AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
A stone is dropped into a quiet lake and
waves move in a circle at a speed of
\( 3.5 c m / \)sec. At the instant when the
radius of the circular wave is \( 7.5 \mathrm{cm} \)
The enclosed area increases as fastly
as.
A \( \cdot 52.5 \pi \mathrm{cm}^{2} / \mathrm{sec} \)
в. \( 50.5 \pi \mathrm{cm}^{2} / \mathrm{sec} \)
\( \mathbf{c} \cdot 57.5 \pi \mathrm{cm}^{2} / \mathrm{sec} \)
D. \( 62.5 \pi \mathrm{cm}^{2} / \mathrm{sec} \)
Subject: Physics
Suppose you walk from home to the bus
stand at \( 4 k m / h \) and immediately return at \( x \) km/h. If the average speed is \( 6 \mathrm{km} / \mathrm{h} \) then \( \mathrm{x} \) is.
\( \mathbf{A} \cdot 8 k m / h \)
в. \( 10 k m / h \)
\( \mathrm{c} .12 \mathrm{km} / \mathrm{h} \)
D. Cannot be determined unless the distance from home to bus stand is known
Subject: Chemistry
\( \ln 2 s p^{2} \) orbital, character of \( 2 p_{z} \) orbital
will be
A. always \( 33.33 \% \)
B. always \( 0 \% \)
c. always \( 66.66 \% \)
D. always \( 33.33 \% \) or \( 0 \% \)
Subject: Biology
After forceful inspiration, the amount of air that can be breathed out by maximum forced expiration is equal to
A. Inspiratory Reserve Volume(IRV) + Expiratory Reserve Volume (ERV) + Tidal Volume (TV)+ Residual Volume(RV)
B. IRV + RV + ERV
c. \( \mid R V+T V+E R V \)
D. \( T V+R V+E R V \)
Subject: Physics
Three identical sphere each of mass \( M \)
are placed at the centre of a right angled triangle with mutually perpendicular sides equal to \( 2 m \) Taking their point of intersection on the origin, the position vector of the centre
of mass is:
\( \left.^{\mathrm{A}} \cdot \frac{2}{3}^{(\hat{\imath}}+\hat{j}\right) \)
B \( \cdot \frac{2}{3}(\hat{i}-\hat{j}) \)
c. Both A and B
D. None of the above
Subject: Maths
The sides of a triangle are \( \mathbf{5 0} \mathrm{cm}, \mathbf{7 8} \mathrm{cm} \) and \( 112 \mathrm{cm} . \) The smallest
altitude is...
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 50 \mathrm{cm} \)
E. None of these
Subject: Maths
20 is written as the product of primes
as:
\( \mathbf{A} \cdot 2 \times 5 \)
в. \( 2 \times 2 \times 3 \times 5 \)
c. \( 2 \times 2 \times 5 \)
D. \( 2 \times 2 \times 3 \)
Subject: Physics
A 10 V battery connected to \( 5 \Omega \)
resistance coil having inductance \( 10 \mathrm{H} \) through a switch drives a constant
current in the circuit. The switch is
suddenly opened and the time taken to open it is 2 ms. The average emf
induced across the coil is
A \( \cdot 4 \times 10^{4} \)
B \( .2 \times 10^{4} \)
\( c \cdot 2 \times 10^{2} \)
D. \( 1 \times 10^{4} \)
Subject: Physics
A cuboid has volume \( \boldsymbol{V}=\mathbf{1} \times \mathbf{2 l} \times \mathbf{3 l} \)
where 1 is the length of one side. If the
relative percentage error in the
measurement of \( l \) is \( 1 \% \), then the
relative percentage error in measurement of \( V \) is
\( \mathbf{A} \cdot 18 \% \)
B. \( 6 \% \)
c. \( 3 \% \)
D. 1\%
Subject: Chemistry
Impure copper containing \( \boldsymbol{F e}, \boldsymbol{A} \boldsymbol{u}, \boldsymbol{A} \boldsymbol{g} \)
as impurities is electrolytically refined. A current of \( 140 A \) for \( 482.5 s \) decreased
the mass of the anode by \( 22.26 g \) and increased the mass of cathode by \( 22.011 g . \) Percentage of iron in impure copper is :
(Given molar mass \( F e=55.5 g m o l^{-1} \)
molar mass \( C u=63.54 g m o l^{-1} \)
A .0 .85
в. 0.90
c. 0.95
D. 0.97
Subject: Maths
Assertion
If \( ^{n} C_{r-1}=36,^{n} C_{r}=84 \) and \( ^{n} C_{r+1}= \)
\( 126, \) then \( ^{r} C_{2}=8 \)
Reason
\( n C_{r}=^{n} C_{n-r} \)
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 and Reason is correct
Subject: Maths
Solve graphically:
\( 2 x-3 y=7 \) and \( 5 x+y=9 \)
A. \( x=2, y=-6 \)
в. \( x=8, y=-9 \)
c. \( x=0, y=-3 \)
D. \( x=2, y=-1 \)
Subject: Chemistry
Bleaching powder contains:
A. \( C a O \) and \( C l_{2} \) are molecules
B. \( C a^{2+} \) and 2 OCl \( ^{-\text {ions }} \)
c. \( C a^{2+}, C l^{-} \) and \( O C l^{-} \) ions
D. \( C a^{2+}, O^{2-} \) ions and \( C l_{2} \) molecule
Subject: Maths
If \( \sin ^{-1} a+\sin ^{-1} b+\sin ^{-1} c=\frac{3 \pi}{2} \) and
\( \boldsymbol{f}(\mathbf{2})=\mathbf{2}, \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})= \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \operatorname{then} \boldsymbol{a}^{f(\boldsymbol{2})}+ \)
\( \boldsymbol{b}^{f(4)}+\boldsymbol{c}^{f(\boldsymbol{6})}-\frac{\boldsymbol{3}\left(\boldsymbol{a}^{f(\boldsymbol{2})} \cdot \boldsymbol{b}^{\boldsymbol{f}(4)} \cdot \boldsymbol{c}^{\boldsymbol{f}(\boldsymbol{6})}\right)}{\boldsymbol{a}^{\boldsymbol{f}(\boldsymbol{2})}+\boldsymbol{b}^{\boldsymbol{f}(4)}+\boldsymbol{c}^{\boldsymbol{f}(\boldsymbol{6})}} \)
equals
\( A \cdot 2 \)
в.
\( c \cdot 6 \)
D.
Subject: Physics
A wire is bent in the form of an
equilateral triangle of side \( 100 \mathrm{cm} \) and
carries a current of \( 2 A . \) It is placed in
the magnetic field of induction \( 2.0 T \)
directed perpendicular to the plane of the paper. The direction and magnitude
of the magnetic force acting on each side of the triangle will be.
A. \( 2 N \) normal to the side towards centre of the triangle
B. \( 2 N \) normal to the side away from the centre of the triangle
c. \( 4 N \) normal to the side towards centre of the triangle
D. None of these
Subject: Physics
Q Type your question
having track,is \( \mathrm{M}=1 \mathrm{kg} \) and rests over a smooth horizontal floor.A cylinder of
radius \( r=10 \mathrm{cm} \) and mass \( \mathrm{m}=0.5 \mathrm{kg} \) is hanging by thread such that axes of cylinder and track are in same level and surface of cylinder is in contact with the track as shown in figure.When the thread is burnt, cylinder starts to move
down the track.Sufficient friction exists
between surface of cylinder and track so that cylinder does not slip. Calculate velocity of axis of cylinder and velocity
of the block when it reaches bottom of
the track.Also find force applied by
block on the floor at that moment. \( (g=10 \)
\( \left.\boldsymbol{m} / \boldsymbol{s}^{2}\right\rangle \)
Subject: Biology
Assertion
WBCs accumulate at the site of wounds
by diapedesis.
Reason
It is the squeezing of leucocytes from
the endothelium.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Physics
has an inductor of inductance \( L \) and a
resistor of resistance it connected in
series. Using the phasar diagram,
explain why the voltage in the circuit
will lead the current in phase.
(b) The potential difference across the
resistor is \( 160 \% \) and that across the
inductor is \( 120 V . \) Find the effective
value of the applied voltage. If the
effective current in the circuit be \( 1.0 A \)
calculate the total impedance of the circuit.
(c) What will be the potential difference
in the circuit when direct current is
passed through the circuit??
Subject: Physics
A person walks at a velocity \( v \) in a
straight line forming an angle \( \alpha \) with
the plane of a plane mirror. the velocity
at which he approaches his image is:
\( A \)
B. \( v \sin \alpha \)
\( \mathbf{c} \cdot 2 v \sin \alpha \)
D. \( 2 v \cos a \)
Subject: Maths
The area of parallegram represented by the vectors. \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}+ \)
\( 4 \hat{j} \) is :-
A. 14 units
B. 7.5 units
c. 10 units
D. 5 units
Subject: Maths
Let \( f(x) \) be a continuous function
whose range is \( [2,6.5] . \) If \( h(x)= \)
\( \left[\frac{\cos x+f(x)}{\lambda}\right], \lambda \in N, \) be continuous
where [.] denotes the greatest integer function, then the least value of \( \lambda \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 7
\( c \cdot 8 \)
D. None of these
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \tan ^{-1}\left(\frac{1-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}\right)= \)
A \( \cdot \frac{2}{1+x^{2}} \)
B \( \cdot \frac{-1}{1+x^{2}} \)
c. \( \frac{1}{1+x^{2}} \)
D. \( \frac{-2}{1+x^{2}} \)
Subject: Chemistry
Conductivity of a saturated solution of a sparingly soluble salt \( A B \) at \( 298 K \) is
\( 1.85 \times 10^{-5} S m^{-1} . \) Solubility product of
the salt \( A B \) at \( 298 K \) is :
\( \left[\text { Given } \boldsymbol{\Lambda}_{\boldsymbol{m}}^{o}(\boldsymbol{A B})=\mathbf{1 4 0} \times\right. \)
\( \left.10^{-4} S m^{2} m o l^{-1}\right] \)
A. \( 1.32 \times 10^{-12} \)
В. \( 1.74 \times 10^{-12} \)
C \( .5 .7 \times 10^{-12} \)
D. \( 7.5 \times 10^{-12} \)
Subject: Maths
If \( \boldsymbol{P}=\left[\begin{array}{ll}\sqrt{\mathbf{3}} / \mathbf{2} & \mathbf{1} / \mathbf{2} \\ -\mathbf{1} / \mathbf{2} & \sqrt{\mathbf{3}} / \mathbf{2}\end{array}\right], \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \)
\( \boldsymbol{Q}=\boldsymbol{P} \boldsymbol{A} \boldsymbol{P}^{\prime}, \operatorname{then} \boldsymbol{P}^{\prime} \boldsymbol{Q}^{2005} \boldsymbol{P} \) is
A. \( \left[\begin{array}{cc}1 & 1 \\ 2005 & 1\end{array}\right] \)
B. \( \left[\begin{array}{cc}1 & 2005 \\ 0 & 1\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{cc}1 & 2005 \\ 2005 & 1\end{array}\right] \)
Subject: Physics
From the figure
\[
F_{1} \sqrt{\longleftarrow} d_{1} \longrightarrow d_{2} \longrightarrow
\]
\( \mathbf{A} \cdot \frac{f_{1}}{d_{1}}=\frac{f_{2}}{d_{2}} \)
\( \mathbf{B} \cdot f_{1} \times d_{2}=f_{2} \times d_{1} \)
\( \mathbf{C} \cdot f_{1} \times d_{1}=f_{2} \times d_{2} \)
D. All
Subject: Maths
Let \( f(x)=\left\{\begin{array}{cc}-2, & -3 \leq x \leq 0 \\ x-2, & x<x \leq 3\end{array} \) and \right.
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(|\boldsymbol{x}|)+\mid \boldsymbol{f}(\boldsymbol{x}) \)
Which of the following statements are correct?
1. \( g(x) \) is continuous at \( x=0 \)
2. \( g(x) \) is continuous at \( x=2 \)
3. \( g(x) \) is continuous at \( x=-1 \)
Select the correct answer using the code given below
A. 1 and 2 only
B. 2 and 3 only
c. 1 and 3 only
D. 1,2 and 3
Subject: Maths
\( \ln \Delta A B C, \angle C=90^{\circ}, \) then the value of
\( \cos ^{2} A+\cos ^{2} B \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
\( c \cdot \frac{1}{2} \)
D. \( \frac{\sqrt{3}}{2} \)
Subject: Physics
Choose the wrong statement when we
measure the temperature of a water
kept in a beaker:
A. Thermometer should be kept vertical so that the bulb does not touch sides or bottom of the beaker
B. Thermometer should be kept vertical so that the bulb touches the bottom of the beaker
C. Thermometer should not be kept tilted so that the bulb touches sides or bottom of the beaker
D. Thermometer should be kept tilted without touching bottom or sides of the beaker
Subject: Chemistry
When a certain metal was irradiated
with a light of \( 8.1 \times 10^{16} \) Hz frequency,
the photoelectron emitted had 1.5 times the kinetic energy as did the photoelectrons emitted when the same metal was irradiated with light \( 5.8 \times \)
\( 10^{16} \mathrm{Hz} \) frequency. If the same metal is
irradiated with light of 3.846 nm
wavelength,what will be the energy of the photoelectron emitted?
A \( .1 .8 \times 10^{2} e V \)
В. \( 3.65 \times 10^{-17} J \)
c. \( 2.28 \times 10^{2} e V \)
D. \( 4.37 \times 10^{-17} J \)
Subject: Biology
Assertion
Phyllotaxy deals with morphology of
Ieaves
Reason
Foliage denotes all leaves of a plant.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Physics
A vibrating tuning fork of frequency \( v \) is
placed near the open end of a long cylindrical tube. The tube has side
opening and is also fitted with a
movable reflecting piston. As the piston
is moved through \( 8.75 c m, \) the intensity
of sound changes from a maximum to minimum. If the speed of sound is
\( 350 m s^{-1}, \) then, \( v \) is
A \( .500 H z \)
В. \( 1000 H z \)
c. \( 2000 H z \)
D. \( 4000 H z \)
Subject: Chemistry
Consider the following half-cell
reactions and associated standard half-
cell potentials and determine the
maximum voltage that can be obtained by combination resulting in
spontaneous processes:
\( \boldsymbol{A u} \boldsymbol{B r}_{4}^{-}(\boldsymbol{a q})+\boldsymbol{3} \boldsymbol{e}^{-} \rightarrow \boldsymbol{A u}(\boldsymbol{s})+ \)
\( 4 B r^{-}(a q) ; E^{\circ}=-0.86 V \)
\( \boldsymbol{E} \boldsymbol{u}^{3+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{e}^{-} \rightarrow \boldsymbol{E} \boldsymbol{u}^{2+}(\boldsymbol{a} \boldsymbol{q}) ; \boldsymbol{E}^{\circ}= \)
\( -0.43 V \)
\( \boldsymbol{S} \boldsymbol{n}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{S} \boldsymbol{n}(\boldsymbol{s}) ; \boldsymbol{E}^{\circ}= \)
\( -0.14 V \)
\( \boldsymbol{I O}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O}(l)+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \)
\( \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) ; \boldsymbol{E}^{\circ}=+\mathbf{0 . 4 9} \boldsymbol{V} \)
\( \mathbf{A} \cdot+0.72 \)
B. +1.54
c. +1.00
D. +1.35
Subject: Maths
If \( \sin ^{2} \theta=\frac{1}{4}, \) then the general solution
of \( \boldsymbol{\theta} \)
A \( \cdot 2 n \pi \pm(-1)^{n} \frac{\pi}{6} \)
в. \( \frac{n \pi}{2} \pm(-1)^{n} \frac{\pi}{6} \)
c. \( n \pi \pm \frac{\pi}{6} \)
D. \( 2 n \pi \pm \frac{\pi}{6} \)
Subject: Physics
If in a circular coil A of radius R, current
is flowing and in another coil B of radius \( 2 \mathrm{R} \) a current 2 I is flowing, then
the ratio of the magnetic fields \( B_{A} \) and
\( \mathrm{B}_{B}, \) produced by them will be
A
B. 2
\( c \cdot 1 / 2 \)
D. 4
Subject: Maths
The rational number lying exactly in between the numbers \( \frac{1}{5} \) and \( \frac{1}{3} \) is
A \( \cdot \frac{1}{2} \)
в.
c. \( \frac{2}{15} \)
D. \( \frac{4}{15} \)
E. \( \frac{8}{15} \)
Subject: Physics
A pump is used to pump a liquid of
density \( \rho^{\prime} \) continuously through a pipe
of cross section area \( A \). If liquid is
flowing with speed \( V \), then power of
pump is:
A \( \cdot \frac{1}{3} \rho A V^{2} \)
B. \( \frac{1}{2} \rho A V^{2} \)
с. \( 2 \rho A V^{2} \)
D \( \cdot \frac{1}{2} \rho A V^{3} \)
Subject: Maths
Let \( g(x)= \) \( \int_{0}^{x} f(t) d t, \quad f \quad \) is such that \( \quad \frac{1}{2} \leq \)
\( \boldsymbol{f}(\boldsymbol{t}) \leq \mathbf{1} \)
for \( \boldsymbol{t} \boldsymbol{\epsilon}[\mathbf{0}, \mathbf{1}] \) and \( \mathbf{0} \leq \boldsymbol{f}(t) \leq \)
\( \frac{1}{2} \) for \( t \epsilon[1,2] . \) Then
\( \boldsymbol{g}(\boldsymbol{2}) \) satisfies the inequality
A \( \cdot-\frac{3}{2} \leq g(2) \leq \frac{1}{2} \)
в. \( 0 \leq g(2) \leq 2 \)
c. \( \frac{3}{2} \leq g(2) \leq \frac{5}{2} \)
D. \( 2 \leq g(2) \leq 4 \)
Subject: Physics
A spherical refractive surface of radius
\( 10 \mathrm{cm} \) separates two media of
refractive indices \( \mu=1 \) and \( \mu=3 / 2 \)
respectively. A point object P starts
from rest at \( t=0 \) with an acceleration
\( 2 \mathrm{cms}^{-2} . \) Find the speed of image at \( t=1 \mathrm{s} \)
A \( \cdot 2 c m s^{-1} \)
B. \( 6 \mathrm{cms}^{-1} \)
\( \mathbf{c} \cdot 3.7 \mathrm{cms}^{-1} \)
D. none of these
Subject: Physics
A ball of mass \( 10 \mathrm{kg} \) is moving with a velocity of \( 10 \mathrm{m} / \mathrm{s} \). It strikes another ball
of mass \( 5 \mathrm{kg} \), which is moving in the same direction with a velocity of \( 4 \mathrm{m} / \mathrm{s} \) If the collision is elastic their
velocities after collision will be
respectively:
A \( \cdot 12 \mathrm{m} / \mathrm{s}, 6 \mathrm{m} / \mathrm{s} \)
B. \( 12 \mathrm{m} / \mathrm{s}, 25 \mathrm{m} / \mathrm{s} \)
\( c \cdot 6 m / s, 12 m / s \)
D. \( 8 \mathrm{m} / \mathrm{s}, 20 \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( f(x)=\frac{4 x+x^{4}}{1+4 x^{3}} \) and \( g(x)= \)
\( \ln \left(\frac{1+x}{1-x}\right), \) then what is the value of \( f \cdot g\left(\frac{e-1}{e+1}\right) \) equal to?
A .2
B. 1
c. 0
D.
Subject: Maths
Find the mean deviation about mean
and median for the following data.
\begin{tabular}{ccccc}
\multirow{2}{*} {\( \boldsymbol{C I} \)} & \( \mathbf{1}- \) & \( \mathbf{6}- \) & \( \mathbf{1 1}- \) & \( \mathbf{1 6}- \) \\
& \( \mathbf{5} \) & \( \mathbf{1 0} \) & \( \mathbf{1 5} \) & \( \mathbf{2 0} \)
\end{tabular}
\[
\begin{array}{l}
2 \\
2
\end{array}
\]
Subject: Chemistry
A compound \( (X) \) gives brick red flame and breaks down on heating giving
oxygen brown gas \( (A) \) and \( (B) \). Identify \( (X),(A) \) and \( (B) \) respectively
A \( \cdot C a\left(N O_{3}\right)_{2}, N O_{2}, C a O \)
в. \( C a\left(N O_{3}\right)_{2}, C a O, N O_{2} \)
c. \( M g\left(N O_{3}\right)_{2}, M g O, N O_{2} \)
D. \( M g\left(N O_{3}\right)_{2}, N O_{2}, M g O \)
Subject: Physics
A ray of light from denser medium strikes a rarer medium at an angle of
incidence i. The reflected and refracted
rays make an angle of \( 90^{\circ} \) with each other. Angle of reflection and refraction
are r \( \& r^{1} . \) The critical angle is
a) \( \sin ^{-1}(\tan r) \)
b) \( \sin ^{-1}(\cot r) \)
c) \( \sin ^{-1}\left(\tan r^{1}\right) \)
d) \( \sin ^{-1}\left(\cot r^{1}\right) \)
A. only a is correct
B. only b is correct
c. a and b are correct
D. a and d are correct
Subject: Maths
\( \int 4^{x}\left[\boldsymbol{g}^{\prime}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{x}) \log \mathbf{4}\right] \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \frac{4^{x}}{\log 4} g(x) \)
в. \( 4^{x} \)
c. \( 4^{x} \log 4 . g(x) \)
D \cdot \( 4^{x} g(x) \)
Subject: Maths
Suppose that of all used cars of a particular year \( 30 \% \) have bad brakes.
You are considering buying a used car of that year. You take the car to a mechanic to have the brakes checked.
The chance that the mechanic will give you the wrong report is \( 20 \% \). Assuming that the car you take to the mechanic is selected at random from the population
of cars of that year. The chance that the
car's brakes are good, given that the mechanic says its brakes are good, is
A \( \frac{28}{130} \)
в. \( \frac{29}{31} \)
c. \( \frac{37}{62} \)
D. \( \frac{29}{62} \)
Subject: Maths
For each \( k \epsilon N, \) let \( C_{k} \) denote the circle
whose equation is \( x^{2}+y^{2}=k^{2} . \) On the
circle \( C_{k}, \) a particle moves k units in the
anticlockwise direction. After
completing its motion on \( C_{k}, \) the
particle moves to \( C_{k+1} \) in the radial direction. The motion of the particle continues in this manner. The particle starts at \( (1,0) . \) If the particle crossed the positive direction of the \( x \) -axis for
the first time of the circle \( C_{n} \) then \( n \) is
A . 7
B. 6
\( c \cdot 2 \)
D. none of these
Subject: Chemistry
Q Type your question
\( \mathbf{U}_{\mathbf{2}} \perp \mathbf{v}_{\mathbf{2}} \overrightarrow{\mathbf{\Delta}}^{\mathbf{\lambda}} \mathbf{A} \)
A can be
This question has multiple correct options
\( \mathbf{A} \)
\( B \)
\( C \)
D.
Subject: Maths
The variance of the random variable \( x \)
whose probability distribution is given
by
\( \boldsymbol{X}=\boldsymbol{x}: \quad \mathbf{0} \quad \mathbf{1} \quad \mathbf{2} \quad \mathbf{3} \)
\( \boldsymbol{p}(\boldsymbol{X}=\boldsymbol{x}): \quad \frac{1}{3} \frac{1}{2} \boldsymbol{0} \frac{1}{\boldsymbol{6}} \)
A . 0.5
B. 1
\( c .1 .5 \)
D. 2.0
Subject: Maths
If three points with position vectors as \( (1, a, b) ;(a, 2, b) \) and \( (a, b, 3) \) are
collinear in space, then the value of \( a+ \)
\( \boldsymbol{b} \) is
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. none
Subject: Chemistry
How many significant figures should be present in the answer of the following calculations?
(i) \( \frac{\mathbf{0 . 0 2 8 5 6} \times \mathbf{2 9 8 . 1 5} \times \mathbf{0 . 1 1 2}}{\mathbf{0 . 5 7 8 5}} \)
(ii) \( 5 \times 5.364 \)
(iii) \( 0.0125+0.7864+0.0215 \)
Subject: Maths
The total number of injective mappings from a set with \( m \) elements to a set
with \( n \) elements, \( m \leq n \), is
\( \mathbf{A} \cdot m^{n} \)
B . \( n^{\text {m }} \)
c. \( \frac{n !}{(n-m) !} \)
D. \( n ! \)
Subject: Maths
Evaluate:
\( \mathbf{1}^{2} \boldsymbol{c}_{1}+\mathbf{2}^{2} \boldsymbol{c}_{2}+\mathbf{3}^{2} \boldsymbol{c}_{3}+\boldsymbol{4}^{2} \boldsymbol{c}_{4}+\ldots \ldots+\boldsymbol{n}^{2} \boldsymbol{c}_{n} \)
Subject: Maths
On the set \( N \) of all natural numbers
define the relation \( R \) by \( a R b \) if and only
if the G.C.D. of \( a \) and \( b \) is 2 . Then \( R \) is:
A. Reflexive, but not symmetrica
B. Symmetric only
C. Reflexive and transitive
D. Reflexive, symmetric and transitive
Subject: Biology
Radioactive \( C^{14} \) is given to \( C 0_{2} \) and
released to atmosphere. This \( C 0_{2} \) is
taken by ribulose diphosphate in a \( C_{3} \)
plant. First radioactive \( C^{14} \) is seen in
which compound?
A. PGAL
B. PEP
c. RMP
D. PGAA
Subject: Physics
The dimensions of Planck's constant
are
\( \mathbf{A} \cdot\left[M L^{-3} T^{-1}\right] \)
в. \( \left[M L^{-2} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{-1} T^{-3}\right. \)
D・ \( \left[M L^{2} T^{-1}\right] \)
Subject: Physics
A rectangular coil of a moving coil galvanometer contains 100 turns, each
having area \( 15 c m^{2} . \) It is suspended in
the radial magnetic field \( 0.03 \mathrm{T} \). The twist constant of suspension fibre is
\( 15 \times 10^{-10} \mathrm{N}-\mathrm{m} / \) degree. Calculate the sensitivity of the moving coil galvanometer.
Subject: Physics
If the acceleration due to gravity g at the earth's surface is \( 9.8 m s^{-2} \) and
mass of the earth is 80 times that of
moon, radius of earth 4 times that of
the moon, the value of \( g \) at the moon's surface will be approximately equal to?
\( \mathbf{A} \cdot 4 m s^{-2} \)
В. \( 1.96 m s^{-2} \)
\( \mathrm{c} \cdot 27 \mathrm{ms}^{-2} \)
D. \( 16 m s^{-2} \)
Subject: Physics
At some instant, a radioactive sample
\( \boldsymbol{S}_{1} \) having an activity \( 5 \mu C i \) has twice the number of nuclei as another sample
\( S_{2} \) which has an activity of \( 10 \mu C \) i. The
half lives of \( S_{1} \) and \( S_{2} \) are
A. 20 years and 5 years, respectively
B. 20 years and 10 years, respectively
c. 10 year each
D. 5 year each
Subject: Maths
If the line joining the points
\( \left(a t_{1}^{2}, 2 a t_{1}\right),\left(a t_{2}^{2}, 2 a t_{2}\right) \) is parallel to \( \mathbf{y}= \)
\( \mathbf{x}, \) then \( \mathbf{t}_{\mathbf{1}}+\mathbf{t}_{\mathbf{2}}= \)
A \( \cdot \frac{1}{2} \)
B. 4
\( c \cdot \frac{1}{4} \)
D. 2
Subject: Chemistry
An amino acid may be represented by general formula \( \boldsymbol{H}_{2} \boldsymbol{N}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{R}- \)
COOH. If \( \boldsymbol{R}=-\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C}_{6} \boldsymbol{H}_{5} \) then it is
phenylananine (Phe) and if \( \boldsymbol{R}=\boldsymbol{C H}_{3} \)
then it is alanine (Ala). Find the
sequence of reagents from those given below to synthesize Phe-Ala.
\( \mathrm{cH}_{3} \)
(1) \( \mathrm{zNH}_{\mathrm{G}}^{\mathrm{HCO}_{3} \mathrm{H}} \)
\( \mathrm{cH}_{2} \mathrm{G}_{5} \)
(2)
(з) ZNHCнсО \( _{2} \) Н
(4) \( \mathrm{H}_{2} \mathrm{NCH} \mathrm{CO}_{2} \mathrm{CH}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \)
A. 1 and 2
B. 1 and 4
\( c \cdot 2 \) and 3
D. 3 and 4
Subject: Chemistry
Assuming that concentration of \( C a^{2+} \)
ions in solution is in equal equivalence ratio to chloride ions, the hardness of water is :
A \( .9 .180 \times 10^{3} \) ppm
B . \( 6.180 \times 10^{3} \) ppm
c. \( 12.180 \times 10^{3} \) ppm
D. \( 4.180 \times 10^{3} \) ppm