AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A spherical solid ball of volume \( V \) is
made of a material of density \( \rho_{1} \) It is
falling through a liquid of density
\( \rho_{1}\left(\rho_{2}<\rho_{1}\right) . \) Assume that the liquid
applies a viscous force on the ball that
is Proportional to the square of its
speed \( \mathbf{v}, \) i.e., \( \boldsymbol{F}_{\boldsymbol{v} i \text {scous}}=-\boldsymbol{k} \boldsymbol{v}^{2}(\boldsymbol{k}>\mathbf{0}) \)
The terminal speed of the ball is:
A \( \cdot \sqrt{\frac{V g\left(\rho_{1}-\rho_{2}\right)}{k}} \)
в. \( \frac{V g \rho_{1}}{k} \)
c. \( \sqrt{\frac{V g \rho_{1}}{k}} \)
D. \( \frac{V g\left(\rho_{2}<\rho_{1}\right)}{k} \)
Subject: Maths
A particle is moving along the curve
\( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{t}^{2}+\boldsymbol{b} \boldsymbol{t}+\boldsymbol{c} \). If \( \boldsymbol{a} \boldsymbol{c}=\boldsymbol{b}^{2}, \) then the
particle would be moving with uniform
A. rotation
B. velocity
c. acceleration
D. retardation
Subject: Maths
STATEMENT - 1: If tangents OR, PR, PQ and drawn respectively at \( A, B, C \) to the circle circumscribing an acute-angled
\( \Delta A B C \) so as the form another \( \Delta P Q R \) then the \( \angle R P Q=\angle B A C \)
STATEMENT - 2: \( \Delta A B C \) is similar to \( \Delta \)
CPB.
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement - 1
B. Statement-1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement- -
c. Statement - 1 is True, Statement- - 2 is False
D. Statement-1 is False, Statement - 2 is True
Subject: Chemistry
Which of the following statement is
wrong?
A. The fibrous nature of Wrought iron is due to the slag present in it.
B. The loss of iron is Bessemer process is due to the formation of \( F e S i O_{3} \) slag.
C. In Bessemer process carbon monoxide formed burns with blue flame at the mouth of the furnace.
D. In blast furnace \( F e_{2} O_{3} \) is reduced to iron mainly by coke.
Subject: Physics
A sphere of radius \( R \) is submerged in
water completely, what force should be
imparted to the sphere, so that every point in it experiences a constant volume stress
A. Force should be proportional to \( R \)
B. Force should be proportional to \( 1 / R \)
C. Force should be proportional to \( R^{2} \)
D. Force should be proportional to \( 1 / R^{2} \)
Subject: Physics
Assertion
\( \gamma \) -radiation emission occurs after \( \boldsymbol{\alpha} \) and
\( \beta \) decay.
Reason
Energy levels occur in nucleus.
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
In hydrogen atom the energy difference between the states \( n=2 \) and \( n=3 \) is
Ee \( V \). The ionisation potential of \( H \)
atom is:
A . \( 3.2 E \)
в. \( 5.6 E \)
\( c .7 .2 E \)
D. \( 13.2 E \)
Subject: Physics
A particle is going with constant speed
along a uniform helical and spiral path
separately as shown in figure then

Essume that the vertical acceleration
of the particle is negligible in case (a)]
A. The velocity of the particle is constant in both cases
B. The magnitude of acceleration of the particle is constant in both cases
C. The magnitude of acceleration is constant in (a) and decreasing in (b)
D. The magnitude of acceleration is decreasing continuously in both the cases
Subject: Physics
\begin{tabular}{l|l|l} 
List & \multicolumn{1}{l} { List } \\
I & II \\
A. & A dusting of a carpet & Inertia of direction \\
B. & Provided with a mudguard & Inertia of motion \\
C. & Fan continues to rotate after switching off & Measure of inertia \\
\hline D. & Mass & Inertia of rest
\end{tabular}
\( \mathbf{A} \)
\( A-(4) ; B-(1) ; C-(3) ; D-(2) \)
\( \mathbf{B} \)
\( A-(4) ; B-(1) ; C-(2) ; D-(3) \)
C \( \cdot A-(4) ; B-(2) ; C-(1) ; D-(3) \)
D. \( A-(1) ; B-(4) ; C-(2) ; D-(3) \)
Subject: Chemistry
By passing electric current, \( N a C l O_{3} \) is
converted into \( N a C l O_{4} \) according to
the following equation \( N a C l O_{3}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \)
How many moles of \( N a C l O_{4} \) will be
formed when three Faradays of charge
is passed through \( N a C l O_{3} ? \)
A . 1.5
в. 1.0
\( c .3 .0 \)
D. 0.75
Subject: Maths
Show that points
\( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}+\boldsymbol{c}), \boldsymbol{B}(\boldsymbol{b}, \boldsymbol{c}+\boldsymbol{a}), \boldsymbol{C}(\boldsymbol{c}, \boldsymbol{a}+\boldsymbol{b}) \)
are collinear.
Subject: Chemistry
Rank the following compounds in order
of decreasing acid strength (most
acidic \( \rightarrow \) least acidic)
\( \mathbf{A} \cdot 2>4>1>3 \)
B. \( 1>3>4>2 \)
\( \mathbf{c} \cdot 3>1>2>4 \)
D. \( 3>1>4>2 \)
Subject: Chemistry
Balance the following equation:
\( \boldsymbol{K} \boldsymbol{C l} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{K} \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{H} \boldsymbol{C l O}_{4}+\boldsymbol{C l O}_{2} \)
A \( \cdot 3 K C l O_{3}+3 H_{2} S O_{4} \rightarrow 3 K H S O_{4}+H C l O_{4}+2 C l O_{2}+ \)
\( H_{2} O \)
в. \( K C l O_{3}+5 H_{2} S O_{4} \rightarrow 3 K H S O_{4}+3 H C l O_{4}+2 C l O_{2}+ \)
\( 3 H_{2} O \)
c. \( 3 K C l O_{3}+4 H_{2} S O_{4} \rightarrow 3 K H S O_{4}+2 H C l O_{4}+ \)
\( 2 C l O_{2}+H_{2} O \)
D. None of these
Subject: Physics
A bullet of mass \( \mathrm{m} \) and velocity v is fired into a large block of wood of mass \( \mathrm{M} \)
The final velocity of the system is :
A. \( v+m+M \)
в. \( (m+M) v \)
c. \( V=\frac{m}{m+M} v \)
D. \( V=\frac{m+M}{m-M} v \)
Subject: Physics
Amit carried a box up the flight of stairs
shown in the diagram

He did \( 150 \mathrm{J} \) of work in the process. The
mass of the box is
A \( .7 .5 \mathrm{kg} \)
B. \( 75 \mathrm{kg} \)
\( \mathbf{c} \cdot 15 k g \)
D. \( 150 \mathrm{kg} \)
Subject: Maths
Solve:
\( \int \frac{1+x+\sqrt{x+x^{2}}}{\sqrt{x}+\sqrt{1+x}} d x \) is equal to
A \( \cdot \frac{1}{2} \sqrt{1+x} C \)
B \( \cdot \frac{2}{3}(1+x)^{3 / 2}+C \)
\( \mathbf{c} \cdot \sqrt{1+x}+C \)
D \( \cdot \frac{3}{2}(1+x)^{32}+C \)
Subject: Maths
Assertion(A): \( f(x)= \) \( \left\{\begin{array}{ll}x^{2} \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array} \) is continuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)
Reason(R): Both \( h(x)=x^{2}, g(x)= \)
\( \left\{\begin{array}{ll}\sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array} \) are continuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)
A. Both A and R are true and R is the correct explanation of
B. Both A and R are true and R is not the correct explanation of
c. \( A \) is true but \( R \) is false
D. R is true but A is false
Subject: Maths
Find \( \boldsymbol{x} \) and \( \boldsymbol{y}, \) when \( \boldsymbol{x}+\boldsymbol{y}=\left[\begin{array}{cc}\mathbf{7} & \mathbf{0} \\ \mathbf{2} & \mathbf{5}\end{array}\right] \)
and \( \boldsymbol{x}-\boldsymbol{y}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{0} \\ \mathbf{0} & \mathbf{3}\end{array}\right] \)
Subject: Physics
The ratio of charge densities on the surface of two conducting spheres is 3:
2. lithe radii of t: the spheres are \( 4 \mathrm{cm} \) and \( 8 \mathrm{cm} \) the ratio of the electric potential on the surfaces of the sphere 2
is
\( A \cdot 3: 4 \)
B. 3:1
\( c \cdot 1: 3 \)
D. 4: 9
Subject: Maths
\( \sin x \frac{d y}{d x}+3 y=\cos x, \) solving it gives
\( \left(\frac{1}{3}+y\right) \tan ^{k} \frac{x}{2}=c+2 \tan \frac{x}{2}-x \)
find k?
\( A \)
B. 2
\( c \cdot 5 \)
\( D \)
Subject: Maths
If \( a=\hat{i}+\hat{j}+\hat{k}, b=4 \hat{i}+3 \hat{j}+4 \hat{k} \) and
\( c=\hat{i}+\alpha \hat{j}+\beta \hat{k} \) are linearly dependent
vectors and \( |c|=\sqrt{3}, \) then the value of
\( \alpha \) and \( \beta \) are respectively
A. ±1,1
в. ±2,1
c. 0,±1
D. None of these
Subject: Chemistry
When a colloidal solution is viewed from
the direction at right angles of the light beam, the path of the beam is
illuminated due to scattering of light. In the given figure (A) and (B) are:
A . A - Tyndall cone, B - Scattered light
B. A - Scattered light, B - Tyndall cone
C. A - Tyndall cone, B - Blind spot
D. A - Tyndall effect.
B - Tyndall cone
Subject: Maths
Hilswer untulury quesuuris Na>tu
on the following.
\( C_{1} \) and \( C_{2} \) are two circles and points
\( \boldsymbol{P}_{1}, \boldsymbol{P}_{2}, \boldsymbol{P}_{3}, \boldsymbol{P}_{4}, \boldsymbol{P}_{5} \) are noted. From which
point tangent is possible to \( C_{2} \) but not
\( C_{1} \)
\( A \cdot P_{2} \)
в. \( P_{3} \)
\( c \cdot P_{4} \)
D. \( P_{5} \)
Subject: Maths
If \( f(x), \phi(x), \varphi(x) \) are continuous
on \( [a, b] \) and differentiable on
\( (a, b) \exists c \epsilon(a, b), \) then
\( \left|\begin{array}{lll}\boldsymbol{f}(\boldsymbol{a}) & \boldsymbol{\phi}(\boldsymbol{a}) & \boldsymbol{\varphi}(\boldsymbol{a}) \\ \boldsymbol{f}(\boldsymbol{b}) & \boldsymbol{\phi}(\boldsymbol{b}) & \boldsymbol{\varphi}(\boldsymbol{b}) \\ \boldsymbol{f}^{\prime}(\boldsymbol{c}) & \boldsymbol{\phi}^{\prime}(\boldsymbol{c}) & \boldsymbol{\varphi}^{\prime}(\boldsymbol{c})\end{array}\right|= \)
\( A \cdot f^{\prime}(c) \)
B. \( \phi^{\prime}(c) \)
c. \( \varphi^{\prime}(c) \)
D.
Subject: Maths
\( \int \frac{e^{x}}{\left(e^{x}+2\right)\left(e^{x}-1\right)} d x= \)
A \( \cdot \frac{1}{3} \log \left|\frac{e^{x}-1}{e^{x}+2}\right|+c \)
в \( \cdot \frac{1}{3} \log \left|\frac{e^{x}+1}{e^{x}-1}\right|+c \)
c. \( \frac{1}{3} \log \left|\frac{e^{x}+1}{e^{x}+2}\right|+c \)
D. \( -\frac{1}{3} \log \left|\frac{e^{x}+1}{e^{x}+2}\right|+c \)
Subject: Chemistry
Arrange the \( p H \) values of \( 0.1 M \)
solution of \( (\boldsymbol{I}) \boldsymbol{H} \boldsymbol{C O O} \boldsymbol{N} \boldsymbol{a} \)
\( (I I) H C O O H,(I I I) C H_{3} C O O N H_{4} \)
\( (I V) N a O H,(V) H C l \) in decreasing order.
\( \mathbf{A} \cdot I V>I I I>I>I I>V \)
в. \( I V>I>I I I>I I>V \)
с. \( I I>I I I>I>I V>V \)
D. \( V>I I>I I I>I>I V \)
Subject: Maths
\( \operatorname{Let} u=\int_{0}^{\infty} \frac{d x}{x^{4}+7 x^{2}+1} \& v= \)
\( \int_{0}^{\infty} \frac{x^{2} d x}{x^{4}+7 x^{2}+1} \) then:
This question has multiple correct options
\( A \cdot v>u \)
B. \( 6 v=\pi \)
c. \( 3 u+2 v=5 \pi / 6 \)
D. \( u+v=\pi / 3 \)
Subject: Maths
The cartesian from of equation a line passing through the point position vector \( 2 \hat{i}-\hat{j}+2 \hat{k} \) and is in the direction of \( -2 \hat{i}+\hat{j}+\hat{k}, \) is
A \( \frac{x-2}{-2}=\frac{y+1}{1}=\frac{z-2}{1} \)
B. \( \frac{x+4}{-2}=\frac{y-1}{1}=\frac{z+2}{1} \)
c. \( \frac{x+2}{4}=\frac{y-1}{-1}=\frac{z-1}{2} \)
D. None of these
Subject: Maths
South African cricket captain lost the
toss of a coin 13 times out of \( 14 . \) The
chance of this happening was
A \( \cdot \frac{7}{2^{13}} \)
в. \( \frac{1}{2^{13}} \)
c. \( \frac{13}{2^{14}} \)
D. \( \frac{13}{2^{13}} \)
Subject: Maths
\( \int \frac{(x-1) e^{x}}{(x+1)^{3}} d x \) is
A \( \cdot \frac{e^{x}}{x+1} \)
В. \( e^{x}\left(\frac{x}{x+1}\right) \)
c. \( \frac{e^{x}(x-1)}{(x+1)^{2}} \)
D. \( \frac{e^{x}}{(x+1)^{2}} \)
Subject: Physics
A block of mass \( M \) is hanging over a
smooth and light pulley through a light string. The other end of the string is
pulled by a constant force \( F \). If kinetic energy of the block increases by \( 20 J \) in
1 s. Then:
A. Tension in the string is \( M g \)
B. Tension in the string is \( F \)
c. work done by the tension on the block is \( 20 \mathrm{J} \) in 1 sec
D. Work done by the force of gravity is \( -20 \mathrm{J} \) in 1 sec.
Subject: Physics
Calculate angular velocity of earth so
that acceleration due to gravity at \( 60^{\circ} \)
latitude becomes zero. (Radius of earth
\( =6400 \mathrm{km}, \) gravitational acceleration
at poles \( \left.=10 m / s^{2}, \cos 60^{\circ}=0.5\right) \)
A . \( 7.8 \times 10^{-2} r a d / s \)
B. \( 0.5 \times 10^{-3} \mathrm{rad} / \mathrm{s} \)
c. \( 1 \times 10^{-3} r a d / s \)
D. \( 2.5 \times 10^{-3} \mathrm{rad} / \mathrm{s} \)
Subject: Chemistry
Which of the following properties are common to the elements manganese,
iron, cobalt, nickel and copper?
(I) Coloured ions in aqueous solution
(II) Oxides of nitrogen on reaction with
concentrated \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
(III) Chlorides of formula \( M C l_{2} \) and
\( M C l_{3} \)
A. ।, ॥।, ॥।
B . ।, ॥
c. ॥, ॥ा
D. I only
Subject: Physics
64 spherical rain drops of equal size are falling vertically through air with a terminal velocity \( 1.5 m s^{-1} . \) If these
drops coalesce to form a big spherical drop, then terminal velocity of big drop is:
\( \mathbf{A} \cdot 8 m s^{-1} \)
В. \( 16 \mathrm{ms}^{-1} \)
c. \( 24 m s^{-1} \)
D. \( 32 \mathrm{ms}^{-1} \)
Subject: Physics
Q Type your question
sy piocuris
equal area A are use dat the four
opening to keep the water in
equilibrium Now an additional force \( F \) is
applied at each piston. The increase
in the pressure at the centre of the
container due to this addition is
\( A \cdot F \)
\( \bar{A} \)
B. \( \frac{2 F}{A} \)
\( c \cdot \frac{4 F}{A} \)
2
Subject: Physics
A charged particle of mass \( 5 \times 10^{-6} \mathrm{kg} \) is
held stationary in space by placing it in an electric field of strength \( 10^{6} N / C \)
directed vertically downwards. The charge on the particle is: \( \left(g=10 m / s^{2}\right) \)
A. \( -20 \times 10^{-5} \mu C \)
B. \( -5 \times 10^{-5} \mu C \)
c. \( 5 \times 10^{-5} \mu C \)
D. \( 20 \times 10^{-5} \mu C \)
Subject: Physics
The distance between the wires of
electric mains is \( 12 \mathrm{cm} . \) These wires
exprience 4 mgwt per unit length. The value of current flowing in each wire will be if they carry current in same direction
A . \( 4.85 \mathrm{A} \)
B. zero
\( \mathbf{c} \cdot 4.85 \times 10^{-2} A \)
D. \( 85 \times 10^{-4} A \)
Subject: Maths
Given the following sequence, determine whether it is arithmetic
progression or not. If it is an Arithmetic Progression, its general term. \( -5,2,9,16,23,30, \dots \dots \dots \)
A \( .7 n-12 \)
в. \( 6 n-12 \)
\( c \cdot 5 n-12 \)
D. \( 4 n-12 \)
Subject: Chemistry
The IUPAC name of the compound is:
A. 1 -bromo-1chloro-4, \( 4^{\prime} \) -bicyclobutane
B. \( 4-\left(4^{\prime}-\text { chlorocyclobutyl }\right)-1 \) -bromocyclobutane
c. 3 -Bromo-3'-chloro-1, 1'-bicyclobutane
D. 4-(4'-bromocyclobutyl)-1-chlorocyclo butane
Subject: Physics
The B-H curve for a ferromagnet is
shown in the figure. The ferromagnet is placed inside a ling solenoid with 1000
turns/cm.. The current that should be passed in the solenoid to demagnetise
the ferromagnet completely is:
\( A \cdot 2 m A \)
В. \( 1 m A \)
\( c .3 m A \)
D. None of these
Subject: Physics
A train is moving with uniform acceleration. The two ends of the train
pass through a point on the track with
velocity \( V_{1} \) and \( V_{2} . \) With what velocity the middle point of the train would pass through the same point?
A \( \cdot\left[\frac{\left(V_{1}^{2}+V_{2}^{2}\right.}{2}\right] \)
B. \( \frac{\left(V_{1}^{2}-V_{2}^{2}\right)}{2} \)
\( c \cdot \frac{v_{1}+v_{2}}{2} \)
\( D \cdot \frac{V_{1}-V_{2}}{2} \)
Subject: Chemistry
Statement-1: Both sodium and hydrogen
have outer electronic configuration \( \boldsymbol{n} \boldsymbol{s}^{1} \)
but hydrogen is less reactive than sodium

Statement-2: Hydrogen has greater ionisation energy.
A. Statement-1 is true, Statement-2 is true; Statementis a correct explanation for Statement-
B. Statement-1 is true, Statement-2 is True; Statementis not a correct explanation for Statement-
c. statement-1 is true, statement-2 is false
D. Statement-1 is false, Statement-2 is true
Subject: Biology
Stage of hydrarch are :
(a) Marsh meadow stage
(b) Reed
swamp stage (c) submerged plant
stage
(d) Phytoplankton stage
(e) Submerged free-floating stage.
Identify the correct sequence:
\( A \cdot d, c, e, b, a \)
B. \( c, e, a, b, d \)
\( c \cdot b, d, c, a, e \)
D. \( d, e, c, b, a \)
E. e, c, b, a, d
Subject: Maths
A stone is dropped into a quiet lake and
waves move in circles at the speed of 5 \( \mathrm{cm} / \mathrm{s} \) At the instant when the radius of
the circular wave is \( 8 \mathrm{cm} \) how fast is the
enclosed area increasing?
\( \mathbf{A} \cdot 84 \pi \mathrm{cm}^{2} / \mathrm{s} \)
B. \( 80 \pi \mathrm{cm}^{2} / \mathrm{s} \)
\( \mathbf{c} \cdot 90 \pi \mathrm{cm}^{2} / \mathrm{s} \)
D. \( 96 \pi \mathrm{cm}^{2} / \mathrm{s} \)
Subject: Maths
Evaluate: \( [\sqrt[3]{\sqrt[6]{5^{9}}}]^{4}[\sqrt[6]{\sqrt[3]{5^{9}}}]^{4} \)
\( A \cdot 5^{2} \)
в. \( 5^{4} \)
\( c \cdot 5^{8} \)
D. \( 5^{12} \)
Subject: Physics
Refraction of the light from the air to glass and from air to water are shown in
the figure (i) and figure (ii) below. The
value of an angle \( \theta \) in the case of
refraction as shown in the figure (iii) will be
A . 30
B. 35 5
\( c \cdot 60 \)
\( D \cdot 4 \)
Subject: Maths
Examine the continuity of:
\[
\begin{aligned}
\boldsymbol{f}(\boldsymbol{x}) &=\boldsymbol{x}^{2}-\boldsymbol{x}+\boldsymbol{9} \text { for } \boldsymbol{x} \leq \mathbf{3} \\
&=\boldsymbol{4} \boldsymbol{x}+\mathbf{3} \quad \text { for } \boldsymbol{x}>\mathbf{3}, \boldsymbol{a} \boldsymbol{t} \boldsymbol{x}=\boldsymbol{3}
\end{aligned}
\]
Subject: Maths
If \( A \) is a \( 3 X 3 \) non-singular matrix such
that \( \boldsymbol{A} \boldsymbol{A}^{\prime}=\boldsymbol{A}^{\prime} \boldsymbol{A} \) and \( \boldsymbol{B}=\boldsymbol{A}^{-1} \boldsymbol{A}^{\prime}, \) then
\( B B^{\prime} \) equals to
\( \mathbf{A} \cdot 1+B \)
B. \( I \)
c. \( B^{-1} \)
D. \( \left(B^{-1}\right)^{\prime} \)
Subject: Maths
Evaluate:
\( \int \frac{x^{4}+4}{x^{2}-2 x+2} d x \)
A \( \cdot \frac{x^{3}}{2}+x^{2}+2 x+C \)
B. \( \frac{x^{3}}{3}+x^{2}+2 x+C \)
c. \( \frac{x^{3}}{3}+x^{2}+x+C \)
D. \( \frac{x^{3}}{3}+x^{2}-2 x+C \)
Subject: Maths
If \( (x)=x^{2}-2 x+4 \) then the set of
values of \( x \) satisfying \( f(x-1)= \)
\( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1}) \) is
\( \mathbf{A} \cdot\{-1\} \)
B . \{-1,1\}
\( c \cdot\{1\} \)
D \( \cdot\{1,2\} \)
Subject: Maths
Find all solution of the equation. \( \frac{(\mathbf{2}|\boldsymbol{x}|-\mathbf{3})^{2}-|\boldsymbol{x}|-\mathbf{6}}{\mathbf{4} \boldsymbol{x}+\mathbf{1}}=\mathbf{0}, \) which
belong to the domain of definition of the
function \( \boldsymbol{y}=(2 \boldsymbol{x}+\mathbf{1}) /\left(\boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{6}\right) \)
Subject: Maths
If \( A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right] \) then \( \operatorname{Adj}(A)= \)
A \( \cdot\left[\begin{array}{ccc}-1 & +8 & -5 \\ 1 & -6 & 3 \\ -1 & 2 & -1\end{array}\right] \)
B. \( \left[\begin{array}{ccc}-1 & +1 & -1 \\ 8 & -6 & 2 \\ -5 & 3 & -1\end{array}\right] \)
C. \( \left[\begin{array}{ccc}1 & -1 & 1 \\ 8 & -6 & 2 \\ -5 & 3 & -1\end{array}\right] \)
D. \( \left[\begin{array}{ccc}-1 & -8 & 5 \\ -1 & 6 & -3 \\ 1 & -2 & 1\end{array}\right] \)
Subject: Maths
The management committee of a residential colony decided to award some of its members (say \( x \) ) for
honesty, some (say \( y \) ) for helping others
and some others (say \( z \) ) for supervising the workers to keep the colony neat and clean. The sum of all the awardees is 12
Three times the sum of awardees for
cooperation and supervision added to two times the number of awardees for
honesty is \( 33 . \) If the sum of the number of awardees for honesty and supervision
is twice the number of awardees for
helping others using matrix category. Apart from these values namely, honesty, cooperation and supervision,
suggest one more value which the
management of the colony must include for awards.
Subject: Physics
A farmer has to go \( 500 m \) due north,
\( 400 m \) due east and \( 200 m \) due south to
reach his field. If he takes 20 minutes to
reach the field. What is the average
velocity of farmer during the walk?
A. \( 25 m / \min \)
в. \( 50 m / \min \)
c. \( 55 m / \min \)
D. \( 110 \mathrm{m} / \mathrm{min} \)
Subject: Maths
If \( \boldsymbol{I}=\int \log (\sqrt{1-\boldsymbol{x}}+\sqrt{1+\boldsymbol{x}}) \boldsymbol{d} \boldsymbol{x} \)
then I is equal to
A \( \cdot x \log (\sqrt{1-x}+\sqrt{1+x})+\frac{1}{2} x+C \)
B・ \( _{x \log (\sqrt{1-x}+\sqrt{1+x})}+\frac{1}{2} \sin ^{-1} x+C \)
c. \( _{x \log (\sqrt{1-x}+\sqrt{1+x})}+\frac{1}{2} \sin ^{-1} x-\frac{1}{2} x+C \)
D. \( x \log (\sqrt{1-x}+\sqrt{1+x})+\frac{1}{2} \sin ^{-1} x+\frac{1}{2} x+C \)
Subject: Chemistry
A divalent metal with atomic number
12 reacts with an acid liberating a gas
\( X . X \) on treatment with a non metal \( Y \)
\( \operatorname{gives} Z, \) which on dissolution in water
produces the same acid. Identify \( \boldsymbol{X}, \boldsymbol{Y} \)
and \( Z \)
A \( \cdot C l_{2}, H_{2}, H C l \)
в. \( H_{2}, H C l, C l_{2} \)
c. \( H C l, H_{2}, C l_{2} \)
D. \( H_{2}, C l_{2}, H C l \)
Subject: Chemistry
In pyrophosphoric acid, \( \boldsymbol{H}_{\mathbf{4}} \boldsymbol{P}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{7}} \)
number of \( \sigma- \) and \( d \pi-p \pi \) bonds
respectively are
A. 8 and 2
B. 6 and 2
c. 12 and zero
D. 12 and 2
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{O}+\boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{C H}= \)
\( O^{H} \stackrel{O^{\theta}, \Delta}{\rightarrow} \) mixture of aldols
\( (z)= \) total number of aldols including stereoisomers.
Report your answer as \( (z-5) \)
Subject: Chemistry
In the pressure-volume diagram given below, the isochoric, isothermal
isobaric and isoentropic parts
respectively are:
A. \( B A, A D, D C, C B \)
B. \( D C, C B, B A, A D D D, D D, C B, B A, A D, D \)
c. \( A B, B C, C D, D A \)
D. \( C D, D A, A B, B C \)
Subject: Chemistry
The redox reaction \( Z n(s)+ \)
\( \boldsymbol{P b C l}_{2}(\boldsymbol{a q}) \longrightarrow \boldsymbol{P b}(\boldsymbol{s})+\boldsymbol{Z n C l}_{2}(\boldsymbol{a q}) \)
can be represented as following half equations \( : Z n(s) \longrightarrow Z n^{2+}(a q)+ \)
\( 2 e^{-}(\text {oxidation }) \) and \( P b^{2+}(a q)+ \)
\( 2 e^{-} \longrightarrow P b(s)(\text { reduction }) \)
If true enter 1 , else enter 0 .
\( A \)
Subject: Physics
Two particle are oscillating along two close parallel straight lines side by side with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is:
A . 0
в. \( 2 \pi / 3 \)
\( c \)
D. \( \pi / 6 \)
Subject: Chemistry
Out of \( N a^{+}, M g^{+2}, O^{-2} \) and \( N^{-3}, \) the pair of species having the minimum and the maximum IP would be?
A \( . N a^{+}, M g^{+2} \)
B . \( M g^{+2}, N^{-3} \)
C . \( N^{-3}, M g^{+2} \)
D. \( O^{-2}, N^{-3} \)
Subject: Maths
The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:
Year \( \begin{array}{lll}1992 & 1993 & 1994 \\ 4 & 19999 & 193\end{array} \)
Loan(in
crores 33
55
of rupees)
With the help of the bar graph, indicate the year in which amount of loan is not increased over that of the preceding
year.
Subject: Maths
If the perpendicular distance of a point \( P \) from the \( x \) -axis is 5 units and the foot
of the perpendicular lines on the negative direction of \( x \) -axis, then the
point P has?
A. \( x \) coordinate \( =5 \)
B. \( y \) coordinate \( =5 \) only
c. \( y \) coordinate \( =-5 \) only
D. \( y \) coordinate \( =5 \) or -5
Subject: Chemistry
Acetylene can be obtained by the reaction:
A \( \cdot H C O O K \frac{\text { Electrolysis }}{\rightarrow} \)
B. \( C H I_{3}+A g \stackrel{\Delta}{\longrightarrow} \)
c. \( C H_{3} C H_{2} O H \frac{\operatorname{conc} . H_{2} S O_{4}}{443 K} \)
D. \( B e_{2} C+H_{2} O \rightarrow \)
Subject: Maths
All possible values of \( x \) for which the
function
\( f(x)=x \ln x-x+1 \) is positive is
A. \( (1, \infty) \)
(n)
B. \( \left(\frac{1}{e}, \infty\right) \)
c. \( [e, \infty) \)
D. \( (0, \infty)-\{1\} \)