AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A machine part is shown in cross
section in figure consists of two homogeneous solid, coaxial cylinders \( A B \) as the common axis. Where is its
centre of mass from A? (in \( \mathrm{m} \) )
\( A \)
\( \overline{7} \)
B. 2 \( \overline{7} \)
c. \( \frac{52}{7} \)
D. 5
Subject: Chemistry
According to CIP Sequence rule, the correct arrangement in order of decreasing priority is :
A. \( -O H>C H_{2} O H>-C H O>-C O O H \)
в. \( -O H>C O O H>-C H O>-C H_{2} O H \)
с. \( -C O O H>O H>-C O H>-C H_{2} O H \)
D. \( -C O O H>C H O>-C H_{2} O H>-O H \)
Subject: Maths
Which of these are correct?
(a) If any two rows or columns of a determinant are identical, then the
value of the determinant is zero.
(b) If the corresponding rows and columns of a determinant are
interchanged, then the value of the determinant does not change.
(c) If any two rows (or column) of a determinant are interchanged, then the value of the determinant changes in
\( \operatorname{sign} \)
A \( \cdot(a) \) and \( (b) \)
B. \( (b) \) and \( (c) \)
c. \( (a) \) and \( (c) \)
D. \( (a),(b) \) and \( (c) \)
Subject: Physics
Suppose the gravitational force varies
inversely as the \( n^{t h} \) power of distance. Then the time period of a planet in
circular orbit of radius \( R \) around the
sun will be proportional to:
B. \( R^{(n-1) / 2} \)
\( c \cdot R^{n} \)
D. \( R^{(n-2) / 2} \)
Subject: Physics
The gravitational potential at the centre of a square of side a when four point masses m each are kept at its vertices will be
A \( \cdot 4 \sqrt{2} \frac{G m}{a} \)
в. \( -4 \sqrt{2} \frac{G m}{a} \)
c. \( _{2 \sqrt{2}} \frac{G m}{a} \)
D. \( -2 \sqrt{2} \frac{G m}{a} \)
Subject: Physics
The maximum and minimum resultant
capacity that can be obtained with \( 2 \mu F, 3 \mu F \) and \( 6 \mu F \) are respectively:
A. \( 11 \mu F, 1 \mu F \)
в. \( 11 \mu F, 6 \mu F \)
c. \( 11 \mu F, 2 \mu F \)
D. \( 11 \mu F, 4 \mu F \)
Subject: Physics
\( 7 / 8 \) fraction of a sample disintegrates in 't' time, how much time it will take to disintegrate \( 15 / 16 \) fraction?
\( \mathbf{A} \cdot \mathbf{t} \)
B. \( 4 / 3 t \)
\( c \cdot 5 / 3 t \)
D. 2t
Subject: Chemistry
The statement that is not correct is :
\( \mathbf{A} \cdot \) in solid state \( P C l_{5} \) exists as \( \left[P C l_{4}\right]^{+}\left[P C l_{6}\right]^{-} \)
B. phosphorous acid on heating disproportionates to give metaphosphoric acid and phosphine
C. hypophosphorous acid reduces silver nitrate to silver
D. pure phosphine is non-inflammable
Subject: Physics
Read the given statements and select
the correct option.

Statement 1: Rahul placed a coloured plastic bottle in front of the beam of a
torch light. Then he placed a transparent sheet of same size on the
other side of bottle. No shadow will form
on the screen.

Statement 2: Translucent objects allow
light to pass through them partially.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1 .
c. Statement 1 is true but statement 2 is false.
D. Statement 1 is false but statement 2 is true
Subject: Physics
An iron rod is placed parallel to the magnetic field of intensity \( 2000 \mathrm{A} / \mathrm{m} \) The magnetic flux through the rod is \( 6 \times 10^{-4} W b \) and its cross-sectional
area is \( 3 \mathrm{cm}^{2} \). The magnetic permeability of the rod in \( \frac{W b}{A-m} \) is:
A \( \cdot 10^{-1} \)
B. \( 10^{-2} \)
\( \mathbf{c} \cdot 10^{-3} \)
D. \( 10^{-4} \)
Subject: Physics
For a junction diode the ratio of forward
current \( \left(I_{f}\right) \) and reserve current \( \left(I_{r}\right) \) is \( [e= \) electronic charges, \( \boldsymbol{V}= \) voltage applied across junction, \( K= \) Boltzmann constant
\( \boldsymbol{T}=\text { temperature in Kelvin }] \)
A \( \cdot e^{-V / K T} \)
\( \mathbf{B} \cdot e^{V / K T} \)
c. \( \left(e^{-e V / K T}+1\right) \)
D. \( e^{e V / K T}-1 \)
Subject: Physics
The armature of a demonstrator
generator consists of a flat square coil
of side \( 4 c m \) and 200 turns. The coil
rotates in a magnetic field of 0.75 T. The
angular speed so that a maximum emf of \( 1.6 V \) is generated is:
A \( \cdot \frac{20}{3} \) rad/s
B. \( \frac{10}{3} \) rotations/s
c. \( \frac{40}{3} \) rpm
D. None of these
Subject: Maths
Evaluate the determinant to the closest nteger: \( \boldsymbol{A}=\left[\begin{array}{cc}\log _{3} \mathbf{5 1 2} & \log _{4} \mathbf{3} \\ \log _{3} \mathbf{8} & \log _{4} \mathbf{9}\end{array}\right] \)
Subject: Maths
If \( \alpha=\beta+\frac{2 \pi}{3} . \) then \( A_{\theta} \) is maximum
when \( \gamma \) equals
A. \( \alpha+\pi / 3 \)
в. \( \alpha-\pi / 3 \)
c. \( \alpha+2 \pi / 3 \)
D. none of these
Subject: Physics
A sinusoidal voltage of peak value \( 283 V \) and angular frequency \( 320 / s \) is applied to a series LCR circuit. Given
that \( \boldsymbol{R}=\mathbf{5} \boldsymbol{\Omega}, \boldsymbol{L}=\mathbf{2 5} \boldsymbol{m} \boldsymbol{H} \) and \( \boldsymbol{C}= \)
1000 \( \mu F \). The total impedance, and
phase difference between the voltage
across the source and the current will
respectively be:
\( \mathbf{A} \cdot 7 \Omega \) and \( 45^{\circ} \)
B. \( 10 \Omega \) and \( \tan ^{-1}\left(\frac{5}{3}\right) \)
c. \( 10 \Omega \) and \( \tan ^{-1}\left(\frac{8}{3}\right) \)
D. \( 7 \Omega \) and \( \tan ^{-1}\left(\frac{5}{3}\right) \)
Subject: Chemistry
Which of the following statements is incorrect?
A \( \cdot K_{4}\left[N i(C N)_{4}\right] \) and \( K_{2}\left[N i(C N)_{4}\right] \) both have same
magnetic moment
B. \( K_{4}\left[N i(C N)_{4}\right] \) is a diamagnetic while \( K_{4}\left[N i\left(C l l_{4}\right] \) is \right.
paramagnetic
\( \mathbf{c} \cdot_{K_{4}}\left[N i(C N)_{4}\right] \) is diamagnetic while \( K_{2}\left[N i(C N)_{4}\right] \) is
tetrahedral
D. \( K_{4}\left[N i(C l)_{4}\right] \) and \( K_{4}\left[N i(C N)_{4}\right] \) both have same
geometrical shapes
Subject: Chemistry
Observe the following statements regarding purification of bauxite:
I. During Hall's process, silica is removed as Si (vapour).
II. Bauxite ore contaminated with
\( F e_{2} O_{3} \) is purified in Baeyer's process.
III. During Serpeck's process, \( A l N \) is formed.
A. I, II and III are correct
B. Only I and II are correct
c. only land III are correct
D. Only II and III are correct
Subject: Chemistry
Pyrolusite is \( M n O_{2} \) used to prepare
\( K M n O_{4} . \) Steps are:
\( M n O_{2} \stackrel{I}{\longrightarrow} M n O_{2}^{2-} \stackrel{I I}{\longrightarrow} M n O_{4}^{-} \)
Steps \( I \) and \( I I \) are respectively:
This question has multiple correct options
A. fuse with \( K O H / \) air, electrolyte oxidation
B. fuse with \( K O H / K N O_{3} \), electrolyte oxidation.
c. fuse with concentrated \( H N O_{3} \) /air, electrolytic reduction
D. dissolve in \( H_{2} O \) oxidation
Subject: Physics
Two particles of equal mass m have respective initial velocties \( u \hat{i} \) and \( u\left(\frac{\hat{i}+\hat{j}}{2}\right) . \) They collide completely inelastically. The energy lost in the
process is?
A \( \cdot \frac{1}{3} m u^{2} \)
B. \( \sqrt{\frac{2}{3}} m u^{2} \)
c. \( \frac{3}{4} m u^{2} \)
D. \( \frac{1}{8} m u^{2} \)
Subject: Maths
If \( \boldsymbol{y}=\cot ^{-1}\left(\frac{1-x}{1+x}\right) \) then \( \frac{d y}{d x}=? \)
A \( \cdot \frac{-1}{\left(1+x^{2}\right)} \)
B. \( \frac{1}{\left(1+x^{2}\right)} \)
c. \( \frac{1}{\left(1+x^{2}\right)^{3 / 2}} \)
D. none of these
Subject: Physics
Two soap bubbles \( A \) and \( B \) are formed
at the two open ends of a tube. The
bubble \( A \) is smaller than bubble \( B \). If
valve \( V \) is opened and air can flow freely
between the bubbles, then
A. There is no change in the size of the bubbles
B. The two bubbles will become of equal size
C. \( A \) will become smaller and \( B \) will become larger
D. \( B \) will become smaller and \( A \) will become larger
Subject: Physics
There are two wires \( a b \) and \( c d \) in a
vertical plane as shown in figure.Direction of current in wire \( a b \) is
rightwards.Choose the correct options
This question has multiple correct options
A. If wire \( a b \) is fixed then wie \( c d \) can be kept in equilibrium by the current in \( c d \) in leftward direction
B. Equilibrium of wie \( c d \) will be stable equilibrium
C. If wire \( c d \) is fixed,then wire \( a b \) can be kept in equilibrium by flowing current in \( c d \) in rightward direction
D. Equilibrium of wire \( a b \) will be stable equilibrium
Subject: Chemistry
The primary valency and secondary valency of central metal ion and the no. of total ions produced in aqueous
solution for \( \boldsymbol{K}\left[\boldsymbol{C o}(\boldsymbol{O} \boldsymbol{X})_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \)
complex respectively is
A. 3,4,2
в. 4,4,2
\( \mathrm{c} .3,6,2 \)
D. 3,6,1
Subject: Physics
In the figure shown, plank is
being pulled to the right with a constant
speed v. If the cylinder does not slip then
This question has multiple correct options
A. the speed of the centre of mass of the cylinder is \( 2 v \)
B. the speed of the centre of mass of the cylinder is zero
c. the angular velocity of the cylinder is \( v / R \)
D. the angular velocity of the cylinder is zero
Subject: Physics
A projectile is thrown in the upward
direction making an angle of \( 60^{\circ} \) with the horizontal direction with a velocity
of \( 147 m s^{-1} . \) Then the time after which
its inclination with the horizontal is \( 45^{\circ} \)
is (Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2} \) )
A . \( 15 s \)
B. \( 10.98 s \)
c. \( 5.49 s \)
D. 2.745 \( s \)
Subject: Maths
If \( \tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\pi \) then
prove that:
\( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{x} \boldsymbol{y} \boldsymbol{z} \)
Subject: Chemistry
Assertion
Reduction of \( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}, \) with \( \mathrm{CO} \) is done
below \( 710^{\circ} \mathrm{C} \)
Reason
\( \Delta G \) is negative at this temperature; thus,process is spontaneous.

Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Statement-1 is true, statement-2 is true; statement- is a correct explanation for statement- -1.
B. Statement-1 is true, statement-2 is true; statement- is NOT a correct explanation for statement- -2.
c. Statement- 1 is true, statement- 2 is false
D. Statement-1 is false, statement-2 is true
Subject: Physics
A particle starts from rest and moves with uniform acceleration. If covers a
displacement of \( y^{2}-x^{2} \) in the first
\( 10 \sec \) and \( y^{2}+x^{2} \) in the next first
\( 10 s e c, \) then
A \( . x=\sqrt{2} y \)
в. \( x=3 y \)
c. \( y=3 x \)
D. \( y=\sqrt{2} x \)
Subject: Maths
The difference between the
circumference and radius of a circle is
\( 30 \pi . \) Find the diameter of circle.
A. \( \frac{30 \pi}{2 \pi-1} \)
в. \( \frac{60 \pi}{2 \pi-1} \)
c. \( \frac{2 \pi-1}{60 \pi} \)
D. None
Subject: Chemistry
Hydrogen peroxide acts both as an oxidising and as a reducing agent, depending upon the nature of the reacting species. In which of the
following cases \( H_{2} O_{2} \) acts as a reducing agent in acid medium?
A. \( M n O_{4} \)
B. \( C r_{2} O_{7}^{2} \)
\( \mathbf{c} \cdot S O_{3}^{2} \)
D. \( K I \)
Subject: Maths
The degree and order of differential
equation \( \left(\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}\right)^{2}=\left(\boldsymbol{y}+\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{\frac{1}{2}} \)
which of the following?
Subject: Chemistry
Find the wavelength associated with an electron which has mass \( 9.1 \times 10^{-28} g \)
and is moving with a velocity of \( 10^{5} \mathrm{cm} \) \( \sec ^{-1} .\left(\text {Given: } h=6.625 \times 10^{-27} \) erg \right.
\( \sec \)
A \( . \lambda=5.28 \times 10^{-5} m \)
в. \( \lambda=7.28 \times 10^{-5} \mathrm{cm} \)
c. \( \lambda=7.28 \times 10^{-5} m \)
D. \( \lambda=5.28 \times 10^{-5} \mathrm{cm} \)
Subject: Maths
Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\begin{array}{c}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y} \\
x y<1 \\
\pi+\tan ^{-1} \frac{x+y}{1-x y}, \quad x y>1 \\
\operatorname{atan}^{-1}\left(\sqrt{\frac{a-b}{a+b}} \tan \frac{\theta}{2}\right)= \\
\cos ^{-1} \frac{a \cos \theta+b}{a+b \cos \theta}
\end{array}
\]
Subject: Maths
In the given figure, a square \( \boldsymbol{O A B C} \) has
been inscribed in the quadrant OPB \( Q \)
If \( \boldsymbol{O} \boldsymbol{A}=\mathbf{2 0} \boldsymbol{c m} \) then the area of the
shaded region is \( [\text {take } \pi=\mathbf{3 . 1 4}] \)
A \( \cdot 214 c m^{2} \)
B. \( 228 c m^{2} \)
\( c \cdot 222 c m^{2} \)
\( \mathrm{D} \cdot 242 \mathrm{cm}^{2} \)
Subject: Biology
Which terms for \( P, Q, R, S, T, U, \) and \( V \) will
make the following paragraph true?
The human excretory system consists
of kidneys, ureters, \( _{-}-P_{--} \) and \( _{-}-Q \) The \( _{--} R_{--} \) brings the dirty blood into kidneys. Kidneys remove the poisonous substances urea, salt and extra water
from the body. The cleaned blood is
carried away from the kidneys by \( S_{--} \cdot_{--} T_{--} \) is the tube that carries
urine from the kidney to the \( _{--} U_{--} \) The urine collected in the bladder is
passed out of the body through the
\( \mathbf{V}_{--} \)
A. P- -bladder; Q-urethra; R_renal artery; S-renal vein; Tureters; U-bladder; V-urethra
B. P- bladder; Q-urethra; R_renal vein; S-renal artery; Tureters; U-bladder; V-urethra
c. P- bladder; Q-urethra; R_renal artery; S-venacava; Tureters; U-bladder; V-urethra
D. None of these
Subject: Maths
\( \ln \) an \( A . P ., \) sum of \( p \) terms \( = \)
sum of q terms, then sum of \( (\boldsymbol{p}+\boldsymbol{q}) \)
terms equal to?
A . 0
B. 2
c. \( -p q \)
\( \mathbf{D} \cdot-(p+q) \)
Subject: Chemistry
How many moles of \( N_{2} \) are needed to
produce 18 moles \( N H_{3} \) in the reaction?
\( N_{2}+3 H_{2} \rightarrow 2 N H_{3} ? \)
\( A \cdot 9 \)
B. 18
\( c \cdot 3 \)
\( D \cdot 2 \)
\( E \)
Subject: Maths
If \( x^{m} \cdot y^{n}=(x+y)^{m+n}, \) then \( \frac{d y}{d x} \) is \( ? \)
A. \( \frac{y}{x} \)
в. \( \frac{x+y}{x y} \)
c. \( x y \)
D. \( \frac{x}{y} \)
Subject: Physics
In a Young's double slit experiment, the
fringes are displaced by a distance \( x \) when a glass plate of refractive index 1.5 is introduced in the path of one of the beams. Then this plate is replaced by another plate of the same thickness, the shift of fringes is \( \frac{3}{2} x . \) The refractive index of the second plate is :
A . 2.25
в. 2.0
c. 1.75
D. 1.25
Subject: Physics
A body starts from rest with uniform
acceleration. If its velocity after \( n \)
seconds is \( v \) then assuming straight line motion, its displacement in the last two seconds is:
A . \( v n \)
B. \( \frac{2 v(n-1)}{n} \)
c. \( \frac{2 v(n+1)}{n} \)
D. \( \frac{v}{n} \)
Subject: Physics
Two bodies, initially separated by \( x \) m
and having an initial velocity \( 2 \mathrm{m} s^{-1} \) each, are moving towards each other along a straight line. If the rate of increase of their speeds is \( 3 \mathrm{m} s^{-2} \) and
\( 2 m s^{-2} \) respectively and the two meet after 4 seconds, find \( x \)
A \( \cdot 12 \)
B. 40
\( c .56 \)
D. 66
Subject: Chemistry
Assuming the formation of an ideal
solution, the boiling point of a mixture
containing 1560 g benzene (molar mass =78) and 1125 g chlorobenzene (molar" mass \( =112.5)^{\prime} \) using the given vapour
pressure vs. temperature diagram against anexternal pressure of 1000
torr, is :
\( \mathbf{A} \cdot 90^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 110^{\circ} C \)
D. \( 120^{\circ} \mathrm{C} \)
Subject: Physics
A galvanometer of resistance \( 50 \Omega \) giving full scale deflection for a current
of 10 milliampere is to be changed into a voltmeter of range \( 100 \mathrm{V} \)

A resistance of \( _{-1}-\ldots_{\text {has to be }} \)
connected in series with the
galvanometer.
A . 9950
B. 10025
c. 10000
D. 9975
Subject: Maths
The ascending order of \( \boldsymbol{A}= \) \( \sin ^{-1}\left(\log _{3} 2\right), B=\cos ^{-1}\left(\log _{3}\left(\frac{1}{2}\right)\right) \)
and \( C=\tan ^{-1}\left(\log _{1 / 3} 2\right) \) is
A. \( \mathrm{C}, \mathrm{B}, \mathrm{A} \)
в. В, А, С
c. \( \mathrm{c}, \mathrm{A}, \mathrm{B} \)
D. B, C, A
Subject: Chemistry
What is the oxidation number for As in
the chemical formula for arsenic acid,
\( \boldsymbol{H}_{3} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4} ? \)
\( A \cdot+1 \)
\( B .+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)
\( E \cdot+5 \)
Subject: Physics
A solid conducting sphere of radius \( 2 R \)
carrying charge \( Q \) is surrounded by two
point charges \( Q \) and \( 2 Q \) as shown in the
figure. The electric field at point \( \boldsymbol{P} \) due
to the induced charge on conducting
sphere is
A \( \cdot \frac{7}{16} \frac{K Q}{R^{2}} \) towards right
B \( \cdot \frac{1}{8} \frac{K Q}{R^{2}} \) towards right
\( \mathrm{C} \cdot \frac{\mathrm{KQ}}{\mathrm{R}^{2}} \) towards right
D. Zero
Subject: Physics
A boy is moving on a straight road against a frictional force of \( 5 N . \) After
travelling a distance of \( 1.5 k m, \) he forgets the correct path at a round about (see fig.) of radius \( 100 m \) However, he moves on the circular path
for one and half cycle and then he moves
forward upto \( 2.0 k m . \) Calculate the work
done by him \( (\pi=3.14) \)
Subject: Physics
Two coherent point sound sources \( \boldsymbol{S}_{1} \)
and \( S_{2} \) are placed as shown in the
figure. Both are emitting sound of
frequency \( 165 \mathrm{Hz} . S_{1} \) is ahead of \( S_{2} \) in
phase by \( \pi- \) radian. (Speed of sound is
\( 330 \mathrm{m} / \mathrm{s} \) ) How many times maximum sound can be observed on line AB?
A. 7
B. 6
\( c \cdot 5 \)
\( D \)
Subject: Chemistry
The chemical formula of feldspar is :
A. \( K A l S i_{2} O_{8} \)
в. \( N a_{3} A l F_{6} \)
c. \( N a A l O_{8} \)
D. \( K_{2} O_{4} A l_{2}\left(S O_{4}\right)_{4} A l(O H)_{4} \)
Subject: Biology
Which of the following represents the
floral characters of Liliaceae?
A. Six sepals, zygomorphic, six stamens, bilocular ovary, axile placentation
B. Tetramerous, actinomorphic, polyphyllous, unilocular ovary, axile placentation
C. Trimerous, actinomorphic, polyandrous, superior ovary, axile placentation
D. Bisexual. zygomorphic, gamophyllous, inferior ovary, marginal placentation
E. Unisexual, actinomorphic, trilocular, inferior ovary, axile placentation
Subject: Maths
If the roots of the equation \( \frac{\alpha}{x-\alpha}+ \) \( \frac{\beta}{\boldsymbol{x}-\beta}=1 \) be equal in magnitude but
opposite in \( \operatorname{sign}, \) then \( \alpha+\beta \) is equal to:
A.
B. 1
\( c \cdot 2 \)
D.
Subject: Maths
If \( 2 \tan ^{-1} x+\sin ^{-1} \frac{2 x}{1+x^{2}} \) is
independent of \( x \) then
A \( \cdot x \epsilon(1,+\infty) \)
В . \( x \epsilon(-1,1) \)
c. \( x \epsilon(-\infty,-1) \)
D. none of these
Subject: Physics
The lateral magnification of the lens with an object located at two different
positions \( u_{1} \) and \( u_{2} \) are \( m_{1} \) and \( m_{2} \) respectively. Then the focal length of the lens is :
\( \mathbf{A} \cdot f=\sqrt{m_{1} m_{2}}\left(u_{2}-u_{1}\right) \)
в. \( \frac{m_{2} u_{2}-m_{1} u_{1}}{m_{2}-m_{1}} \)
c. \( \frac{\left(u_{2}-u_{1}\right)}{\sqrt{m_{2} m_{1}}} \)
D. \( \frac{\left(u_{2}-u_{1}\right)}{\left(m_{2}\right)^{-1}-\left(m_{1}\right)^{-1}} \)
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ccc}|\boldsymbol{x}-\mathbf{2}|+\mathbf{1} & \boldsymbol{i} \boldsymbol{f} & \boldsymbol{x}<\mathbf{2} \\ \mathbf{2} & \boldsymbol{i} \boldsymbol{f} & \boldsymbol{x}=\mathbf{2} \\ |\boldsymbol{x}-\mathbf{2}|-\mathbf{1} & \boldsymbol{i} \boldsymbol{f} & \boldsymbol{x}>\mathbf{2}\end{array}\right\} \)
If \( \lim _{x \rightarrow a} f(x) \) exists then
A \( . a=2 \)
\( \mathbf{B} \cdot a \epsilon R \)
\( \mathbf{c} \cdot a \epsilon R-\{2\} \)
D \( \cdot a \epsilon R-\{1,2\} \)
Subject: Maths
A factory has three machines \( A, B \) and \( C \) which produce 100,200 and 300 items of a particular type daily. The machines produce \( 2 \%, 3 \% \) and \( 5 \% \) defective items respectively. One day when the production was over, an item was picked up randomly and it was found to be defective. Find the probability that it was produced by machine \( A \)
Subject: Chemistry
One end of metal bar of area of cross
section \( 5 c m^{2} \) and \( 25 c m \) in length is in stream and other end is in contact with
ice. The amount of ice melts in one
minute is :
\( (\boldsymbol{L}=\mathbf{8 0} \mathbf{c a l} / \boldsymbol{g} \boldsymbol{m}, \boldsymbol{K}=\mathbf{0 . 8} \boldsymbol{c g} \boldsymbol{s} \boldsymbol{u n i t s}) \)
\( \mathbf{A} \cdot 16 g m \)
в. \( 12 g m \)
\( \mathrm{c} \cdot 24 g m \)
D. \( 36 g m \)
Subject: Physics
Assertion
Magnification of a convex mirror is always positive, but that of a concave mirror may be both positive or negative.
Reason
It depends on the sign convention
chosen.
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 reaction \( \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C}(\boldsymbol{g})+ \)
\( D(g) \) is elementry \( 2^{n d} \) order reaction.
When started with equimolar amounts of \( A \) and \( B, \) at equilibrium, it is found that the concentration of \( A \) is twice that
of C. Specific rate for forward reaction is \( 2 \times 10^{-3} \) mol \( ^{-1} \) Lsec \( ^{-1} \). The specific
rate constant for backward reaction is:
B. \( 8 \times 10^{-3} M^{-1} \)sec\( ^{-1} \)
c. \( 1.5 \times 10^{2} M^{-1} \sec ^{-1} \)
D. None of these
Subject: Physics
Position vector of a particle is given by \( \vec{r}=a \cos \omega t \hat{i}+a \sin \omega t \hat{j} . \) Which of the
following is/are true? This question has multiple correct options
A. velocity vector is parallel to position vector
B. velocity vector is perpendicular to position vector
c. acceleration vector is directed towards the origin
D. acceleration vector is directed away from the origin
Subject: Physics
The acceleration due to gravity on the moon is one sixth that on the earth. \( A \)
high jumper canjump \( 2 \mathrm{m} \) on earth. What distance can he jump on the moon?
\( A \cdot 2 m \)
B. \( 6 \mathrm{m} \)
\( c \cdot 12 m \)
D. 18
Subject: Physics
A man slides down a snow covered hill
along a curved path and falls \( 20 \mathrm{m} \) below his initial position. The velocity in \( \mathrm{m} / \mathrm{sec} \) with which he finally strikes the
ground is? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s e c}^{2}\right) \)
A . 20
в. 400
c. 200
D. 40
Subject: Physics
Which pair of following forces will never give resultant force of \( 2 \mathrm{N} \)
A. \( 2 \mathrm{N} \) and \( 2 \mathrm{N} \)
B. 1 N and 1 N
c. \( 1 \mathrm{N} \) and \( 3 \mathrm{N} \)
D. \( 1 \mathrm{N} \) and \( 4 \mathrm{N} \)
Subject: Chemistry
\( \mathbf{2} \boldsymbol{C} \boldsymbol{u}^{2+}(\boldsymbol{a} \boldsymbol{q})+\mathbf{5} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{I}_{2}(\boldsymbol{s})+ \)
\( \boldsymbol{I}_{3}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
\( I_{3}^{-}(a q)+2 S_{2} O_{3}^{2-}(a q) \rightarrow \)
\( \boldsymbol{S}_{4} \boldsymbol{O}_{6}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{3} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
When copper containing alloy of weight \( 0.3175 g \) is dissolved in an acid and an excess of \( K I \) is added, 25 mL of
\( 0.10 M N a_{2} S_{2} O_{3} \) is required, then \( C u \)
present in alloy is
A . \( 20 \% \)
в. \( 40 \% \)
\( c .45 \% \)
D. \( 50 \% \)
Subject: Chemistry
With a mixture of conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) and
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) anisole
gives
A. ortho nitro anisole
B. para nitro anisole
c. ortho and para nitro anisole
D. meta nitro anisole