AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
\( \boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{3}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \rightleftharpoons \boldsymbol{N} \boldsymbol{a} \boldsymbol{B} \boldsymbol{O}_{2}+ \)
\( \boldsymbol{N} \boldsymbol{a}\left[\boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{4}\right]+\boldsymbol{H}_{2} \boldsymbol{O} \)
How can this reaction is made to
proceed in forward direction?
A. Addition of cis 1,2 diol
B. Addition of borax
c. Addition of trans 1,2 dio
D. Addition of \( N a_{2} H P O_{4} \)
Subject: Maths
If \( \sum_{r=0}^{25}\left\{^{50} C_{r} .^{50-r} C_{25-r}\right\}=K\left(^{50} C_{25}\right) \)
then \( K \) is equal to:
A \( \cdot 2^{25}-1 \)
B . \( (25)^{2} \)
\( c \cdot 2^{25} \)
\( D \cdot 2^{2} \)
Subject: Maths
If the difference between the mean and
variance of binomial distribution for 5
trials is \( 5 / 9, \) the distribution is of the
form
A \( \cdot\left(5, \frac{1}{2}, \frac{1}{2}\right) \)
B. \( \left(5, \frac{1}{3}, \frac{2}{3}\right) \)
\( ^{c} \cdot\left(5, \frac{3}{4}, \frac{1}{4}\right) \)
D. \( \left(5, \frac{3}{5}, \frac{2}{5}\right) \)
Subject: Chemistry
The total vapour pressure of a mixture of 1 mol \( A\left(P_{A}^{O}=150 \text { tor } r\right) \) and 2 mol \( B \)
\( \left(P_{B}^{o}=240 \text { tor } r\right) \) is \( 200 \mathrm{mm} . \) In this
case:
A. there is positive deviation from Raoult's law
B. there is negative deviation from Raoult's law.
c. there is no deviation from Raoult's law
D. molecular masses of A and B are also required.
Subject: Chemistry
A solution is prepared by dissolving 9.8
\( g \) of \( H_{2} S O_{4} \) in 54 g of water. What is the
mole fraction of \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} ? \)
A. 0.03
B. 0.04
c. 0.01
D. 0.02
Subject: Biology
Assertion
Cytokinin treatment results in the
increase in the RNA content.
Reason
Cytokinin inhibits protein degradation.
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: Physics
A heavy nucleus having mass number 200 gets disintegrated into two small fragments of mass number 80 and 120
If binding energy per nucleon for parent atom is 6.5 MeV and for daughter nucle
is \( 7 \mathrm{MeV} \) and \( 8 \mathrm{MeV} \) respectively, then the energy released in the decay is \( X \times \)
\( 110 M e V \).Find the value of \( X \)
\( A \cdot 3 \)
B. 4
\( c \cdot 2 \)
\( D \)
Subject: Physics
Light is incident on a prism with an
equilateral triangular cross-section
making an angle of \( \theta \) w.r.t the normal as
shown in the figure. The index of
refraction of the prism is \( \frac{2}{\sqrt{3}} . \) If the
angle \( \theta \) starts at \( 60^{\circ} \) and is gradually made smaller until no light exist from side BC, the final value of \( \theta \) in degrees is
Subject: Physics
The electric potential at a point in free space due to a charge \( Q \) coulomb is
\( Q \times 10^{11} \) volts. The electric field at that
point is -
\( \mathbf{A} \cdot 4 \pi \epsilon_{0} \times 10^{20} \) volt \( / \mathrm{m} \)
B . \( 12 \pi \epsilon_{0} \times 10^{22} \)volt\( / m \)
C . \( 4 \pi \epsilon_{0} \times 10^{22} \) volt \( / m \)
D . \( 12 \pi \epsilon_{0} \times 10^{20} \) volt \( / m \)
Subject: Chemistry
Find the \( p H \) of the resulting solution and then mark the option in which \( p H \) exists between color transition range of an indicator.
\( 100 \mathrm{ml} \) of \( 0.8 \mathrm{M} \mathrm{HCO}_{3}^{-}+100 \mathrm{ml} \) of \( 0.4 \mathrm{M} \)
\( \boldsymbol{C O}_{3}^{2-} \)
[For \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3}: \boldsymbol{K}_{\boldsymbol{a}_{1}}=\boldsymbol{4} \times \mathbf{1 0}^{-\boldsymbol{7}} \boldsymbol{\&} \boldsymbol{K}_{\boldsymbol{a}_{2}}= \)
\( \left.4 \times 10^{-11}\right] \)
A. phenol red \( (6.8 \text { to } 8.4) \)
B. propyl red \( (4.6 \text { to } 6.4) \)
c. phenolphthalein \( (8.3 \text { to } 10.1) \)
D. Malachite green (11.4 to 13)
Subject: Chemistry
Which of the following represent
saponification reaction?
\( \mathbf{A} \cdot C H_{3} C O O H+N a O H \stackrel{C a O}{\longrightarrow} C H_{4}+N a_{2} C O_{3} \)
B \( \cdot C H_{3} C O O H+C_{2} H_{5} O H \frac{H_{2} S O_{4}}{\longrightarrow} C H_{3} C O O C_{2} H_{5}+ \)
\( H_{2} O \)
\( \mathbf{c} \cdot 2 C H_{3} C O O H+2 N a \rightarrow C H_{3} C O O N a+H_{2} \)
D. \( C H_{3} C O O C_{2} H_{5}+N a O H \rightarrow C H_{3} C O O N a+C_{2} H_{5} O H \)
Subject: Chemistry
STATEMENT-1: Silver extraction is done
by dissolving its ore into cyanide solution.
STATEMENT-2: In cyanide process, the silver is precipitated from soluble
complex of silver of zinc-dust.
A. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is a correct explanation for STATEMENT-
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
A gas at \( 27^{\circ} \mathrm{C} \) and pressure of \( 30 \mathrm{atm} \)
is allowed to expand to atmospheric pressure and volume 15 times larger. The final temperature of gas is
\( A \cdot 123^{0} C \)
B . - \( 123^{\circ} \mathrm{C} \)
c. \( 400 \mathrm{k} \)
D. None
Subject: Physics
A block of mass \( 30 \mathrm{kg} \) is being brought down by a chain. If the block acquires a speed of \( 40 \mathrm{cm} / \mathrm{s} \) in dropping down \( 2 \mathrm{m} \) Find the work done by the chain during
the process. \( \left(g=10 m / s^{2}\right) \)
A . - 297.6
B . -375 J
c. - -597.6
D. -674.6
Subject: Chemistry
Assertion
Ammonia is a compound.
Reason
Ammonia \( \left(N H_{3}\right) \) consists of molecules
of two different elements, nitrogen and hydrogen, bonded together.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
The values of \( a \) and \( b \) for which the
function \( \boldsymbol{y}=\boldsymbol{a} \log _{e} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{x}, \) has
extremum at the points \( x_{1}=1 \) and
\( \boldsymbol{x}_{2}=2 \) are
\( ^{A} \cdot_{a}=\frac{2}{3}, b=-\frac{1}{6} \)
B. \( \quad a=-\frac{2}{3}, b=-\frac{1}{6} \)
c. \( _{a=-\frac{2}{3}, b=\frac{1}{6}} \)
D. \( _{a=-\frac{1}{3}, b=-\frac{1}{6}} \)
Subject: Chemistry
Two moles of \( N_{2} \) and two moles of \( H_{2} \)
are taken in a closed vessel of 5 liters
capacity and suitable conditions are provided for the reaction. When the equilibrium is reached, it is found that
a half mole of \( N_{2} \) is used up. The
equilibrium concentration of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is:
A . 0.3
B. 0.4
\( c .0 .2 \)
D. 0.1
Subject: Physics
The V-I graph for conductor at
temperatures \( T_{1} \) and \( T_{2} \) are shown in
the figure. \( \left(T_{2}-T_{1}\right) \) is proportional to
A \( . \cos 2 \theta \)
B. \( \sin 2 \theta \)
\( c \cdot \cot 2 \theta \)
D. \( \tan 2 \theta \)
Subject: Maths
The general value of \( \theta \) satisfying the equation \( \sin ^{2} \theta-3 \cos \theta+\frac{3}{4}=0 \)
A \( \cdot 2 n \pi \pm \frac{\pi}{3} \)
В \( \cdot 2 n \pi \pm \frac{\pi}{6} \)
\( \mathbf{c} \cdot 2 n \pi \pm \frac{\pi}{4} \)
D. None
Subject: Physics
A capacitor of \( 10 \mu F \) charged upto \( 250 \mathrm{V} \) is connected in parallel with another capacitor of \( 5 \mu F \) charged upto \( 100 \mathrm{V} \) The common potential is :
A . 200
B. 300
c. \( 400 \mathrm{v} \)
D. 500
Subject: Chemistry
Given the polymers
\( A= \) Nylon 6,\( 6 ; B= \) Buna-S; \( C= \) Polythene.
Arrange these in decreasing order of their intermolecular forces.
\( A \cdot A>B>C \)
в. \( B>C>A \)
c. \( B<C<A \)
D. \( C<A<B \)
Subject: Chemistry
The vapour pressure of water is \( 12.3 k P a \) at \( 300 K . \) Calculate the vapour
pressure 1 molal solution of a non-
volatile solute in it
\( \mathbf{A} \cdot 12.08 k P a \)
B. 1.208 Ppa
\( \mathrm{c} .2 .4 \mathrm{kPa} \)
D. \( 0.4 k P a \)
Subject: Maths
The time(in seconds) taken by a group of people to walk across a pedestrian crossing is given in the table below.
Time
(in
\( \sec \)
\( \begin{array}{llll}5- & 10- & 15- & 20- \\ 10 & 15 & 20 & 25\end{array} \)
No. of people
If variation is \( 36.76, \) so calculate
standard deviation of the data.
Subject: Chemistry
Assertion (A): Paracetamol is widely used as analgesic even though it is an
antipyretic.
Reason (R): It is administrated to
aspirin-sensitive patients.
Choose the correct option.
A. A is true, R is true and R is the correct explanation of A
B. A is true, R is true and \( R \) is not the correct explanation of A
c. A is true, R is false
D. A is false, R is true
Subject: Maths
To find out the concentration of \( S O_{2} \) in
the air (in parts per million, i.e., \( p p m \) ),
the data was collected for 30 localities
in certain city and is presented below:
Concentration of \( S O_{2} \) \( f(\operatorname{in} p p m) \) Frequency \( 2^{2} \) reeter
\( 0.00-0.04 \)
\( 0.04-0.08 \)
\( 0.08-0.12 \) 9
\( 0.12-0.16 \) 2
\( 0.16-0.20 \) 4
\( 0.20-0.24 \) 2
Find the mean concentration of \( S O_{2} \) in
the air.
Subject: Maths
The value of
\( \lim _{n \rightarrow \infty} \frac{1}{(n+1)}+\frac{1}{(n+2)}+\frac{1}{(n+3)}+\dots \)
\( ? \)
A \( \cdot \log 4 \)
в. \( \log 2 \)
\( c \cdot \log 3 \)
D. \( \log 5 \)
Subject: Chemistry
The formula of Dolomite is :
A. \( M g C O_{3} . C a C l_{2} \)
в. \( M g C O_{3} . C a C O_{3} \)
c. \( M g C O_{3} . \) CaS \( O_{4} \)
D. \( M g C l_{2} . C a C O_{3} \)
Subject: Maths
The radius and height of an ice cream cone are in the ratio 4: 3 and area of its
base is \( 154 \mathrm{cm}^{2} \). Find its curved surface
area.
A \( \cdot 192.5 \mathrm{cm}^{3} \)
В. \( 150 \mathrm{cm}^{3} \)
c. \( 176.3 \mathrm{cm}^{3} \)
D. \( 115.36 \mathrm{cm}^{3} \)
E . None of these
Subject: Maths
What is the value of \( k \) if \( (k, 5) \) is the solution of the simultaneous equations
\( 4 x+3 y=19 \) and \( 4 x-3 y=-11 ? \)
\( A \cdot 4 \)
B. \( -1 / 3 \)
c. 5
\( D \)
Subject: Physics
In a series \( L C R \) circuit the frequency of
a \( 10 V, A C \) voltage source id adjusted in such a fashion that the reluctance of
the inductor or measures \( 15 \Omega \) and that
of the capacitor \( 11 \Omega . \) If \( R=3 \Omega, \) the
potential difference across the series combination of \( L \) and \( C \) will be:
\( A \cdot 8 V \)
B. \( 10 V \)
\( c \cdot 22 V \)
D. \( 52 V \)
Subject: Chemistry
Arsine produces hydrogen gas on heating. The pressure of produced hydrogen was measured, at consant
volume and temperature, as follows:
Time \( \quad \) o \( \quad 5.5 \quad 6.5 \) (hours)

Pressure \( \quad \) 0.965 \( \quad \) 1.060 \( \quad 1.076 \) \( (a+m) \)
Calculate the specific rate and half-life
peroid of reaction assuming the reaction to be of first-order.
Subject: Chemistry
Assertion
Equivalent mass of \( N_{2} H_{4} \) is 8 in acidic
medium or basic medium
Reason
It is oxidised to \( N_{2} \) with loss of four
electron per \( N_{2} H_{4} \) unit
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 and Reason both are incorrect
Subject: Chemistry
fan electron is moving with velocity
\( \mathbf{5 0 0 m s}^{-1}, \) which is accurate up to 0.005
\( \% \) then calculate uncertainty in its position.
\( \left[\boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J}-\boldsymbol{s}, \quad \boldsymbol{m a s s}\right. \)
Subject: Maths
In the figure, there are shown sectors of
two concentric circles of radii \( 7 \mathrm{cm} \) and
\( 3.5 \mathrm{cm} . \) Find the area of the shaded region. \( \left(\boldsymbol{U} \boldsymbol{s e} \boldsymbol{\pi}=\frac{\boldsymbol{2} \boldsymbol{2}}{\boldsymbol{7}}\right) \)
A. 10.425 sq. \( \mathrm{cm} \)
B. 10.125 sq. \( \mathrm{cm} \)
c. 9.625 sq. \( \mathrm{cm} \)
D. 9.152 sq. \( \mathrm{cm} \)
Subject: Physics
A body starts rolling down an inclined plane of length \( L \) and height \( h \) This body reaches the bottom of the plane in time \( t . \) The relation between \( L \)
and \( t \) is
\( \mathbf{A} \cdot t \propto L \)
в. \( t \propto \frac{1}{L} \)
c. \( L \propto t^{2} \)
D \( \cdot t \propto \frac{1}{L^{2}} \)
Subject: Physics
Assertion
Two thin blankets put together are warmer than a single blanket of double the thickness.
Reason
Thickness increases because of air
layer enclosed between the two blankets.
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
Find the area of the region enclosed by
parabola \( \boldsymbol{y}=\boldsymbol{x}^{2}+\boldsymbol{2} \) and lines \( \boldsymbol{y}= \)
\( \boldsymbol{x}, \boldsymbol{x}=\mathbf{3} \) and \( \boldsymbol{x}=\mathbf{0} \)
Subject: Maths
A variable triangle is inscribed in a circle of radius \( \mathrm{R} \). If the rate of change of
side is \( R \) times the rate of change of the opposite angle, then that angle is
\( \mathbf{A} \cdot \pi / 6 \)
в. \( \pi / 4 \)
c. \( \pi / 3 \)
D. \( \pi / 2 \)
Subject: Physics
For a particular heat engine, 3,000 J of energy goes in at \( 700 \mathrm{K} \) and \( 2000 \mathrm{J} \) comes out at \( 200 \mathrm{K} \). The rest of the
energy is used work.

What is the actual efficiency of this engine?
A . 0.71
B. 0.33
c. 0.67
D. 0.29
E . 1.5
Subject: Physics
In a primary coil \( 5 A \) current is flowing
on 220 volts. If the secondary coil produces \( 2200 V \) voltage. Then the
ratio of number of turns in secondary coil and primary coil will be
\( \mathbf{A} \cdot 1: 10 \)
B. 10: 1
c. 1: 1
D. 11: 1
Subject: Physics
Two resistors, with resistances \( R_{1} \) and
\( R_{2}, \) are connected in parallel
The resistance \( R_{1} \) is greater than the
resistance \( \boldsymbol{R}_{2} \)

What is the resistance of the parallel
combination?
A. Less than either \( R_{1} \) or \( R_{2} \)
B. Equal to \( R_{1} \)
c. Equal to \( R_{2} \)
D. The average of \( R_{1} \) and \( R_{2} \)
Subject: Chemistry
\( A l_{2} O_{3} \) can be converted to anhydrous
\( A l C l_{3} \) by heating:
A . Hydrated \( A l_{2} O_{3} \) with \( C l_{2} \) gas
в. \( A l_{2} O_{3} \) with aqueous \( H C l \)
c. \( A l_{2} O_{3} \) with \( N a C l \) in solid state
D. A mixture of \( A l_{2} O_{3} \) and carbon in dry \( C l_{2} \) gas
Subject: Physics
A ball Of \( 0.1 k g \) strikes a wall at right
angle with a speed of \( 6 m / s \) and rebounds along its original path at
\( 4 m / s . \) The change in momentum in Newton - sec is-
A \( \cdot 10^{3} \)
B. \( 10^{2} \)
c. 10
D.
Subject: Physics
A system has two charges \( \boldsymbol{q}_{\boldsymbol{A}}=\boldsymbol{2 . 5} \times \)
\( \mathbf{1 0}^{-7} \boldsymbol{C} \) and \( \boldsymbol{q}_{B}=-\mathbf{2 . 5} \times \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{C} \) located
at points \( \boldsymbol{A}:(\mathbf{0}, \mathbf{0}, \mathbf{1 5} \mathbf{c m}) \) and \( \boldsymbol{B} \)
\( (0,0,+15 c m), \) respectively. What are
the total charge and electric dipole
moment of the system?
Subject: Chemistry
Q Type your question
reaction as shown below. Write the
structures of \( A, B, C, D \) and \( E \) in the
following reactions:
OR
(a) Write the structures of main
products when benzene diazonium chloride reacts with the following regents:
(i) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
\( (\text { ii }) C u C N / K C N \)
\( (\text { iii }) \boldsymbol{H}_{2} \boldsymbol{O} \)
(b) Arrange the following in the increasing order of their basic character in an aqueous solutions:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{N} \boldsymbol{H},\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{3} \boldsymbol{N} \)
(c) Give a simple chemical test to distinguish between the following pair
of compounds:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5}-\boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{a n d} \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{N} \boldsymbol{H}- \)
\( \boldsymbol{C H}_{3} \)
Subject: Chemistry
At \( 800 \mathrm{K} \) a reaction mixture contained
0.5 mole of \( S O_{2} .0 .12 \) mole of \( O_{2} \) and 5
mole of \( S O_{3} \) at equilibrium. \( K_{c} \) for the
equilibrium \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \) is 833
lit/ mole. If the voiume of the container
is 1 litre, calculate how much \( O_{2} \) is to be added at this equilibrium in order to get
5.2 moles of \( S O_{3} \) at the same temperature.
A. 2.34 mole
B. 0.34 mole
c. 1.43 mole
D. 3.23 mole
Subject: Physics
A current of \( 1 \mathrm{A} \) is flowing along positive x-axis through a straight wire of length \( 0.5 \mathrm{m} \) placed in a region of a magnetic field given by \( \vec{B}=(2 \hat{i}+4 \hat{j}) \) T. The magnitude and the direction of the force experienced by the wire
respectively are:
A \( \cdot \sqrt{18} N, \) along positive z-axis
B. \( \sqrt{20} N \), along positive \( x \) -axis
c. \( 2 N, \) along positive z-axis
D. \( 4 N \), along positive y-axis
Subject: Chemistry
The equilibrium constant \( \boldsymbol{K}_{c} \) for the reaction:
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q} \cdot) \rightleftharpoons \boldsymbol{C} \boldsymbol{u}^{2+}(\boldsymbol{a} \boldsymbol{q} \cdot)+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})\left(\boldsymbol{E}_{c e l l}^{\circ}=\mathbf{0 . 4 6} \boldsymbol{V}\right) \) will be:
A. antilog 15.6
B. antilog 2.5
c. antilog 1.5
D. antilog 12.2
Subject: Maths
If all the angles of a 14 -sided figure are equal, then the measure of each angle is equal to?
\( ^{A} \cdot\left(184 \frac{2}{7}\right)^{\circ} \)
B. \( \left(164 \frac{2}{7}\right) \)
\( ^{c} \cdot\left(134 \frac{2}{7}\right)^{\circ} \)
\( ^{\mathrm{D}} \cdot\left(154 \frac{2}{7}\right) \)
Subject: Chemistry
The radius of \( \boldsymbol{H}- \) atom in its ground
state is \( 0.53 A^{\circ} . \) The radius of \( L i^{2+} \) in
the similar is:
\( \mathbf{A} \cdot 0.058 A^{\circ} \)
B. \( 0.171 A^{\circ} \)
c. \( 0.706 A^{\circ} \)
D. \( 1.06 A^{\circ} \)
Subject: Chemistry
What is the equation for the
equilibrium constant \( \left(K_{c}\right) \) for the
following equilibrium reaction?
\( \frac{1}{2} A(g)+\frac{1}{3} B(g) \rightleftharpoons \frac{3}{2} C(g) \)
\( ^{\mathbf{A}} \cdot_{K_{C}}=\frac{[A]^{\frac{1}{2}}[B]^{\frac{1}{3}}}{[C]^{\frac{3}{2}}} \)
\( ^{\mathrm{B}} K_{C}=\frac{[C]^{\frac{3}{2}}}{[A]^{2}[B]^{2}} \)
\( ^{\mathbf{c}}_{K_{C}}=\frac{[C]^{\frac{3}{2}}}{[A]^{\frac{1}{2}}[B]^{\frac{1}{5}}} \)
\( ^{\mathrm{D}} K_{C}=\frac{[C]^{\frac{3}{2}}}{[A]^{\frac{1}{2}}+[B]^{\frac{1}{3}}} \)
Subject: Physics
A body of mass \( 2 k g \) is sliding with a
constant velocity of \( 4 m / s \) on a
frictionless horizontal table. The net
force required to keep the body moving with the same velocity is
A. \( 8 N \)
в. \( 0 N \)
c. \( 4 N \)
D. \( \frac{1}{2} N \)
Subject: Physics
A block of mass \( 3 k g \) which is on a
smooth inclined plane making an angle
of \( 30^{\circ} \) to the horizontal is connected by
second block of mass \( 2 k g \) hanging
vertically, What is the acceleration of each block and what is the tension of the
cord?
A \( \cdot 0.98 m / s^{2} ; 17.6 N \)
B . \( 1.98 m / s^{2} ; 19.6 N \)
c. \( 0.49 m / s^{2} ; 9.8 N \)
D. \( 1.47 m / s^{2} ; 4.9 N \)
Subject: Chemistry
The charge/size ratio of a cation determines its polarising power. Which one of the following sequences represents the increasing order of the polarising power of cationic species?
\( \left[\boldsymbol{K}^{+}, \boldsymbol{C} \boldsymbol{a}^{2+}, \boldsymbol{M} \boldsymbol{g}^{2+}, \boldsymbol{B} \boldsymbol{e}^{2+}\right] \)
A \( \cdot M g^{2+}<B e^{2+}<K^{+}<C a^{2+} \)
B . \( B e^{2+}<K^{+}<C a^{2+}<M g^{2+} \)
C \( \cdot K^{+}<C a^{2+}<M g^{2+}<B e^{2+} \)
D. \( C a^{2+}<M g^{2+}<B e^{2+}<K^{+} \)
Subject: Maths
Let a sequence be defined by \( a_{1}= \)
\( \mathbf{1}, \boldsymbol{a}_{\mathbf{2}}=\mathbf{1} \) and \( , \boldsymbol{a}_{\boldsymbol{n}}=\boldsymbol{a}_{\boldsymbol{n}-\mathbf{1}}+\boldsymbol{a}_{\boldsymbol{n}-\mathbf{2}} \) for al
\( \boldsymbol{n}>2 \)
find \( \frac{\boldsymbol{a}_{\boldsymbol{n}+1}}{\boldsymbol{a}_{\boldsymbol{n}}} \) for \( \boldsymbol{n}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3}, \boldsymbol{4} \)
Subject: Chemistry
Heat evolved in the reaction \( \boldsymbol{H}_{2}+ \)
\( C l_{2} \rightarrow 2 H C l \) is \( 182 k J \)
(Bond energies \( \boldsymbol{H}-\boldsymbol{H}= \)
\( 430 k J / m o l e, C l-C l-242 k J / m o l e) \)
The \( H-C l \) bond energy is:
A. \( 763 k J / \) mole
в. \( 427 k J / \) mole
c. \( 336 k J / \) mole
D. \( 154 k J / \) mole
Subject: Maths
If \( \overrightarrow{\boldsymbol{a}} \cdot \hat{\boldsymbol{i}}=\overrightarrow{\boldsymbol{a}} \cdot(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}})=\overrightarrow{\boldsymbol{a}} \cdot(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}})= \)
1 then \( \vec{a}= \)
A. \( \hat{i}+\hat{j} \)
в. \( \hat{i}-\hat{k} \)
\( c \)
D. \( \hat{i}+\hat{j}-\hat{k} \)
Subject: Maths
The coefficient of \( \boldsymbol{x}^{r}[\mathbf{0} \leq \boldsymbol{r} \leq \boldsymbol{n}-\mathbf{1}] \) in
the expression of \( (x+2)^{n-1}+(x+ \)
2) \( ^{n-2} \cdot(x+1)+(x+2)^{n-3} \cdot(x+1)^{2}+ \)
\( \ldots+(x+1)^{n-1} \) is
A \( \cdot^{n} C_{r}\left(2^{r}-1\right) \)
B. \( ^{n} C_{r}\left(2^{n-r}-1\right) \)
c. \( ^{n} C_{r}\left(2^{r}+1\right) \)
D. \( ^{n} C_{r}\left(2^{n-r}+1\right) \)
Subject: Maths
CP and \( \mathrm{CQ} \) are tangents to a circle with
centre \( 0 . A R B \) is another tangent
touching the circle at \( \mathrm{R} . \) If \( C P= \)
\( 11 c m, B C=7 c m, \) then the length BR is
\( A \cdot 11 c m \)
B. \( 7 \mathrm{cm} \)
\( c .3 c m \)
\( \mathrm{D} \cdot 4 \mathrm{cm} \)
Subject: Maths
If \( \bar{e}=\bar{l} \bar{i}+m \bar{j}+n \bar{k} \) is a unit vector, the
maximum value of \( l m+m n+n l \) is
A \( \cdot-\frac{1}{2} \)
B. 0
c. 1
D. \( \frac{3}{2} \)
Subject: Maths
\( f\left(\alpha, \beta \text { are the roots of } x^{2}+x+1=0\right. \)
\( \operatorname{then}\left|\begin{array}{ccc}\boldsymbol{y}+\mathbf{1} & \boldsymbol{\beta} & \boldsymbol{\alpha} \\ \boldsymbol{\beta} & \boldsymbol{y}+\boldsymbol{\alpha} & \mathbf{1} \\ \boldsymbol{\alpha} & \mathbf{1} & \boldsymbol{y}+\boldsymbol{\beta}\end{array}\right|=? \)
A \( \cdot y^{2}-1 \)
В . \( y\left(y^{2}-1\right) \)
c. \( y^{2}-y \)
D. \( y^{3} \)
Subject: Maths
If \( a, b, c \) are vectors such that \( a+b+ \)
\( \boldsymbol{c}=\mathbf{0} \) and \( |\boldsymbol{a}|=\mathbf{7},|\boldsymbol{b}|=\mathbf{5},|\boldsymbol{c}|=\mathbf{3}, \) then
the angle between \( c \) and \( b \) is
A \( \cdot \frac{\pi}{3} \)
в.
c.
D.
Subject: Maths
The coordinates of the vertices of a
triangle are \( \left(x_{2}, y_{2}\right) \) and \( \left(x_{3}, y_{3}\right) . \) The line joining the first two is divided in the ratio I : \( k \), and the line joining this point of division to the opposite angular point is then divided in the ratio \( \mathrm{m}: \mathrm{k}+ \)
I. Find the coordinates of the latter point of section.
Subject: Chemistry
Select the correct statements.
This question has multiple correct options
A. Vapour may be condensed to liquid by the application of pressure.
B. To liquefy a gas one must lower the temperature below \( T_{c} \) and apply pressure.
C \( . \) At \( T_{c} \) there is no distinction between liquid and vapour
states
D. At the \( T_{c} \), density of liquid is very high as compared to its gaseous state.