AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A particle accelerates from rest at a constant rate for some time and attains
a velocity of \( 8 m / \) sec. Afterwards it
decelerates with the constant rate and
comes to rest. If the total time taken is
4 sec, the distance travelled is
A . \( 32 m \)
B. \( 16 m \)
\( c .4 m \)
D. None of the above
Subject: Maths
Discuss the applicability of Rolle's theorem to \( f(x)=\log \left[\frac{x^{2}+a b}{(a+b) x}\right], \) in
the interval \( [a, b] \)
A. Yes Rolle's theorem is applicable and the stationary point is \( x=\sqrt{a b} \)
B. No Rolle's theorem is not applicable due to the discontinuity in the given interval
C. Yes Rolle's theorem is applicable and the stationary point is \( x=a b \)
D. none of these
Subject: Maths
f a non-zero function \( f \) satisfies the
relation \( f(x+y)+f(x-y)=2 f(x) \cdot f(y) \)
for all \( x, y \) in \( R \) and \( f(0) \neq 0 ; \) then \( f(10)- \)
\( f(-10)= \)
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3
Subject: Physics
A physicist took a hollow metallic sphere of radius \( 4 \mathrm{cm} \) at a temperature
of \( 27^{\circ} \mathrm{C} . \) He heated metallic sphere up
to \( 127^{\circ} \mathrm{C} \) and found that diameter of the
sphere increased to \( 8.2 \mathrm{cm}, \) then what is the coefficient of real expansion.
Subject: Physics
Three bodies \( A, B \) and \( C \) are in thermal
equilibrium.

The temperature of \( B \) is \( 45^{\circ} C . \) Then the
temperature of \( ^{\prime} C^{\prime} \) is
\( \mathbf{A} \cdot 45^{\circ} C \)
B \( .50^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} C \)
D. Any temperature
Subject: Chemistry
Pressure of \( 1 \mathrm{g} \) of an ideal \( \operatorname{gas} \mathrm{A} \) at \( 27^{\circ} \mathrm{C} \) is found to be 2 bar. When 2 g of another ideal gas \( \mathrm{B} \) is introduced in the same
flask at same temperature the pressure becomes 3 bar. What is the relationship between their molecular masses?
A \( \cdot 2 M_{B}=M_{A} \)
В . \( M_{B}=M_{A} \)
C \( . M_{B}=4 M_{A} \)
D. \( M_{B}=2 M_{A} \)
Subject: Chemistry
The compound \( C_{7} H_{8} \) undergoes the following reactions:
\( \boldsymbol{C}_{7} \boldsymbol{H}_{8} \frac{3 C l_{2} / \Delta}{\longrightarrow} \boldsymbol{A} \frac{B r_{2} / \boldsymbol{F} e}{\longrightarrow} \boldsymbol{B} \frac{\boldsymbol{Z} \boldsymbol{n} / \boldsymbol{H} C l}{\longrightarrow} \boldsymbol{C} \)
The product \( C \) is:
A. 3 -bromo -2,4,6 -trichlorotoluene
B. \( m \) -bromotoluene
c. \( p \) -bromotoluene
D. \( o \) -bromotoluene
Subject: Chemistry
Stability constants of \( \left[\boldsymbol{C d}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{2-} \) and
\( \left[N i(C N)_{4}\right]^{2-} \) are \( 1.28 \times 10^{17} \) and \( 1.0 \times \)
\( 10^{31} \) respectively. Which is more stable?
\( \mathbf{A} \cdot\left[N i(C N)_{4}\right]^{2} \)
B . \( \left[C d(C N)_{6}\right]^{2} \)
c. Both are equally stable
D. None of the above
Subject: Physics
Two particles of equal mass have initial velocities \( 2 \hat{i} m s^{-1} \) and \( 2 \hat{j} m s^{-1} . \) First
particle has a constant acceleration \( (\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}) \boldsymbol{m} \boldsymbol{s}^{-1} \) while the acceleration of
the second particle is always zero. The centre of mass of the two particles moves in:
A . Circle
B. Parabola
c. Ellipse
D. Straight line
Subject: Chemistry
Consider the following equilibrium
reaction:
\( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{4}^{+}+\boldsymbol{N} \boldsymbol{H}_{2} \)
Find the ionic product of the above equilibrium reaction?
Subject: Physics
An \( \alpha \) -particle describes a circular path of radius \( r \) in a magnetic field \( B \). The
radius of the circular path described by the proton of same energy in the same magnetic field is :
A \( \cdot \frac{r}{2} \)
B.
\( c \cdot \sqrt{2} r \)
D. \( 2 r \)
Subject: Maths
To construct a triangle similar to given \( \Delta A B C \) with its sides \( \frac{3}{5} \) of that of \( \Delta A B C, \) a ray \( B X \) is drawn at acute
angle with \( B C \). How many minimum no
of points should be marked on \( B X ? \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Maths
Let \( \boldsymbol{A}=\{1,2,3,4\} ; B=\{3,5,7,9\} \)
\( C=\{7,23,47,79\} \) and \( f: A \rightarrow B, g: \)
\( B \rightarrow C \) be defined as \( f(x)=2 x+1 \)
and \( g(x)=x^{2}+x . \) Express \( (g \circ f)^{-1} \)
and \( f^{-1} \circ g^{-1} \) as the sets of ordered
pairs and verify and \( (\boldsymbol{g} \circ \boldsymbol{f})^{-1}=\boldsymbol{f}^{-1} \circ \)
\( \boldsymbol{g}^{-1} \)
Subject: Chemistry
Which of the following is produced by
the reaction of zinc metal, \( Z n \) and
hydrochloric acid, \( \boldsymbol{H} \boldsymbol{C l} \) ?
I. \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
II. \( C l_{2}(g) \)
III. \( Z n^{2+}(a q) \)
A. Il only
B. III only
c. I and II only
D. I and III only
E . I, II, and III
Subject: Physics
The position vector of a particle \( \vec{R} \) as a function of time is given by:
\( \overrightarrow{\boldsymbol{R}}=\boldsymbol{4} \sin (2 \pi t) \hat{\hat{i}}+4 \cos (2 \pi t) \hat{j} \)
where \( R \) is in meters, \( t \) is in seconds
and \( \hat{i} \) and \( \hat{j} \) denote unit vectors along \( x \) and y- directions, respectively. Which one of the following statements is wrong for the motion of particle?
A. Path of the particle is a circle of radius \( 4 \mathrm{m} \)
B. Acceleration vector is along \( -\vec{R} \).
C. Magnitude of acceleration vector is \( \frac{v^{2}}{R} \), where \( v \) is th velocity of particle
D. Magnitude of the velocity of particle is \( 8 \mathrm{m} / \mathrm{s} \)
Subject: Maths
\( \boldsymbol{a}^{\boldsymbol{x}}=\boldsymbol{b}, \boldsymbol{b}^{\boldsymbol{y}}=\boldsymbol{c}, \boldsymbol{c}^{\boldsymbol{z}}=\boldsymbol{a} \)
Find the value of \( x, y, z \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. Not valid
c. -1
D.
Subject: Physics
An \( 1800 W \) toaster, a \( 1.3 K W \) electric
fan and \( 100 W \) lamp are plugged in the same \( 120 V \) circuit i.e., all the three
devices are in parallel. What is the approximate value of the total current
(i.e. sum of the current drawn by the
three devices) through circuit?
A \( .40 A \)
в. \( 120 A \)
\( c .18 A \)
D. \( 27 A \)
Subject: Maths
Obtain the mean and standard
deviation for the following data set:
\[
x
\]
२० \( \begin{array}{lll}\text { 30 } & \text { 40 } & \text { 50 }\end{array} \) 10
\( Y \) \( \begin{array}{llll}05 & 15 & 30 & 35\end{array} \)
Subject: Physics
is the Moment of inertia of \( \triangle A B C \)
(equilateral) about and an axis passing through 0 (D,E,F are midpoints). And
point 0 is the center of \( \triangle A B C . I_{o} \) is a
moment of inertia of a remaining
triangle when \( \triangle \) DEF is cut from \( \triangle A B C \).
A \( \cdot \frac{15}{16} I \)
в. \( \frac{3}{1} I \)
c. \( \frac{I_{o}}{4} \)
D. \( \frac{16}{15} I \)
Subject: Physics
If the gravitational constant is expressed in terms of dynesm\( ^{-2} \boldsymbol{k g}^{2} \)
how will the value of G change:
A \( .6 .67 \times 10^{-11} \) dynes \( k g^{2} m^{-2} \)
B . \( 6.67 \times 10^{-8} \) dynes \( k g^{2} m^{-2} \)
c. \( 6.67 \times 10^{-6} \) dynes \( k g^{2} m^{-2} \)
D. \( 6.67 \times 10^{-3} \) dynes \( \operatorname{kg}^{2} m^{-2} \)
Subject: Biology
Oxidative decarboxylation of pyruvic acid results in the formation of
I. Acetyl CoA
Il. \( C O_{2} \)
III. ATPIV. NADH \( +\boldsymbol{H}^{+} \)
A. I only
B. I and II only
c. I, Il and III only
D. I, II and IV only
E. III and IV only
Subject: Physics
The equation of a transverse wave travelling along positive \( X \) axis with amplitude \( 0.2 m, \) velocity \( 360 m / s \) and wavelength 60 m can be written as:
A \( \cdot y=0.2 \sin \pi\left[6 t+\frac{x}{60}\right] \)
B. \( y=0.2 \sin \pi\left[6 t-\frac{x}{60}\right] \)
c. \( y=0.2 \sin 2 \pi\left[6 t-\frac{x}{60}\right] \)
D. \( y=0.2 \sin 2 \pi\left[6 t+\frac{x}{60}\right. \)
Subject: Physics
A horizontal uniform glass tube of \( 100 \mathrm{cm} \) length is sealed at both ends contains 10 \( \mathrm{cm} \) mercury column in the middle the
temperature and pressure of air on either side of mercury column are respectively \( 31^{0} \mathrm{C} \) and \( 76 \mathrm{cm} \) of mercury if the air
column at one end is kept at \( 0^{0} \mathrm{C} \) and the other end at \( 273^{0} \mathrm{C} \) the pressure of
air which is at \( 0^{0} \mathrm{C} \) is (in \( \mathrm{cm} \) of \( \mathrm{Hg} \) )
A. 76
B. 88.2
c. 102.4
D. 122
Subject: Physics
A light source is placed \( 100 \mathrm{cm} \) away from a screen. A converging lens placed at a certain position between the source and the screen focuses the image of the source on the screen. The lens is moved
a distance of \( 40 \mathrm{cm} \) and it is found that
it again focuses the image of the source on the screen. The focal length of the lens is
\( A \cdot 21 \mathrm{cm} \)
B. 30 cm
c. \( 40 \mathrm{cm} \)
D. \( 67 \mathrm{cm} \)
Subject: Physics
If \( c \) is the speed, \( \nu \) is frequency and \( \lambda \) is wavelength of EM waves, then
A \( . c=\nu \lambda \)
B. \( \frac{\lambda}{\nu}=c \)
c. \( \frac{\nu}{\lambda}=c \)
D. \( \frac{1}{\lambda}=\frac{c}{\nu} \)
Subject: Maths
The angles \( A, B, C, D \) in the
parallelogram ABCD are
\( \mathbf{A} \cdot 90^{\circ}, 90^{\circ}, 90^{\circ}, 90^{\circ} \)
В \( \cdot 90^{\circ}, 45^{\circ}, 30^{\circ}, 15^{\circ} \)
c. \( 30^{\circ}, 60^{\circ}, 20^{\circ}, 40^{\circ} \)
D. \( 90^{\circ}, 45^{\circ}, 15^{\circ}, 20^{\circ} \)
Subject: Physics
Fig shows some of the equipotential
surfaces of the magnetic scalar potential
The magnetic field \( B \) at a point in the
region is:
A \( \cdot 2 \times 10^{-3} T \)
B . \( 4 \times 10^{-4} T \)
c. \( 2 \times 10^{-4} T \)
D. \( 4 \times 10^{-3} T \)
Subject: Maths
If \( \cos ^{-1} x+\cos ^{-1} y=2 \pi \) then
\( \sin ^{-1} x+\sin ^{-1} y= \)
\( A \cdot \pi \)
в. \( -\pi \)
\( c \cdot \frac{\pi}{2} \)
D. None of these
Subject: Physics
A charged particle 'q' lies at 'P' and the line \( \mathrm{PC} \) is perpendicular to the surface of \( A B C \) (part of disc). Find the flux passing through the surface ABC.
A \( \cdot \frac{q}{4 \varepsilon_{0}} \)
в. \( \frac{q}{16 \varepsilon_{0}} \)
c. \( \frac{q}{32 \varepsilon_{0}} \)
D. \( \frac{q}{48 \varepsilon_{0}} \)
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{\sin (a+1) x+\sin x}{x} \text { if } x<0 \\ \frac{\left(x+b x^{2}\right)^{\frac{1}{2}-x^{\frac{1}{2}}}}{b x^{3 / 2}} \text { if } x>0\end{array}\right. \)
\( f(0)=c \) is continuous at \( x=0 \) then
A \( \cdot a=\frac{-3}{2}, c=\frac{1}{2}, b \neq 0 \)
B \cdot \( a=b=\frac{1}{2}, c=0 \)
C \( \cdot a=b=\frac{1}{2}, c=0 \)
D \( \cdot a=\frac{1}{2} b \neq 0 c=1 \)
Subject: Maths
\( 2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x) \) then
\( \boldsymbol{x}=? \)
\( \mathbf{A} \cdot \pi / 4 \)
в. \( \pi / 6 \)
c. \( \pi / 2 \)
D. no solution
Subject: Maths
Given \( : f(x)=4 x^{3}-6 x^{2} \cos 2 a+ \)
\( 3 x \sin 2 a \cdot \sin 6 a+\sqrt{\ln \left(2 a-a^{2}\right)} \) then
A. \( f(x) \) is not defined at \( x=\frac{1}{2} \)
B \( \cdot f^{\prime}\left(\frac{1}{2}\right)<0 \)
C \( \cdot f^{\prime}(x) \) is not defined at \( x=\frac{1}{2} \)
D \( \cdot f^{\prime}\left(\frac{1}{2}\right)>0 \)
Subject: Maths
The \( D . E \) of the family of circles
touching \( X- \) axis at (0,0) is
The \( D . E \) of the family of circle passing through the origin and having their centre on \( \boldsymbol{Y}-\boldsymbol{a} \boldsymbol{x} \boldsymbol{i} \boldsymbol{s} \) is
A \( \cdot \frac{d y}{d x}=\frac{2 x y}{x^{2}-y^{2}} \)
в. \( \frac{d y}{d x}=\frac{x^{2}-y^{2}}{2 x y} \)
c. \( \frac{d y}{d x}=x^{2}-y^{2} \)
D. \( \frac{d y}{d x}+\frac{x}{y}=0 \)
Subject: Maths
\( \operatorname{Let} A=\left|\begin{array}{ll}\mathbf{5} & \mathbf{0} \\ \mathbf{1} & \mathbf{0}\end{array}\right| \) and \( \boldsymbol{B}=\left|\begin{array}{ll}\mathbf{2 0} & \mathbf{5} \mid \\ -\mathbf{1} & \mathbf{0}\end{array}\right| \)
\( \mathbf{4} \boldsymbol{A}+\mathbf{5} \boldsymbol{B}-\boldsymbol{C}=\mathbf{0}, \) then \( \boldsymbol{C} \) is
\( \mathbf{A} \cdot\left|\begin{array}{cc}5 & 25 \\ -1 & 0\end{array}\right| \)
\( \mathbf{B} \cdot\left|\begin{array}{cc}120 & 25 \\ -1 & 0\end{array}\right| \)
\( \mathbf{c} \cdot\left|\begin{array}{cc}5 & -1 \\ 0 & 25\end{array}\right| \)
\( \mathbf{D} \cdot\left|\begin{array}{cc}5 & 25 \\ -1 & 5\end{array}\right| \)
Subject: Biology
Assertion
Heavy metals such as cadmium,
mercury, nickel etc. are water
pollutants.
Reason
Heavy metals are not harmful to
humans.
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
Let \( R \) be the relation on \( Z \) defined by
\( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{Z}, \boldsymbol{a}-\boldsymbol{b} \) is an
integer \( \} . \) Find the domain and range of
\( \mathrm{R} \)
Subject: Maths
The coordinates of the point which is
equidistant from the three vertices of the \( \Delta A O B \) as shown in the given
figure
\( \mathbf{A} \cdot(x, y) \)
B . \( (y, x) \)
c. \( \frac{x}{2}, \frac{y}{2} \)
D. \( \frac{y}{2}, \frac{x}{2} \)
Subject: Physics
A non-zero vector \( \vec{a} \) is parallel to the line
of intersection of the plane \( \boldsymbol{P}_{1} \) determined by \( \hat{i}+\hat{j} \) and \( \hat{i}-2 \hat{j} \) and plane \( P_{2} \) determined by vector \( 2 \hat{i}+ \) \( \hat{j} \) and \( 3 \hat{i}+2 \hat{k}, \) then angle between \( \vec{a} \) and vector \( \hat{i}-2 \hat{j}+2 \hat{k} \) is
A \( \cdot \frac{\pi}{4} \)
в.
\( c \cdot \frac{\pi}{3} \)
D. \( \pi \)
Subject: Maths
Let \( \boldsymbol{A}=\{\boldsymbol{p}, \boldsymbol{q}, \boldsymbol{r}\} . \) Which of the following
is an equivalence relation in \( A \) ?
A \( \cdot R_{1}=\{(p, q),(q, r),(p, r),(p, p)\} \)
B . \( R_{2}=\{(r, q),(r, p),(r, r),(q, q)\} \)
C . \( R_{3}=\{(p, p),(q, q),(r, r),(p, q)\} \)
D. None of these
Subject: Physics
He was a professor of mathematics at St. Petersburg University, Prof. of anatomy and physics at the University of Groningen, and prof. of physics, anatomy and botany at the University of Basle. But he is most famous for what is
known as 'Bernouilli's theorem'. Name
the outstanding mathematician- of a
well-known Swiss family.
A. Johann Bernouill
B. Jacob Bernouilli
c. Danial Bernouill
D. None of these
Subject: Chemistry
In sulphur detection of an organic compound, sodium nitropruside solution is added to sodium extract.
Formation of violet colour is due to the
formation of:
A \( \cdot \operatorname{Na}_{3} \) Fe \( (C N)_{6} \)
B . \( \operatorname{Na}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS} \mathrm{Na}\right] \)
c. \( \operatorname{Na}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NS}\right] \)
D. \( F e(C N S)_{3} \)
Subject: Physics
A magnet of dipole moment \( 2 A m^{2} \) is
deflected through \( 30^{\circ} \) from magnetic meridian. The required deflecting
torque is \( \left(B_{H}=0.4 \times 10^{-4} T\right) \)
A \( \cdot 0.4 \times 10^{-4} \mathrm{Nm} \)
B. \( 0.4 \mathrm{Nm} \)
c. \( 0.2 \times 10^{-4} N m \)
D. None of these
Subject: Biology
Nirenberg synthesized an mRNA containing 34 poly-Adenine (A-A-A-A-A\( \left.A^{-}-\cdots-\right) \) and found a polypeptide formed of 11 poly-lysine this proved that genetic code for lysine was
A. One-adenine
B. A-A doublet
c. A-A-A triplet
D. Many adenines
Subject: Physics
Figure shows \( (x, t),(y, t) \) diagram of a
particle moving in 2-dimensions. If the particle has a mass of \( 500 \mathrm{g} \), the force acting on the particle is
A. \( 1 \mathrm{N} \) along \( \mathrm{y} \) -axis
B. 1 N along x-axis
c. \( 0.5 \mathrm{N} \) along \( \mathrm{x} \) -axis
D. 0.5 N along y-axis
Subject: Chemistry
The wave number of first line of Balmer
series of hydrogen is \( 15200 \mathrm{cm}^{-1} . \) The
wave number of the first Balmer line of
\( L i^{2+} \) ion is:
A \( \cdot 15,200 \mathrm{cm}^{-1} \)
В. \( 60,800 \mathrm{cm}^{-1} \)
c. \( 76,000 \mathrm{cm}^{-1} \)
D. \( 1,36,800 \mathrm{cm}^{-1} \)
Subject: Chemistry
Oxidation numbers of \( M n \) in its
compounds \( M n C l_{2}, M n(O H)_{3} \)
\( M n O_{2} \) and \( K M n O_{4} \) respectively are:
\( A \cdot+2,+4,+7,+3 \)
B. +2,+3,+4,+7
\( c \cdot+7,+3,+2,+4 \)
\( D \cdot+7,+4,+3,+2 \)
Subject: Maths
\begin{tabular}{|ccc} 
if \( \boldsymbol{f}(\boldsymbol{x})= \) & \\
\( \mathbf{1} \) & \( \boldsymbol{x} \) & \( \boldsymbol{x}+ \) \\
\( \boldsymbol{2} \boldsymbol{x} \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( (\boldsymbol{x}+ \) \\
\( \boldsymbol{3} \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2}) \) & \( (\boldsymbol{x}+\mathbf{1}) \boldsymbol{x} \)
\end{tabular}
then \( f(100) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
\( c .100 \)
D. -
Subject: Physics
The frequency of a source is \( 20 \mathrm{kHz} \). The frequencies of sound wave produced by it in water and air will be :
A. Same as that of source \( \simeq 20 \mathrm{kHz} \)
B . > 20 kHz
\( \mathrm{c} .<20 \mathrm{kHz} \)
D. Depends upon velocity
Subject: Chemistry
Identify the conjugate acids and bases in the following equation:
\( N H_{3}+H_{2} O \rightleftharpoons N H_{4}^{+}+O H^{-} \)
A \( \cdot\left(H_{2} O, O H^{-}\right) \) and \( \left(N H_{2}^{+}, N H_{3}\right) \)
B . \( \left(H_{2} O, O H^{-}\right) \) and \( \left(N H_{4}^{+}, N H_{2}^{2-}\right) \)
c. \( \left(H_{2} O, O H\right) \) and \( \left(N H_{3}, N H_{4}\right) \)
D. \( \left(H_{2} O, O H^{-}\right) \) and \( \left(N H_{4}^{+}, N H_{3}\right) \)
Subject: Maths
A cylindrical vessel \( 60 \mathrm{cm} \) in diameter is partially filled with water. A sphere, \( 54 \mathrm{cm} \) in diameter is gently dropped into the vessel. To what further height will water rise in the cylinder?
A \( .20 .02 \mathrm{cm} \)
B . \( 30.29 \mathrm{cm} \)
c. \( 29.16 \mathrm{cm} \)
D. \( 25 \mathrm{cm} \)
Subject: Physics
In a hydraulic lift, used at a service station the radius of the large and small piston are in the ratio of \( 20: 1 . \) What
weight placed on the small piston will be sufficient to lift a car of mass \( 1500 k g ? \)
A. \( 3.75 k g \)
в. \( 37.5 k g \)
c. \( 7.5 k g \)
D. \( 75 k g \)
Subject: Chemistry
Which of the following is an example of
weak electrolyte?
A \( \cdot C H_{3} C O O H \rightarrow C H_{3} C O O^{-}+H^{+} \)
в. \( K O H \rightarrow K^{+}+O H^{-} \)
\( \mathrm{c} \cdot A g N O_{3} \rightarrow A g^{+}+N O_{3} \)
D. all of the above
Subject: Chemistry
If the radius of first Bohr orbit is \( x, \) then
de Broglie wavelength of an electron in
\( 4^{t h} \) orbit is nearly:
\( \mathbf{A} \cdot 6 \pi x \)
в. \( 16 \pi x \)
\( c .8 \pi x \)
D. None of these
Subject: Maths
State true or false:
Let \( \left|\left(\bar{z}_{1}-2 \bar{z}_{2}\right) /\left(2-z_{1} \bar{z}_{2}\right)\right|=1 \) and
\( \left|z_{2}\right| \neq 1, \) where \( z_{1} \) and \( z_{2} \) are complex
numbers, then \( \left|z_{1}\right|=2 \)
Subject: Maths
If \( z=\frac{-1}{2}+i \frac{\sqrt{3}}{2}, \) then \( 8+10 z+7 z^{2} \) is
equal to:
A \( \cdot-\frac{1}{2}-i \frac{\sqrt{3}}{2} \)
B \( \cdot \frac{1}{2}+i \frac{\sqrt{3}}{2} \)
\( ^{\mathrm{C}}-\frac{1}{2}+i \frac{3 \sqrt{3}}{2} \)
D. \( \frac{\sqrt{3}}{2} \)
E \( -\frac{\sqrt{3}}{2} i \)
Subject: Chemistry
Using the Gibbs change, \( \Delta G^{o}= \)
\( +63.3 k J, \) for the following reaction, the
\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C} \boldsymbol{O}_{3}(s) \) in water at \( \boldsymbol{2} \boldsymbol{5}^{o} \boldsymbol{C} \) is :
\( A g_{2} C O_{3}(g) \rightleftharpoons 2 A g^{+}(a q)+C O_{3}^{2-}(a q) \)
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)
A. \( 3.2 \times 10^{-26} \)
B. \( 8.0 \times 10^{-12} \)
c. \( 2.9 \times 10^{-3} \)
D. \( 7.9 \times 10^{-2} \)
Subject: Physics
A uniform conduction wire of length
\( 10 g \) and resistance \( R \) is wound up into
four turns as a current carrying coil in
the shape of equilateral triangle of side
\( a . \) If current \( I \) is flowing through the coil
then the magnetic moment of the coil is
A \( \cdot \frac{\sqrt{3}}{2} a^{2} I \)
B. \( \frac{a^{2} I}{\sqrt{3}} \)
c. \( \sqrt{3} a^{2} I \)
D. \( \frac{2 a^{2} I}{\sqrt{3}} \)
Subject: Maths
From a well shuffled pack of 52 playing cards two cards drawn at random. The
probability that either both are red or both are kings is:
\( ^{\mathrm{A}} \cdot \frac{\left(^{26} C_{2}+^{4} C_{2}\right)}{^{52} C_{2}} \)
B. \( \frac{\left(^{26} C_{2}+^{4} C_{2}-^{2} C_{2}\right)}{^{52} C_{2}} \)
\( ^{\mathrm{c}} \cdot \frac{30}{^{52} C_{2}} \)
D. \( \frac{39}{52} C_{2} \)
Subject: Physics
The room temperature is \( +20^{\circ} \mathrm{C} \) when
outside temperature is \( -20^{\circ} \mathrm{C} . \) Room
temperature is \( +10^{\circ} \mathrm{C} \) when outside
temperature is \( -40^{\circ} \mathrm{C} \). The
temperature of the radiator heating the
room is:
A \( \cdot 70^{\circ} \mathrm{C} \)
В. \( 60^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 50^{\circ} \mathrm{C} \)
D. \( 40^{\circ} \mathrm{C} \)
Subject: Physics
In a hydraulic lift, used at a service station the radius of the large and small
piston are in the ratio of \( 20: 1 . \) What
weight placed on the small piston will be sufficient to lift a car of mass
\( 1500 k g ? \)
A. \( 3.75 k g \)
в. \( 37.5 k g \)
c. \( 7.5 k g \)
D. \( 75 k g \)
Subject: Biology
How many of the following statements
are correct?
(i) Axillary buds are present in axil of leaflets
(ii) In Salvia filaments of stamens are
same length.
(iii) Apocarpous condition can be seen in lotus and rose.
(iv)Endospermous seeds can be seen in solanaceae.
(v) Sterile stamens are called
staminodes.
A. Three
B. Four
c. Two
D. one
Subject: Physics
A ball with a weight of 20 N is thrown vertically upward. What is the acceleration of the ball just as it
reaches the top of its path?
A. \( 10 m / s^{2} \) downward
B. \( 10 \mathrm{m} / \mathrm{s}^{2} \) upward
c. \( 20 m / s^{2} \) downward
D. \( 20 m / s^{2} \) upward
E. zero
Subject: Maths
If the matrix \( \left[\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} & \mathbf{3} \\ \mathbf{2} & \boldsymbol{b} & \mathbf{- 1} \\ \boldsymbol{c} & \mathbf{1} & \mathbf{0}\end{array}\right] \) is a skew
symmetric matrix, find \( a, b \) and \( c \)
Subject: Physics
On comparing the emf's \( E_{1} \) and
\( \boldsymbol{E}_{2}\left(\boldsymbol{E}_{1}>\boldsymbol{E}_{2}\right) \) of two cells by a
potentiometer, the balancing lengths
come out to be \( l_{1} \) and \( l_{2} \) respectively,
then
A \( \cdot l_{1}<l_{2} \)
В. \( l_{1}-l_{2} \)
c. \( l_{1}>l_{2} \)
D. none of the above
Subject: Maths
Directions: In following quesiton, choose the missing term out of the given alternatives Reference:
\( A B C D E F G H I J K L M \)
N O P Q R ST U V W X Y Z
\( Z, X, V, T, R, \dots \dots \)
A. \( O, K \)
в. \( N, M \)
c. \( K, S \)
D. \( M, N \)
E . \( P, N \)
Subject: Chemistry
A neutral organic compound A has
formula \( C_{9} H_{16} O_{3} \) and rotates plane
polarized light. A on acid hydrolysis
produces \( \mathrm{B} \) and \( C\left(C_{3} H_{8} O\right) . \) C on partial
oxidation with PCC gives \( D\left(C_{3} H_{6} O\right) \) which does not give iodoform test. D on treatment with dilute solution of
\( N a O H \operatorname{gives} E\left(C_{6} H_{12} O_{2}\right) \) which is
diastereomeric. E on treatment with the
acidic solution of \( K M n O_{4} \) produces \( B \)
Deduce structures of A to E.
Subject: Physics
The work function of a metal in \( 4 e V . \) For
the emission of photoelectrons of zero velocity from the metal surface, the wavelength of the incident radiation should be
\( \mathbf{A} \cdot 1700 \hat{A} \)
в. 2700 А
\( c \cdot 3100 \hat{A} \)
D \( \cdot 5900 \),
Subject: Maths
If \( I=\int_{0}^{2 \pi} e^{x / 2} \sin \left(\frac{x}{2}+\frac{\pi}{4}\right) d x, \) then \( I \)
equals
\( A \)
B.
\( \mathbf{c} \cdot-\pi / 2 \)
D. \( 2 \pi \)