AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( A \) and \( B \) are events such that \( P(A)= \) \( \frac{3}{8}, P(B)=\frac{5}{8} \) and \( P(A \cup B)=\frac{3}{4}, \) then
\( P\left(\frac{A}{B}\right)= \)
\( A \cdot \frac{2}{3} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Maths
f \( y=\left(\tan ^{-1} x\right)^{2}, \) show that \( (1+ \)
\( \left.x^{2}\right)^{2} \frac{d^{2} y}{d x^{2}}+2 x\left(1+x^{2}\right) \frac{d y}{d x}-2=0 \)
Subject: Chemistry
Which of the following does not contain \( O-O \) bond?
This question has multiple correct options
\( A \cdot S_{2} O_{8}^{2-} \)
B. \( S_{4} O_{6}^{2-} \)
\( \mathbf{c} \cdot S O_{5}^{2-} \)
D. \( S_{2} O_{7}^{2} \)
Subject: Chemistry
List \( A \) List \( \mathrm{B} \)
A. Dry Cell
(P) Primary cell
B. Lead storage battery
(Q) \( 38 \% H_{2} S O_{4} \)
C. Ni-Cd cell
\( (\mathrm{R}) M n O_{2}+C \)
D. \( H_{2}-O_{2} \) fuel cell
(S) Secondary cell
A \( \cdot \) A-P,R: B-Q,S:C-S:D-S
B. A-Q,R: B-P,S:C.C-P:D-Q
c. A-P, B-S:C-P,S :D-Q,R
D. A-R: B-Q:C-Q,S:D-P
Subject: Physics
An electric motor exerts a constant
torque \( 10 \mathrm{N}-\mathrm{m} \) on a grind stone mounted on a shaft. MOI of the grind stone about
the shaft is \( 2 \mathrm{kg} m^{-2} . \) If the system
starts from rest, find the work done in
\( 8 s \)
A . \( 1600 J \)
B. \( 1200 J \)
\( c .800 J \)
D. \( 600 J \)
Subject: Physics
A capacitor of capacitance \( C \) has initial
charge \( Q_{0} \) and connected to an inductor
of inductance \( L \) as shown. At \( t=0 \) switch
S is closed. The current through the inductor when energy in the capacitor is three times the energy of inductor is
A \( \cdot \frac{Q_{0}}{2 \sqrt{L C}} \)
в. \( \frac{Q_{0}}{\sqrt{L C}} \)
c. \( \frac{2 Q_{0}}{\sqrt{L C}} \)
D. \( \frac{4 Q_{0}}{\sqrt{L C}} \)
Subject: Physics
A \( 10 \mathrm{kg} \) mass moves along \( \mathrm{X} \) -axis. Its
acceleration as a functions of its
position is shown in the figure. What is
the total work done on the mass by the
force as the mass moves from \( x=0 \) to
\( x=8 \mathrm{cm} ? \)
\( \mathbf{A} \cdot 8 \times 10^{-2} J \)
В. \( 16 \times 10^{-2} J \)
C. \( 4 \times 10^{-4} J \)
D. \( 1.6 \times 10^{-3} J \)
Subject: Maths
The sum of the series \( \frac{1}{(1 \times 2)}+ \) \( \frac{1}{(2 \times 3)}+\frac{1}{(3 \times 4)}+\ldots \ldots+ \)
\( \frac{1}{(100 \times 101)} \) is equal to
A \( \cdot \frac{20}{1010} \)
в. \( \frac{100}{1010} \)
c. \( \frac{50}{101} \)
D. \( \frac{25}{101} \)
Subject: Chemistry
The normal boiling point of a liquid \( A \) is
\( 350 \mathrm{K} . \Delta \boldsymbol{H}_{\boldsymbol{v a p}} \) at normal boiling point
is \( 35 \mathrm{KJ} / \mathrm{mole} \). Pick out the correct
statement(s). (Assume \( \Delta H_{v a p} \) to be independent of pressure)
A. \( \Delta S_{\text {vaporisation}}>100 \mathrm{J} / \mathrm{K} \) mole at \( 350 \mathrm{K} \) and \( 0.5 \mathrm{atm} \)
B. \( \Delta S_{\text {vapprisation}}<100 \mathrm{J} / \mathrm{K} \) mole at \( 350 \mathrm{K} \) and \( 0.5 \mathrm{atm} \)
C. \( \Delta S_{\text {vaporisation}}<100 \) J/K mole at \( 350 \mathrm{K} \) and 2 atm
D. \( \Delta S_{\text {vaporisation}}=100 \mathrm{J} / \mathrm{K} \) mole at \( 350 \mathrm{K} \) and \( 2 \mathrm{atm} \)
Subject: Physics
Two spheres \( A \) and \( B \) moving in opposite
directions have velocities of \( 10 m s^{-1} \)
and \( 20 m s^{-1} . \) The two spheres collide
with each other elastically. If \( A \) continues to move in the same
direction at \( 4 m s^{-1}, \) the velocity of
sphere B just after the collision is
A. \( 34 m / s \) in the same direction
B. \( 34 m / s \) in the opposite direction
c. \( 26 m / s \) in the same direction
D. \( 34 m / s \) in the opposit direction
Subject: Maths
\( \$ \$ \operatorname{lint}|,| \operatorname{left}\left[x \sin ^{\wedge}\{-1\} x \mid, \text { lleft } \mid\{1\right. \)
\( \left|\operatorname{sqrt}\left\{\left(1|,-|, \mathbf{x}^{\wedge} 2\right\}|,| r i g h t \mid\right\} \wedge\{-1\}\right| \)
|right \( ] \wedge \mid, \$ \$ d x \)
Subject: Maths
Graph shows the number of units
consumed by a family for six months.
Find the cost of energy for four months
from March to June if M.S.E.B increased
its unit rate from Rs.3.50 to Rs. 4.50 for
April and May and again decreased by
Rs.2 for June:
A. Rs.6000
B. Rs.6, 030
c. Rs.6, 300
D. Rs.6, 200
Subject: Chemistry
A weak acid \( H X \) has the dissociation
constant \( 1 \times 10^{-5} M . \) It forms a salt
\( N a X \) on reaction with alkali. The
percentage hydrolysis of \( 0.1 \mathrm{M} \) solutions of \( N a X \) is:
A. \( 0.0001 \% \)
B . \( 0.01 \% \)
c. \( 0.1 \% \)
D. \( 0.15 \% \) \%
Subject: Maths
If \( \frac{x^{a^{2}}}{x^{b^{2}}}=x^{16}, x>1, \) and \( a+b=2, \) what
is the value of \( a-b ? \)
\( A \cdot 8 \)
B. 14
\( c \cdot 16 \)
D. 18
Subject: Physics
Consider two conducting spheres of
radii \( R_{1} \) and \( R_{2} \) with \( R_{1}>R_{2} \). If the two
are at the same potential, and the larger sphere has more charge than the smaller sphere, then
A. the charge density of smaller sphere is less than that of larger sphere
B. the charge density of smaller sphere is more than that of larger sphere.
c. both spheres may have same charge density
D. None of these.
Subject: Chemistry
Select the correct statements about
greenhouse gases:
A. Carbon dioxide is the only gas in the atmosphere which causes global warming.
B. The greenhouse gases trap heat and do not allow heat to escape into outer
space
C. Water vapours do not contribute to the greenhouse effect.
D. The presence of excessive greenhouse gases in the atmosphere is responsible for global warming.
A. A and B
B. B and D
c. \( c \) and \( B \)
D. D and A
Subject: Maths
In the following figure, \( \Delta A B C \) is an isosceles triangles with perimeter
\( 40 \mathrm{cm} . \) The base \( A C \) is of length \( 10 \mathrm{cm} \)
Side \( A B \) and side \( B C \) are congruent. \( A \)
circle touches the three sides as shown
in the figure below. Find the length of
the tangent segment from point \( B \) to
the circle.
Subject: Maths
If \( \mathbf{A}=\left\{\begin{array}{ll}\mathbf{2} & \mathbf{2} \\ \mathbf{- 3} & \mathbf{2}\end{array}\right\}, \mathbf{B}=\left\{\begin{array}{ll}\mathbf{0} & -\mathbf{1} \\ \mathbf{1} & \mathbf{0}\end{array}\right\} \)
\( \operatorname{then}\left(\boldsymbol{B}^{-\mathbf{1}} \boldsymbol{A}^{-1}\right)^{-\mathbf{1}_{=}} \)
\( \mathbf{A} \cdot\left\{\begin{array}{ll}2 & -2 \\ 2 & 3\end{array}\right\} \)
в. \( \left\{\begin{array}{ll}3 & -2 \\ 2 & 2\end{array}\right\} \)
c. \( \frac{1}{10}\left\{\begin{array}{ll}2 & 2 \\ -2 & 3\end{array}\right\} \)
D \( \cdot \frac{1}{10}\left\{\begin{array}{ll}3 & 2 \\ -2 & 2\end{array}\right\} \)
Subject: Physics
The potential energy of a particle of
mass \( 1 k g \) in motion along the \( x \) -axis is given by \( U=4(1-\cos 2 x) J . \) Here \( x \) is
in meter. The period of small oscillations (in sec) is
\( \mathbf{A} \cdot 2 \pi \)
в. \( \pi \)
\( c \cdot \frac{\pi}{2} \)
D. \( \sqrt{2 \pi} \)
Subject: Physics
A bone fragment found in a cave contains 0.21 times as much \( _{6}^{14} \mathrm{C} \) as in equal amount of carbon in air when the organism containing bone died. Find the approximate age of fragment \( t_{1 / 2} \) of
\( \frac{14}{6} \mathbf{C}=5730 \) years
A \( \cdot 1.15 \times 10^{4} y \)
B. \( 1.3 \times 10^{4} y \)
c. \( 1.24 \times 10^{4} y \)
D. \( 1.4 \times 10^{4} y \)
Subject: Physics
The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is \( 6 V \) and the load resistance is
\( R_{L}=4 k \Omega . \) The series resistance of the
circuit is \( R_{i}=1 k \Omega . \) If the battery
voltage \( V_{B} \) varies from \( 8 V \) to \( 16 V \), what
are the minimum and maximum values
of the current through Zener diode?
A. \( 0.5 \mathrm{mA} ; 6 \mathrm{mA} \)
B. \( 0.5 \mathrm{mA} ; 8.5 \mathrm{mA} \)
c. \( 1.5 m A ; 8.5 m A \)
D. \( 1 \mathrm{mA} ; 8.5 \mathrm{mA} \)
Subject: Chemistry
Potash alum is represented by the formula:
A \( \cdot K_{2} S O_{4} \cdot A l_{2}\left(S O_{4}\right)_{3} \cdot 24 H_{2} O \)
B . \( K \cdot A l\left(S O_{4}\right)_{2} \cdot 12 H_{2} O \)
c. Both (a) and (b)
D. None of these
Subject: Chemistry
The compounds \( (C) \) and \( (D) \)
respectively are:
\( \mathbf{A} \cdot E t N H_{2} \) and \( \operatorname{Pr} C H=O \)
B. \( E t-N H- \)Pr and \( H C O O H \)
\( \mathbf{C} \cdot \operatorname{Pr} N H_{2} \) and \( E t C H=O \)
D. \( E t N H_{2} \) and \( \operatorname{Pr} C H_{2} O H \)
Subject: Maths
If \( y=f(x)=\frac{x+2}{x-1}, \) than it is incorrect
to say:
A. \( x=\frac{y+2}{y-1} \)
B. \( f(0)=-2 \)
c. \( f(1)=0 \)
D. \( f(-2)=0 \)
E . \( f(y)=x \)
Subject: Chemistry
Identify isostructural pairs from \( N F_{3}(I), N O_{3}^{-}(I I), B F_{3}(I I I), H_{3} O^{+}(I L \)
A . । \& ॥, ॥ा \& ।
B. I \& V, II \& III
c. । \& ाए, ॥ \& ॥
D. I \& IV, III \& v
Subject: Chemistry
Which one of the following species has maximum conductance in their
aqueous solutions?
A \( \cdot K_{2} P t C l_{6} \)
в. \( P t C l_{4} \cdot 2 N H_{3} \)
c. \( P t C l_{4} \cdot 3 N H_{3} \)
D. \( P t C l_{4} \cdot 5 N H_{3} \)
Subject: Physics
A solenoid of length \( 0.4 m \) and diameter
\( 0.6 m \) consists of a single layer of 1000
turns of fine wire carrying a current of
\( \mathbf{5} \times \mathbf{1 0}^{-\mathbf{3}} \) A. Calculate the magnetic
field on the axis at the middle and at
the end of the solenoid:
A \( \cdot 8.7 \times 10^{-6} T, 6.28 \times 10^{-6} T \)
B . \( 6.28 \times 10^{-6} T, 8.7 \times 10^{-6} T \)
D. \( 8.7 \times 10^{-6} T, 8.28 \times 10^{-6} T \)
Subject: Physics
A boy moving with a velocity of \( 20 k m / h \)
along a straight line joining two stationary objects. According to him both objects
A. move in the same direction with the same speed of
\( 20 \mathrm{km} / \mathrm{h} \)
B. move in different direction with the same speed of \( 20 \mathrm{km} / \mathrm{h} \)
c. move towards him
D. remains stationary
Subject: Maths
Component of \( \vec{a}=\hat{i}-\hat{j}-\hat{k} \)
perpendicular to the vector \( \overrightarrow{\boldsymbol{b}}=2 \hat{\boldsymbol{i}}+ \) \( \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) is?
A \( \cdot \frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k}) \)
B \( \cdot \frac{1}{3}(\hat{i}-4 \hat{j}-2 \hat{k}) \)
c \( \cdot \frac{1}{3}(\hat{i}+4 \hat{j}+2 \hat{k}) \)
D \( \cdot \frac{1}{3}(\hat{i}+2 \hat{j}+\hat{k}) \)
Subject: Physics
If a vector \( 2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to the vector \( 4 \hat{i}-4 \hat{j}+\alpha \hat{k}, \) then value of
\( \boldsymbol{\alpha} \) is:
A . -1
в. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D. 1
Subject: Maths
Given \( : a x+b y=d \) and \( y=m x+c \)
Find \( x \) in terms of \( b, c, d \) and \( m \)
A \( \cdot x=\frac{d-b c}{a-b m} \)
B. \( x=\frac{d+b c}{a+b m} \)
c. \( _{x}=\frac{d-b c}{a+c m} \)
D. \( x=\frac{d-b c}{a+b m} \)
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C H}+\boldsymbol{H}_{2} \boldsymbol{O} \frac{\boldsymbol{H} \boldsymbol{g} \boldsymbol{S O}_{4}}{\boldsymbol{H}_{2} \boldsymbol{S O}_{4}}(\boldsymbol{A}) \)
The product \( A \) in above reaction is:
A. propanal
B. propanone
c. propene
D. both (a) and (b)
Subject: Chemistry
Which of the following order of acidity is
correct?
(I) \( \quad \mathbf{C H}_{3}-\mathbf{N H}_{2} \)
(II) \( \mathbf{H}-\mathbf{C} \equiv \mathbf{C}-\mathbf{H} \)
(III)
(IV)
A. \( I I I>I V>I>I I \)
В. \( I I I>I V>I I>I \)
c. \( I V>I I I>I>I I \)
D. \( I V>I I I>I I>I \)
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^{2}}= \)
\( A \cdot 2 \)
B. - 2
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \)
Subject: Chemistry
The equilibrium constant , Kp for
thegaseous reaction \( A \Leftrightarrow 2 B \) is related
to degree of dissociation \( \alpha \) of \( A \) and
total pressure \( P \) as
A \( \frac{4 \alpha^{2} P}{1-\alpha^{2}} \)
B. \( \frac{4 \alpha^{2} P^{2}}{1-\alpha^{2}} \)
c. \( \frac{4 \alpha^{2} P^{2}}{1-\alpha} \)
D. \( \frac{4 \alpha^{2} P}{1-\alpha} \)
Subject: Maths
Show that each of the relation \( R \) in the
\( \operatorname{set} A=\{x \in Z: 0 \leq x \leq 12\}, \) given by
is an equivalence relation. Find the set of all elements related to 1 in each case
\( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}=\boldsymbol{b}\} \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
\( \mathbf{8} \boldsymbol{x}^{2}+\boldsymbol{9} \boldsymbol{y}=\boldsymbol{6} \boldsymbol{x}+\boldsymbol{2} \)
Subject: Maths
n figure OPQR is a rhombus, three of whose vertices lie on the circle with
centre \( 0 . \) If the area of rhombus is 32
\( \sqrt{3} \mathrm{cm}^{2}, \) find the radius of the circle.
\( 4.6 \mathrm{cm} \)
B. 2 cm
\( c .4 \mathrm{cm} \)
\( D \)
Subject: Physics
\( A 60 \mu F \) capacitor is connected to a 110 \( \mathrm{V}(\mathrm{rms}), 60 \mathrm{Hz} \) ac supply. The rms value of Current in the circuit is:
A . 1.49 A
B. 14.9 A
c. 2.49 A
D. 24.9 A
Subject: Chemistry
Find the ratio of the following: \( (\operatorname{Max}(\mathrm{M}) \) \( +\operatorname{Max}(\mathrm{N})) /(\operatorname{Max}(\mathrm{K})+\operatorname{Max}(\mathrm{L})) \) where
Max denotes the maximum number of
electrons. \( K, L, M, N \) represent the shells.
A . 4
B. 5
\( c .6 \)
\( D .7 \)
Subject: Physics
Unpolarized light of intensity \( I \) is incident on a system of two polarizes, \( A \)
followed by \( B \). The intensity of emergent light is \( I / 2 . \) If a third polarizer \( C \) is placed between \( A \) and \( B \), the intensity
of emergent light is reduced to \( I / 3 . \) The
angle between the polarizers \( A \) and \( C \) is
\( \theta . \) Then
\( ^{\mathrm{A}} \cdot \cos \theta=\left(\frac{2}{3}\right)^{1 / 4} \)
в. \( \cos \theta=\left(\frac{1}{3}\right)^{1 / 4} \)
\( ^{\mathrm{c}} \cos \theta=\left(\frac{1}{3}\right)^{1 / 2} \)
Des \( \theta=\left(\frac{2}{3}\right)^{1 / 2} \)
Subject: Maths
If \( y=\frac{5 x}{(1-x)^{2 / 3}}+\cos ^{2}(2 x+1), \) find
\( \frac{d y}{d x} \)
A. \( \frac{5}{3(1-x)^{5 / 9}}(3-x)-2 \sin (4 x+2) \)
в. \( \frac{-5}{3(1-x)^{5 / 9}}(3-x)-2 \sin (4 x+2) \)
c. \( \frac{4}{3(1-x)^{5 / 9}}(3-x)-2 \sin (4 x+2) \)
D. \( \frac{5}{3(1-x)^{5 / 9}}(3-x)-\sin (4 x+2) \)
Subject: Chemistry
A galvanic cell is constructed using the
redox reaction, it is represented as:
\( \frac{1}{2} H_{2}(g)+A g C l(s) \rightleftharpoons H^{+}(a q)+ \)
\( \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
\( \mathbf{A} \cdot P t\left|H_{2}(g)\right| H C l(s o l n .) \| A g N O_{3}(s o l n .) \mid A g \)
B \( \cdot A g|A g C l(s)| K C l(s o l n .) \mid H C l(\text {soln.}), H_{2}(g) \mid P t \)
\( \mathbf{c} \cdot P t\left|H_{2}(g)\right| K C l(s o l n .) \| A g C l(s) \mid A g \)
\( \mathbf{D} \cdot P t\left|H_{2}(g), H C l(s o l n .) \| A g C l(s)\right| A g \)
Subject: Maths
The solution to the differential equation \( (x+1) \frac{d y}{d x}-y=e^{3 x}(x+1)^{2} \) is
A \( \cdot y=(x+1) e^{3 x}+c \)
B. \( 3 y=(x+1)+e^{3 x}+c \)
c. \( \frac{3 y}{x+1}=e^{3 x}+c \)
D. \( y e^{-3 x}=3(x+1)+c \)
Subject: Physics
A radioactive element \( X \) distintegrates
successively \( \boldsymbol{X} \stackrel{\boldsymbol{\beta}^{-}}{\longrightarrow} \boldsymbol{X}_{\mathbf{1}} \stackrel{\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{X}_{2} \stackrel{\boldsymbol{\beta}^{-}}{\longrightarrow} \boldsymbol{X}_{\mathbf{3}} \stackrel{\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{X}_{\mathbf{4}} \)
If atomic number and atomic mass
number of \( X \) are respectively 72 and \( 180, \) what are the corresponding values
for \( \boldsymbol{X}_{4} ? \)
A .69,172
B. 69,176
c. 71,176
D. 70,172
Subject: Chemistry
Assertion
Statement-I: In the extraction of Ag the
\( \operatorname{complex} N a\left[A g(C N)_{2}\right] \) is reacted with
Zn.
Reason
Statement- - II : Zn is transition metal
according to electronic theory.

Read the above assertion and reason
and choose the correct option regarding
¡t.
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
Match the following items in column I
with the corresponding items in column
\( \| \)
Column I
Portland
(i) \( N a_{2} C O_{3} \cdot 10 H_{2} O \)
(A) \( \quad \) cement ingredient
castner
(ii)
\[
M g\left(H C O_{3}\right)_{2}
\]
(B) \( \quad \) Keller process
(iii) \( \quad N a O H \) Solvay
(C) process
Temporary
\( \begin{array}{llll}\text { (iv) } & \mathrm{Ca}_{3} \mathrm{Al}_{2} \mathrm{O}_{6} & \text { (D) } & \text { hardness }\end{array} \)
A \( \cdot(i) \rightarrow(C) ;(i i) \rightarrow(B) ;(i i i) \rightarrow(D) ;(i v) \rightarrow(A) \)
B . \( (i) \rightarrow(C) ;(i i) \rightarrow(D) ;(i i i) \rightarrow(B) ;(i v) \rightarrow(A) \)
c. \( (i) \rightarrow(D) ;(i i) \rightarrow(A) ;(i i i) \rightarrow(B) ;(i v) \rightarrow(C) \)
D. \( (i) \rightarrow(B) ;(i i) \rightarrow(C) ;(i i i) \rightarrow(A) ;(i v) \rightarrow(D) \)
Subject: Maths
Solve:
\( \int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{\boldsymbol{x}+\mathbf{1}}+\sqrt{\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \frac{4}{3}(\sqrt{2}+1) \)
B. \( \frac{4}{3}(\sqrt{2}-1) \)
c. \( \frac{3}{4}(\sqrt{2}-1) \)
D. \( \frac{3}{4}(\sqrt{2}-2) \)
Subject: Chemistry
Assertion
Unreacted \( A g N O_{3} \) of photographic plate is removed by \( N a_{2} S_{2} O_{3} \) (hypo)
Reason
\( N a_{3}\left[A g\left(S_{2} O_{3}\right)_{2}\right] \) is soluble complex.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( \boldsymbol{x} \in\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right], \) the number of solutions of
the equation, \( \sin 7 x+\sin 4 x+ \)
\( \sin x=0 \) is
A . 3
B. 5
\( c \cdot 6 \)
D. None
Subject: Chemistry
If an electron is moving with velocity
\( 500 m s^{-1}, \) which is accurate up to
\( 0.005 \% \) then calculate uncertainty in its
position. \( \left[\boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\right. \)
\( s, \) mass of electron \( =9.1 \times \)
\( \left.\mathbf{1 0}^{-\mathbf{3 1}} \quad \boldsymbol{K} \boldsymbol{g}\right] \)
Subject: Chemistry
For the reaction, \( \boldsymbol{C l}_{2}+\mathbf{2} \boldsymbol{I}^{-} \rightarrow \boldsymbol{I}_{2}+ \)
\( 2 C l^{-}, \) the initial concentration of \( I^{-} \)
was 0.20 mol \( l i t^{-1} \) and the
concentration after 20 min was
0.18 mol lit\( ^{-1} . \) Then, the rate of
formation of \( I_{2} \) in \( \operatorname{mol} l i t^{-1} \min ^{-1} \)
would be:
A \( \cdot 1 \times 10^{-3} \)
B . \( 5 \times 10^{-4} \)
c. \( 1 \times 10^{-4} \)
D . \( 5 \times 10^{-3} \)
Subject: Maths
The percentage of marks obtained by the
students in a class of 50 are given below.
Find the mode for the following data.
Marks \( \begin{array}{lll}\mathbf{4 0}- & \mathbf{5 0}- & \mathbf{6 0}- \\ \mathbf{5 0} & \mathbf{6 0} & \mathbf{7 0}\end{array} \)
\( (\%) \)
Number
of 6
12
14
horses
A .62 .5
B. 63.5
c. 64.5
D. 65.5
Subject: Physics
A parallel plate air capacitor has a
initial capacitance \( C . \) If plate
separation is slowly increased from \( \boldsymbol{d}_{1} \)
to \( d_{2} \), then mark the correct
statement(s). (Take potential of the
capacitor to be constant, i.e. throughout the process it remains connected to battery.) This question has multiple correct options
A. Work done by electric force= negative of work done by the external agent.
B. Work done by external force \( -\int \vec{F} . \overrightarrow{d x} \), where \( \vec{F} \) is the electric force of attraction between the plates at plate separation \( x \)
c. work done by electric force \( \neq \) negative of work done by external agent
D. work done by battery = two times the change in electric potential energy stored in capacitor.
Subject: Maths
Evaluate: \( \int 3 x-5 d x \)
A \( \frac{3 x^{2}}{2}-5 x+C \)
B. \( \frac{3 x^{2}}{2}-7 x+C \)
c. \( \frac{3 x^{2}}{2}-4 x+C \)
D. \( \frac{3 x^{2}}{2}-6 x+C \)
Subject: Maths
Assertion
If \( A \) is a non-singular symmetric matrix, then its inverse is also symmetric. Because
Reason
\( \left(A^{-1}\right)^{T}=\left(A^{T}\right)^{-1}, \) where \( A \) is a non-
singular symmetric matrix.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
A hydrogen gas. electron is made by dipping platinum wire in a solution of \( H C I \) of \( p H=10 \) and by passing hydrogen gas around the platinum wire at one atm pressure.The oxidation potential of electrode would be?
A . \( 1.18 V \)
в. \( 0.059 V \)
c. \( -0.59 V \)
D. \( 0.118 \mathrm{V} \)
Subject: Maths
If the coefficient of 4 consecutive terms
in the expansion of \( (1+x)^{n} \) are
\( a_{1}, a_{2}, a_{3}, a_{4} \) respectively, then show
that:
\( \frac{\boldsymbol{a}_{\mathbf{1}}}{\boldsymbol{a}_{\mathbf{1}}+\boldsymbol{a}_{\mathbf{2}}}+\frac{\boldsymbol{a}_{\mathbf{3}}}{\boldsymbol{a}_{\mathbf{3}}+\boldsymbol{a}_{\boldsymbol{4}}}=\frac{\mathbf{2} \boldsymbol{a}_{\boldsymbol{3}}}{\boldsymbol{a}_{\mathbf{2}}+\boldsymbol{a}_{\boldsymbol{3}}} \)
Subject: Chemistry
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \stackrel{\Delta}{\longrightarrow}(\boldsymbol{X})+\boldsymbol{P} \boldsymbol{H}_{3} \) is :
A. Dehydration reaction
B. Oxidation reaction
c. Dispropportionation reaction
D. Dephosphorelation reaction
Subject: Chemistry
An aqueous solution of \( 0.24 M \) aniline
\( \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{4} . \mathbf{1 6 6} \times \mathbf{1 0}^{-\mathbf{1 0}} \) ) is mixed with
Na \( O H \) solution to maintain anilinium
ion concentration to \( 1 \times 10^{-8} M \)

The \( p O H \) of \( N a O H \) solution used was:
Subject: Physics
A particle of mass \( m \) is located in a unidimensional potential field, where
the potential energy of the particle
depends on the coordinates as \( U(x)= \)
\( U_{0}(1-\sin b x) ; \) where \( U_{0} \) and \( b \) are
constant. find the period of small
oscillations that the particle performs about the equilibrium position.
A \( \cdot \frac{2 \pi}{b^{2}} \sqrt{\frac{m}{U_{0}}} \)
В. \( \frac{\pi}{b} \sqrt{\frac{m}{U_{0}}} \)
c. \( \frac{\pi^{2}}{2 b} \sqrt{\frac{m}{U_{0}}} \)
D. \( \frac{2 \pi}{b} \sqrt{\frac{m}{U_{0}}} \)
Subject: Maths
A man buys eggs at 2 for Rs 1 and an equal number at 3 for \( \operatorname{Rs} 2 \) and sells the whole at 5 for Rs \( 3 . \) His gain or loss
percent is-
A \( \cdot 2 \frac{2}{7} \% \) loss
B \( \cdot 3 \frac{6}{7} \) \% gain
c. \( 3 \frac{2}{7} \) \% loss
D. \( _{2} \frac{6}{7} \) \%
Subject: Physics
Assertion
Sound shadows are generally not so well defined as those of light.
Reason
The wavelength of sound waves are very large in comparison to that of light
waves.
A. Statement 1 is True and Statement 2 is True and is correct explanation of statement 1
B. Statement 1 is True and Statement 2 is True but not correct explanation for Statement
c. Statement 1 is True and Statement 2 is False.
D. Statement 1 is False and Statement 2 is True
Subject: Chemistry
In the given reaction, alkaline \( \mathrm{KMnO}_{4} \) behaves as :
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{O H} \stackrel{\text {Alkaline } \boldsymbol{K M n O}_{4}+\boldsymbol{H e a t}}{\boldsymbol{N}} \boldsymbol{C H}_{3}- \)
COOH
A. reducing agent
B. oxidising agent
c. catalyst
D. dehydrating agent