AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A choke coil is needed to operate an arc \( \operatorname{lamp} \operatorname{at} 160 V(\mathrm{rms}) \) and \( 50 \mathrm{Hz} \). The arc
lamp has an effective resistance of \( 5 \Omega \) when running at \( 10 A(\mathrm{rms}) . \) Calculate
the inductance of the choke coil. If the
same arc lamp is to be operated on \( 160 V \) DC, what additional resistance
would be required. Compare the power losses in both the cases.
Subject: Chemistry
\( K_{1} \) and \( K_{2} \) are the velocity constants of the forward and backward reactions.
The equilibrium constant K of the reaction is:
A. \( k_{1} \times k_{2} \)
в. \( k_{1}-k_{2} \)
c. \( \frac{k_{1}}{k_{2}} \)
D. \( \frac{k_{2}}{k_{1}} \)
Subject: Maths
N, the set of natural numbers, is
partitioned into subsets \( \boldsymbol{S}_{1}= \) \( \{1\}, S_{2}=\{2,3\}, S_{3}=\{4,5,6\}, S_{4}= \)
\( \{7,8,9,10\} . \) The last term of these
groups is \( 1,1+2,1+2+3,1+2+ \)
\( 3+4, \) so on. Find the sum of the
elements in the subset \( S_{50} \)
Subject: Physics
Two concentric shells have radii \( \mathbf{R} \) and
2R, charges \( q_{A} \) and \( q_{B} \) and potentials \( 2 V \)
and \( (3 / 2) \vee \) respectively. Now shell \( B \) is
earthed and let charges on them
become \( \boldsymbol{q}_{\boldsymbol{A}}^{\prime} \) and \( \boldsymbol{q}_{\boldsymbol{B}}^{\prime} . \) Then:
This question has multiple correct options
\( \mathbf{A} \cdot q_{A} / q_{B}=1 / 2 \)
\( \mathbf{B} \cdot\left|q_{A}^{\prime}\right| /\left|q_{B}^{\prime}\right|=1 \)
C. Potential of A after earthing becomes (3/2)V
D. Potential difference between A and B after earthing becomes V/2
Subject: Maths
The slope and y-intercept of the following line are respectively
\( 5 x-2 y=3 \)
A \( \cdot \) slope \( =m=-\frac{5}{2} \quad \) and \( \quad y- \) intercept \( =-\frac{3}{2} \)
B \( \cdot \) slope \( =m=\frac{5}{2} \quad \) and \( \quad y- \) intercept \( =\frac{3}{2} \)
C \( \cdot \) slope \( =m=\frac{5}{2} \quad \) and \( \quad y- \) intercept \( =-\frac{3}{2} \)
D. slope \( =m=-\frac{5}{2} \quad \) and \( \quad y- \) intercept \( =\frac{3}{2} \)
Subject: Maths
Solve and graph the inequality. Give
answer in interval notation.
\( -6 x+12>-7 x+17 \)
\( A \cdot(5, \infty) \)
В \( \cdot(-\infty, 5) \)
\( c \cdot(29, \infty) \)
\( \mathbf{D} \cdot(-\infty, 29) \)
Subject: Chemistry
Balance the following equations by
oxidation number method.
\( \boldsymbol{K} \boldsymbol{I}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{I}_{2}+\boldsymbol{S} \boldsymbol{O}_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
A solid cylinder of mass \( 10 k g \) is rolling
perfectly on a plane of inclination \( 30^{0} \) The force of friction between the
cylinder and surface of the inclined
plane is :
A . \( 49 N \)
в. \( 24.5 \mathrm{N} \)
c. \( \frac{49}{3} N \)
D. \( 12.25 N \)
Subject: Physics
Specific heat of aluminium is
\( 0.25 c a l / g^{o} C . \) The water equivalent of an aluminium vessel of mass one
kilogram is
\( \mathbf{A} \cdot 40 g m \)
в. \( 250 g m \)
\( \mathbf{c} \cdot 25 g m \)
D. \( 2.5 g m \)
Subject: Chemistry
In an alkaline solution, the following equilibrium exists.
\( S^{2-}+S \leftrightharpoons S_{2}^{2-}, K_{1}=12 \)
\( \boldsymbol{S}_{2}^{2-}+\boldsymbol{S} \leftrightharpoons \boldsymbol{S}_{3}^{2-}, \boldsymbol{K}_{2}=\mathbf{1 1} \)
What is the equilibrium constant for the given equilibrium?
\( S_{3}^{2-} \leftrightharpoons S^{2-}+2 S \)
A \( \cdot 23 \)
в. 132
\( c \cdot 1 / 132 \)
D. \( 1 / 32 \)
Subject: Biology
From which of the following algae, agar is commercially extracted?
a) Gracilaria
b) Fucus
c) Sargassum
d) Gelidium
e) Turbinaria
A. c and e
B. b and c
\( c . \) d and \( e \)
D. a and b
\( E \cdot \) a and \( d \)
Subject: Maths
Consider the following statements:
1. If \( A \) and \( B \) are exhaustive events, then
their union is the sample space.
2. If \( A \) and \( B \) are exhaustive events,
then their intersection must be an
empty event. Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Chemistry
Select the correct statement(s) out of
the following:
i) A sigma
(s) bond is formed when
two s-orbitals overlap.
ii) \( A \) pi \( (p) \) bond is formed when two \( p \) orbitals overlap sideways.
iii) An sigma bond is weaker than pi
bond.
B. ii and iii
c. i only
D. ii only
Subject: Maths
Assertion
Consider the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x} \)
and \( \boldsymbol{g}(\boldsymbol{x})=-|\boldsymbol{x}| \)
The composite function \( \boldsymbol{F}(\boldsymbol{x})= \)
\( \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x})) \) is not derivable at \( \boldsymbol{x}=\mathbf{0} \)
Reason
\( \boldsymbol{f}^{\prime}\left(\mathbf{0}^{+}\right)=\mathbf{2} \) and \( \boldsymbol{f}^{\prime}\left(\mathbf{0}^{-}\right)=-\mathbf{2} \)
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
If \( \cos A=\frac{4}{5}, \cos B=\frac{12}{13}, \frac{3 \pi}{2}< \)
\( A, B<2 \pi, \) find the values of the
following.
\( (\mathrm{i}) \cos (\boldsymbol{A}+\boldsymbol{B}) \)
(ii) \( \sin (A-B) \)
Subject: Chemistry
Paramagnetic species are :
A. \( N O, N O_{2}, O_{2} \)
в. \( N_{2} O_{2}, N_{2} O_{2}, N_{2} O_{4}, O_{3} \)
c. \( N O^{+}, N O_{2}^{+}, O_{2}^{+} \)
D. \( O_{2}, C O, C O_{2} \)
Subject: Maths
Two complex numbers are represented
by ordered pairs \( z_{1}:(a, b) \& z_{2}:(c, d) \)
when these two complex numbers are
equal?
A. If and only if \( a=-c, b=-d \)
B. If and only if \( a=d, b=c \)
c. If and only if \( a=c, b=d \)
D. None of these
Subject: Physics
A particle having mass 1 g and electric
charge \( 10^{-8} \mathrm{C} \) travels from a point \( \mathrm{A} \)
having electric potential \( 600 \mathrm{V} \) to the point B having zero potential. What would be the change in its kinetic
energy?
A . \( -6 \times 10^{-6} \) erg
В. \( -6 \times 10^{-6} \) j
c. \( 6 \times 10^{-6} \) j
D. \( 6 \times 10^{-6} \) erg
Subject: Physics
A Pelton wheel develops \( 1750 k W \) under
a head of 100 metres while running at 200 r.p.m. and discharging 2500 litres of water per second. The unit power of the wheel is
A. \( 1.75 K V \)
В. \( 0.25 K v \)
c. \( 0.75 K v \)
D. \( 1 K v \)
Subject: Biology
Cloning is the production of an exact copy of a cell, any other living part of a complete organism. A sheep named Dolly was the first mammal to be cloned by lan Wilmut and his colleagues at the
Roslin Institute in Edinburgh. Find out the incorrect statements about the
cloning of Dolly.
(i) Dolly was born on 5th July 1996
(ii) Dolly was given birth by the Finn Dorset sheep.
(iii) Dolly was found to be absolutely identical to the Scottish blackface ewe.
(iv) The nucleus of the mammary gland cell from the Finn Dorsett sheep was inserted into the egg of the Scottish blackface ewe whose nucleus had been
removed.
A. (i) only
B. (i) and (iii) only
c. (i), (ii) and (iii) only
D. All of the above
Subject: Physics
Three particles, each of mass \( m \), are
placed at the corner of right angle triangle as shown in the figure. if \( \mathrm{OA}=\mathrm{a} \)
and \( \mathrm{OB}=\mathrm{b}, \) the position vector of the
centre of mass is :
(here \( \hat{i} \) and \( \hat{j} \) are unit vector along \( \times \) and \( y \) axes, respectively
A \( \cdot \frac{1}{3}(a \hat{i}+b \hat{j}) \)
B \( \cdot \frac{1}{3}(a \hat{i}-b \hat{j}) \)
c \( \cdot \frac{2}{3}(a \hat{i}+b \hat{j}) \)
\( D \)
Subject: Physics
A current \( i \) passes through a wire of length \( L, \) radius \( R \) and resistively \( \rho . \) The rate of heat generated is
A \( \cdot \frac{i \rho L}{\pi r^{2}} \)
В. \( i^{2}\left(\frac{L \rho}{\pi r^{2}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{i^{2} \rho L}{r}\right) \)
D. none of these
Subject: Physics
The elastic limit of steel cable is \( 3.0 \times \)
\( 10^{8} N / m^{2} \) and the cross-section area is
\( 4 c m^{2} . \) Find the maximum upward
acceleration that can be given to a \( 900 k g \) elevator supported by the cable if the stress is not to exceed one-third of
the elastic limit.lf your answer is \( x, \) then mark the value of \( \frac{x}{5} \)
Subject: Chemistry
Orthophosphoric acid \( \frac{\text {gentleheat}}{220^{\circ}} \boldsymbol{X} \)
What is/are correct about \( X ? \)
A. it is a tetra basic acid
B. It contains one P- - -0- - -P bond
c. It is a dibasic acid
D. on hydrolysis it produces metaphosphoric acid.
Subject: Biology
select the correct option from the given
codes.
\( \mathbf{A} \)
\( A-(i), B-(i i) ;(i v) ;(i x), C-(i i i) ;(v i), D-(v i i) \) ; (viii), , E-(V)
\( B \)
\( A-(i), B-(i i) ;(i v), C-(i i i) \) ; (vi); ; (ix), D-(vii);(viii), E-(v)
\( ;(i x), D-(v i i) \)
\( \mathbf{C} \cdot A-(i), B-(i i) ;(i v) ;(i x), C-(i i i) \)
; (viii), , E-(v); (vi)
D. \( A-(i) \) \( \mathrm{B}-(\mathrm{iv}) ;(\mathrm{i} \mathrm{x}), \mathrm{C}-(\mathrm{ii}) ;(\mathrm{iii}) ;(\mathrm{vi}), \mathrm{D}-(\mathrm{vii}) ;(\mathrm{viii}), \mathrm{E}-(\mathrm{v}) \)
Subject: Physics
A particle of charge \( q \) and mass \( m \)
moves in a circular orbit of radius \( r \)
with angular speed \( \omega . \) The ratio of the
magnitude of its magnetic moment to that of its angular momentum depends
on
A. \( \omega \) and \( q \)
B. \( \omega, q \) and \( m \)
c. \( q \) and \( m \)
D. \( \omega \) and \( m \)
Subject: Maths
The solution of differential equation \( \frac{d y}{d x}+y \tan x=2 x+x^{2} \tan x \) is?
A \( \cdot y=x^{2}+c \cos x \)
B . \( y=2 x^{2}-c \cos x \)
C \( \cdot y+x^{2}=c \cos x \)
D. \( y+2 x^{2}=c \cos x \)
Subject: Chemistry
When \( F e C l_{3} \) is ignited in an
atmosphere of pure oxygen, the following reaction takes place:
\( 4 F e C l_{3}(s)+3 O_{2}(g) \rightarrow \)
\( 2 F e_{2} O_{3}(s)+6 C l_{2}(g) \)
If 3 moles of \( F e C l_{3} \) are ignited in the
presence of 2 moles of \( O_{2} \) gas, how
much of which reagent is present in excess and therefore, remains
unreacted?
A. 0.33 mole \( F e C l_{3} \) remains unreacted
B. 0.67 mole \( F e C l_{3} \) remains unreacted
C. 0.25 mole \( O_{2} \) remains unreacted
D. 0.50 mole \( O_{2} \) remains unreacted
Subject: Maths
Find the matrix \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{2} & \mathbf{1} \\ \mathbf{2} & \mathbf{1} & \mathbf{0}\end{array}\right], \) which
of the following is correct
A. \( A^{3}+3 A^{2}-I=0 \)
B. \( A^{3}-3 A^{2}-I=0 \)
c. \( A^{3}+2 A^{2}-I=0 \)
D. \( A^{3}-A^{2}+I=0 \)
Subject: Chemistry
Which one of the following has the maximum number of \( \boldsymbol{P}-\boldsymbol{O H} \) bonds?
A \( . H_{3} P O_{2} \)
в. \( H_{3} P O_{4} \)
c. \( H_{3} P O_{3} \)
D. \( H_{4} P_{2} O_{5} \)
E \( . H_{4} P_{2} O_{6} \)
Subject: Chemistry
Titration curves for \( 0.1 \mathrm{M} \) solutions of
three weak acids \( H A_{1}, H A_{2} \) ans \( H A_{3} \)
with ionization constants \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and
\( K_{3} \) respectively are plotted in the figure.which of the following is/are
true?
\( \mathbf{A} \cdot K_{2}=\left(K_{1}+K_{3}\right) / 2 \)
B . \( K_{1}<K_{3} \)
\( \mathbf{c} \cdot K_{1}>K_{2} \)
D. \( K_{2}>K_{3} \)
Subject: Chemistry
Which of the following molecules are expected to exhibit intermolecular \( \mathrm{H} \) bonding?
: Acetic acid II : \( o \) -nitrophenol Ill: \( m \) -nitrophenol IV: \( o \) -boric acid Select the correct option.
\( \mathbf{A} \cdot \) ।, ॥।, ॥ ।
B. ।, ॥।, IV
c. ।, ॥ा, ।V
D. II, III, IV
Subject: Chemistry
The air pollutant NO is produced in
automobile engines from the high
temperature reaction \( N_{2}(g)+ \)
\( O_{2}(g) \rightleftharpoons 2 N O(g) ; K_{c}=1.7 \times 10^{-3} \mathrm{at} \)
2300K. If the initial concentrations of
\( N_{2} \) and \( O_{2} \) at \( 2300 K \) are both \( 1.40 M \)
what are the concentrations of \( N O, N_{2} \)
and \( O_{2} \) when the reaction mixture
reaches equilibrium?
A \( \cdot[N O]=0.056 M,\left[N_{2}\right]=\left[O_{2}\right]=1.37 M \)
B . \( [N O]=0.045 M,\left[N_{2}\right]=0.23 M,\left[O_{2}\right]=1.37 M \)
C \( \cdot[N O]=0.367 M,\left[N_{2}\right]=\left[O_{2}\right]=2.03 M \)
D \cdot \( [N O]=0.056 M,\left[N_{2}\right]=0.57 M,\left[O_{2}\right]=0.12 M \)
Subject: Chemistry
Assertion
Among all elements of the Group-16 sulphur has the largest tendency to catenation.
Reason
Sulphur-Sulphur bond energy is very high.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Which reactions are used for the
preparation of the halogen acid? This question has multiple correct options
\( \mathbf{A} \cdot 2 K B r+H_{2} S O_{4} \rightarrow K_{2} S O_{4}+2 H B r \)
(conc.)
B \( \cdot C a F_{2}+H_{2} S O_{4} \rightarrow C a S O_{4}+2 H F \)
(conc.)
c. \( N a C l+H_{2} S O_{4} \rightarrow N a H S O_{4}+H C l \)
(conc.)
D. \( 2 K I+H_{2} S O_{4} \rightarrow K_{2} S O_{4}+2 H I \)
(conc.)
Subject: Maths
If \( a^{3}-3 a^{2} b+3 a b^{2}-b^{3} \) is divided by
\( (a-b), \) then the remainder is
A \( \cdot a^{2}-a b+b^{2} \)
B \( \cdot a^{2}+a b+b^{2} \)
\( c \)
D.
Subject: Maths
Evaluate \( \lim _{n \rightarrow \infty}\left(\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{6 n}\right) \)
\( A \cdot \log 6 \)
B. \( 3 \log 2 \)
c. \( 2 \log 3 \)
D. \( \log 3 \)
Subject: Maths
\( \mathbf{f}_{\boldsymbol{f}(\boldsymbol{x})}=\left\{\begin{array}{ll}\frac{\boldsymbol{x}^{2}-\boldsymbol{9}}{\boldsymbol{x}-\mathbf{3}}+\boldsymbol{\alpha} & , \text { for } \boldsymbol{x}>\mathbf{3} \\ \mathbf{5} & , \text { for } \boldsymbol{x}=\mathbf{3} \\ \mathbf{2} \boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}+\boldsymbol{\beta} & , \text { for } \boldsymbol{x}<\mathbf{3}\end{array}\right. \)
is continuous at \( x=3, \) find \( \alpha \) and \( \beta \)
Subject: Chemistry
Which of following is not correctly matched?
A. d-block element: electronic configuration is \( n s^{0-2}(n-1) d^{1-1} \)
B. p-block element : electronic configuration is \( n s^{2} n p^{1-6} \)
C. s-block element: electronic configuration is \( n s^{1-2} \)
D. None of these
Subject: Chemistry
In the alkane
\( \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{C H}_{2} \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
identify \( 1^{\circ}, 2^{\circ}, 3^{\circ} \) carbonatoms and give the number of H atoms bonded to
each one of these.
Subject: Maths
If
\( a, b, c \) all are non-zero and unequal and \( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{a} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{b} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{c}\end{array}\right|=\mathbf{0}, \) then
\( 1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \) is equal to?
Subject: Maths
After expressing the following as a rational number of the form \( \frac{\boldsymbol{p}}{\boldsymbol{q}} \) \( \frac{-\mathbf{7}}{\mathbf{4}}+\frac{\mathbf{5}}{\mathbf{3}}+\frac{-\mathbf{1}}{\mathbf{2}}+\frac{-\mathbf{5}}{\mathbf{6}}+\mathbf{2}, \) then the
value equivalent to \( p \) is
Subject: Chemistry
Out of the following metals, which will
give \( H_{2} \) on reaction with \( N a O H ? \)
\( \boldsymbol{I}: \boldsymbol{Z} \boldsymbol{n} \)
\( \boldsymbol{I} \boldsymbol{I}: \boldsymbol{M} \boldsymbol{g} \)
\( \boldsymbol{I I I}: \boldsymbol{A l} \)
\( \boldsymbol{I} \boldsymbol{V}: \boldsymbol{B} \boldsymbol{e} \)
A. \( I, I I, I I I, I V \)
в. \( I, I I I, I V \)
c. \( I I, I V \)
D. \( I, I I I \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{c}-1 \\ 2 \\ \mathbf{3}\end{array}\right], \boldsymbol{B}=[-\mathbf{2},-\mathbf{1},-\mathbf{4}] \) verify
that \( (\boldsymbol{A B})^{T}=\boldsymbol{B}^{\boldsymbol{T}} \boldsymbol{A}^{\boldsymbol{T}} \)
Subject: Maths
Two events \( A \) and \( B \) are such that
\( P(A)=\frac{1}{4}, P(A \mid B)=\frac{1}{4} \) and \( P(B \mid A)= \)
\( \mathbf{1} \)
\( \overline{2} \)
Consider the following statements:
(I) \( P(\bar{A} \mid \bar{B})=\frac{3}{4} \)
(II) \( A \) and \( B \) are mutually exclusive
\( (\| I) P(A \mid B)+P(A \mid \bar{B})=1 \)
Then
A. Only (I) is correct
B. Only (I) and (II) are correct
C. Only (I) and (III) are correct
D. Only (II) and (III) are correct
Subject: Maths
If \( \omega \) is a complex cube root of unity, the \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \boldsymbol{1} \\ \boldsymbol{\omega}^{2} & \boldsymbol{1} & \boldsymbol{\omega}\end{array}\right| \) is equal to
A . -1
B.
\( c \cdot 0 \)
D.
Subject: Chemistry
Number of intramolecular aldol
condensation product is:
\[
\begin{array}{c}
\stackrel{0}{\|} \\
\mathrm{CH}_{3}-\mathrm{C}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{I}-\mathrm{H} \\
\mid \mathrm{KOH}
\end{array}
\]
\( A \)
B.
\( c \cdot 3 \)
\( D \)
Subject: Maths
Find \( a_{1}+a_{6}+a_{11}+a_{16} \) if it is known
that \( a_{1}, a_{2} \dots . \) is an A.P. and \( a_{1}+a_{4}+ \)
\( \boldsymbol{a}_{\boldsymbol{7}}+\ldots+\boldsymbol{a}_{\mathbf{1 6}}=\mathbf{1 4 7} \)
Subject: Chemistry
If we create vacuum in container \( A \) at
\( 25^{\circ} C \) then:
Container
\( (\mathbf{A}) \)
A. water will be completely vaporised in the container
B. there will be no vaporisation in the container
C. the equilibrium will establish in between water vapour and liquid \( H_{2} O \) and vapour pressure of water will
remain same as it would be in presence of atmospheric pressure
D. the equilibrium in between \( H_{2} O(v) \) and \( H_{2} O(l) \) will
establish but vapour pressure of \( H_{2} O(v) \) will be more
than as it would be in presence of atmospheric
pressure
Subject: Physics
A body of mass Mkg is on the top point of a smooth hemisphere of radius \( 5 \mathrm{m} \). It is released to slide down the surface of
hemisphere it leaves the surface when its velocity is \( 5 m s^{-1} \) At this instant the
angle made by the radius vector of the body with the vertical is \( \left(g=10 m s^{-2}\right) \)
A \( \cdot \cos ^{-1}\left(\frac{3}{4}\right) \)
B . \( 45^{\circ} \)
\( c \cdot 60 \)
D. \( 90^{\circ} \)
Subject: Maths
Let \( \vec{a}, \vec{b} \) be the position vectors of points \( A \) and \( B \) with respect to \( O \) and \( |\vec{a}|=a,|\vec{b}|=b \) the points \( C \) and \( D \)
divides \( A \) internally and externally in the ratio 2: 3 If \( \overrightarrow{O C} \) and \( \overrightarrow{O D} \) are
perpendicular then
A \( \cdot 9 a^{2}=4 b^{2} \)
В. \( 4 a^{2}=9 b^{2} \)
c. \( 9 a=4 b \)
D. \( 4 a=9 b \)
Subject: Chemistry
For the hypothetical reactions, the equilibrium constant (K) values are given:
\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} ; \boldsymbol{K}_{1}=\mathbf{2} ; \boldsymbol{B} \rightleftharpoons \boldsymbol{C} ; \boldsymbol{K}_{2}=\mathbf{4} ; \boldsymbol{C} \rightleftharpoons \)
\( \boldsymbol{D} ; \boldsymbol{K}_{3}=\boldsymbol{3} \)
The equilibrium constant (K) for the
reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{D} \) is:
A. 48
B. 6
\( c \cdot 24 \)
D. 12
Subject: Chemistry
A solid compound 'X' on heating gives
\( C O_{2} \) gas and a residue. The residue
mixed with water forms 'Y'. On passing
an excess of \( C O_{2} \) through 'Y' in water, a clear solution 'Z' is obtained. On boiling
Z', compound 'X' is reformed. The compound 'X' is :
A \( \cdot C a\left(H C O_{3}\right)_{2} \)
в. \( C a C O_{3} \)
c. \( N a_{2} C O_{3} \)
D. \( K_{2} C O_{3} \)
Subject: Physics
A uniform sphere of mass 500 g rolls without slipping on a plane surface so that its centre moves at a speed of 0.02 \( \mathrm{m} / \mathrm{s} . \) The total kinetic energy of rolling sphere would be (in J)
A \( .1 .4 \times 10^{-4} J \)
B. \( 0.75 \times 10^{-3} J \)
c. \( 5.75 \times 10^{-3} J \)
D. \( 4.9 \times 10^{-5} J \)
Subject: Chemistry
\( \mathrm{CaO} \) and \( \mathrm{NaCl} \) have the same crystal
structure and approximately the same
ionic radii. If \( U \) is the lattice energy of
Na \( C l \), the approximate lattice energy
of \( C a O \) is:
A. \( U / 2 \)
B. \( U \)
\( c .2 U \)
D. \( 4 U \)
Subject: Physics
Electrons traveling at a velocity of
\( 2.4 \times 10^{6} m s^{-1} \) enter a region of cross
electric and magnetic fields as shown in fig. If the electric field is \( 3.0 x \)
\( 10^{6} V m \) and the flux density of the
magnetic field is \( 1.5 \mathrm{T} \), the electron upon
entering the region of the crossed fields
will
A. continue to travel undeflected in their original direction
c. be deflected downward on the plane of the diagram
D. none of the above
Subject: Maths
If \( A \) and \( G \) be \( A . M \) and \( G . M, \) respectively
between two positive numbers. prove that the numbers are \( \boldsymbol{A} \pm \) \( \sqrt{(\boldsymbol{A}+\boldsymbol{G})(\boldsymbol{A}-\boldsymbol{G})} \)
Subject: Physics
A man of height \( 170 \mathrm{cm} \) wants to see his complete image in a plane mirror (while standing). His eyes are at a height of \( 160 \mathrm{cm} \) from the ground.
A. minimum length of the mirror \( =80 \mathrm{cm} \)
B. minimum length of the mirror = 85 cm
c. bottom of the mirror should be at a height 80 cm or
more
D. bottom of the mirror should be at a height \( 85 \mathrm{cm} \)
Subject: Chemistry
\( N a_{2} O, M g O, A l_{2} O_{3} \) and \( S i O_{2} \) have
heat of formation equal to -416,-602,-1676 and -911
\( k J m o l^{-1} \) respectively. The most stable oxide is:
A. \( N a_{2} O \)
в. \( M g O \)
c. \( A l_{2} O_{3} \)
D. \( \operatorname{si} O_{2} \)
Subject: Physics
A sinusoidal wave travelling in the positive direction of \( x \) on a stretched string has amplitude \( 2.0 \mathrm{cm} \) wavelength \( 1 \mathrm{m} \) and wave velocity 5.0 \( \mathrm{m} / \mathrm{s} \cdot \mathrm{At} \mathrm{x}=0 \) and \( \mathrm{t}=0, \) it is given that
displacement \( y=0 \) and \( \frac{\partial y}{\partial t}<0 . \) Express the wave function correctly in the from \( y \) \( =f(x, t):- \)
A \( \cdot y=(0.04 \mathrm{m})\left[\sin \left(\pi m^{-1} 1\right) \mathrm{x}-\left(10 \pi s^{-1} 1\right) t\right] \)
B. \( y=(0.02 \mathrm{m}) \cos 2 \pi(x-5 t) \)
c. \( y=(0.02 \mathrm{m})\left[\sin \left(2 \pi m^{-1} 1\right) x-\left(10 \pi s^{-1}\right)\right] t \)
D \( \cdot y=(0.02 \mathrm{m}) \cos \pi\left(x-5 t+\frac{1}{4}\right) \)
Subject: Physics
The radius \( (r), \) length \( (l) \) and resistance
\( (R) \) of a thin wire are \( (0.20 \pm 0.01) \mathrm{cm} \)
\( (800 \pm 0.1) \mathrm{cm}, \) and \( (301 \pm 1) \Omega \)
respectively. The error in the specific resistance is :
A . 10.34\%
B . 45.4\%
c. 26\%
D. 27.5\%
Subject: Physics
Which of the two switches \( S_{1} \) and \( S_{2} \)
shown in figure will produce short-
circuiting?
\( A \cdot S_{1} \)
B. \( S_{2} \)
c. Both \( S_{1} \) and \( S_{2} \)
D. Neither \( S_{1} \) nor \( S_{2} \)
Subject: Physics
The elevator shown in figure is descending, with an acceleration of 2
\( m / s^{2} . \) The mass of the block \( A \) is 0.5 kg.
The force exerted by the block A on the block B is -
\( A \cdot 2 N \)
в. 4 ।
\( c \cdot 6 N \)
\( D \cdot 8 n \)
Subject: Maths
Find the value of \( \cos \theta-\cos 3 \theta+\cos 4 \theta \)
when \( \boldsymbol{\theta}=\mathbf{4 5}^{\circ} \)
A. \( \frac{\sqrt{3}}{2} \)
B. \( \sqrt{3}-1 \)
\( c \cdot \frac{1}{2} \)
D. \( \sqrt{2}-1 \)
Subject: Maths
The mode of the following series is 36 Find the missing frequency in it
\( \begin{array}{lllll}\text { Class } & 0- & 10- & 20- & 30- \\ \text { interval } & 10 & 20 & 30 & 40\end{array} \)
Frequency 1 8 10 \( \dots \)
A . 10
B. 15
c. 16
D. 12
Subject: Physics
Which of the following conclusions regarding the structure of atom is based on Rutherford's \( \alpha \) -particle scattering experiment?
A. Th positive charge is concentrated in a very smal volume of the atom
B. The positive charge is scattered with the electrons throughout the atom.
c. The volume occupied by the nucleus is half of the volume of atom.
D. Most of the space in the atom is occupied by the neutrons