AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The radius of a circle is \( 13 \mathrm{cm} \) and the
length of one of its chords is \( 10 \mathrm{cm} \). The distance of the chord from the centre is
A. \( 8 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( \mathrm{c} \cdot 12 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Physics
A ball is shot vertically upward with a
given initial velocity. It reaches a maximum height of \( 100 \mathrm{m} \). If on a second shot, the initial velocity is doubled then the ball will reach a maximum height of
\( A .70 .7 \mathrm{m} \)
B. \( 141.4 \mathrm{m} \)
c. \( 200 \mathrm{m} \)
D. \( 400 \mathrm{m} \)
Subject: Maths
In the figure above (not to scale) ABCD
is trapezium in which \( \overline{\boldsymbol{A B}} \| \overline{\boldsymbol{C D}}, \mathbf{A D}= \)
\( \mathrm{CD} \) and \( \mathrm{AB}=2 \mathrm{CD} \)
If \( \angle A D C=100^{\circ} \) then find \( \angle A B C \)
A \( \cdot 40^{\circ} \)
B .50
\( c \cdot 60^{\circ} \)
D. 70
Subject: Maths
Find the profit per cent or loss per cent made, when the S.P. of 15 identical
articles is equal to the C.P. of 20 articles.
A ' profit \( =33 \frac{1}{3} \% \)
B. Profit \( =23 \frac{1}{2} \% \)
c. profit \( =23 \frac{1}{3} \% \)
D. \( \operatorname{Loss}=31 \frac{1}{8} \% \)
Subject: Physics
Monochromatic green light of wavelength 550 nm illuminates two parallel narrow slits \( 7.7 \mu \mathrm{m} \) apart. The
angular deviation \( \theta \) of third order (for \( m \)
\( =3 \) ) bright fringe in radian and in degrees respectively are:
A \( .21 .6,12.4^{\circ} \)
в. \( 0.216,1.24^{\circ} \)
c. \( 0.216,12.4^{\circ} \)
D. \( 216,1.24^{\circ} \)
Subject: Chemistry
For a reaction \( \boldsymbol{X} \longrightarrow \boldsymbol{Y}, \) the graph of
the product concentration (x) versus time (t) came out to be straight line passing through the origin. Hence the \( \operatorname{graph} \) of \( \frac{-\boldsymbol{d}[\boldsymbol{X}]}{\boldsymbol{d} \boldsymbol{t}} \) and time would be:
A. straight line with a negative slope and an intercept on y-axis
B. straight line with positive slope and an intercept on \( y \) axis
c. a straight line parallel to x-axiss
D. a hyperbola
Subject: Maths
If \( (a+i b)(c+i d)(e+i f)(g+i h)= \)
\( A+i B, \) then show that
\( \left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right)\left(e^{2}+f^{2}\right)\left(g^{2}+h^{2}\right)= \)
\( A^{2}+B^{2} \)
Subject: Maths
\( \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{5} & \mathbf{2} \\ \mathbf{7} & \mathbf{3}\end{array}\right) \) and \( \boldsymbol{B}=\left(\begin{array}{cc}\mathbf{2} & \mathbf{- 1} \\ \mathbf{- 1} & \mathbf{2}\end{array}\right) \)
verify that \( (\boldsymbol{A B})^{\boldsymbol{T}}=\boldsymbol{B}^{\boldsymbol{T}} \boldsymbol{A}^{\boldsymbol{T}} \)
Subject: Chemistry
Structure of some important polymers
are given. Which one represents Buna-
S?
\( A \)
\[
\begin{array}{c}
\mathrm{CH}_{3} \\
\left(-\mathrm{CH}_{2}-\mathrm{C}=\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}}
\end{array}
\]
в.
\[
\begin{array}{c}
\left(-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}} \\
\mathrm{C}_{6} \mathrm{H}_{5}
\end{array}
\]
\( c \)
\[
\begin{array}{c}
\left(-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}} \\
\mathrm{CN}
\end{array}
\]
\( D \)
\[
\left(-\mathrm{CH}_{2}-\mathrm{C}^{\prime}=\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}}
\]
Subject: Chemistry
Chemical equilibria is (I) in nature. It occurs in (2)
reactions only. At equilibria, all (3) properties becomes constant. Chemical equilibrium gets affected by change in temperature, pressure, concentration, volume etc but
is not altered by addition of
(4) \( -\dots-\dots-\dots \)
two types (5) and
homogeneous equilibria.
A. (1) dynamic
(2) reversible (3) observable (4) catalyst
(5) homogeneous
B. (1) static
(2) irreversible
(4) reactants
(3) observable
(5) heterogeneous
c. (1) dynamic
(2) irreversible
(3) observable (4) reactants
(5) homogeneous
D. (1) dynamic
(2) reversible
(3) observable
(4) catalyst
(5) heterogeneous
Subject: Chemistry
Give the name of the complex
compound \( \boldsymbol{K}_{3}\left[\boldsymbol{F} e\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \) according
to IUPAC system:
A. Potassium Ferric oxalate
B. Potassium trioxalatoiron(II)
c. Potassium trioxalatoferrate(III)
D. Tripotassium trioxalatoferrate(III)
Subject: Maths
If \( \omega \) is a cube root of unity, then \( (3+ \) \( \left.\mathbf{5} \boldsymbol{\omega}+\mathbf{3} \boldsymbol{\omega}^{2}\right)^{2}+\left(\mathbf{3}+\mathbf{3} \boldsymbol{\omega}+\mathbf{5} \boldsymbol{\omega}^{2}\right)^{2} \) is equal
to
A . 4
B.
\( c \cdot-4 \)
D. None of these
Subject: Physics
A spherical capacitor consists of two concentric spherical conductors of
inner one of radius \( R_{1} \) maintained at
potential \( V_{1} \) and the outer one of radius
\( \boldsymbol{R}_{2} \) at potential \( \boldsymbol{V}_{2} . \) The potential at a
point \( p \) at a distance \( x \) from the centre
\( \left(R_{2}>x>R_{1}\right) \) is:
A \( \cdot \frac{V_{1}-V_{2}}{R_{2}-R_{1}}\left(x-R_{1}\right) \)
B. \( \frac{V_{1} R_{1}\left(R_{2}-x\right)+V_{2} R_{2}\left(x-R_{1}\right)}{x\left(R_{2}-R_{1}\right)} \)
C \( \cdot V_{1}+\frac{V_{2} x}{R_{2}-R_{1}} \)
D. \( \frac{V_{1}+V_{2}}{R_{2}+R_{1}} x \)
Subject: Chemistry
Assertion
Statement -1: Boron does not show
univalent nature but unipositive nature
of thallium is quite stable.
Reason
Statement -2: Inert pair effect
predominates in thallium.
A. Statement -1 is true, Statement -2 is true and Statement -2 is correct explanation for Statement -
1.
B. Statement -1 is true, Statement -2 is true and Statement - 2 is not the correct explanation for Statement - 1
c. Statement - 1 is true, Statement - 2 is false.
D. Statement -1 is false, Statement -2 is true
Subject: Chemistry
There is a stream of neutrons with a
kinetic energy of \( 0.0327 \mathrm{eV} \). If the half-
life of neutrons is 700 second, the
percentage fraction of neutron will
decay before they travel a distance of 10 \( \mathrm{km} \) is (multiply answer by 20). (mass of neutron \( =1.675 \times \)
\( \left.10^{-27} k g\right) \)
Subject: Chemistry
The lattice energy of the carbonates of
Mg, Ca, Sr and Ba follow the order:
A. \( M g C O_{3}>C a C O_{3}>S r C O_{3}>B a C O_{3} \)
в. \( C a C O_{3}>S r C O_{3}>B a C O_{3}>M g C O_{3} \)
c. \( B a C O_{3}>S r C O_{3}>C a C O_{3}>M g C O_{3} \)
D. \( \operatorname{Sr} \mathrm{rCO}_{3}>\mathrm{MgCO}_{3}>\mathrm{CaCO}_{3}>\mathrm{BaCO}_{3} \)
Subject: Maths
A bag contains 40 balls out of which some are red, some are blue and
remaining are black. If the probability of drawing a red ball is \( \frac{11}{20} \) and that of blue ball is \( \frac{1}{5}, \) then the number of black ball is?
\( \mathbf{A} \cdot \mathbf{5} \)
B . 25
c. 10
D. 30
Subject: Physics
sinusoidal waves \( 5.00 \mathrm{cm} \) in amplitude are to be transmitted along a string having a linear mass density equal to
\( 4.00 \times 10^{-2} k g / m . \) If the source can
deliver an average power of \( 90 W \) and the string is under a tension of \( 100 N \)
then find the frequency at which the source can operate. (take \( \left.\pi^{2}=10\right) \)
Subject: Chemistry
During the developing process in photography, unexposed \( A g B r \) is washed away by complexation of \( A g(I) \) by sodium thiosulphate solution. These washings are often disposed of as waste. However, metallic silver can be
recovered from them by adding cyanide, followed by zinc. What is the hybridization of zinc is the complex formed during the recovery of silver?
A \( \cdot s p^{3} d^{2} \)
B \( \cdot d^{2} s p^{3} \)
\( c \cdot s p^{3} \)
D \( \cdot d s p^{2} \)
Subject: Physics
Dimensions of specific heat are :
A \( \cdot\left[M L^{2} T^{-2} K\right] \)
\( \mathbf{B} \cdot\left[M L^{2} T^{-2} K^{-1}\right] \)
C \( \cdot\left[M L^{2} T^{2} K^{-1}\right] \)
D・ \( \left[L^{2} T^{-2} K^{-1}\right] \)
Subject: Physics
A system consists of two identical
small balls of mass 2 kg each
connected to the two ends of a 1 m long light rod. The system is rotating about a fixed axis through the centre of the rod and perpendicular to it at an angular speed of 9 rad/s. An impulsive force of
average magnitude \( 10 N \) acts on one of the masses in the direction of its
velocity for \( 0.20 s . \) Calculate the new
angular velocity of the system.
Subject: Chemistry
Which reaction occurs in blast furnace
at \( 1270 K \) temperature?
\( A \cdot 3 F e_{2} O_{3}+C O \rightarrow \)
в. \( F e_{3} O_{4}+C O \)
c. \( F e_{2} O_{3}+C O \rightarrow \)
D. \( F e O+C O \rightarrow \)
Subject: Physics
wo lutitical vedus, tach ndve d mass
\( m \) and charge \( q . \) When placed in
a hemispherical bowl of radius \( \boldsymbol{R} \) with
frictionless, non-conducting walls,
the beads move and at equilibrium they
are at a distance \( R \) apart (as shown in
figure). Determine the charge on each
bead:
\( ^{\mathbf{A}} \cdot\left(\frac{4 \pi \varepsilon_{0} m g R^{2}}{\sqrt{3}}\right)^{1 / 2} \)
\( ^{\mathbf{B}}\left(\frac{2 \pi \varepsilon_{0} m g R^{2}}{\sqrt{3}}\right)^{1 / 2} \)
\( \left(\frac{4 \pi \varepsilon_{0} m g R^{2}}{\sqrt{6}}\right)^{1 / 2} \)
\( \left(\frac{\pi \varepsilon_{0} m g R^{2}}{\sqrt{3}}\right)^{1 / 2} \)
Subject: Chemistry
How many gm of solid \( K O H \) must be
added to \( 100 m L \) of a buffer solution,
which is \( 0.1 ~ M \) each with respect to
acid \( H A \) and salt \( K A \) to make the \( p H \)
of the solution \( 6.0 ? \)
\( \left[\text { Given: } \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{A})=\mathbf{5}\right] \)
A .0 .458
B. 0.327
c. 5.19
D. None of the above
Subject: Chemistry
Important constituent of Portland and high alumina cements is?
A. \( C a_{3} A l_{2} O_{6} \)
в. \( \operatorname{casi} O_{3} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \)
D. \( F e_{2} C O_{3} \)
Subject: Maths
Use remainder theorem to find
remainder when \( p(x) \) is divided by \( q(x) \) in the following questions:
\( \boldsymbol{p}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\mathbf{7}, \boldsymbol{q}(\boldsymbol{x})=\boldsymbol{x}-\mathbf{1} \)
Subject: Maths
Solve \( \int_{0}^{\pi / 2}(2 \log \sin x-\log \sin 2 x) d x \)
A \( \cdot \frac{\pi}{2} \log 2 \)
B. \( -\frac{\pi}{2} \log 2 \)
c. \( \frac{\pi}{4} \log 2 \)
D. None
Subject: Physics
Statement 1: The magnitude of velocity of two boats relative to river is same.
Both starts simultaneously from same point on one bank and they may reach opposite bank simultaneously moving along different paths.
Statement 2: For boats to cross the
river in same time.The component of their velocity relative to river in direction normal to flow should be
same.
A. Statement-1 is false, Statement- 2 is true
B. Statement-1 is true, Statement-2 is true, Statementis a correct explanation for statement- -
c. statement-1 is true, statement- 2 is true; statementis not a correct explanation for statement-
D. Statement-1 is true, Statement-2 is false.
Subject: Maths
\( \operatorname{Let} \boldsymbol{E}=\left[\frac{\mathbf{1}}{\mathbf{3}}+\frac{\mathbf{1}}{\mathbf{5 0}}\right]+\left[\frac{\mathbf{1}}{\mathbf{3}}+\frac{\mathbf{2}}{\mathbf{5 0}}\right]+\ldots+ \)
up to 50 terms, then which of the
following is true? Here \( \square \) denotes the greatest integer function.
This question has multiple correct options
A. \( E \) is divisible by exactly 2 primes
B. \( E \) is prime
c. \( E \leq 30 \)
D. \( E \geq 35 \)
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{4} & -\mathbf{2} & \mathbf{5}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{l}\mathbf{2} \\ \mathbf{0} \\ \mathbf{3}\end{array}\right], \) then
\( \boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{B} \boldsymbol{A})= \)
\( A \cdot\left\{\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right\} \)
\( \mathbf{B} \cdot\left\{\begin{array}{lll}8 & -4 & 10 \\ 0 & 0 & 0 \\ 12 & -6 & 15\end{array}\right\} \)
\( \mathbf{c} \cdot\left\{\begin{array}{ccc}8 & 0 & 12 \\ -4 & 0 & -6 \\ 10 & 0 & 5\end{array}\right\} \)
D. None of the above
Subject: Maths
Let \( S=\{1,2,3, \dots .40\} \) and let \( A \) be a
subset of \( S \) such that no two elements
in \( A \) have their sum divisible by 5 What
is the maximum number of elements
possible in \( \boldsymbol{A} \) ?
A . 10
B . 13
c. 17
D. 20
Subject: Physics
The nuclear radius is given by \( \boldsymbol{R}= \) \( r_{0} A^{1 / 3}, \) where \( r_{0} \) is constant and \( A \) is
the atomic mass number.
Then :
A. The nuclear mass density of \( U^{238} \) is twice that of \( S n^{119} \)
B. The nuclear mass density of \( U^{238} \) is thrice that of \( S n^{11} \)
C. The nuclear mass density of \( U^{238} \) is the same as that of \( S n^{11} \)
D. The nuclear mass density of \( U^{238} \) is half that of \( S n^{119} \)
Subject: Chemistry
The oxidation number of oxygen in
\( \mathrm{K}_{2} \mathrm{O}, \mathrm{K}_{2} \mathrm{O}_{2} \) and \( \mathrm{KO}_{2} \) are respecitvely:
A \( \cdot-2,-1,-\frac{1}{2} \)
в. \( -\frac{1}{2},-1,-2 \)
\( c \cdot_{-1,-2,-\frac{1}{2}} \)
D. \( _{-2,-\frac{1}{2},-1} \)
Subject: Maths
\( \mathrm{n} \) the Fig., if \( \boldsymbol{O} \boldsymbol{X}=\frac{1}{2} \boldsymbol{X} \boldsymbol{Y}, \boldsymbol{P} \boldsymbol{X}=\frac{1}{2} \boldsymbol{X} \boldsymbol{Z} \)
and \( O X=P X \), then
A. \( X Y=Y Z \)
В. \( X Y=X Z \)
c. \( X Z=Y Z \)
D. None of these
Subject: Maths
If Rolle's theorem is applicable to the function \( f(x)=\frac{\ln x}{x},(x>0) \) over the interval \( [a, b] \) where \( a \epsilon I, b \epsilon I, \) then the value of \( a^{2}+b^{2} \) can be
A . 20
B . 25
c. 45
D. 10
Subject: Chemistry
The oxidation of \( S O_{2} \) by \( O_{2} \) to \( S O_{3} \) is an
exothermic reaction. The yield of \( \boldsymbol{S O}_{3} \)
will be maximum if:
A. temperature is increased and pressure is kept constant
B. temperature is reduced and pressure is increased
c. both temperature and pressure are increased
D. both temperature and pressure are reduced
Subject: Physics
A batsman deflects a ball by an angle of
\( 45^{\circ} \) without changing its initial speed
which is equal to \( 54 \mathrm{km} / \mathrm{hr} \). Mass of the
ball is \( 0.15 \mathrm{kg} \). What is the impulse imparted to the ball?
A. \( 4.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \) in the direction of the final velocity
B. \( 4.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \) in the direction of the initial velocity
c. \( 4.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \) in the direction opposite to the initial velocity
D. \( 4.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \) directed along the bisector of the initial and the final directions of the velocity
Subject: Physics
Range of nuclear force is approximately
A \( \cdot 2 \times 10^{-15} m \)
B . \( 1.5 \times 10^{-20} m \)
c. \( 7.2 \times 10^{-4} m \)
D. \( 1.4 \times 10^{-15} \mathrm{m} \)
Subject: Maths
From 7 gentlemen and 4 ladies, a
committee of 5 is to be formed. The
probability that this can be one so as to include at least one lady is
A \( \cdot \frac{^{7} C_{5}}{^{11} C_{5}} \)
в. \( \frac{4}{^{11} C_{5}} \)
\( ^{\mathbf{C}} \cdot_{1-\frac{^{7} C_{5}}{11} C_{5}} \)
D. \( _{1-\frac{4}{11} C_{5}} \)
Subject: Maths
Assertion
The system of linear equations \( \boldsymbol{x}+(\sin \boldsymbol{\alpha}) \boldsymbol{y}+(\cos \boldsymbol{\alpha}) \boldsymbol{z}=\mathbf{0} \)
\( x+(\cos \alpha) y+(\sin \alpha) z=0 \quad \) has a non
\( -\boldsymbol{x}+(\sin \boldsymbol{\alpha}) \boldsymbol{y}-(\cos \boldsymbol{\alpha}) \boldsymbol{z}=\mathbf{0} \)
trivial solution for only one value of \( \boldsymbol{\alpha} \)
Iying between 0 and \( \pi \)
Reason \( \left|\begin{array}{ccc}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0 \) has no
solution in the interval \( -\frac{\pi}{4}<x<\frac{\pi}{4} \)
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: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}x+2 & (x \leq-1) \\ x^{2} & (-1<x<1) \text { then the value } \\ 2-x & (x \geq 1)\end{array}\right. \)
of \( \boldsymbol{f}(-1)+\boldsymbol{f}(\mathbf{0})+\boldsymbol{f}(1) \) is
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. -
Subject: Physics
A block of mass \( \mathrm{m} \) is suspended by a
light thread from an elevator.The
elevator is accelerating upward with uniform acceleration a. The work done
by tension on the block during t seconds is \( (1=0) \)
A \( \cdot \frac{m}{2}(g+a) a t^{2} \)
B \( \cdot \frac{m}{2}(g-a) a t^{2} \)
c. \( \frac{m}{2} g a t^{2} \)
D.
Subject: Biology
Which of the following factors raise the
\( P_{50} \) and shifts the \( H b O_{2} \) dissociation curve to right and vice
versa?
a. Rise in \( \boldsymbol{P} \boldsymbol{c o}_{2} \)
b. Fall in temperature
c. Rise in \( \boldsymbol{H}^{+}(=\text {fall in } \mathrm{pH} \) )
d. Fall in diphosphoglyceric acid
A. a and b are correct
B. b and d are correct
c. a and c are correct
D. a, b and c are correct
Subject: Physics
The unit of \( \frac{G}{g} \) can be written as
\( \mathbf{A} \cdot \frac{K g}{m} \)
B. \( \frac{K g}{m^{2}} \)
\( ^{\mathbf{C}} \cdot \frac{m^{2}}{K g} \)
D. \( \frac{m}{K g} \)
Subject: Chemistry
How many \( \sigma \) - and \( \pi \) -bonds are present in each of the following molecules?
(a) \( \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
(b) \( \boldsymbol{C H}_{2}=\boldsymbol{C}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
Subject: Physics
Suppose you push a spring with a force
\( F_{1} \) as shown in figure, the spring also
pushes up on your hand with a force \( F_{2} \)
What is the relationship between \( \boldsymbol{F}_{1} \)
and \( F_{2} ? \)
A \( \cdot F_{1}>F_{2} \)
B \( . F_{1}=2 F_{2} \)
\( \mathrm{c} \cdot F_{1}<F_{2} \)
D. \( F_{1}=F_{2} \)
Subject: Chemistry
Assertion
The first IE of \( B e \) is greater than that of
\( \boldsymbol{B} \)
Reason
\( 2 p \) -orbital is lower in energy than \( 2 s \)
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: Maths
The equation of the base of an equilateral triangle is \( \mathbf{x}+\mathbf{y}-\mathbf{2}=\mathbf{0} \)
and the vertex is \( (2,-1), \) then the
length of side is
A . 1
в. 2
\( c .3 \)
D. \( \sqrt{\frac{2}{3}} \)
Subject: Physics
An object of length \( 4 \mathrm{cm} \) is placed in front of a concave mirror at a distance
of \( 30 \mathrm{cm} . \) The focal length of mirror is
\( 15 \mathrm{cm} . \) What will be the length of image?
A. \( 1 ~ c m \)
в. 2 ст
\( c .4 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Maths
If \( \sin a=\frac{3}{7} \) and \( \cos a<0, \) what is the
value of \( \tan a \)
A \( \cdot \frac{-(3 \sqrt{20})}{10} \)
B. \( \frac{-(\sqrt{10})}{10} \)
c. \( \frac{-(3 \sqrt{10})}{20} \)
D. \( \frac{(2 \sqrt{5})}{10} \)
Subject: Chemistry
Each pair forms ideal solution except :
A. \( C_{2} H_{5} B r \) and \( C_{2} H_{5} I \)
в. \( C_{6} H_{5} C l \) and \( C_{6} H_{5} B r \)
c. \( C_{6} H_{6} \) and \( C_{6} H_{5} C H_{3} \)
D. \( C_{2} H_{6} I \) and \( C_{2} H_{5} O H \)
Subject: Maths
Area bounded by the parabola \( y^{2}=x- \)
3 and \( x=5, \) is \( \dots . s q \) units
\( A \cdot \frac{8 \sqrt{2}}{3} \)
B. \( 4 \sqrt{2} \)
\( \mathrm{c} \cdot 3 \sqrt{2} \)
D. \( 5 \sqrt{2} \)
Subject: Maths
If the \( n^{t h} \) term of geometric progression
\( 5,-\frac{5}{2}, \frac{5}{4},-\frac{5}{8}, \ldots . \) is \( \frac{5}{1024}, \) then the value
of \( n \) is
A . 11
B. 10
\( c .9 \)
\( D \)
Subject: Chemistry
Calculate the vapour pressure of solution having 3.42 g of canesugar in 180 g water at \( 40^{\circ} C \) and \( 100^{\circ} \) C. Given that, the boiling point of water is \( 100^{\circ} \mathrm{C} \) and heat of vaporisation is 10 kcal
\( m o l^{-1} \) in the given temperature range. Also, calculate the lowering in vapour pressure of 0.2 molal cane-sugar at
\( 40^{\circ} C: \)
\( \mathbf{A} .58 \mathrm{mm} \)
B. \( 13 \mathrm{mm} \)
c. \( 78 \mathrm{mm} \)
D. none of these
Subject: Maths
Given that: \( \sqrt{\mathbf{2}}=\mathbf{1 . 4 1 4}, \sqrt{\mathbf{3}}= \)
\( 1.732, \sqrt{5}=2.236 \) and \( \sqrt{7}=2.646 \)
evaluate each of the following:
\( \sqrt{\frac{2500}{3}} \)
Subject: Physics
Assuming the earth to be a homogeneous sphere, determine the
density of the earth from the following data:
\( g=9.8 \mathrm{m} / \mathrm{s}^{2}, \mathrm{G}=6.673 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2} \)
\( R=6400 \mathrm{km} \)
Subject: Maths
If the median of data
\( \mathbf{3 1}, \mathbf{3 3}, \mathbf{3 5}, \boldsymbol{x}, \boldsymbol{x}+\mathbf{1 0}, \mathbf{4 8}, \mathbf{4 8}, \mathbf{5 0} \) is \( \mathbf{4 0} \)
than find the value of \( x \)
Subject: Maths
Consider the function for \( \boldsymbol{x}=[-\mathbf{2}, \mathbf{3}] \)
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}\boldsymbol{x}^{\mathbf{3}}-\mathbf{2} \boldsymbol{x}^{\mathbf{2}}-\mathbf{5} \boldsymbol{x}+\mathbf{6} & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \neq \mathbf{1} \\ \boldsymbol{x}-\mathbf{1} & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x}=\mathbf{1}\end{array}\right. \)
then
A. \( f \) is discontinuous at \( x=1 \Rightarrow \) Rolles theorem is not
applicable in [-2,3]
B. \( f(-2) \neq f(3) \Rightarrow \) Rolles theorem is not applicable in [-2,3]
C. \( f \) is not derivable in (-2,3)\( \Rightarrow \) Rolles theorem is not applicable
D. Rolles theorem is applicable as \( f \) satisfies all the
conditions and \( c \) of Rolles theorem is
Subject: Maths
Assertion \( \operatorname{Let} a, b \in R, \) and \( I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \) and \( J= \)
\( \left[\begin{array}{cc}\mathbf{0} & \mathbf{1} \\ -\mathbf{1} & \mathbf{0}\end{array}\right] \)
Inverse of \( a I+b J \) is \( c I+d J \) if and only
if
\( \boldsymbol{a c}-\boldsymbol{b d} \neq \mathbf{0} \) and \( \boldsymbol{a} \boldsymbol{d}+\boldsymbol{b} \boldsymbol{c}=\mathbf{0} \)
Reason
\( (\boldsymbol{a} \boldsymbol{I}+\boldsymbol{b} \boldsymbol{J})(\boldsymbol{c} \boldsymbol{I}+\boldsymbol{d} \boldsymbol{J})=(\boldsymbol{a} \boldsymbol{c}-\boldsymbol{b} \boldsymbol{d}) \boldsymbol{I}+ \)
\( (a d+b c) J \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
A beam of light containing two wavelengths \( 5200 A \) and \( 6500 A \) is used in Young's experiment to obtain interference fringes. What is the least distance from the central maximum on
the screen where the bright fringes due to both wavelengths concide? (Given distance between slits is 2 \( \mathrm{mm} \) and
distance of screen from slits is 120
\( \mathrm{mm} \)
A. \( 0.156 \mathrm{mm} \)
B. \( 0.312 \mathrm{mm} \)
\( c .0 .78 \mathrm{mm} \)
D. \( 1.1 \mathrm{mm} \)
Subject: Physics
\( A \) thin rod of length \( \frac{f}{3} \) is placed along the optic axis of a concave mirror of focal length f such that its image which is real and elongated just touches the rod. The magnification is:
A \( \cdot \frac{3}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
D. None of the above
Subject: Physics
The amount of heat energy required to raise the temperature of \( 1 g \) of helium
in a container of volume \( 10 L, \) from \( T_{1} K \)
to \( T_{2} K \) is \( \left(N_{a}= \) Avogadros number, \right.
\( k_{B}= \) Boltzmann constant
A \( \cdot \frac{3}{2} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
в. \( \frac{3}{7} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
c. \( \frac{3}{4} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
D \( \cdot \frac{3}{8} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)