AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
An equiconvex lens, \( f_{1}=10 c m, \) is
placed \( 40 \mathrm{cm} \) in front of a concave
mirror, \( f_{2}=7.50 \mathrm{cm}, \) as shown in fig. An
object \( 2 \mathrm{cm} \) high is placed \( 20 \mathrm{cm} \) to the left of the lens. If overall magnification
is X/1000. Then find out the value of X?
Subject: Maths
The value of \( 2 \cos ^{-1} x \) is:
\( A \cdot \cos ^{-1}\left(2 x^{2}+1\right) \)
B. \( \cos ^{-1} \frac{2 x}{1+x^{2}} \)
C \( \cos ^{-1}\left(2 x^{2}-1\right) \)
D. \( \tan ^{-1} \frac{2 x}{1-x^{2}} \)
Subject: Maths
If \( a_{1}, a_{2}, \dots a_{n} \) are positive real numbers
whose product is a fixed number \( c \), then
the minimum value of \( \boldsymbol{a}_{1}+ \)
\( \boldsymbol{a}_{2}+, \dots \boldsymbol{a}_{\boldsymbol{n}-1}+\boldsymbol{2} \boldsymbol{a}_{\boldsymbol{n}} \)
A \( \cdot n(2 c)^{1 / n} \)
B . \( (n+1) c^{1 / n} \)
\( \mathbf{c} \cdot 2 n c^{1 / n} \)
D. \( (n+1)(2 c)^{1 / n} \)
Subject: Chemistry
When one mole of an ideal gas is compressed to half its initial volume and simultaneously heated to twice its initial temperature, the change in
entropy \( (\triangle S) \) is :
A \( . C_{V} \) ln2
B. \( C_{P} \) ln2
c. \( R l n 2 \)
D \( \cdot\left(C_{V}-R\right) \ln 2 \)
Subject: Physics
A person standing symmetrically between two cliffs claps his hands and starts hearing series of echoes at intervals of 1 sec. If speed of sound in air is \( 340 \mathrm{m} / \mathrm{s} \), the distance between the parallel cliff must be
A. 340 \( m \)
B. 680 \( m \)
c. \( 1020 \mathrm{m} \)
D. \( 170 \mathrm{m} \)
Subject: Maths
If 5 of a company's 10 delivery trucks do not meet emission standard and 3 of
them are chosen for inspection, then what is the probability that none of the trucks chosen will meet emission
standards ?
A \( \cdot \frac{1}{8} \)
в. \( \frac{3}{8} \)
c. \( \frac{1}{12} \)
D.
Subject: Maths
In the given figure, the area of the
shaded portion APB is?
A \( -\frac{1}{4} \pi r^{2} \)
B. \( \frac{1}{4}(\pi-2) r^{2} \)
c. \( \frac{1}{4}(\pi-1) r^{2} \)
D. None of these
Subject: Physics
The adjacent graph shows the extension
(1) of a wire of length \( 1 \mathrm{m} \) suspended from the top of a roof at one end and
with load 'W' connected to the other end.
If the cross-sectional area of the wire is
\( 10^{-6} m^{-2}, \) calculate the Young modulus
of the material of the wire:
A \( \cdot 2 \times 10^{-11} \)
В. \( 2 \times 10^{10} \)
\( c \cdot 2 \times 10^{11} \)
D. \( 2 \times 10^{-10} \)
Subject: Chemistry
\( \left[_{\boldsymbol{A} \mathbf{1}} \boldsymbol{C u}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{3}(\boldsymbol{O} \boldsymbol{H})\right]^{+}+ \)
\( \left[\boldsymbol{A l}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{O} \boldsymbol{H})\right]^{2+} \)
Choose the correct statement:
A \( . A_{1} \) is a base and \( A_{3} \) is an acid
B. \( A_{3} \) is conjugate acid of \( A_{1} \) and \( A_{4} \) is conjugate base of
\( A_{2} \)
C. \( A_{3} \) is conjugate base of \( A_{1} \) and \( A_{4} \) is conjugate acid of \( A_{2} \)
D. Noneofthese
Subject: Physics
apacitor ( (1) so as to fill the gap eeping the battery remainc charge on each capacit
\( \frac{2 m}{1+(1 / 1 / k)} \)
\( \frac{\omega(10)}{1} \)
\( \frac{2 \omega}{(1+k)} \)
\( \frac{2 w}{10-k} \)
Subject: Physics
A wire of length \( L \) and 3 identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised at \( \triangle T \) in time \( t . N \) number of similar cells
is now connected in series with a wire of
the same material and cross-section
but of length \( 2 L \). The temperature of the
wire is raised by the same amount \( \triangle \boldsymbol{T} \) in the same time \( t \). The value of \( \boldsymbol{N} \) is:
\( A \)
B. 6
\( c \cdot 8 \)
\( D \)
Subject: Chemistry
Assertion
Gaseous molecules are assumed to be
point masses' occupying no volume.
Reason

Gaseous molecules suffer no energy
loss due to friction.
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: Physics
A sphere \( ^{\prime} \boldsymbol{P}^{\prime} \) of mass \( ^{\prime} \boldsymbol{m}^{\prime} \) moving with
velocity \( ^{\prime} u^{\prime} \) collides head-on with
another sphere \( ^{\prime} Q^{\prime} \) of mass \( ^{\prime} m^{\prime} \) which is at rest. The ratio of final velocity of \( ^{\prime} Q^{\prime} \)
to initial velocity of \( ^{\prime} \boldsymbol{P}^{\prime} \) is
\( (e=\operatorname{coefficient} \) of restitution)
A \( \cdot \frac{e-1}{2} \)
B. \( \left[\frac{e+1}{2}\right]^{1 / 2} \)
c. \( \frac{e+1}{2} \)
D. \( \left[\frac{e+1}{2}\right]^{2} \)
Subject: Physics
The breaking stress of aluminium is \( \mathbf{7 . 5} \times \mathbf{1 0}^{7} \mathbf{N m}^{-\mathbf{2}} . \) Find the greatest
length of aluminium wire that can hang vertically without breaking. Density of aluminium is \( 2.7 \times 10^{3} \mathrm{Kgm}^{-3} \)
Subject: Physics
An AND gate is followed by a NOT gate in series. With two inputs \( \boldsymbol{A} \& \boldsymbol{B} \), the
Boolean expression for the out put \( Y \) will be :
A. \( A . B \)
B. \( A+B \)
\( c \cdot \overline{A+B} \)
D. \( \overline{A . B} \)
Subject: Chemistry
Three faradays of electricity are passed
through molten \( A l_{2} O_{3}, \) aqueous
solution of \( C u S O_{4} \) and molten \( N a C l \)
taken in three different electrolytic cells. The amount of \( A l, C u \) and \( N a \) deposited at the cathodes will be in the
ratio of
A. 1 mole : 1 mole : 1 mole
B. 1 mole : 1.5 mole: 3 mole
c. 3 mole : 2 mole : 1 mole
D. 1 mole : 1.5 mole: 2 mole
Subject: Physics
The self inductance of a choke coil is 10
mH. When it is connected with a 10 V
D.C. source, then the loss of power is 20
watt. When it is connected with 10 volt
A.C. source loss of power is 10 watt. The frequency of A.C. source will be.
A . 50 нz
в. 60 на
c. 80 Нz
D. 100 Н \( z \)
Subject: Maths
The differential coefficient of log (tan
\( x \) )is
A \( .2 \sec 2 x \)
B. \( 2 \cos e c 2 x \)
\( \mathbf{c} \cdot 2 \sec ^{2} x \)
D. \( 2 \cos e c^{2} 2 x \)
Subject: Physics
A metal rod moves at a constant
velocity in a direction perpendicular to its length. A constant uniform magnetic
field exists in space in a direction perpendicular to the rod as well its
velocity. Select correct statements from the following
A. the entire rod is at the same potential
B. there is an electric field in the rod
c. the electric potential is highest at the centre
D. the electric potential is lowest at its centre and increases towards its ends
Subject: Maths
The distance between the parallel lines \( 3 \cos \theta+4 \sin \theta+\frac{5}{r}=0 \) and \( 6 \cos \theta+ \)
\( 8 \sin \theta+\frac{7}{r}=0 \) is
\( A \cdot \frac{3}{5} \)
в. \( \frac{3}{10} \)
\( c \cdot \frac{3}{20} \)
D.
Subject: Chemistry
If the salts, \( M_{2} X, Q Y_{2} \) and \( P Z_{3} \) have
same solubilities \( \left(\left\langle\langle<1), \text { their } \boldsymbol{K}_{s p}\right.\right. \) values are related as:
\( \mathbf{A} \cdot M_{2} X>Q Y_{2}>P Z_{3} \)
в. \( M_{2} X<Q Y_{2}>P Z_{3} \)
c. \( M_{2} X=Q Y_{2}>P Z_{3} \)
D. \( M_{2} X=Q Y_{2}=P Z_{3} \)
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is \( \boldsymbol{4} . \boldsymbol{7} 4 \) and \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{A}^{-}, \boldsymbol{B}^{-} \)
and \( C^{-} \) are 4,5 and 6 respectively.
Aqueous solution of \( 0.01 M \) has \( p H \) in
the increasing order.
A \( . N H_{4} A<N H_{4} B<N H_{4} C \)
B. \( N H_{4} C<N H_{4} B<N H_{4} A \)
C . \( N H_{4} C<N H_{4} A<N H_{4} B \)
D. All have equal \( p H \)
Subject: Maths
If \( A_{1} A_{2} ; G_{1} G_{2} ; H_{1} H_{2} \) be two A.M.s
G.M.s and H.M.s between two numbers then prove: \( \frac{\boldsymbol{G}_{1} \boldsymbol{G}_{2}}{\boldsymbol{H}_{1} \boldsymbol{H}_{2}}=\frac{\boldsymbol{A}_{1}+\boldsymbol{A}_{2}}{\boldsymbol{H}_{1}+\boldsymbol{H}_{2}} \)
Subject: Physics
Due to some force \( \boldsymbol{F}_{1}, \) a body oscillates with period \( 4 / 5 \) second and due to other
force \( F_{2} \) it oscillates with the period of \( 3 / 5 \) sec. If both forces act simultaneously new period will be
A . 0.72 s
B. 0.64 s
c. 0.48 s
D. 0.36 s
Subject: Chemistry
Which of the following reactions defines
\( \Delta H_{f}^{o} ? \)
A. \( C_{\text {diamond}}+O_{2}(g) \rightarrow C O_{2}(g) \)
B \( \cdot \frac{1}{2} H_{2}(g)+\frac{1}{2} F_{2}(g) \rightarrow H F(g) \)
C. \( N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
\( ^{\mathrm{D}} \cdot_{C O(g)}+\frac{1}{2} O_{2}(g) \rightarrow C O_{2}(g) \)
Subject: Maths
If \( A \) is matrix of order \( m \times n \) and \( B \) is a
matrix of order \( n \times p, \) then the order of
\( A B \) is
\( \mathbf{A} \cdot p \times m \)
в. \( p \times n \)
c. \( n \times p \)
D. \( m \times p \)
Subject: Maths
Evaluate the following:
\( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{\lambda} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{\lambda} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{\lambda}\end{array}\right| \)
Subject: Physics
If \( \chi \) stands for the magnetic
susceptibility of a substance, \( \mu \) for its
magnetic permeability and \( \mu_{0} \) for the permeability of free space, then This question has multiple correct options
A. For a paramagnetic substance: \( \chi>0, \mu>0 \)
B. For a paramagnetic substance: \( \quad \chi>0, \quad \mu>\mu_{0} \)
c. For a diamagnetic substance: \( \chi<0, \mu<0 \)
D. For a ferromagnetic substance: \( \quad \chi>1, \mu<\mu_{0} \)
Subject: Maths
Let \( (a b c=8, a, b, c \geq 0) \) and the real
valued function \( f(x)=b c(a x-1)^{2}+ \)
\( c a(b x-1)^{2}+a b(c x-1)^{2} \) has
minimum value at \( x=\frac{1}{2}, \) then the
value of \( \boldsymbol{a}^{16}+\boldsymbol{b}^{17}+\boldsymbol{c}^{16} \)
A \( \cdot 2^{15} \)
B . \( 2^{16} \)
\( c \cdot 2^{17} \)
D. \( 2^{18} \)
Subject: Physics
Suppose gravitational force between two masses were to be given by \( \boldsymbol{F}= \) \( k \frac{\sqrt{m_{1} m_{2}}}{d^{3}} \) where \( k \) is some constant
two equal masses attract each other with a certain force when the distance
is d. If each of the masses is doubled,
than what value the distance between
them must be maintained for the force
to remain the same as earlier?
A. \( \sqrt[3]{3 d} \)
B. "3/3d
\( c \cdot \sqrt[13]{2 d} \)
D. \( \sqrt[3]{2 d} \)
Subject: Chemistry
A well is dug in a bed of rock containing
fluorspar \( \left(C a F_{2}\right) . \) If the well contains \( 20000 \mathrm{L} \) of water, what is the amount of
\( \boldsymbol{F}^{-} \) in it \( ?\left(\boldsymbol{K}_{s p}=\boldsymbol{4} \times \mathbf{1 0}^{-11}\right) \)
A . 4.2 mol
B . 13.6 mol
c. 8.6 mol
D. 10 mol
Subject: Physics
An automobile engine absorbs \( 1600 J \) of heat from a hot reservoir and expel
\( 1000 J \) to a cold reservoir in each cycle.
What is the power output of engine if it
operates at 200 cycle per minute?
\( \mathbf{A} \cdot 3 H P \)
B. \( 4 \mathrm{HP} \)
c. 2.7 НР
D. 3.7 НР
Subject: Physics
A thin rod of length \( 3 \mathrm{L} \) is bent at right
angles at a distance \( L \) from one end.
Locate the centre of mass of the
arrangement w.r.t the corner (see figure). (Given, \( L=1 \mathrm{m} \) )
\( \mathbf{A} \cdot r_{C O M}=(0.2 \hat{i}+0.8 \hat{j}) \mathrm{m} \)
B \( \cdot r_{C O M}=(0.4 \hat{i}+0.6 \hat{j}) \mathrm{m} \)
\( \mathbf{c} \cdot r_{C O M}=(0.5 \hat{i}+\hat{j}) m \)
\( \mathbf{D} \cdot r_{C O M}=(0.2 \hat{i}+0.6 \hat{j}) m \)
Subject: Maths
Lot \( A \) consists of \( 3 G \) and \( 2 D \) articles.
Lot \( B \) consists of \( 4 G 1 D \) article. A new
lot \( C \) is formed by taking 3 articles from \( A \) articles from \( A \) and 2 form \( B \). The
probability that an article chosen at random from \( C \) is
A . \( 1 / 3 \)
в. 2 /
c. \( 8 / 25 \)
D. none
Subject: Physics
A \( 10 \Omega \) resistance, \( 5 \mathrm{mH} \) coil and \( 10 \mu \mathrm{F} \)
capacitor are joined in series. When a suitable frequency alternating current source is joined to the combination, the circuit resonates. If the resistance is
halved the resonance frequency is
A. halved
B. doubled
c. remains same
D. quadrupled
Subject: Chemistry
The ground glass stopper is often seen
to get stuck in the neck of glass bottles
containing aq NaOH solution This is
due to:
A. formation of solid \( N a_{2} C O_{3} \) around the neck of the
bottle due to NaoH reacting with atmospheric \( C O_{2} \)
B. formation of solid \( N a_{2} S i O_{3} \) around the neck of the
bottle
C. creation of partial vacuum due to highly hygroscopic nature of \( N a O H \)
D. high coefficient of thermal expansion of glass
Subject: Chemistry
When hydrogen peroxide is treated with
a cold acidified \( \boldsymbol{K}_{\mathbf{2}} \boldsymbol{C r}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{7}} \) solution
containing ether, blue colour is obtained. This is due to:
A. perchromic acid
B. potassium chromate
c. chromium sulphate
D. chromium trioxide
Subject: Chemistry
A: Polymethyl methacrylate is also
known as plexi glass.
R: PMMA is used in decorative articles.
\( A . \) Both \( A \) and \( R \) are correct and \( R \) is the correct explanation of the \( A \)
B. Both A and R are correct but R is not the correct explanation of the \( A \)
C. A is correct but R is in correct
D. A is incorrect but \( R \) is correct
Subject: Maths
For two events \( A \) and \( B \) with \( P(B) \neq 1 \)
prove that \( \boldsymbol{P}\left(\boldsymbol{A} \mid \boldsymbol{B}^{\prime}\right)= \)
\( \frac{\boldsymbol{P}(\boldsymbol{A})-\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})}{1-\boldsymbol{P}(\boldsymbol{B})} \)
Subject: Physics
A ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and the latter is equal to \( \frac{3^{t h}}{4} \) angle of prism. What will be the
deviation?
A \( \cdot 45^{\circ} \)
В. \( 37^{\circ} \)
\( c \cdot 20^{0} \)
D. 30
Subject: Maths
The area of a parallelogram is \( y \mathrm{cm}^{2} \) and its height is \( h \) cm. The base of
another parallelogram is \( x \) cm more
than the base of the first parallelogram
and its area is twice the area of the first.
Find, in terms of \( y, h \) and \( x, \) the expression for the height of the second
parallelogram.
A \( \frac{h y}{y h-x} \)
B. \( \frac{y}{y-x h} \)
c. \( \frac{2 h y}{y+x h} \)
D. None of these
Subject: Chemistry
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{4} \boldsymbol{I}_{2}+\boldsymbol{3} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \rightarrow \boldsymbol{X}+ \)
\( \boldsymbol{H} \boldsymbol{C O O N} \boldsymbol{a}+\mathbf{5} \boldsymbol{N a I}+\mathbf{3} \boldsymbol{C O}_{2}+\mathbf{2 H}_{2} \boldsymbol{O} \)
In the above reaction \( ^{\prime} X^{\prime} \) is :
A. Di iodo methane
B. Tri iodo methane
c. lodo methane
D. Tetra iodo methane
Subject: Maths
The set of all points where \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sqrt[3]{x^{2}|x|}-|x|-1 \) is not differentiable is
\( A \cdot\{0\} \)
B \( \cdot\{-1,0,1\} \)
\( \mathbf{c} \cdot\{0,1\} \)
D. None of these
Subject: Chemistry
Alkali metals (M) dissolve in liquid
\( N H_{3} \) to give:
A \( \cdot M N H_{2} \)
в. \( M H \)
C \( \cdot\left[M\left(N H_{3}\right)_{x}\right]^{+}+\left[e\left(N H_{3}\right)_{y}\right] \)
D. \( M_{3} N \)
Subject: Physics
The relation between time \( t \) and
distance of \( x \) s is \( t=a x^{2}+b x \) where \( a \)
and \( b \) are constant. The acceleration is
A. \( -2 a b v^{2} \)
B . \( 2 b v^{3} \)
c. \( -2 a v^{3} \)
D. \( 2 a v^{2} \)
Subject: Chemistry
The specific conductance of a saturated solution of AgCl in water is \( 1.826 \times \) \( 10^{-6} \Omega^{-1} \mathrm{cm}^{-1} \) at \( 25^{\circ} \mathrm{C} \) calculate its
solubility in water at \( 25^{\circ} \mathrm{C} \)
Given that \( :-\lambda^{\circ}\left(A g^{+}\right)=61.92 \)
\[
\boldsymbol{\lambda}^{\circ}\left(\mathbf{C l}^{-}\right)=\mathbf{7 6 . 3 4}
\]
Subject: Physics
Two bulbs of \( 100 \mathrm{W} \) and \( 40 \mathrm{W} \) are
connected in series. The current
through the 100 W bulb is 1A. The
current through the 40 W bulb will be
A \( .0 .4 A \)
в. \( 0.6 A \)
\( c .0 .8 A \)
D. \( 1 A \)
Subject: Physics
From the top of a \( 40 \mathrm{m} \) tall multi-
storeyed building, a boy projects a stone vertically upwards with an initial velocity \( 10 \mathrm{m} s^{-2} \) such that, it eventually falls to the ground. After how long will the stone strike the ground? (Take \( g=10 \)
\( \left.m s^{-2}\right)(\text {in sec }) \)
Subject: Physics
The electron in a hydrogen atom first jumps from the third excited state to the second excited state and
subsequently to the first excited state. The ratio of the respective wavelengths,
\( \lambda_{1} / \lambda_{2} \) of the photons emitted in this
process is:
A \( \cdot \frac{9}{7} \)
B. \( \frac{7}{5} \)
c. \( \frac{27}{5} \)
D. \( \frac{20}{7} \)
Subject: Physics
Two soap bubbles of radius \( r_{1}=r \) and
\( r_{2}=2 r \) coalesce to form a double as
shown, then angle \( p j i, \) is equal to
\( A \cdot 60^{\circ} \)
В \( \cdot 90^{\circ} \)
\( c \cdot 120^{\circ} \)
D. It depends on surface tension of soap solution
Subject: Chemistry
The total number of possible isomer for
the complex comp.:
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C} \boldsymbol{I}_{4}\right] \)
A. 3
B. 6
\( c \cdot 5 \)
D.
Subject: Maths
A solid is in the form of a right circular
cone mounted on a hemisphere. The
radius of the hemisphere is \( 3.5 \mathrm{cm} \) and
the height of the cone is \( 4 \mathrm{cm} . \) The solid
is placed in a cylindrical tub, full of
water, in such a way that the whole
solid is submerged in water. If the
radius of the cylinder is \( 5 \mathrm{cm} \) and its
height is \( 10.5 \mathrm{cm}, \) find the volume of
water left in the cylindrical tub \( \left(\boldsymbol{U} \boldsymbol{s e} \boldsymbol{\pi}=\frac{\boldsymbol{2} \boldsymbol{2}}{\boldsymbol{7}}\right) \)
Subject: Maths
If \( A \) and \( B \) are events such that \( P(A)= \) \( \frac{1}{2}, P(B)=\frac{1}{3} \) and \( P(A \cap B)=\frac{1}{4}, \) then
find \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) \)
Subject: Maths
The equations of \( L_{1} \) and \( L_{2} \) are \( y=m x \)
and \( \boldsymbol{y}=\boldsymbol{n} \boldsymbol{x}, \) respectively. Suppose \( \boldsymbol{L}_{\mathbf{1}} \)
makes twice as large of an angle with the horizontal(measured
counterclockwise from the positive \( x- \)
axis) as does \( L_{2} \) and that \( L_{1} \) has 4
times the slope of \( L_{2} . \) If \( L_{1} \) is not
horizontal, then the value of the
product(mn) equals.
\( A \cdot \frac{\sqrt{2}}{2} \)
B. \( -\frac{\sqrt{2}}{2} \)
c. 2
D. -2
Subject: Maths
\( \mathbf{0}<\mathbf{x}<\mathbf{2} \boldsymbol{\pi} ; \mathbf{0}<\mathbf{y}<\mathbf{2} \boldsymbol{\pi} \) and
\( 3^{\sin x+\cos y}=1 \) and \( 25^{\sin x^{2}+\cos ^{2} y}=5 \) then
\( (x, y) \) is This question has multiple correct options
\( ^{\mathrm{A}} \cdot\left(\frac{7 \pi}{6}, \frac{\pi}{3}\right. \)
В. \( \left(\frac{7 \pi}{6}, \frac{5 \pi}{3}\right) \)
c. \( \left(\frac{11 \pi}{6}, \frac{\pi}{3}\right) \)
D. \( \left(\frac{11 \pi}{6}, \frac{5 \pi}{3}\right) \)
Subject: Maths
Range of \( \boldsymbol{f}(\boldsymbol{x})=\left(\sin ^{-1} \boldsymbol{x}+\tan ^{-1} \boldsymbol{x}+\right. \)
\( \left.\sec ^{-1} x\right) \) is
A \( \cdot\left(\frac{\pi}{4}, \frac{3 \pi}{4}\right) \)
В. \( \left[\frac{\pi}{4}, \frac{3 \pi}{4}\right] \)
c. \( \left\{\frac{\pi}{4}, \frac{3 \pi}{4}\right\} \)
D \( \cdot\left\{0, \frac{\pi}{4}\right\} \)
Subject: Chemistry
Formula of oleum is:
\( \mathbf{A} \cdot H_{2} S O_{3} \)
\( \mathbf{B} \cdot H_{2} S O_{4} \)
\( \mathbf{c} \cdot H_{2} S O_{5} \)
D. \( H_{2} S_{2} O_{7} \)
Subject: Chemistry
A barometer made of very narrow tube
is placed at normal temperature and pressure. The coefficient of volume
expansion of mercury is 0.00018 per \( ^{\circ} C \) and that of the tube is negligible. The temperature of mercury in the
barometer is now raised by \( 1^{\circ} \mathrm{C} \), but the
temperature of the atmosphere does
not change. Then the mercury height in the tube remains unchanged.
A. True
B. False
Subject: Physics
Monochromatic light of wave length \( 667 \mathrm{nm} \) is produced by a helium neon laser. The power emitted is \( 9 \mathrm{mW} \). The
number of photons arriving per second on the average at a target irradiated by this beam is
A \( \cdot 3 \times 10^{16} \)
В . \( 3 \times 10^{19} \)
\( \mathrm{c} \cdot 9 \times 10^{15} \)
D. \( 9 \times 10^{17} \)
Subject: Chemistry
The equilibrium \( \boldsymbol{A}_{4}(\boldsymbol{g})+\boldsymbol{6} \boldsymbol{B}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 4 A B_{3}(g) \) is established in a closed
container by taking equal moles of
\( A_{4}(g) \) and \( B_{2}(g) . \) Which of the following options must be correct at equilibrium?
\( \mathbf{A} \cdot\left[A_{4}\right]<[B]_{2} \)
B . \( \left[B_{2}\right]>\left[A B_{3}\right] \)
c. \( \left[A_{4}\right]<\left[A B_{3}\right] \)
D. None of the above
Subject: Maths
If \( \mathbf{A}=\left[\begin{array}{ll}\mathbf{3} & -\mathbf{4} \\ \mathbf{1} & -\mathbf{1}\end{array}\right] \) then \( \boldsymbol{A}^{k}= \)
\( \left[\begin{array}{cc}\mathbf{1}+\mathbf{2} \boldsymbol{k} & -\mathbf{4} \boldsymbol{k} \\ \boldsymbol{k} & \mathbf{1}-\mathbf{2} \boldsymbol{k}\end{array}\right] \)
where \( k \) is any \( + \) ve integer
Subject: Maths
If \( \mathbf{0} \leq[\boldsymbol{x}]<\mathbf{2},-\mathbf{1} \leq[\boldsymbol{y}]<\mathbf{1} \) and \( \mathbf{1} \leq \)
\( [z]<3([.] \) denotes the greatest integer
function) then the maximum value of
determinant
\( \boldsymbol{\Delta}=\left|\begin{array}{ccc}{[\boldsymbol{x}]+\mathbf{1}} & {[\boldsymbol{y}]} & {[\boldsymbol{z}]} \\ {[\boldsymbol{x}]} & {[\boldsymbol{y}]+\mathbf{1}} & {[\boldsymbol{z}]} \\ {[\boldsymbol{x}]} & {[\boldsymbol{y}]} & {[\boldsymbol{z}]+\mathbf{1}}\end{array}\right| \)
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)
Subject: Maths
If \( a \) and \( b \) are the two vectors such that
\( |\boldsymbol{a}|=\mathbf{3} \sqrt{\mathbf{3}},|\boldsymbol{b}|=\mathbf{4} \) and \( |\boldsymbol{a}+\boldsymbol{b}|=\sqrt{\mathbf{7}} \)
then the angle between \( a \) and \( b \) is
\( \mathbf{A} \cdot 120^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 150^{\circ} \)
Subject: Physics
Assertion
In the motion of projectile the horizontal component of velocity remains constant
Reason
The force on the projectile is gravitational force which acts only in vertically downward direction
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
Compare thermal stability of \( L i_{2} C O_{3} \)
and \( B e C O_{3}: \)
A. \( L i_{2} C O_{3}>B e C O_{3} \)
в. \( L i_{2} C O_{3}<B e C O_{3} \)
c. \( L i_{2} C O_{3}=B e C O_{3} \)
D. None of these
Subject: Chemistry
Assertion
\( C l_{2} \) or \( B r_{2} \) changes \( K I \) into \( I_{2} \) (violet in
\( C C l_{4} \) layer), \( C l_{2} \) changes \( K B r \) into \( B r_{2} \)
(orange-yellow in \( C C l_{4} \) layer). Thus, \( C l_{2} \) would change mixture of \( K I \) and \( K B r \) into violet layer in
\( \boldsymbol{C C l}_{4} \)
Reason
Oxidising power is in order \( \boldsymbol{I}_{2}<\boldsymbol{B} \boldsymbol{r}_{2}< \)
\( \boldsymbol{C l}_{2}<\boldsymbol{F}_{2} \)
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.