AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Using the principle of mathematical induction, find \( \tan \alpha+2 \tan 2 \alpha+ \)
\( 2^{2} \tan 2^{2} \alpha+\ldots . \) to \( n \) terms:
A \( \cdot \tan \alpha-2^{n} \cdot \tan \left(2^{n} \cdot \alpha\right) \)
B. \( \cot \alpha-2^{n} \cdot \cot \left(2^{n} \cdot \alpha\right) \)
c. \( \sec \alpha-2^{n} \cdot \sec \left(2^{n} \cdot \alpha\right) \)
D. None of these
Subject: Maths
State true or false:
In triangle \( A B C, \) angle \( B \) is obtuse. \( D \)
and \( E \) are mid-points of sides \( A B \) and \( B C \) respectively and \( F \) is a point in
side \( A C \) such that \( E F \) is parallel to \( A B \)
Then, \( B E F D \) is a parallelogram.
A. True
B. False
Subject: Maths
The range of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sec \left(\frac{\pi}{4} \cos ^{2} x\right) \cdot-\infty<x<\infty \) is
A \( \cdot[1, \sqrt{2}] \)
B . \( [1, \infty] \)
c. \( [-\sqrt{2},-1] \cup[1, \sqrt{2}] \)
D \( \cdot[-\infty,-1] \cup[1, \infty] \)
Subject: Physics
The mass of the earth is \( 6 \times 10^{22} k g \)
and that of the moon is \( 7.4 \times 10^{22} \) kg. If
the distance between the earth and the
moon is \( 3.84 \times 10^{5} k m, \) calculate the
force exerted by the earth on the moon. \( G=6.7 \times 10^{-11} N m^{2} k g^{-2} \)
Subject: Chemistry
Calculate the potential of a half cell
having reaction: \( \quad A g_{2} S(s)+2 e^{-} \rightleftharpoons \)
\( 2 A g(s)+S^{2-}(a q) \) in a solution
buffered at \( p H=3 \) and which is also
saturated with \( 0.1 M H_{2} S(a q) \)
\( \left[\text { Given: } \boldsymbol{K}_{s p}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}\right)=\right. \)
\( \mathbf{1 0}^{-49}, \boldsymbol{K}_{\boldsymbol{a}_{1}} \cdot \boldsymbol{K}_{\boldsymbol{a}_{2}}=\mathbf{1 0}^{-\mathbf{2 1}} \)
A . 1.18
B. 0.19
c. \( -0.19 V \)
D. None of these
Subject: Biology
Consider the statements given below regarding contraception and answer as directed thereafter
(a) Medical Termination of Pregnancy (MTP) during first trimester is generally safe.
(b) Generally chances of conception are nil until mother breast-feeds the infant
upto two years.
(c) Intrauterine devices like copper \( T \)
are effective contraceptives.
(d) Contraception pills may be taken upto one week after coitus to prevent conception. Which two of the above statements are
correct?
A. a and c
B. a and b
\( \mathbf{C} \cdot \mathbf{b} \) and \( c \)
D. \( c \) and \( d \)
Subject: Physics
State the amount of charge on each
particle in a cathode ray tube
A. \( -3.2 \times 10^{-19} \mathrm{C} \)
В. \( -1.6 \times 10^{-19} \mathrm{C} \)
c. \( +1.6 \times 10^{-19} C \)
D. \( +3.2 \times 10^{-19} \mathrm{C} \)
Subject: Physics
The coefficient of friction between two
blocks of masses \( 1 \mathrm{kg} \) and \( 4 \mathrm{kg} \) as
shown in figure is \( \mu \) and the horizontal
plane is smooth. If the system is slightly displaced and released it will execute
S.H.M. The maximum amplitude if the
upper block does not slip relative to lower block will be (k is spring constant)
\( A \cdot \frac{5 \mu g}{k} \)
в. \( \frac{\mu g}{k} \)
\( c \cdot \frac{3 \mu g}{k} \)
D. \( \frac{2 \mu g}{k} \)
Subject: Maths
\( \int \frac{\sin 2 x}{1+\cos ^{4} x} d x \) is equal to
\( \mathbf{A} \cdot \cos ^{-1}\left(\cos ^{2} x\right)+c \)
B. \( \sin ^{-1}\left(\cos ^{2} x\right)+c \)
C \( \cdot \cot ^{-1}\left(\cos ^{2} x\right)+c \)
D. None of these
Subject: Physics
A particle executes SHM with a time
period of 16 s. \( A t \) time \( t=2 s, \) the
particle crosses the mean position
while at \( t=4 s, \) its velocity is \( 4 m s^{-1} \)
The amplitude of motion in metre is?
A \( \cdot \sqrt{2} \pi \)
В. \( 16 \sqrt{2} \pi \)
c. \( 32 \sqrt{2} / \pi \)
D. \( 4 / \pi \)
Subject: Chemistry
\( N a H_{2} P O_{4} \stackrel{230^{\circ} C}{\rightarrow} N a_{3}\left(P_{3} O_{9}\right) \stackrel{638^{\circ} C}{\rightarrow}(D) \)
Compound (D) contains \( 200\left(P O_{4}\right) \) units and called:
A. Bunsen's salt
B. Graham's salt
c. Reimann's salt
D. werner's salt
Subject: Physics
A starts from rest and moves with
acceleration \( a_{1} . \) Two seconds later, \( \mathrm{B} \)
starts from rest and moves with an
acceleration \( a_{2} . \) If the displacement of \( A \)
in the \( 5^{t h} \) second is the same as that of
\( \mathrm{B} \) in the same interval, the ratio of \( a_{1} \) to
\( a_{2} \) is
A 9: 5
5
B. 5: 9
c. 1: 1
D. 1: 3
Subject: Chemistry
A certain mass of gas is expanded from \( (1 L, 10 a t m) \) to \( (4 L, 5 a t m) \) against a
constant external pressure of 1 atm. If the initial temperature of the gas is \( 300 K \) and the heat capacity of the
process is \( 50 J /^{\circ} C . \) Then the enthalpy change during the process is:
\( (1 L a t m \simeq 100 J) \)
A \( . \triangle H=15 k J \)
в. \( \triangle H=15.7 k J \)
c. \( \triangle H=14.4 k J \)
D. \( \triangle H=14.7 k J \)
Subject: Maths
\( \tan ^{-1} x+2 \cot ^{-1} x=\frac{2 \pi}{3}, \) then the
value of \( x \) is-
A \( \cdot \sqrt{2} \)
B. 3
\( c \cdot \sqrt{3} \)
D. \( \frac{\sqrt{3}-1}{\sqrt{3}+1} \)
Subject: Chemistry
Which of the following statement(s) is/are correct when a mixture of \( N a C l \)
and \( K_{2} C r_{2} O_{7} \) is gently warmed with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
This question has multiple correct options
A. A deep red vapor is evolved.
B. The vapor when passed into NaOH solution gives yellow solution of \( N a_{2} C r O_{4} \)
c. chlorine gas is evolved.
D. chromyl chloride is formed.
Subject: Chemistry
Half life period of a first order reaction, \( A \rightarrow \) product is 6.93 hour. What is the value of rate constant?
A \( \cdot 1.596 h^{-1} \)
B. \( 0.1 h^{-1} \)
c. \( 4.802 h^{-1} \)
D. \( 10 h^{-1} \)
Subject: Chemistry
An experiment requires minimum \( \beta \)
activity produced at the rate of \( 346 \beta \)
particles per minute. The half-life period of \( _{42}^{99} \) Mo which is a \( \beta \) -emitter is 66.6 hr. The minimum amount of \( _{42}^{99} \) Mo required to carry out the experiment in 6.909 hour is :
A \( \cdot 6.78 \times 10^{-16} g \)
В. \( 3.52 \times 10^{-16} g \)
c. \( 5.21 \times 10^{-16} g \)
D. none of these
Subject: Chemistry
Which of the following reactions is/are not correct to get cinnamic acid?
A \( \cdot C_{6} H_{5} C H O \frac{ }{\left(C H_{3} C O\right)_{2} O / C H_{3} C O O N a} \)
B. \( C_{6} H_{5} C H O \frac{1) C H_{2}\left(C O O C_{2} H_{2}\right)_{2}, p y r i \text { dine }}{2 / H_{3} O+, \Delta} \)
c. \( C_{6} H_{5} \) СНО \( \stackrel{\text {СНз} \text {сно} / \text {ОН}}{\text { - }} \)
D. \( C_{6} H_{5} C H O \frac{1) B r C H_{2} C O O C_{2} H_{3} / Z n I \Delta}{2) H_{2} O / H+/ \Delta} \)
Subject: Physics
Three point charges of \( +2 q,+2 q \) and
\( -4 q \) are placed at the corners \( A, B \) and \( C \) of an equilateral triangle \( A B C \) of side ' \( x \) '. The magnitude of the electric
dipole moment of this system is :
A \( \cdot 2 \sqrt{3} q x \)
в. \( 2 q x \)
\( \mathbf{c} \cdot 3 q x \)
D. \( 3 \sqrt{2} q x \)
Subject: Physics
A thin spherical conducting shell of radius \( R \) has a charge \( q \). Another charge
\( Q \) is placed at the centre of the shell. The electrostatic potential at a point \( \mathrm{P} \) at a distance \( \boldsymbol{R} / \mathbf{2} \) from the centre of the
shell is :
\( ^{A} \cdot \frac{2 Q}{4 \pi \varepsilon_{\Omega} R} \)
в. \( \frac{2 Q}{4 \pi \varepsilon_{0} R}-\frac{2 q}{4 \pi \varepsilon_{0} R} \)
c. \( \frac{2 Q}{4 \pi \varepsilon_{0} R}+\frac{q}{4 \pi \varepsilon_{0} R} \)
D. \( \frac{(q+Q) 2}{4 \pi \varepsilon R R} \)
Subject: Physics
A progressive wave of wavelength \( 5 \mathrm{cm} \) moves along \( +\mathrm{X} \) axis. What is the phase difference between two points on the wave separated by a distance of \( 3 \mathrm{cm} \) at
any instant
A . \( 3 \pi / 5 \)
в. \( 6 \pi / 5 \)
c. \( 2 \pi / 5 \)
D. \( 7 \pi / 5 \)
Subject: Biology
Assertion
In dicot stem, the endodermis is also referred to as the starch sheath.
Reason
The cells of the endodermis are rich in
starch grains.
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 \( z=x+i y \) and \( w=\frac{(1-i z)}{(z-i)}, \) then
\( |\boldsymbol{w}|=1 \) implies that, in the complex
plane
A. \( z \) lies on the imaginary axis
B. \( z \) lies on the real axis
c. \( z \) lies on the unit circle
D. None of these
Subject: Physics
(a) Three resistors \( 2 \Omega, 4 \Omega \) and \( 5 \Omega \) are
combined in parallel. What is the total resistance of the combination?
(b) If the combination is connected to a
battery of emf \( 20 \mathrm{V} \) and negligible internal resistance, determine the
current through each resistor, and the total current drawn from the battery.
Subject: Maths
If \( a, b, c, p, q, r \) are three non-zero complex number such that \( \frac{p}{a}+\frac{q}{b}+ \) \( \frac{r}{c}=1+i \) and \( \frac{a}{p}+\frac{b}{q}+\frac{c}{r}=0, \) then
value of \( \frac{p^{2}}{a^{2}}+\frac{q^{2}}{b^{2}}+\frac{r^{2}}{c^{2}} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot 2 i \)
D. \( -2 i \)
Subject: Physics
In an A.C. circuit, the instantaneous
values of e.m.f. and current are \( \boldsymbol{E}= \)
\( 200 \sin 314 t \) volts and \( I=\sin (314 t+ \)
\( \pi / 3) \) ampere then the average power
consumed in watts is
A . 200
B. 100
\( c \cdot 0 \)
D. 50
Subject: Maths
\( \left|\begin{array}{ccc}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & 1\end{array}\right|=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3}\end{array}\right| \) then the
two triangles whose vertices are
\( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(\left(x_{3}, y_{3}\right) \) and \right.
\( \left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right),\left(a_{13}, b_{3}\right), \) are
A . congruent
B. similar
c. equal in area
D. none of these
Subject: Chemistry
(a) Complete the following chemical reaction equations
(i) \( P_{4}+S O_{2} C l_{2} \rightarrow \)
(ii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
(b) Predict the shape and the asked angle \( \left(90^{\circ} \) or more or less) in each of \right.
the following cases:
(i) \( S O_{3}^{2-} \) and the angle \( O-S-O \)
(ii) \( C l F_{3} \) and the angle \( F-C l-F \)
(iii) \( X e F_{2} \) and the angle \( F-X e-F \)
Subject: Maths
From a piece of cardboard, in the shape
of a trapezium \( A B C D, \) and \( A B \| C D \) and \( \angle \)
\( \mathrm{BCD}=90^{\circ}, \) quarter circle is removed
Given \( A B=B C=3.5 \mathrm{cm} \) and \( \mathrm{DE}=2 \mathrm{cm} \)
Calculate the area of the remaining
piece of the cardboard.(Take \( \pi \) to be \( \frac{22}{7} \)
A \( .9 .625 \mathrm{cm}^{3} \)
в. \( 6.125 . \) ст
\( \mathbf{c} \cdot 2.625 \mathrm{cm}^{2} \)
D. None of these
Subject: Physics
A body travels \( 200 \mathrm{cm} \) in the first 2 s
and \( 220 \mathrm{cm} \) in the next 4 s with deceleration. The velocity of the body at the end of the seventh second is
A. \( 5 \mathrm{cm} / \mathrm{s} \)
в. \( 10 \mathrm{cm} / \mathrm{s} \)
\( \mathrm{c} \cdot 15 \mathrm{cm} / \mathrm{s} \)
D. 20cm/s
Subject: Maths
A force \( \vec{F}=4 \hat{i}+6 \hat{j}+3 \hat{k} \) acting on a particle produces a displacement of \( \vec{S}= \) \( 2 \hat{i}+3 \hat{j}+5 \hat{k} \) where \( F \) is expressed in
Newtonn and \( S \) in the metre. Find the
work done by the force.
Subject: Chemistry
The vapour pressure of pure water at 25
\( ^{o} \mathrm{C} \) is 23.76 torr. The vapour pressure of a solution containing 5.40 g of a nonvolatile substance in 90.0 g water in 23.32 torr. Compute the molecular weight of the solute
A. 58.82 g/mol
B. \( 58.20 \mathrm{g} / \mathrm{mol} \)
c. 59.25 g/mol
D. \( 60.24 \mathrm{g} / \mathrm{mol} \)
Subject: Physics
A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation(T) of the liquid drop depends on radius \( (r) \) of the drop, density \( (\rho) \) and surface tension(s) of the liquid. Which among the following will be a possible expression for T(where k is a dimensionless constant)?
A \( \cdot k \sqrt{\frac{\rho r}{s}} \)
B. \( k \sqrt{\frac{\rho^{2} r}{s}} \)
\( ^{\mathrm{c}} \cdot \sqrt[k]{\frac{\rho r^{3}}{s}} \)
D. \( k \sqrt{\frac{\rho r^{3}}{s^{2}}} \)
Subject: Physics
A large solenoid of windings of 400
turns per meter carries a current \( 5 \mathrm{A} \)
The magnetic field at the centre of the solenoid is about:
A . \( 1.2 \mathrm{mT} \)
B. zero
c. \( 5.0 \mathrm{mT} \)
D. 2.5 mT
Subject: Maths
If \( f(a)=\log \left(\frac{2+a}{2-a}\right), 0<a<2 \) then
\( \frac{1}{2} f\left(\frac{8 a}{4+a^{2}}\right)= \)
A. \( f(a) \)
B. \( 2 f(a) \)
c. \( \frac{1}{2} f(a) \)
D. \( -f(a) \)
Subject: Physics
The graph shows the behaviour of a
steel wire in the region for which the wire obeys Hooke's law.The graph is a part of a parabola. The variables x and y might represent
A. \( x= \) stress \( ; y= \) strain
B. \( x= \) strain ; \( y=\operatorname{str} e s \)
c. \( x= \) strain \( ; y= \) elastic energy
D. \( x= \) elastic energy \( ; y= \) strain
Subject: Biology
Dryopithecus occurred about
\( A \cdot 2.5 \times 10^{6} \) years back
B. \( 25 \times 10^{6} \) years back
\( \mathbf{C} \cdot 50 \times 10^{6} \) years back
D. \( 75 \times 10^{6} \) years back
Subject: Biology
A lake near a village suffered heavy mortally of fishes within a few days. Consider the following reasons for this.
(A) Lots of urea and phosphate fertilizers were used in the crops in the vicinity.
(B) The area was sprayed with DDT by an aircraft.
(C) The lake water turned green and stinky
(D) Phytoplankton populations in the lake declined initially thereby greatly reducing photosynthesis. Which two of the above were the main
causes of fish mortality in the lake?
\( A \cdot(A),(C) \)
B. (A), (B)
\( c \cdot(B),(C) \)
D. (c), (D)
Subject: Maths
Point \( D \) has coordinates as (3,4,5)
Referring to the given figure, find the
coordinates of point \( C \)
\( \mathbf{A} \cdot(4,0,0) \)
\( \mathbf{B} \cdot(0,3,4) \)
C. (0,3,0)
D. (0,4,0)
Subject: Chemistry
Assertion
\( H_{2} S \) is more acidic than \( H_{2} O \)
Reason
\( H-S \) bond is more polar than \( H-O \)
bond.
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
For \( _{24} C r, \) which of the following statements is/are correct?

This question has multiple correct options
A. Number of electrons with principle quantum number is 13
B. Number of electrons with azimuthal quantum number is 12
c. Number of electrons with magnetic quantum number 0 is 12
D. Number of minimum or maximum electrons with spin quantum number \( +1 / 2 \) is 9 or 15
Subject: Physics
A spring block system is placed on a horizontal surface so as to just fit within two vertical walls. The spring is initially unstretched. The coefficient of restitution for collison is \( e=\frac{1}{2} . \) The block is pulled to the left by a distance \( x=1 c m \) and released from rest. The
time between second and third collision
of the block with the
wall is
A \( \cdot 2 \pi \sqrt{\frac{m}{k}} \)
В. \( \pi \sqrt{\frac{m}{k}} \)
c. \( \frac{\pi}{2} \sqrt{\frac{m}{k}} \)
D. \( \frac{\pi}{4} \sqrt{\frac{m}{k}} \)
Subject: Physics
In Wheatstone bridge, three resistors
\( P, Q, R \) are connected in three arms in
order and 4 th arm \( s \) is formed by two
resistors \( s_{1} \) and \( s_{2} \) connected in
parallel. The condition for bridge to be balanced is \( \frac{\boldsymbol{P}}{\boldsymbol{Q}}= \)
A \( \cdot \frac{R\left(s_{1}+s_{2}\right)}{s_{1} s_{2}} \)
В. \( \frac{s_{1} s_{2}}{R\left(s_{1}+s_{2}\right)} \)
c. \( \frac{R s_{1} s_{2}}{\left(s_{1}+s_{2}\right)} \)
D. \( \frac{\left(s_{1}+s_{2}\right)}{R s_{1} s_{2}} \)
Subject: Maths
If the normal at the end of latus rectum of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) passes
through \( (0,-b), \) then \( e^{4}+e^{2} \) (where \( E \) is eccentricity) equals
A \cdot eccentricity of the ellipse is \( \sqrt{\frac{\sqrt{5}-1}{2}} \)
B. ratio of the minor and major axes is \( \frac{\sqrt{5}+1}{2} \)
c. square of the eccentricity is equal to the ratio of the minor and major axes
D. none of these
Subject: Maths
The degree and order of
the differential equation
\( \left[1+2\left(\frac{d y}{d x}\right)^{2}\right]^{1 / 2}=5 \frac{d^{2} y}{d x^{2}} \) are
\( A \cdot 1,2 \)
B. 2,
c. 3,1
D. 4,3
Subject: Physics
The focal length of a convex lens is \( 5 \mathrm{cm} \) where should the object be placed to get a real image with same size as that
of object:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 60 \mathrm{cm} \)
D. None of these
Subject: Maths
Solve the equations using cross
multiplication method: \( x-y=12 \) and
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{1 4} \)
A . \( x=13, y=1 \)
В. \( x=13, y=-1 \)
c. \( x=-13, y=-1 \)
D. \( x=-13, y=1 \)
Subject: Physics
How long will it be moving until it stops for the first time?
A \( \cdot t=2 \frac{\pi}{\omega} \)
В \( \cdot t=3 \frac{\pi}{\omega} \)
c. \( t=4 \frac{\pi}{\omega} \)
D・ \( t=\frac{\pi}{\omega} \)
Subject: Physics
A narrow tube is bent in the form of a
circle of radius \( R, \) as shown in the
figure. Two small holes \( S \) and \( D \) are made in the tube at the positions right angle to each other. A source placed at S generated a wave of intensity \( l_{0} \) which
is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point \( D \) where a detector is placed. The maximum value of \( \lambda \) to produce a
maxima at D is given by :
A \( . \pi R \)
В. \( 2 \pi R \)
c. \( \frac{\pi R}{2} \)
D. \( \frac{3 \pi R}{2} \)
Subject: Maths
The number of \( \boldsymbol{A} \) in \( \boldsymbol{T}_{\boldsymbol{p}} \) such that \( \boldsymbol{A} \) is either symmetric or skew-symmetric or both, and det(A) divisible by \( p \) is:
A \( \cdot(p-1)^{2} \)
в. \( 2(p-1) \)
c. \( (p-1)^{2}+1 \)
D. \( 2 p-1 \)
Subject: Physics
Let \( \omega \) be the angular velocity of the earth's rotation about its axis. Assume
that the acceleration due to gravity on the earth's surface has the same value
at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth a below earth's surface at a pole \( (d<< \)
\( \boldsymbol{R} \) ) The value of \( \boldsymbol{d} \) is
\( ^{\mathrm{A}} \cdot \frac{\omega^{2} R^{2}}{g} \)
B. \( \frac{\omega^{2} R^{2}}{2 g} \)
\( ^{\mathrm{c}} \cdot \frac{2 \omega^{2} R^{2}}{g} \)
D. \( \frac{\sqrt{R g}}{g} \)
Subject: Maths
\( \int \frac{\operatorname{cosec} x}{\cos ^{2}\left(1+\log \tan \frac{x}{2}\right)} d x \) is equal to
\( A \cdot \sin ^{2}\left[1+\log \tan \frac{x}{2}\right]+C \)
B \cdot \( \tan \left[1+\log \tan \frac{x}{2}\right]+C \)
c. \( \sec ^{2}\left[1+\log \tan \frac{x}{2}\right]+C \)
D. \( -\tan \left[1+\log \tan \frac{x}{2}\right]+C \)
Subject: Chemistry
The critical constant \( P_{C} \& T_{C} \) for
methane are 45 atm and 189 K. The
correct statement is-(Single option correct
\( \begin{array}{ll}\text { A. } V_{C}=1.2 & L \\ \end{array} \)
В. \( b=0.8 \quad L / m o l \)
c. \( V_{C}=2.4 \quad L \)
D. \( b=0.04 \quad L / m o l \)
Subject: Physics
The de-Broglie wavelength associated with an electron accelearated to
potential difference of V volt is:
A. \( V \times 10^{-10} m \)
в. \( \sqrt{\frac{150}{V}} A^{0} \)
c. \( \frac{150}{V} A^{0} \)
D. \( 150 V \times 10^{-8} \mathrm{m} \)
Subject: Physics
A bullet of mass \( 40 g \) is fired from a gun
of mass \( 10 \mathrm{kg} \). If velocity of bullet is \( 400 m / s, \) then the recoil velocity of the gun will be
A. \( 1.6 \mathrm{m} / \mathrm{s} \) in the direction of the bullet
B. \( 1.6 \mathrm{m} / \mathrm{s} \) opposite to the direction of the bullet
c. \( 1.8 m / s \) in the direction of the bullet
D. \( 1.8 \mathrm{m} / \mathrm{s} \) opposite to the direction of the bullet
Subject: Physics
Atomic mass number of an element is
232 and its atomic number of \( 90 . \) The
end product of this radioactive element is an isotopes of lead (atomic mass 208
and atomic number 82 ). The number of
\( \alpha \) and \( \beta- \) particles emitted are :
A. \( \alpha=3, \beta=3 \)
в. \( \alpha=6, \beta=4 \)
c. \( \alpha=6, \beta=0 \)
D. \( \alpha=4, \beta=6 \)
Subject: Maths
If, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left[\begin{array}{cc}\boldsymbol{x} \tan ^{-1} \boldsymbol{x}+\sec ^{-1} \frac{1}{x} & , \boldsymbol{x} \boldsymbol{\epsilon}(-1,1)-\mathbf{0} \\ \frac{\boldsymbol{\pi}}{2} & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x}=\mathbf{0}\end{array}\right] \)
then \( \boldsymbol{f}^{\prime}(\mathbf{0}) \) is
A. equal to -
B. equal to 0
c. equal to 1
D. non existent
Subject: Physics
A box of mass \( 50 k g \) is pulled along on
an inclined plane of \( 12 m \) length and \( 2 m \)
height by a constant force of \( 100 N \) from rest. It acquires a velocity of \( 2 m / s \) when
it reaches the top of the plane. The work done against friction in joules is
A . 50
B. 100
\( c \cdot 150 \)
D. 200
Subject: Maths
If \( \mathbf{A B}=\mathbf{0}, \) then
\( \mathbf{A} \cdot \mathbf{A}=0 \)
\( \mathbf{B} \cdot \mathbf{B}=0 \)
C. \( A \) and \( B \) need not be zero matrices
D. \( A \) and \( B \) are zero matrices
Subject: Physics
Assertion
A steady current is flowing in a conductor hence there is an electric
field within the conductor and
Reason
In case of steady current, there can be
no accumulation of charges, so no
electric field can be established.
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
Equal volumes of \( 1 \mathrm{M} K_{2} S O_{4} \) and \( 1 \mathrm{M} \)
\( A l_{2}\left(S O_{4}\right)_{3} \) solutions are mixed. Which
of the following is incorrect?
A. The concentration of \( K^{+} \) is 1 M
B. The concentration of \( A l^{3+} \) is 1M
C. The concentration of \( S O_{4}^{2-} \) is 2 M
D. The concentration of all the three ions is 1 M
Subject: Maths
If \( y=2 \sin x-3 x^{4}+8, \) then \( \frac{d y}{d x} \) is
B . \( 2 \cos x-12 x^{3} \)
\( \mathbf{c} \cdot 2 \cos x+12 x^{3} \)
D. \( 2 \sin x+12 x^{3} \)
Subject: Chemistry
Select the correct order of acidic nature
of non-metal oxide:
This question has multiple correct options
А. \( C O>C O_{2} \)
в. \( C O_{2}> \) СО
\( \mathrm{c} \cdot \mathrm{CO}_{2}>\mathrm{SiO}_{2} \)
D. \( C O_{2}< \) SiO \( _{2} \)
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{a}\end{array}\right] \) and \( \boldsymbol{A}^{2}=\left[\begin{array}{ll}\boldsymbol{\alpha} & \boldsymbol{\beta} \\ \boldsymbol{\beta} & \boldsymbol{\alpha}\end{array}\right] \) then
\( \mathbf{A} \cdot \alpha=a^{2}+b^{2}, \beta=2 a b \)
B . \( \alpha=a^{2}+b^{2}, \beta=a^{2}-b^{2} \)
C \( \cdot \alpha=2 a b, \beta=a^{2}+b^{2} \)
D . \( \alpha=a^{2}+b^{2}, \beta=a b \)
Subject: Physics
Car A and car B start moving simultaneously in the same direction along the line joining them car A with a constant acceleration \( \boldsymbol{a}=\mathbf{4} \boldsymbol{m} / \boldsymbol{s}^{2} \) while
car \( \mathrm{B} \) moves with a constant velocity \( \mathrm{V}= \) \( 1 \mathrm{m} / \mathrm{s} . \) At \( \mathrm{t}=0 \) car \( \mathrm{A} \) is \( 10 \mathrm{m} \) behind car \( \mathrm{B} \)
Find the time when car A over takes car
B.
A . 2 s
в. 2.5
\( c \cdot 1 s \)
D. 1.5 \( s \)