AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A loop carrying a current \( i \), lying in the
plane of the paper, is in the field of a
long straight wire with current \( \boldsymbol{i}_{0} \) (inward) as shown in figure. If the
torque acting on the loop is given by
\( \tau=\frac{\mu_{0} i i_{0}}{x \pi r}[\sin \theta](b-a) . \) Find \( x \)
Subject: Maths
\( \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{3} & \mathbf{2} \\ -\mathbf{1} & \mathbf{4}\end{array}\right), \boldsymbol{B}=\left(\begin{array}{cc}-\mathbf{2} & \mathbf{5} \\ \mathbf{6} & \mathbf{7}\end{array}\right) \) and
\( C=\left(\begin{array}{cc}1 & 1 \\ -5 & 3\end{array}\right), \) then verify that
\( \boldsymbol{A}(\boldsymbol{B}+\boldsymbol{C})=\boldsymbol{A} \boldsymbol{B}+\boldsymbol{A} \boldsymbol{C} \)
Subject: Physics
Two cars \( A \) and \( B \) are running at
velocities of \( 60 \mathrm{km} h^{-1} \) and \( 45 \mathrm{km} h^{-1} \)
What is the relative velocity of car \( A \) with respect to car \( \mathrm{B} \), if both are moving eastward?
A \( \cdot 15 \mathrm{km} h^{-1} \)
B. \( 45 \mathrm{km} h^{-1} \)
\( c \cdot 60 \mathrm{km} h^{-1} \)
D. \( 105 \mathrm{km} h^{-1} \)
Subject: Physics
The maximum stress that can be
applied to the material of a wire
employed to suspend an elevator is \( \frac{3}{\pi} \times 10^{8} N / m^{2} . \) If the mass of the
elevator is \( 900 \mathrm{kg} \) and it moves up with
an acceleration of \( 2.2 m / s^{2} \) then calculate the minimum radius of the
wire.
Subject: Physics
Force acting on a block is \( \boldsymbol{F}=(-4 x+ \)
8). Here \( F \) is in Newton and \( x \) the position of block on \( x \) -axis in meters
A. motion of the block is periodic but not simple harmonic
B. motion of the block is not periodic
c. motion of the block is simple harmonic about origin, \( x=0 \)
D. motion of the block is simple harmonic about \( x=2 m \).
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\int_{0}^{x}\{1+|1-t|\} d t & \text { if } x>2 \\ \mathbf{5 x - 7} & \text { if } x \leq 2\end{array} \) then \right.
A. \( f \) is not continuous at \( x=2 \)
B. \( f \) is continuous but not differentiable at \( x=2 \)
c. \( f \) is differentiable everywhere
D \( \cdot f^{\prime}(2+) \) doesn't exist
Subject: Maths
Find the mean variance and standard
deviation using short-cut method
\( \begin{array}{ll}\begin{array}{l}\text { Height } \\ \text { in cms }\end{array} & \text { No. of children } \\ \text { 70-75 } & 3 \\ \text { 75-80 } & 4 \\ 80-85 & 7 \\ \text { 85-90 } & \text { 7 } \\ \text { 90-95 } & 15 \\ \text { 95-100 } & 9 \\ \text { 100-105 } & 6 \\ \text { 105-110 } & 6 \\ \text { 110-115 } & \text { 3 }\end{array} \)
Subject: Physics
A hydraulic machine exerts a force of \( 900 \mathrm{N} \) on a piston of diameter \( 1.80 \mathrm{cm} \) The output force is exerted on a piston of diameter \( 36 \mathrm{cm} . \) What will be the output force?
\( \mathbf{A} \cdot 12 \times 10^{4} N \)
В . \( 16 \times 10^{4} N \)
\( \mathbf{c} \cdot 36 \times 10^{4} N \)
D. \( 38 \times 10^{4} N \)
Subject: Chemistry
All the systems are closed system and at equilibrium. A decrease in the total volume of each container will increase
the number of moles of product(s) for which system?
A \( \cdot 2 N H_{3}(g) \rightleftharpoons N_{2}(g)+3 H_{2}(g) \)
B . \( H_{2}(g)+C l_{2}(g) \rightleftharpoons 2 H C l(g) \)
c. \( 2 N O(g)+O_{2}(g) \rightleftharpoons 2 N O_{2}(g) \)
D. \( \operatorname{CO}(g)+H_{2} O(g) \rightleftharpoons C O_{2}(g)+H_{2}(g) \)
E \( \cdot F e_{3} O_{4}(s)+4 H_{2}(g) \rightleftharpoons 3 F e(s)+4 H_{2} O(g) \)
Subject: Maths
A balloon which always remains spherical, has a variable diameter \( \frac{3}{2}(2 x+3) . \) The rate of change of volume with respect to \( x \) will be
A \( \cdot \frac{27 \pi}{8}(2 x-3)^{2} \)
в. \( \frac{27 \pi}{8}(2 x+3)^{2} \)
c. \( \frac{27 \pi}{8}(3 x-2)^{2} \)
D. \( \frac{8}{27 \pi}(2 x+3)^{2} \)
Subject: Maths
\( \operatorname{Given} \frac{x-x \tan ^{2} 30^{\circ}}{1+\tan ^{2} 30^{\circ}}=\sin ^{2} 30^{\circ}+ \)
\( 4 \cot ^{2} 45^{\circ}-\sec ^{2} 45^{\circ} . \) Then the value of
\( \boldsymbol{x} \)
\( A \cdot \frac{3}{2} \)
в. \( \frac{5}{2} \)
\( c \cdot \frac{9}{2} \)
D. none of these
Subject: Maths
\( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x}{\cos ^{-1}\left[\frac{1}{4}(3 \sin x-\sin 3 x)\right]} \)
D denotes integer function, is-
A \( \cdot \frac{\sqrt{2}}{\pi} \)
B. 1
\( c \cdot \frac{4}{\pi} \)
D. does not exist
Subject: Maths
The resultant complex number when \( (4+6 i) \) is divided by \( (10-5 i) \) is
A \( \cdot \frac{2}{25}+\frac{16}{25} i \)
B \( \cdot \frac{2}{25}-\frac{16}{25} i \)
c. \( \frac{2}{5}+\frac{6}{5} \)
D. \( \frac{2}{5}-\frac{6}{5} \)
Subject: Chemistry
Assertion
Benzyl bromide when kept in acetone
and \( H_{2} O \) produces benzyl alcohol.
Reason
The reaction follows \( S_{N} 2 \) mechanism.
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 are correct
Subject: Physics
For which of the following dependence of
drift velocity \( v_{d} \) on electric field \( \mathrm{E} \), is
Ohm's law obeyed?
A \( \cdot v_{d} \propto E^{2} \)
B. \( v_{d}=E^{1 / 2} \)
\( \mathbf{c} \cdot v_{d}= \) constant
D. \( v_{d} \propto E \)
Subject: Maths
\( f\left(\frac{1+i}{1-i}\right)^{3}-\left(\frac{1-i}{1+i}\right)^{3}=A+i B \)
\( \operatorname{then} A, B= \)
A . 0,2
B. 0,-2
\( c .2,0 \)
D. -2,0
Subject: Maths
If the system of equations of \( 3 x-2 y+ \)
\( \boldsymbol{z}=\mathbf{0}, \boldsymbol{k} \boldsymbol{x}-\mathbf{1 4} \boldsymbol{y}+\mathbf{1 5 z}=\mathbf{0}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+ \)
\( \mathbf{3} z=\mathbf{0} \) has non trivial solution then \( \boldsymbol{k}= \)
A . 29
B . 26
\( c \cdot 23 \)
D. 19
Subject: Physics
A girl stands on a box having \( 60 \mathrm{cm} \) length, \( 40 \mathrm{cm} \) breadth and \( 20 \mathrm{cm} \) width in three ways. The pressure exerted by the box will be:
A. maximum when length and breadth form the base
B. maximum when breadth and width form the base
c. maximum when width and length form the base
D. the same in all the above three cases
Subject: Maths
Find the value of \( x \) which satisfy
equation \( : 2 \tan ^{-1}(\cos x)= \)
\( \tan ^{-1}(2 \csc x) \)
A \( \cdot x=n \pi+\frac{\pi}{4} \)
B \cdot \( x=n \pi-\frac{\pi}{4} \)
c. \( x=n \pi+\frac{\pi}{2} \)
D. \( x=n \pi-\frac{\pi}{2} \)
Subject: Chemistry
An acid-base indicator has \( \boldsymbol{K}_{\boldsymbol{H} \text { In }}= \)
\( 3.0 \times 10^{-5} . \) The acid form of the
indicator is red and the basic form is
blue. The change in \( \left[\boldsymbol{H}^{+}\right] \) required to
change the indicator from \( 75 \% \) red to
\( 75 \% \) blue is:
A \( \cdot 8 \times 10^{-5} \) М
В. \( 9 \times 10^{-5} \) М
c. \( 1 \times 10^{-5} \) М
D. \( 3 \times 10^{-4} \mathrm{M} \)
Subject: Maths
On the ellipse, \( 9 x^{2}+25 y^{2}=225, \) find
the point whose distance to the focus
\( F_{1} \) is four times the distance to the
other focus \( \boldsymbol{F}_{2} \)
\( \mathbf{A} \cdot[-15, \sqrt{63}] \)
\( ^{\text {В }} \cdot\left(\frac{-15}{4}, \frac{\sqrt{63}}{2}\right) \)
\( ^{\mathrm{c}} \cdot\left(\frac{-15}{4}, \frac{\sqrt{63}}{4}\right) \)
D. \( \left(\frac{-15}{2}, \frac{\sqrt{63}}{2}\right) \)
Subject: Maths
The angles is to be bisected to obtain an
angle of \( 90^{0} \) is
A \( \cdot 60^{0} \) and \( 45^{0} \)
B. \( 60^{0} \) and \( 120^{\circ} \)
\( \mathrm{c} \cdot 120^{0} \) and \( 180^{\circ} \)
D. \( 30^{\circ} \) and \( 60^{\circ} \)
Subject: Physics
A hollow smooth uniform sphere \( \boldsymbol{A} \) of
mass \( m \) rolls without sliding on a
smooth horizontal surface. It collides
elastically and head-on with another
stationary smooth hollow sphere \( \boldsymbol{B} \) of
the same mass mm and same radius.
The ratio of the kinetic energy of \( \boldsymbol{B} \) to that of \( A \) just after the collision is
A . 1: 1
B. 2: 3
\( c \cdot 3: 2 \)
D. None
Subject: Maths
Each year for 4 years, a farmer increased the number of trees in a certain orchard by \( \frac{1}{4} \) of the number of trees in the orchard the preceding year.
If all of the trees thrived and there were
6,250 trees in the orchard at the end of
the 4 -year period, how many trees were in the orchard at the beginning of the 4 year period?
A . 1250
B. 1563
\( \mathbf{c} .2250 \)
D. 2560
E . 2752
Subject: Maths
Find the differential equation corresponding to the family of curves
\( y=k(x-k)^{2} \) where \( k \) is an arbitrary
constant.
\( ^{\mathbf{A}} \cdot\left(\frac{d y}{d x}\right)^{3}-4 x y \frac{d y}{d x}+8 y^{2}=0 \)
\( ^{\mathrm{B}}\left(\frac{d y}{d x}\right)^{3}+4 x y \frac{d y}{d x}+8 y^{2}=0 \)
\( ^{\mathrm{c}}\left(\frac{d y}{d x}\right)^{3}-2 x y \frac{d y}{d x}+8 y^{2}=0 \)
\( ^{\mathrm{D} \cdot}\left(\frac{d y}{d x}\right)^{3}+2 x y \frac{d y}{d x}+8 y^{2}=0 \)
Subject: Chemistry
The elements of one period are given below in order from left to right
\( \boldsymbol{L} \boldsymbol{i}, \boldsymbol{B} \boldsymbol{e}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{O}, \boldsymbol{F}, \boldsymbol{N} \boldsymbol{e} \)
Which is the missing element?
A . Na a
B.
c. \( c 1 \)
\( D \)
Subject: Maths
An ellipse \( \frac{x^{z}}{4}+\frac{y^{z}}{3}=1 \) confocal with
hyperbola \( \frac{x^{2}}{\cos ^{2} \theta}-\frac{y^{2}}{\sin ^{2} \theta}=1 \) then the
set of value of \( ^{\prime} \mathbf{0}^{\prime} \)
A. \( R \)
В . \( R-\{n \pi, n \epsilon z\} \)
\( ^{\mathrm{c}} \cdot_{R}-\left\{(2 n+1) \frac{\pi}{2}, n \epsilon z\right\} \)
D. \( _{R-}\left\{\frac{n \pi}{2}, n \epsilon z\right\} \)
Subject: Chemistry
At \( 30^{\circ} C, \) the degree of dissociation of
\( \mathbf{0 . 0 6 6} \boldsymbol{M} \boldsymbol{H} \boldsymbol{A} \) is \( \mathbf{0 . 0 1 4 5 .} \) The degree of
dissociation of \( 0.02 M \) solution of acid
at the same temperature is \( x, \) then find
the value of \( x \times 100 \) to the nearest
integer
Subject: Chemistry
gram sample of \( N H_{4} N O_{3} \) is decomposed in a bomb calorimeter. The temperature of the calorimeter increases by 6.12 K. The heat capacity of the system is 1.23 kJ/g-deg. What is the molar heat of decomposition for
\( N H_{4} N O_{3} ? \)
A . -7.53 kJ/mol
B. -398.1 kJ/mol
c. - -16.1 kJ/mol
D. 602 kJ/mol
Subject: Chemistry
The hybrid states of phosphorous atoms
in \( P C l_{5} \) and \( P B r_{3} \) in gaseous phase
\( \operatorname{are} s p^{3} d . \) But in solid \( P C l_{5} \)
phosphorous shows \( s p^{3} d^{2} \) hybrid state. While \( P \) in \( P B r \) is in \( s p^{3} \) hybrid state. This is because:
This question has multiple correct options
A. \( P C l_{5} \) in solid form exists as \( \left[P C l_{4}\right]^{+}\left[P C l_{6}\right] \)
B. \( P B r_{5} \) in solid form exists as \( \left[P C l_{4}\right]^{+}\left[P B r_{6}\right]^{-} \)
c. \( P C l_{5} \) in solid form exists as \( \left[P C l_{4}\right]^{+} C l^{-} \)
D. \( P B r_{5} \) in solid form exists as \( \left[P B r_{4}\right]^{+} B r^{-} \)
Subject: Maths
If \( \alpha \) is a real number for which \( f(x)= \)
\( \log _{e} \cos ^{-1} x \) is defined, then a possible
value of \( [\boldsymbol{\alpha}] \) (where [] denotes the
greatest function) is This question has multiple correct options
A . 0
B.
\( c \cdot-1 \)
D. - -
Subject: Chemistry
The efficiency of an hypothetical cell is about \( 84 \% \) which involves the following
reaction:
\( \boldsymbol{A}(s)+\boldsymbol{B}^{2+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{A}^{2+}(\boldsymbol{a} \boldsymbol{q})+ \)
\( B(s): \Delta H=-285 k J \)
Then, the standard electrode potential of the cell will be: (Assume as \( \Delta S=0 \) )
A . 1.20
B. 2.40
c. \( 1.10 v \)
D. 1.24
Subject: Maths
Find the solution of \( (2 x+y+1) d x+ \)
\( (4 x+2 y-1) d y=0 \)
A \( \cdot 2 y-x+\log (2 x+y-1)=k \)
B . \( y+x+\log (2 x+y-1)=k \)
c. \( y-x+\log (2 x+y-1)=k \)
D. \( 2 y+x+\log (2 x+y-1)=k \)
Subject: Maths
The direction cosines of the ray
\( \boldsymbol{P}(1,-2,4) \) and \( Q(-1,1,-2) \) are
A \( \cdot(-2,-3,-6) \)
B \( \cdot(2,-3,-6) \)
\( ^{C} \cdot\left(\frac{2}{7}, \frac{3}{7}, \frac{6}{7}\right) \)
D \( \cdot\left(-\frac{2}{7}, \frac{3}{7},-\frac{6}{7}\right) \)
Subject: Maths
If the slope of a line through \( (-2,3),(4, a) \) is \( \frac{-5}{3} \)
then equation of the line is.
A. \( 5 x-3 y-1=0 \)
B. \( 5 x+3 y+1=0 \)
c. \( 3 x-5 y+1=0 \)
D. \( 5 x+3 y=0 \)
Subject: Maths
The slope of the normal to the curve \( x=1-a \sin \theta, y=b \cos ^{2} \theta \) at \( \theta=\frac{\pi}{2} \) is
A \( \cdot \frac{a}{2 b b} \)
в. \( \frac{2 a}{b} \)
c. \( \frac{a}{b} \)
D. \( \frac{-a}{2 b} \)
Subject: Maths
If \( \frac{x}{y}=\frac{\cos A}{\cos B} \operatorname{then} \frac{x \tan A+y \tan B}{x+y}= \)
A. \( \cot \frac{A+B}{2} \)
B. \( \cot \frac{A-B}{2} \)
c. \( \tan \frac{A-B}{2} \)
D. \( \tan \frac{A+B}{2} \)
Subject: Maths
Which of following statements is/are
INCORRECT?
I. If \( f(x) \) and \( g(x) \) are one-one, then \( f(x)+g(x) \) is also one-one.
II. If \( f(x) \) and \( g(x) \) are one-one, then \( f(x) \cdot g(x) \) is also one-one.
III. If \( \boldsymbol{f}(\boldsymbol{x}) \) is odd, then it is necessarily
one to one.
A. I and II only
B. II and III only
c. III and I only
D. I, II and III
Subject: Maths
Find the sum of the series
\( \frac{3 \cdot 5}{5 \cdot 10}+\frac{3 \cdot 5 \cdot 7}{5 \cdot 10 \cdot 15}+\frac{3 \cdot 5 \cdot 7 \cdot 9}{5 \cdot 10 \cdot 15 \cdot 20}+ \)
\( \dots \infty \)
Subject: Maths
In what ratio does the plane \( 2 x+y- \)
\( z=3 \) divide line segment joining the
point \( \boldsymbol{a}=(\mathbf{2}, \mathbf{1}, \mathbf{3}), \boldsymbol{b}=(\mathbf{9},-\mathbf{2}, \mathbf{5}) \)
Subject: Physics
The torque of force \( \overrightarrow{\boldsymbol{F}}=(2 \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}}) \)
N acting at the point \( \vec{r}= \) \( (3 \hat{i}+2 \hat{j}+3 \hat{k}) m \) about origin is (in \( \mathrm{N}- \)
\( \mathrm{m}) \)
A . \( 6 \hat{i}-6 \hat{j}+12 \hat{k} \)
B . \( 17 \hat{i}-6 \hat{j}-13 \hat{k} \)
c. \( -6 \hat{i}+6 \hat{j}-12 \hat{k} \)
D. \( -17 \hat{i}+6 \hat{j}+13 \hat{k} \)
Subject: Physics
Using an A.C. voltmeter the potential
difference in the electrical line in a
house is read to be 234 volts. If the line
frequency is known to be 50 cycles/second, the equation for the line voltage is
A. \( V=165 \sin (100 \pi t) \)
B. \( V=331 \sin (100 \pi t) \)
c. \( V=220 \sin (100 \pi t) \)
D. \( V=420 \sin (100 \pi t) \)
Subject: Maths
The position vectors of points \( \overrightarrow{\boldsymbol{A}}, \overrightarrow{\boldsymbol{B}}, \overrightarrow{\boldsymbol{C}} \)
are respectively \( \vec{a}, \vec{b}, \vec{c} \). If \( P \) divides \( \overrightarrow{A B} \) in the ratio 3: 4 and \( Q \) divides \( \overrightarrow{B C} \) in
the ratio 2: 1 both externally then \( \overrightarrow{P Q} \)
is
A. \( \vec{b}+\vec{c}-\overrightarrow{2 a} \)
and
В . \( 2(\vec{b}+\vec{c}-\overrightarrow{2 a}) \)
c. \( 4 \vec{a}-\vec{b}-\vec{c} \)
D. \( \frac{-2 \vec{a}-\vec{b}-\vec{c}}{2} \)
Subject: Chemistry
In a buffer solution, the concentration of
\( \boldsymbol{X}^{-} \) and \( \mathrm{HX} \) are equivalent. If \( \boldsymbol{K}_{\boldsymbol{b}} \) for \( \boldsymbol{X}^{-} \)
is \( 10^{-10} \) then pH of the solution would
be:
(PMT, Rajasthan, 1997)
A \( \cdot 14 \)
B. 10
\( c \cdot 4 \)
D. 8
Subject: Physics
Write down the sequence of radiations
emitted in the following radioactive
processes. \( z+2 \boldsymbol{X}^{\boldsymbol{A}} \rightarrow_{z} \boldsymbol{Y}^{\boldsymbol{A}-\mathbf{4}} \rightarrow_{\boldsymbol{z}+\mathbf{1}} \boldsymbol{Y}^{\boldsymbol{A}-\mathbf{4}} \rightarrow_{\boldsymbol{z}-\mathbf{1}} \)
\( \boldsymbol{K}^{\boldsymbol{A}-\boldsymbol{8}} \)
A. \( \gamma-\beta-\alpha \)
B . \( \gamma-\alpha-\beta \)
c. \( \beta-\gamma-\alpha \)
D. \( \alpha-\beta-\alpha \)
Subject: Physics
The percentage errors in the measurement of mass and speed are
\( 2 \% \) and \( 3 \% \), respectively. How much will be the maximum error in the
estimation of KE obtained by
measuring mass and speed?
A . \( 5 \% \)
B. 1\%
\( c .8 \% \)
D. \( 11 \% \)
Subject: Physics
A loop carrying current \( I \) lies in the \( x \)
\( \boldsymbol{y} \) plane as shown in figure. The unit
vector \( \hat{k} \) is coming out of the plane of the paper. The magnetic moment of the
current loop is
\( \mathbf{A} \cdot a^{2} I \hat{k} \)
B \cdot \( \left(\frac{\pi}{2}+1\right) a^{2} I \hat{k} \)
c. \( -\left(\frac{\pi}{2}+1\right) a^{2} I \hat{k} \)
D. \( (2 \pi+1) a^{2} I \hat{k} \)
Subject: Maths
\( \ln \Delta A B C, \) if \( \angle A+\angle B=90^{\circ}, \cot B= \)
\( \frac{3}{4}, \) then the value of \( \tan A \) is :
A \( \cdot \frac{4}{5} \)
в. \( \frac{3}{4} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{3}{5} \)
Subject: Maths
A flag-staff stands on a tower which is on level ground. The total height of the flag-staff and tower taken together is
300 metres. The flag-staff subtends an angle of \( \tan ^{-1}\left(\frac{1}{5}\right) \) at a point \( P \) on the level ground at a distance 300 metres from the foot of the tower. The height of the tower is:
A. 100 metres
B. 200 metres
c. 250 metres
D. 300 metres
Subject: Chemistry
Assertion
The conversion of diamond into
graphite is an endothermic reaction.
Reason
The conversion of diamond into
graphite is kinetically very slow.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Physics
A sphere of mass \( m_{1} \) in motion hits
directly another sphere of mass \( m_{2} \) at
rest and sticks to it, the total kinetic
energy after collision is \( 2 / 3 \) of their total
K.E before the collision. Find the ratio
\( \boldsymbol{m}_{1}: \boldsymbol{m}_{2} \)
Subject: Chemistry
Select the correct options:
A. Due to lanthanide contraction \( Z r \) and \( H f \) have almost equal size.
B. \( d \) - and \( f \) -orbitals do not shield the nuclear charge very effectively
c. Both
(A) \( \&(\mathrm{B}) \) are correct statements.
D. Both
(A) \&
(B) are incorrect statements.
Subject: Physics
A man is stranded in the middle of a
perfectly smooth island of ice, where there is no friction between the ground
and his feet. Under these
circumstances,
A. he can reach the desired corner by throwing any object in the same direction
B. he can reach the desired corner by throwing any object in the opposite direction
C. he has no chance of reaching any corner of the island
D. he can reach the desired corner by walking on the ground in that direction
Subject: Chemistry
What is the correct relationship
between the \( p H^{\prime} s \) of isomolar solutions
of sodium oxide \( \left(p H_{1}\right), \) sodium
sulphide \( \left(p H_{2}\right), \) sodium selenide \( \left(p H_{3}\right. \)
)and sodium telluride \( \left(p H_{4}\right) ? \)
A \( . p H_{1}<p H_{2}<p H_{3}<p H_{4} \)
в. \( p H_{1}>p H_{2}>p H_{3}>p H_{4} \)
c. \( p H_{1}<p H_{2}<p H_{3} \approx p H_{4} \)
D. \( p H_{1}>p H_{2} \approx p H_{3}>p H_{4} \)
Subject: Chemistry
Which Oxide of Nitrogen is most stable?
A \( \cdot 2 N O_{2(g)} \rightleftharpoons N_{2(g)}+2 O_{2(g)} \)
\[
K=6.7 \times 10^{16} \mathrm{mol} L^{-1}
\]
B. \( 2 N O_{(g)} \rightleftharpoons N_{2(g)}+O_{2(g)} \)
\[
K=2.2 \times 10^{30}
\]
\( \mathbf{c} \cdot 2 N_{2} O_{5(g)} \rightleftharpoons 2 N_{2(g)}+5 O_{2(g)} \)
\[
K=1.2 \times 10^{34} \mathrm{mol}^{5} \mathrm{L}^{-5}
\]
D. \( 2 N_{2} O_{(g)} \rightleftharpoons 2 N_{2(g)}+O_{2(g)} \)
\[
K=3.5 \times 10^{33} \mathrm{mol} L^{-1}
\]
Subject: Maths
\( \frac{\cot \theta-\cot 2 \theta}{\cot \theta} \) is equal to
\( \mathbf{A} \cdot \frac{x}{z} \)
\( \mathbf{B} \cdot \frac{y}{z} \)
\( \mathbf{c} \cdot \frac{y}{x} \)
D. \( \frac{x}{y} \)
Subject: Physics
A closed coil with a resistance R is
placed in a magnetic field. The flux linked with the coil is \( \phi \). If the magnetic
field is suddenly reversed in direction, the charge that flows through the coil will be:
A. \( \frac{\phi}{2 R} \)
в. \( \frac{\phi}{R} \)
c. \( _{2} \frac{\phi}{R} \)
D. zero
Subject: Chemistry
Imole of \( 50 \% \) pure \( C a C_{2} \) on hydrolysis followed by passing through red hot copper tube. How many moles of benzene is formed?
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{6} \)
D. \( \frac{1}{8} \)
Subject: Maths
Express \( -\overline{\mathbf{i}}-\mathbf{3} \overline{\mathbf{j}}+\mathbf{4} \overline{\mathbf{k}} \) as a linear
combination of \( 2 \bar{\imath}+\bar{\jmath}-4 \bar{k}, 2 \bar{\imath}-\bar{\jmath}+3 \bar{k} \)
and \( 3 \bar{\imath}+\bar{\jmath}-2 \bar{k} \)
Subject: Physics
In the geiger-marsden experiment what
percentage of the \( \alpha \) particles were
deflected by an angle more than \( 1^{\circ} \)
\( \mathbf{A} \cdot<0.15 \% \)
в. \( <15 \% \)
\( \mathbf{c} .>99.85 \% \)
D. \( 100 \% \)
Subject: Biology
Name the virus and labels given in the
figure.
A. HIV (Retovira), A- Protein coats, B- Envelope, \( C \) Glycoprotein, D- RNA, E- Reverse transcriptase
B. Adenovira (Retovira), A- Protein coats, B- Envelope, CGlycoprotein, E- RNA, F- Reverse transcriptase
C. HIV (Retovira), A- Envelope, B- Glycoprotein, C- Protein coat, D- RNA, E- Reverse transcriptase
D. TMV (Retrovira), A- Protein coats, B- Envelope, CGlycoprotein, D- RNA, E- Reverse transcriptase
Subject: Biology
Select the correct option:
Which of the following statements about cell junctions are correct?
(i) All the cells of the epithelium are held together with little intercellular
materials
(ii) In almost all animal tissues
specialised junctions provide both structural and functional link between
its individual cells
(iii) Tight junctions prevent substances from leaking across a tissue
(iv) Adhering junctions provide cementing to keep neighbouring cells together.
(v) Gap junctions provide cytoplasmic channels between cells for passage of
ions, small molecules and sometimes
big molecules.
A. (ii) and (iii)
B. (i), (ii) and (iii)
c. (iv) and (v)
D. (i), (ii), (iii), (iv) and (v)
Subject: Physics
If the time taken by the planet to move
from position \( \mathrm{P} \) to \( \mathrm{X} \) and \( \mathrm{Q} \) to \( \mathrm{Y} \) is equal
then the ratio of \( A_{1} \) to \( A_{2} \) is:
A. Greater than one
B. Less than one
c. Equal to one
D. Data insufficient
Subject: Physics
A transparent cube of side \( \boldsymbol{d}, \) made ot a
material of refractive index \( \mu_{2}, \) is
immersed in a liquid of refractive index
\( \mu_{1}\left(\mu_{1}<\mu_{2}\right) . \) A ray is incident on the
face \( A B \) at an angle \( \theta \) (shown in the
figure). Total internal reflection takes
place at point \( \boldsymbol{E} \) on the face \( \boldsymbol{B} \boldsymbol{C} \)
The \( \theta \) must satisfy:
\( \mathbf{A} \cdot \theta<\sin ^{-1} \frac{\mu_{1}}{\mu_{2}} \)
B \( \cdot \quad \theta<\sin ^{-1} \sqrt{\frac{\mu_{2}^{2}}{\mu_{1}^{2}}-1} \)
c. \( \theta>\sin ^{-1} \frac{\mu_{1}}{\mu_{2}} \)
\( ^{\mathrm{D}} \theta>\sin ^{-1} \sqrt{\frac{\mu_{2}^{2}}{\mu_{1}^{2}}-1} \)
Subject: Maths
Find the area of the region bounded by
the curve \( y=4-x^{2}, x \) -axis and the line
\( x=0 \) and \( x=2 \)
A \( \cdot \frac{11}{3} \)
в. \( \frac{16}{3} \)
\( c \cdot \frac{16}{5} \)
D.
Subject: Maths
Arrange the points: \( \mathbf{A}(1,2- \) \( \mathbf{3}), \mathbf{B}(-\mathbf{1}, \mathbf{2},-\mathbf{3}), \mathbf{C}(-\mathbf{1},-\mathbf{2}-\mathbf{3}) \) and
\( \mathbf{D}(\mathbf{1},-\mathbf{2},-\mathbf{3}) \) in the increasing order of
their octant numbers:
A. \( A, B, C, D \)
в. \( B, C, D, A \)
c. \( C, D, A, B \)
D. \( D, C, B, A \)
Subject: Chemistry
Nitrogen has unique ability to form \( \boldsymbol{P} \boldsymbol{\pi}-\boldsymbol{P} \boldsymbol{\pi} \) multiple bonds with itself and
with other elements due to:
A. small size and low electronegativity
B. large size and high electronegativity
c. large size and low electronegativity
D. small size and high electronegativity
Subject: Chemistry
The oxidation states of \( P \) atom in
\( \boldsymbol{P O C l}_{3}, \boldsymbol{H}_{2} \boldsymbol{P O}_{3} \) and \( \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{6} \)
respectively are:
\( \mathbf{A} \cdot+5,+4,+4 \)
B. +5,+5,+4
\( \mathbf{c} \cdot+4,+4,+5 \)
\( \mathbf{D} \cdot+3,+4,+5 \)