( \mathrm{cm} \) and one diagonal is \( 12 \mathrm{cm} \). The length of second diagonal is
A . \( 19 \mathrm{cm} \)
B. 18 \( \mathrm{cm} \)
\( c \cdot 17 \mathrm{cm} \)
D. \( 16 \mathrm{cm} \)
Subject: Maths
100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the
maximum number of surnames lie.
\begin{tabular}{|c|c|}
\hline Number of letters & Number of surnames \\
\hline \( 1-4 \) & 6 \\
\( 4-6 \) & 30 \\
\( 6-8 \) & 44 \\
\( 8-12 \) & 16 \\
\( 12-20 \) & 4 \\
\hline
\end{tabular}
Subject: Maths
If \( X \) is a \( 2 \times 3 \) matrix such that
\( \left|\boldsymbol{X}^{\boldsymbol{T}} \boldsymbol{X}\right| \neq \mathbf{0} \) and \( \boldsymbol{A}=\boldsymbol{I}_{2}- \)
\( X\left(X^{T} X\right)^{-1} X^{T} \) then \( A^{2} \) is equal to:
\( \left(X^{T} \text { denotes transpose of matrix } X\right) \)
A. \( A \)
B. \( I \)
\( c \cdot A^{-1} \)
D. \( A X \)
Subject: Chemistry
Assertion
\( s p^{3} \) hybrid carbon atom is more electronegative than sp hybrid carbon
atom.
Reason
\( s p^{3} \) hybrid orbitals are more closer to
the nucleus
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
The equation \( 2 x^{2}+3 y^{2}-8 x-18 y+ \)
\( \mathbf{3 5}=\boldsymbol{\lambda} \) represents?
A . A circle for all \( \lambda \)
B. An ellipse if \( \lambda<0 \)
c. The empty set if \( \lambda>0 \)
D. A-point if \( \lambda=0 \)
Subject: Physics
A vehicle starts from rest and moves at
uniform acceleration such that its
velocity increases by \( 3 m s^{-1} \) per every second. If diameter of wheel of that vehicle is \( 60 \mathrm{cm}, \) the angular acceleration of wheel is:
A .5 rads\( ^{-2} \)
B. 10 rads\( ^{-2} \)
C .15 rads\( ^{-2} \)
D. 20 rads \( ^{-2} \)
Subject: Maths
The unit vector perpendicular to the plane determined by \( \boldsymbol{P}(\mathbf{1},-\mathbf{1}, \mathbf{2}) \)
\( Q(2,0,-1), R(0,2,1) \) is
A \( \cdot \frac{i+2 j+k}{\sqrt{6}} \)
в. \( \frac{i-2 j+2 k}{\sqrt{6}} \)
c. \( \frac{2 i+j+k}{\sqrt{6}} \)
D. none of these
Subject: Chemistry
Q Type your question
by \( \boldsymbol{S}_{N} \mathbf{1} \) IS \( \boldsymbol{3}^{v}>\boldsymbol{Z}^{v} \mathbf{1}^{v} \boldsymbol{K} \boldsymbol{X} \) and \( \mathbf{b} \mathbf{y} \boldsymbol{\nabla} \boldsymbol{V}^{-} \)
path is \( 1^{\circ}>2^{\circ}>3^{\circ} R X \)
Which of the following statements are
correct for the above energy diagras of
\( \boldsymbol{S}_{N} \mathbf{1} \) and \( \boldsymbol{S}_{N} \mathbf{2} \) reactions?
\( (a) \)
Fig. \( (\mathbf{b}) \)
This question has multiple correct options
\( \mathbf{A} \cdot(I) \) is Fig (a) and \( (I V) \) in Fig. (b) represent \( S_{N} 1 \) reaction
B. \( (I I) \) is Fig (a) and \( (I I I) \) in Fig. (b) represent \( S_{N} 2 \) reaction
\( \mathbf{C} \cdot \) Fig.
(a) and Fig. (b) are the energy diagrams for \( 1^{\circ} R X \)
and \( 3^{\circ} R X \) respectively
\( D \cdot F i g \)
(a) and Fig. (b) are the energy diagrams for \( 3^{\circ} \) RX
and \( 1^{\circ} R X \) respectively
Subject: Physics
\( Q \) amount of electric charge is present
on the surface of a sphere having radius
\( \boldsymbol{R} \). Then electrical potential energy of this system is
\( \mathbf{A} \cdot \frac{K Q^{2}}{R^{2}} \)
в. \( \frac{K Q^{2}}{R} \)
c. \( \frac{1}{2} \frac{K Q^{2}}{R} \)
D. \( \frac{1}{2} \frac{K Q^{2}}{R^{2}} \)
Subject: Physics
An aeroplane is flying in a horizontal direction at \( 600 k m / h r \) at a height of \( 6 k m s \) and is advancing towards a point
which is exactly over a target on earth. At that instant the pilot releases a ball which on descending the earth strike
the target. The falling ball appears-
A. To the pilot in the aeroplane, as falling along a parabolic path
B. To a person standing near the target, as falling exactly vertical
c. To a person standing near the target, as describing a parabolic path
D. To the pilot sitting in the aeroplane, as falling in a zigzag path
Subject: Physics
A conductor of uniform resistance (per
unit length) bent in the form of an
equilateral triangle of side a. It is
enclosing on inward magnetic field \( \vec{B}=B_{0} \cos ^{2} \omega t(-\hat{k}) . \) Then
This question has multiple correct options
A \( \cdot \) During \( 0<t<\frac{\pi}{2 \omega} \) an clockwise current is induced in
the coil.
B. During \( 0<t<\frac{\pi}{\omega} \) an anticlockwise current is induced
in the coil
C . During \( \frac{\pi}{2 \omega}<t<\frac{\pi}{\omega} \) an anticlockwise current flows
through it
D. During \( \frac{\pi}{\omega}<t<\frac{3 \pi}{2 \omega} \) a clockwise current flows through
it
Subject: Physics
The acceleration - time graph for a particle in rectilinear motion is as
shown in the figure. Find the average
acceleration in first twenty seconds.
\( A \cdot 10 m s^{-2} \)
B. \( 15 \mathrm{ms}^{-2} \)
\( \mathrm{c} \cdot 20 \mathrm{ms}^{-2} \)
D. \( 25 \mathrm{ms}^{-2} \)
Subject: Physics
Vectors \( \vec{a} \) and \( \vec{b} \) make an angle \( \theta=\frac{2 \pi}{3} \) If \( |\vec{a}|=1,|\vec{b}|=2 \) then
\( \{(\vec{a}+3 \vec{b}) \times(3 \vec{a}-\vec{b})\}^{2}= \)
A . 225
B. 250
c. 275
D. 300
Subject: Chemistry
A crystalline hydrated salt on being rendered anhydrous, loses \( 45.6 \% \) of its weight. The percentage composition of anhydrous salt is : \( A I=10.5 \%, K=15.1 \%, S \) \( =24.8 \% \) and \( I=49.6 \% . \) Find the
empirical formula of the salt.
A . \( K A l S_{2} I \)
в. \( K_{2} \) А \( l S_{2} I \)
c. \( K A l S_{2} I .12 H_{2} O \)
D. \( K_{2} A l S_{2} I .12 H_{2} O \)
Subject: Physics
A sinusoidal wave is travelling along a rope. The oscillator that generates the wave completes 60 vibrations in 30 s. Also a given maximum travels \( 425 \mathrm{cm} \) along the rope in 10.0 s. What is the
wavelength of the wave?
A. \( 21.25 \mathrm{cm} \)
B. 36.32 \( \mathrm{cm} \)
c. \( 48.26 \mathrm{cm} \)
D. 42.50 \( \mathrm{cm} \)
Subject: Chemistry
Arrange the following \( (\mathbf{w}, \mathbf{x}, \mathbf{y}, \mathbf{z}, \mathbf{)} \) in
decreasing order of their boiling points:
\( \mathbf{A} \cdot w>x>z>y \)
в. \( w>x>y>z \)
с. \( w>z>y>x \)
D. \( w>z>x>y \)
Subject: Physics
A electric charge \( 10^{-8} C \) is placed at the
point \( (4 m, 7 m, 2 m) . \) At the point \( (1 m, 3 m, 2 m) \) the electric
A. potential will be \( 18 V \)
B. field has no \( Y \) -component
c. field will be along \( Z \) -axis
D. potential will be \( 1.8 V \)
Subject: Physics
Assertion - The sound emitted by the
source travels in all directions.

Reason - The relative velocity of sound with respect to the observer is the sum
of velocity of sound and velocity of
observer.
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 the various terms in the below-given expressions have usual meanings, the van't Hoff factor ( \( i \) ) cannot be calculated
by which of the following expression?
A \( . \pi V=\sqrt{i n R T} \)
B. \( \Delta T_{f}=i K_{f}-m \)
c. \( \Delta T_{b}=i K_{b}-m \)
\( \frac{P_{\text {solvent}}^{o}-P_{\text {solution}}}{P_{\text {solvent}}^{o}}=i\left(\frac{n}{N+n}\right) \)
Subject: Maths
If \( \mathbf{y}=\mathbf{b} \cos \log \left(\frac{\boldsymbol{x}}{\boldsymbol{n}}\right)^{\boldsymbol{n}}, \boldsymbol{t h e n} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot \frac{-n b \sin \log (x)^{n}}{x} \)
B. \( n b \sin \log \left(\frac{x}{n}\right)^{n} \)
c. \( _{-n b \sin \log }\left(\frac{x}{n}\right)^{n} \)
D. None of these
Subject: Maths
Find the value of \( \lambda \) for which the four
points \( A, B, C, D \) with position vectors \( -\widehat{\boldsymbol{j}}-\widehat{\boldsymbol{k}} ; \boldsymbol{4} \hat{\boldsymbol{i}}+\boldsymbol{5} \hat{\boldsymbol{j}}+\boldsymbol{\lambda} \hat{\boldsymbol{k}} ; \boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{9} \hat{\boldsymbol{j}}+\boldsymbol{4} \widehat{\boldsymbol{k}} \) and
\( -4 \hat{i}+4 \widehat{j}+4 \widehat{k} \) are coplanar.
Subject: Chemistry
The product formed in the reaction is
\( B C l_{3}+H_{2} O \longrightarrow \) Product :
\( \mathbf{A} \cdot H_{3} B O_{3}+H C l \)
в. \( B_{2} O_{3}+ \) НОС\( l \)
c. \( B_{2} H_{6}+H C l \)
D. no reaction
Subject: Maths
The value of \( \triangle= \)
\( \begin{array}{cc}\mathbf{2} & \boldsymbol{a}+\boldsymbol{r}+\mathbf{2} \\ \boldsymbol{a}+\boldsymbol{r}+\mathbf{2} & \mathbf{2}(\boldsymbol{a}+\mathbf{1})(\boldsymbol{r}+\mathbf{1}) \\ \boldsymbol{a}+\boldsymbol{r} & \boldsymbol{a}(\boldsymbol{r}+\mathbf{1})+\boldsymbol{r}(\boldsymbol{a}+\mathbf{1})\end{array} \)
\( A \)
в. \( -2 a(r+1) \)
c. \( a(a r+r+a) \)
D. -1
Subject: Chemistry
Assertion
Alkyl halides are colourless when pure.
Reason
Bromides and lodides develop colour
when exposed to light.
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 temperature of gas is increased
from \( 27^{\circ} \mathrm{C} \) to \( 127^{\circ} \mathrm{C} \). The ratio of its mean
kinetic energies will be
A \( \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
c. \( \frac{9}{16} \)
D. \( \frac{16}{9} \)
Subject: Physics
Intensity of central fringe in interference pattern is \( 0.1 W / m^{2} \) then find intensity at a point having path difference \( \lambda / 3 \) on screen from centre
\( \left.\operatorname{in} m W / m^{2}\right): \)
A . 2.5
B. 5
c. 7.5
D. 10
Subject: Maths
If \( N \) denote the set of all natural
numbers and \( R \) be the relation on \( N \times \)
\( N \) defined by \( (a, b) R(c, d) . \) if \( a d(b+ \)
\( c)=b c(a+d), \) then \( R \) is
A. Symmetric only
B. Reflexive only
c. Transitive only
D. An equivalence relation
Subject: Chemistry
Statement 1: Bakelite is hard and has
high melting point.

Statement 2: Intermolecular forces of
attraction in it are H-bonding.
A. Statement 1 is true; statement 2 is true; statement 2 is the correct explanation of statement
B. Statement 1 is true; statement 2 is true; statement 2 is not the correct explanation of statement 1
c. Statement 1 is true; statement 2 is false
D. Statement 1 is false; statement 2 is true
Subject: Physics
A person sitting on the top of a tall building is dropping balls at regular intervals of one second. Find the
position of the \( 3 r d, 4 \) th and 5 th ball when the 6 th ball is being dropped
A. \( 24.1 \mathrm{m}, 19.6 \mathrm{m} \) and \( 4.9 \mathrm{m} \) above the top
B. 44.1 \( \mathrm{m}, 19.6 \mathrm{m} \) and 4.9 \( \mathrm{m} \) bellow the top
c. \( 44.1 \mathrm{m}, 12.6 \mathrm{m} \) and \( 4.9 \mathrm{m} \) bellow the top
D. \( 41.4 \mathrm{m}, 29.6 \mathrm{m} \) and \( 4.9 \mathrm{m} \) bellow the top
Subject: Maths
f \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi}, \) then
\( \left|\begin{array}{ccc}\sin (\boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}) & \sin \boldsymbol{B} & \cos \boldsymbol{C} \\ -\sin \boldsymbol{B} & \boldsymbol{0} & \tan \boldsymbol{A} \\ \cos (\boldsymbol{A}+\boldsymbol{B}) & -\tan \boldsymbol{A} & 0\end{array}\right| \)
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 2 \sin B \tan A \cos C \)
\( c .1 \)
D. None of these
Subject: Physics
In an adiabatic change, the pressure
and temperature of a monoatomic gas
are related with relation as \( \boldsymbol{P} \propto \boldsymbol{T}^{C} \)
where \( C \) is equal to
A \( \cdot \frac{5}{4} \)
B. \( \frac{5}{3} \)
\( c \cdot \frac{5}{2} \)
D. \( \frac{3}{5} \)
Subject: Physics
Two current carrying loops having \( N_{1} \)
turns and \( N_{2} \) turns respectively both
carrying a current equal to \( I \) in the same direction, are placed inside a magnetic field \( B \). If the radii of both
loops are in the ratio 1: 3 then what will
be the ratio of the potential energy of loops in that magnetic field?
A \( \cdot \frac{N_{1}}{N_{2}} \)
B. \( \frac{2 N_{1}}{N_{2}} \)
c. \( \frac{N_{1}}{3 N_{2}} \)
D. \( \frac{N_{1}}{9 N_{2}} \)
Subject: Physics
Astronomical unit (AU) is the distance
between earth and the sun, 1 AU is equal
to the
A \( \cdot 1.496 \times 10^{8} k m \)
В. \( 9.46 \times 10^{12} k m \)
c. \( 3.084 \times 10^{13} k m \)
D. \( 4.596 \times 10^{15} \mathrm{km} \)
Subject: Physics
Equation of trajectory of a projectile is
given by \( y=-x^{2}+10 x \) where \( x \) and \( y \)
are in meters and \( x \) is along horizontal
and y is vertically upward and particle is projected from origin. Then which of the following options is/are correct.
\( \left(g=10 m / s^{2}\right) \)
A. Initial velocity of particle is \( \sqrt{505} \mathrm{m} / \mathrm{s} \)
B. Horizontal range is \( 10 \mathrm{m} \)
c. Maximum height is 25 m
D. Angle of projection with horizontal is \( \tan ^{-1}(5) \)
Subject: Chemistry
Which of the above synthetic scheme
can be used to prepare the oct-2,7dione?
A. React acetylene with \( N a N H_{2} / N H_{3} \); add half of an equivalent of 1,4-dibromobutane; then add \( H_{2} O / H_{2} S O_{4} / H g S O_{4} \)
B. React 1,6-octadiene with \( O_{3} \) followed by \( Z n \) -acetic acid
C . React 1,2-dimethylcyclohexene with \( K M n O_{4} / H^{+} \)
D. Both (a) and (c) may work.
Subject: Chemistry
Which hybrid orbitals are used by carbon atoms in the following molecules?
\( (a) C H_{3}-C H_{3} \)
\( (b) C H_{3}-C H=C H_{2} \)
\( (c) C H_{3}-C H_{2}-O H \)
\( (\boldsymbol{d}) \boldsymbol{C H}_{3}-\boldsymbol{C H O} \)
\( (e) C H_{3} C O O H \)
Subject: Physics
A rocket is moving in a gravity free space with a constant acceleration of
\( 2 m s^{-2} \) along \( +x \) direction (see figure) The length of a chamber inside the rocket is \( 4 m . \) A ball is thrown from the
left end of the chamber in \( +x \) direction
with a speed of \( 0.3 m s^{-1} \) relative to the
rocket. At the same time, another ball is thrown in - - x direction with a speed of
\( 0.2 m s^{-1} \) from its right end relative to the rocket. The time in seconds when
the two balls hit each other is
Subject: Physics
If an electron describes half a revolution
in a circle of radius \( r \) in a magnetic field
B, the energy acquired by it is
A. zero
B. \( \frac{1}{2} m v^{2} \)
c. \( \frac{1}{4} m v^{2} \)
\( \mathbf{D} \cdot \mu_{r} \times B e v \)