AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following process under desired conditions show endothermic
change? This question has multiple correct options
A \( \cdot N_{2}+\frac{1}{2} O_{2} \rightarrow N_{2} O \)
в. \( N_{2}+O_{2} \rightarrow 2 N O \)
\( \mathbf{c} \cdot F_{2}+\frac{1}{2} O_{2} \rightarrow F_{2} O \)
D. \( C+\frac{1}{2} O_{2} \longrightarrow C O \)
Subject: Maths
Let \( \lim _{x \rightarrow a} f(x) \) exists but it is not equal to \( f(a) \). Then \( f(x) \) is discontinuous
at \( x=a \) and a is called a removable
discontinuity. If \( \lim _{x \rightarrow a^{-}} f(x)= \)
\( l \) and \( \lim _{x \rightarrow a^{+}} f(x)=m \) exist but \( l \neq \)
\( m . \) Then a is called a jump
discontinuity. If one of the limits (left hand limit or right hand limit ) does not exist, then a is called an infinite discontinuity.
\( \operatorname{Let} f(x)\left\{\begin{array}{cc}2|x|, & x \leq-1 \\ 2 x, & -1 \leq x \leq 0 \\ x+1, & 0<x \leq 1 \\ 2 & x>1\end{array} \) Then \right.
\( f(x) \) at
This question has multiple correct options
A. \( x=-1 \) is a removable discontinuity
B. \( x=0 \) is a jump discontinuity
c. \( x=1 \) is a removable discontinuity
D. \( x=-1 \) is a jump discontinuity
Subject: Maths
\( A, B, C \) and \( D \) have position vectors \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d}, \) respectively, such that \( \vec{a}- \) \( \vec{b}=2(\vec{d}-\vec{c}), \) then
A. \( A B \) and \( C D \) bisect each other
B. \( A B \) and \( C D \) trisect each other
c. \( B D \) and \( A C \) bisect each other
D. \( B D \) and \( A C \) trisect each other
Subject: Maths
Assume that a factory has two
machines \( A \) and \( B \). Past records shows
that machine \( A \) produces \( 60 \% \) of the
items of output and machine \( \boldsymbol{B} \) produces \( 40 \% \) of the items. Further, \( 2 \% \) of the items produced by machine \( \boldsymbol{A} \)
were defective and only \( 1 \% \) produced by
machine \( B \) were defective. If a detective
item is drawn at random, what is the
probability that it was produced by machine \( \boldsymbol{A} \) ?
Subject: Maths
A lawn is the form of a square of side
\( 30 m . A \) cow is tied with a rope of \( 10 m \) to
a pole standing at one of its corners. The maximum area of the lawn grazed by this cow is
\( \mathbf{A} \cdot 300 m^{2} \)
B. \( 150 m^{2} \)
c. \( 78.5 m^{2} \)
D. \( 450 m^{2} \)
Subject: Physics
A ray of light incident on an equilateral
prism shows minimum deviation of \( 30^{\circ} \)
The speed of light through the glass prism is :
A \( .2 .5 \times 10^{8} \mathrm{m} / \mathrm{s} \)
B. \( 2.121 \times 10^{8} \mathrm{m} / \mathrm{s} \)
c. \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. \( 3.2 \times 10^{8} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
\( N_{2(g)}+3 H_{2(g)} \leftrightarrow 2 N H_{3(g)} \) If some \( H C l \)
gas is passed into the reaction mixture at the equilibrium of this reaction,then:
A. Equilibrium position shifts towards left
B. Equilibrium position shifts towards right
c. concentration of \( H_{2} \) increases
D. The equilibrium position is not affected
Subject: Physics
Two open pipes of length \( 25 \mathrm{cm} \) and 25.5 cm produced 10 beat/second. The velocity of sound will be:
A. \( 255 \mathrm{m} / \mathrm{s} \)
B. 250 m/s
c. \( 350 \mathrm{m} / \mathrm{s} \)
D. None of these
Subject: Chemistry
The oxidation states of \( S \) atoms in
\( S_{4} O_{6}^{2-} \) from left to right respectively
are:
\( \boldsymbol{O}-\underbrace{\boldsymbol{O}}{\boldsymbol{S}}-\boldsymbol{S}-\boldsymbol{S}-\underset{\boldsymbol{V}}{\|}^{\boldsymbol{O}}-\boldsymbol{O}^{-} \)
\( A \cdot+6,0,0,+6 \)
B. +3,1,+1,+3
\( c \cdot+5,0,0,+5 \)
D. None of above
Subject: Physics
An electron of mass 'm' and charge 'w' initially at rest gets accelerated by a constant electric field 'E'. The rate of
change of de-Broglie wavelength of this electron at time 't' ignoring relativistic effects is
\( ^{A} \cdot-\frac{h}{e E t^{2}} \)
B. \( -\frac{e h t}{E} \)
c. \( -\frac{m h}{e E t^{2}} \)
D. \( \frac{h}{e E} \)
Subject: Maths
Solve for \( \boldsymbol{x} \)
\( \left|\begin{array}{ccc}1-x & 2 & 3 \\ 0 & x & 0 \\ 0 & 0 & x\end{array}\right|=0 \)
\( \mathbf{A} \cdot 1,0,0 \)
B. 1,1,0
c. 1,1,1
D. 0,0,0
Subject: Physics
The radii of curvature of the surfaces of
a double convex lens are \( 20 \mathrm{cm} \) and 40
\( \mathrm{cm} \) respectively, and its focal length is \( 20 \mathrm{cm} . \) What is the refractive index of
the material of the lens.?
A \( \cdot \frac{5}{2} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{5}{3} \)
D. \( \frac{4}{5} \)
Subject: Maths
Draw a square of \( 4 \mathrm{cm} . \) Constuct angle bisectors of 4 angles.Let all meet at 0 measure \( A O \) and \( 0 C . \) Then \( A O^{2}+O C^{2}= \)
\( \mathbf{A} \cdot \mathbf{8} \)
B. 4
c. 16
D. 32
Subject: Chemistry
A sulphate of a metal (M) on healing evolves two gases \( (\mathrm{B}) \) and \( (\mathrm{C}) \) and an oxide (D). Gas (B) turns acidified
dichromate paper green while gas \( (\mathrm{C}) \) forms a trimer. Compound (D) forms a Lewis acid (E) with HCI (g).
If, the number of \( S \) -S bonds in trimer of
gas
(C) be 'n' and the number of
equivalent M-Cl bonds in one molecule of anhydrous (E) be 'm', Then, \( (m+n) \) is:
Subject: Maths
A mans walks along a straight path at a speed of \( 4 f t / \) sec.A scarch light is
located on the ground \( 20 f t \) from the path and is kept focused on man. At what rate is the scarch light rotating when the man is \( 15 f t \) from the point on
the path closest to the search light.
A . 0.128 rad/sec
B. 1.6rad/sec
c. \( 0.8 \mathrm{rad} / \mathrm{sec} \)
D. \( 0.24 \mathrm{rad} / \mathrm{sec} \)
Subject: Maths
\( \operatorname{Let} g(x)=1+x-[x] \quad \) and \( f(x)= \)
\( \left\{\begin{array}{lll}-1 & \text { if } & \boldsymbol{x}<\mathbf{0} \\ \mathbf{0} & \text { if } & \boldsymbol{x}=\mathbf{0}, \text { then } \forall \boldsymbol{x}, \boldsymbol{f} \boldsymbol{o} \boldsymbol{g}(\boldsymbol{x}) \\ \mathbf{1} & \boldsymbol{i f} & \boldsymbol{x}>\mathbf{0}\end{array}\right. \)
equals
\( A \)
B.
c. \( f(x) \)
D. \( g(x) \)
Subject: Chemistry
The wave function for \( 1 s \) orbital of the
hydrogen atom is given by
\[
\mathbf{\Psi}_{1 s}=\frac{\boldsymbol{\pi}}{\sqrt{\mathbf{2}}} \boldsymbol{e}^{-\boldsymbol{r} / \boldsymbol{a}_{0}}
\]
where \( a_{0}= \) Radius of first Bohr orbit \( r= \) Distance from the nucleus
(Probability of finding the electron varies with respect to it)
What will be the ratio of probabilities of finding the electrons at the nucleus to
first Bohr's orbit \( a_{0} ? \)
\( A \)
B \( \cdot e^{2} \)
\( c \cdot 1 / e^{2} \)
D. zero
Subject: Physics
Take the mean distance of the moon
and the sun from the earth to be \( 0.4 \times \)
\( 10^{6} k m \) and \( 150 \times 10^{6} k m \) respectively.
Their masses are \( 8 \times 10^{22} k g \) and \( 2 \times \)
\( 10^{30} k g \) respectively. The radius of the
earth is \( 6400 \mathrm{km} \). Let \( \Delta F_{1} \) be the difference in the forces exerted by the
moon at the nearest and farthest points
on the earth and \( \Delta F_{2} \) be the difference
in the force exerted by the sun at the nearest and farthest points o the earth. Then, the number closest to \( \frac{\Delta F_{1}}{\Delta F_{2}} \) is :
A .2
B. \( 10^{-2} \)
\( c .0 .6 \)
D.
Subject: Chemistry
Out of list 1 , select the cation which has
less polarizing power than \( C a^{2+} \) and from list II, select the anion having more polarisability:
List \( \mathrm{I}: M g^{2+}, S c^{3+}, K^{+} \)
List II: \( \boldsymbol{O}^{2-}, \boldsymbol{C l}^{-}, \boldsymbol{P}^{3-} \)
\( \mathbf{A} \cdot M g^{2+}, O^{2+} \)
B. \( K^{+}, P^{3-} \)
\( \mathbf{c} \cdot S c^{3+}, P^{3-} \)
D. \( M g^{2+}, C l^{-} \)
Subject: Chemistry
The colour of the solution/precipitate obtained in the elemental analysis of an organic compound and the molecule/ion responsible for the colour are given below. Choose the incorrectly matched pair.
A. Prussian blue - \( F e_{4}\left[F e(C N)_{6}\right]_{3} \) ] \( \cdot x H_{2} O \)
B. Black - PbS
C. Violet colour - \( \left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right]^{4-} \)
D. Blood red colour - \( \left[\mathrm{Fe}(S C N)^{2}\right. \)
E. Yellow - \( \left(N H_{4}\right)_{2} M o O_{4} \)
Subject: Chemistry
The normal boiling point of a liquid' \( \boldsymbol{X}^{\prime} \) is \( 400 K . \) Which of the following statement(s) is/are true about the
process \( X(l) \longrightarrow X(g) ? \)
This question has multiple correct options
A. at \( 400 K \) and 1 atm pressure \( \Delta G=0 \)
B. at \( 400 K \) and 2 atm pressure \( \Delta G=+v e \)
C. at \( 400 K \) and 0.1 atm pressure \( \Delta G=-v e \)
D. at \( 410 K \) and 1 atm pressure \( \Delta G=+v e \)
Subject: Physics
Two light rays having the same
wavelength \( \lambda \) in vacuum are in phase initially. Then the first ray travels a path \( L_{1} \) through a medium of refractive
index \( n_{1} \) while the second ray travels a
path of length \( L_{2} \) through a medium of
refractive index \( n_{2} \). The two waves are
then combined to produce interference. The phase difference between the two
waves is:
A \( \cdot \frac{2 \pi}{\lambda}\left(L_{2}-L_{1}\right) \)
в. \( \frac{2 \pi}{\lambda}\left(n_{1} L_{1}-n_{2} L_{2}\right) \)
c. \( \frac{2 \pi}{\lambda}\left(n_{2} L_{1}-n_{1} L_{2}\right) \)
D \( \cdot \frac{2 \pi}{\lambda}\left(\frac{L_{1}}{n_{1}}-\frac{L_{2}}{n_{2}}\right) \)
Subject: Chemistry
The structure of 6-hydroxyheptanal is:
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H(O H)-C H_{2}-C H_{2}-C H_{2}- \)
\( C H O \)
B. \( C H_{3}-C H_{2}-C H_{2}-C H(O H)-C H_{2}-C H O \)
\( \mathbf{c} \cdot C H_{3}-C H(O H)-C H_{2}-C H_{2}-C H_{2}-C H O \)
D. \( C H_{3}-C H(O H)-C H_{2}-C H_{2}-C H_{2}-C H_{2}- \)
\( C H O \)
Subject: Physics
ACCELERATION DUE TO GRAVITY OF THE
EARTH

Radius of earth is \( 6400 \mathrm{km} \) and that of
mars is \( 3200 \mathrm{km} \). Mass of mars is 0.1
that of earth's mass. Then the acceleration due to gravity on mars is nearly.
A \( \cdot 1 \mathrm{m} / \mathrm{s}^{2} \)
B \( .2 .5 m / s^{2} \)
c. \( 4 m / s^{2} \)
D. \( 5 m / s^{2} \)
Subject: Physics
At two different places the angles of dip
are respectively \( 30^{0} \) and \( 45^{0} . \) At these
two places the ratio of horizontal component of earths magnetic field is
A. \( \sqrt{3}: \sqrt{2} \)
B. \( 1: \sqrt{2} \)
c. 1: 2
D. \( 1: \sqrt{5} \)
Subject: Physics
Arrange the following radiations in the order of their increasing wavelength:
\( X \) -rays, infra red rays, radio waves,
gamma rays and micro waves.
A. Gamma rays, X -rays, infra red rays, radio waves micro waves
B. Gamma rays, micro waves, X-rays, infra red rays radio waves.
c. Gamma rays, infra red rays, \( X \) -rays, micro waves radio waves.
D. Gamma rays, \( X \) -rays, infra red rays, micro waves radio waves
Subject: Physics
n identical cells, each of emf \( \varepsilon \) and
internal resistance \( r, \) are joined in
series to form a closed circuit. One cell
\( A \) is joined with reversed polarity. The potential difference across each cell, except \( A \), is
A \( \cdot \frac{2 \varepsilon}{n} \)
в. \( \frac{n-1}{n} \)
c. \( \frac{n-2}{n} \)
D. \( \frac{2 n}{n-2} \)
Subject: Maths
If \( |\vec{A} \times \vec{B}|=\sqrt{3} \vec{A} \cdot \vec{B} \) then the value of
\( |\vec{A}+\vec{B}| \) is:
\( ^{A} \cdot\left(A^{2}+B^{2}+\frac{A B}{\sqrt{3}}\right)^{1 / 2} \)
в. \( A+B \)
c. \( \left(A^{2}+B^{2}+\sqrt{3} A B\right)^{1 / 2} \)
D. \( \left(A^{2}+B^{2}+A B\right)^{1 / 2} \)
Subject: Chemistry
Let us suppose that you have discovered a new element of the atomic
number \( 162, \) which you choose to name
khalidium (Kh). Assume that the
normal order of filling of orbitals still prevails in the eighth period.

The new type of orbital used in Kh that
is not used in any known atom is:
\( A \cdot h \)
B.
\( c \cdot f \)
D.
Subject: Physics
The corecivity of a small magnet where the ferromagnet gets demagnetized is
\( 3 \times 10^{3} A m^{-1} . \) The current required to
be passed in a solenoid of length \( 10 \mathrm{cm} \)
and number of turns \( 100, \) so that the magnet gets demagnetized when inside the solenoid is:
\( A \cdot 3 A \)
в. \( 6 A \)
\( c .30 m A \)
D. \( 60 m A \)
Subject: Maths
What must be added to \( x^{3}-3 x^{2}- \)
\( 12 x+19, \) so that the result is exactly
divisible by \( x^{2}+x-6 ? \)
A \( .2 x+5 \)
в. \( 4 x-4 \)
c. \( 2 x+3 \)
D. \( -2 x-5 \)
Subject: Maths
An article is marked at Rs. \( 2,250 . \) By selling it at a discount of \( 12 \%, \) the dealer makes a profit of \( 10 \% \). Find the cost price of the article for the dealer
A . Rs. 1,500
B. Rs. 1, 600
c. Rs. 1,700
D. Rs. 1, 800
Subject: Physics
A moving sidewalk in an airport terminal building moves at a speed of
\( 1.0 m s^{-1} \) and is \( 35.0 \mathrm{m} \) long. If a woman
steps on at one end and walks at 1.5
\( m s^{-1} \) relative to the moving sidewalk,
then find the time that she requires to
reach the opposite end
(a) when she
walks in the same direction the
sidewalk is moving and
(b) when she
walks in the opposite direction.
Subject: Physics
A convex mirror of focal length \( f \) forms
an image which is \( \frac{1}{n} \) times the object. The distance of the object from the mirror is :
\( ^{\mathbf{A}} \cdot\left(\frac{n-1}{n}\right) f \)
\( ^{\mathbf{B}} \cdot\left(\frac{n+1}{n}\right) f \)
\( \mathbf{c} \cdot(n+1) f \)
D. \( (n-1) f \)
Subject: Physics
A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black
(i) The image will be shifted downward
\( (i i) \) The image will be shifted upward
\( (i i i) \) The image will not be shifted
\( (i v) \) The intensity of the image will decrease
A. (i) and ( \( (i) \) )
B. (ii) and (iii)
c. \( (i i i) \) and \( (i v) \)
D. only \( (i v) \)
Subject: Chemistry
Pure water boils at \( 99.725^{\circ} C \) at shimla.
If \( K_{b} \) for water is \( 0.51 K m o l^{-1} k g, \) the
boiling point of 0.69 molal urea solution will be:
A . 100.35
B. 100.08
c .99 .37
D. None of these
Subject: Physics
The radius of the sun is \( 7 \times 10^{8} m \) and
its mass is \( 2 \times 10^{30} k g \). What is the
order of magnitude of density of the
sun?
\( \mathbf{A} \cdot 1.4 \times 10^{3} k g / m^{3} \)
В \( \cdot 10^{7} k g / m^{3} \)
c. \( 1.5 \times 10^{3} k g / m^{3} \)
D. \( 10^{3} k g / m^{3} \)
Subject: Chemistry
Monoclinic sulphur is an example of
monoclinic crystal system. What are the
characteristics of the crystal system?
\( \mathbf{A} \cdot \mathbf{a} \neq b \neq c, \alpha=\beta=\gamma=90^{\circ} \)
B \( \cdot a \neq b \neq c, \alpha \neq \beta \neq \gamma \neq 90^{\circ} \)
\( \mathbf{C} \cdot a=b \neq c, \alpha=\beta=\gamma=90^{\circ} \)
D \( \cdot a \neq b \neq c, \alpha=\gamma=90^{\circ}, \beta \neq 90^{\circ} \)
Subject: Chemistry
The ratio of magnetic moments of \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \)
\( \& C o^{3+} \) is:
B. \( \sqrt{35}: \sqrt{24} \)
\( c \cdot 7: 3 \)
D. \( \sqrt{24}: \sqrt{15} \)
Subject: Physics
In the circuit shown, the switch \( S_{1} \) is
closed for long time and at \( t=0 \) s, the
switch \( S_{2} \) is closed and \( S_{1} \) is opened
simultaneously. What is the maximum charge (in the unit of \( \mu C \) ) on the \( 4 \mu F \)
capacitor?
A \( \cdot q_{0}=3 \mu C \)
В \( \cdot q_{0}=6 \mu C \)
c. \( q_{0}=3.4 \mu C \)
D \( \cdot q_{0}=6.8 \mu C \)
Subject: Physics
Two identical calorimeter \( \boldsymbol{A} \) and \( \boldsymbol{B} \)
contain equal quantity of water at \( 20^{\circ} C \)
A \( 5 g m \) piece of metal \( X \) of specific
heat 0.2 cal \( g^{-1}\left(C^{\circ}\right)^{-1} \) is dropped into
\( A \) and a \( 5 g m \) piece of metal \( Y \) into \( B \) The equilibrium temperature in \( A \) is
\( 22^{\circ} \mathrm{C} \) and in \( B 23^{\circ} \mathrm{C} . \) The initial
temperature of both the metals is \( 40^{\circ} \mathrm{C} \)
Find the specific heat of metal \( Y \) in cal
\( \boldsymbol{g}^{-1}\left(\boldsymbol{C}^{\circ}\right)^{-1} \)
Subject: Physics
The refractive index of water with
respect to air is \( _{a} \mu_{w} \) and of glass with respect to air is \( _{a} \mu_{\mathrm{g} \cdot} \) So, \( \frac{a \mu_{g}}{a \mu_{w}} \) should
express:
A. refractive index of glass with respect to water
B. refractive index of water with respect to glass
C. refractive index of air
D. none of these
Subject: Maths
The population of a city increases at the rate of \( 4 \% \) per year. If in time \( t, \) the
population becomes \( p \), then equation of
\( p \) in terms of \( t \) is
A.
\[
p=e^{\frac{t}{25}}
\]
В. \( \quad p=4 . e^{\frac{t}{25}} \)
c. \( \quad_{p=c . e} \frac{t}{25} \)
D.
\[
p=\frac{1}{25} e^{4 t}
\]
Subject: Chemistry
The \( \boldsymbol{K}_{s p} \) for \( \mathrm{AgCl} \) is \( 2.8 \times 10^{-10} \) at \( \mathrm{a} \)
given temperature. The solubility of AgCl in 0.01 molar \( \mathrm{HCl} \) solution at
this temperature will be :
A . \( 2.8 \times 10^{-12} \mathrm{molL}^{-1} \)
В. \( 2.8 \times 10^{-8} \) molL\( ^{-1} \)
c. \( 5.6 \times 10^{-8} \) molL\( ^{-1} \)
D. \( 2.8 \times 10^{-4} \mathrm{molL}^{-1} \)
Subject: Maths
What is the value of \( \sin ^{-1}\left(\sin 160^{\circ}\right) ? \)
\( \mathbf{A} \cdot 160^{\circ} \)
В. \( 70^{\circ} \)
\( \mathbf{c} \cdot-20^{0} \)
D. \( 20^{\circ} \)
Subject: Physics
An oscillator consists of a block
attached to spring \( (\mathrm{K}=1,1,400 \mathrm{l}, \mathrm{N} / \mathrm{m}), \mathrm{At} \)
some time \( t, \) the position (measured from the system's equilibrium location), velocity and acceleration of
the block are \( \boldsymbol{x}=\mathbf{0 . 1 0 0 m}, \boldsymbol{v}= \)
\( -15.0 m / s, \) and \( a=-90 m / s^{2} . \) The
amplitude of the motion and the mass of the block are :
A. \( 0.2 m, 0.84 k g \)
\( g \)
в. \( 0.3 m, 0.76 k g \)
\( \mathrm{c} .0 .4 m, 0.54 \mathrm{kg} \)
D. \( 0.5 m, 0.44 k g \)
Subject: Chemistry
Which of the following does not give oxygen on heating?
A. \( K C l O_{3} \)
B. \( Z n\left(C l O_{3}\right)_{2} \)
c. \( K_{2} C r_{2} O_{7} \)
D. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)
Subject: Maths
The area of region bounded by curve \( y=\cos 2 x, \) line \( x=0 \) and \( x=\frac{\pi}{3} \) is
A \( \cdot \frac{2-\sqrt{3}}{4} \)
B. \( \frac{\sqrt{3}}{4} \)
c. \( \frac{4-\sqrt{3}}{4} \)
D. \( \frac{\sqrt{3}-4}{4} \)
Subject: Physics
A particle starts from a point \( \mathrm{P} \) at \( \mathrm{a} \) distance of A/2 from the mean position
0 and travels towards left as shown in
the figure. If the time period of \( \mathrm{SHM} \) executed about 0 is \( \mathrm{T} \) and amplitude \( \mathrm{A} \)
then the equation of the motion of
particle is:
This question has multiple correct options
A \( \cdot x=A \sin \left(\frac{2 \pi}{T} t+\frac{\pi}{6}\right) \)
B. \( x=A \sin \left(\frac{2 \pi}{T} t+\frac{5 \pi}{6}\right) \)
c. \( x=A \cos \left(\frac{2 \pi}{T} t+\frac{\pi}{6}\right) \)
D. \( x=A \cos \left(\frac{2 \pi}{T} t+\frac{\pi}{3}\right) \)
Subject: Chemistry
Amongst the following the total number
of elements, which produce \( \boldsymbol{H}_{2} \) gas with sodium hydroxide is:
\( \mathrm{Zn}, \mathrm{Al}, \mathrm{Sn}, \mathrm{Pb}, \mathrm{P}, \mathrm{Si} \)
A. 3
B. 4
\( c \cdot 5 \)
\( D \cdot 6 \)
Subject: Maths
For what values of \( x \) is the rate of
increase of \( x^{3}-5 x^{2}+5 x+8 \) is twice
the rate of increase of \( x ? \)
A \( \cdot-3,-\frac{1}{3} \)
в. \( _{-3, \frac{1}{3}} \)
c. \( _{3,-\frac{1}{3}} \)
D. \( _{3, \frac{1}{3}} \)
Subject: Maths
\( \int e^{\tan ^{-1} x}\left(1+x+x^{2}\right) d\left(\cot ^{-1} x\right) \) is
equal to
A \( \cdot-e^{\tan ^{-1} x}+c \)
B - \( e^{\tan ^{-1} x}+c \)
C. \( _{-x e^{\tan ^{-1} x}+c} \)
D. \( x e^{\tan ^{-1} x}+c \)
Subject: Physics
There photo dlodes \( D_{1}, D_{2} \) and \( D_{3} \) are made of semiconductor having band
\( \operatorname{gap} 2.5 e V, 2 e V \) and \( 3 e V \) respectively. Which one will be able to detect light of
wavelength \( 6000 A^{\circ} ? \)
A. \( D_{1} \)
в. \( D_{2} \)
\( c \cdot D_{3} \)
D. \( D_{1} \) and \( D_{2} \) both
Subject: Maths
\( \frac{1-\sin A}{\cos A} \) is equal to
\( A \cdot \frac{\cos A}{1+\sin A} \)
B. \( \frac{\sin A}{1-\cos A} \)
c. \( \frac{\tan A}{1+\tan A} \)
D. \( \frac{\tan A}{1+\cos A} \)
Subject: Chemistry
Knowing that the chemistry of lanthanoids \( (L n) \) is dominated by its
+3 oxidation state, which of the
following statements is incorrect?
A. \( L n(I I I) \) hydroxides are mainly basic in character
B. The ionic sizes of \( \operatorname{Ln}(I I I) \) decrease in general with increasing atomic number
c. Because of the large size of the \( L n(I I I) \) ions the bonding in its compounds is predominantly ionic in character
D. \( L n(I I I) \) compounds are generally colourless
Subject: Maths
Let \( n>2 \) be an integer and \( f: P \rightarrow R \) a
function defined on the set of points in the plane, with the property that for any
regular n-gon \( \boldsymbol{A}_{\mathbf{1}} \boldsymbol{A}_{\mathbf{2}} \ldots \boldsymbol{A}_{\boldsymbol{n}}, \boldsymbol{f}\left(\boldsymbol{A}_{\mathbf{1}}\right)+ \)
\( \boldsymbol{f}\left(\boldsymbol{A}_{2}\right)+\ldots+\boldsymbol{F}\left(\boldsymbol{A}_{n}\right)=\mathbf{0} . \) Prove that
is the zero function.
A. fis zero function.
B. fis not a zero function
c. f is indefinite function.
D. fis not a function
Subject: Maths
For any integer \( n \geq 1 \), the sum \( \sum_{k=1}^{n} k(k+2) \) is equal to
A \( \cdot \frac{n(n+1)(n+2)}{6} \)
B. \( \frac{n(n+1)(2 n+1)}{6} \)
c. \( \frac{n(n+1)(2 n+7)}{6} \)
D. \( \frac{n(n+1)(2 n+9)}{6} \)
Subject: Chemistry
The reagent(s) for the following conversion,
is/are
A. alcoholic KOH
B. alcoholic KOH followed by NaNHa
c. aqueous KOH followed by \( \mathrm{NaNH}_{2} \)
D. \( \mathrm{Zn} / \mathrm{CH}_{3} \mathrm{OH} \)
Subject: Maths
The length of the longest rod that can be fitted in a cubical vessel of edge \( 10 \mathrm{cm} \)
long, is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
В. \( 10 \sqrt{2} \mathrm{cm} \)
c. \( 10 \sqrt{3} \mathrm{cm} \)
D. \( 20 c m \)
Subject: Chemistry
If a molecule \( M X_{3} \) has zero dipole
moment, the \( \sigma \) - bonding orbitals used by M (atomic number \( <21 \) ) is:
A . pure \( p \)
B. \( s p \) - hybridized
c. \( s p^{2} \) - hybridized
D. \( s p^{3} \) - hybridized
Subject: Physics
A square loop of side \( 10 \mathrm{cm} \) and resistance \( 0.5 \Omega \) is placed vertically in the east-west plane. A uniform
magnetic field of \( 0.10 \mathrm{T} \) is set up across the plane in the north-east direction. The magnetic field is decreased to zero
in 0.70 s at a steady rate. The magnitudes of induced emf and current during this time-interval is then
\( A \cdot 1 \mathrm{mV}, 2 \mathrm{mA} \)
B. \( 1 \mathrm{mV}, 1 \mathrm{ma} \)
c. \( 2 \mathrm{mv}, 2 \mathrm{mA} \)
D. \( 2 \mathrm{mV}, 1 \mathrm{mA} \)
Subject: Physics
STATEMENT-1
In a Meter Bridge experiment, null point for an unknown resistance is measured.
Now, the unknown resistance is
put inside an enclosure maintained at a
higher temperature. The null point can be obtained at the same point as before
by decreasing the value of the standard resistance.
STATEMENT-2
Resistance of a metal increases with
increase in temperature.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT -1 is False, STATEMENT-2 is True
Subject: Physics
The displacement \( x \) of a particle varies
with time according to the relation \( x= \) \( \frac{a}{b}\left(1-e^{-b t}\right) . \) Which of the following
statements is incorrect?
A \( \cdot \) At \( t=\frac{1}{b}, \) the displacement of the particle is nearly \( \frac{2}{3}\left(\frac{a}{b}\right) \)
B. the velocity and acceleration of the particle at \( t=0 \) are \( a \) and \( -a b \) respectively
C . the particle cannot go beyond \( x=\frac{a}{b} \)
D. the particle will come back to its starting point at \( t \rightarrow \) \( \infty \)
Subject: Maths
The value of \( c \) in Lagranges mean value
theorem for \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{l} \boldsymbol{x}^{2}+\boldsymbol{m} \boldsymbol{x}+ \)
\( \boldsymbol{n},(\boldsymbol{l} \neq \mathbf{0}) \) on \( [\boldsymbol{a}, \boldsymbol{b}] \) is
A \( \cdot \frac{a}{2} \)
B. \( \frac{b}{2} \)
c. \( \frac{(a-b)}{2} \)
D. \( \frac{(a+b)}{2} \)