AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Find the angle of incidence and angle of
reflection from the diagram.
A \( \cdot 45^{\circ}, 40^{\circ} \)
B . \( 55^{\circ}, 55^{\circ} \)
\( \mathbf{c} \cdot 60^{\circ}, 60^{\circ} \)
D. \( 30^{\circ}, 30^{\circ} \)
Subject: Maths
Divide \( 4 x^{2} y^{2}(6 x-24) \div 4 x y(x-4) \)
\( \mathbf{A} \cdot 6 x y \)
B. \( 4 x y \)
c. \( x-4 \)
D. \( x y(x-4) \)
Subject: Chemistry
Consider the above sequence of reactions. Find \( \boldsymbol{A}, \boldsymbol{B} \) and \( \boldsymbol{C} \)
\( \overbrace{\mathrm{CH}}_{2} \mathrm{OH} \stackrel{\mathrm{HBr}}{\longrightarrow} \mathrm{A}^{\mathrm{O}_{3} / \text { reduction }}>\mathrm{B}+\mathrm{c} \)
\( \mathbf{A} \)
\( \overbrace{\mathrm{CH}}_{2} \mathrm{Br}, \mathrm{CH}_{2}=\mathrm{O}, \mathrm{O}=\mathrm{CH}-^{*} \mathrm{CH}_{2} \mathrm{Br} \)
B. \( \overbrace{x}_{\mathrm{CH}_{2} \mathrm{Br}}, \stackrel{*}{\mathrm{CH}_{2}=} 0, \mathrm{O}=\mathrm{CH}-\mathrm{CH}_{2} \mathrm{Br} \)
\( c \)
\( \overbrace{x}_{\mathrm{CH}_{2} \mathrm{Br}}, \) HCOOH \( , \mathrm{O}=\mathrm{CH}-\dot{\mathrm{CH}}_{2} \mathrm{Br} \)
D. \( \overbrace{x}_{\mathrm{CH}_{2} \mathrm{Br}}, \) HCOOH \( , \mathrm{HOOC}-\stackrel{*}{\mathrm{CH}_{2}} \mathrm{Br} \)
Subject: Physics
Let a total charge \( 2 Q \) be distributed in a
sphere of radius \( R, \) with the charge
density given by \( \rho(r)=k r, \) where \( r \) is
the distance from the centre. Two
charges \( A \) and \( B, \) of \( -Q \) each, are
placed on diametrically opposite points, at equal distance, a form the centre. If \( \boldsymbol{A} \)
and \( B \) do not experience any force, then:
A \( \cdot a=\frac{3 R}{2^{1 / 4}} \)
B. \( a=\frac{R}{\sqrt{3}} \)
C \( \cdot a=8^{-1 / 4} R \)
D . \( a=2^{-1 / 4} R \)
Subject: Physics
Find the dimensions of capacitance :
\( \mathbf{A} \cdot=\left[M^{-1} L^{2} T^{4} A^{-2}\right] \)
B . \( =\left[M^{-1} L^{-2} T^{-4} A^{2}\right] \)
\( \mathbf{c} \cdot=\left[M^{-1} L^{-1} T^{4} A^{2}\right] \)
D. \( =\left[M^{-1} L^{-2} T^{4} A^{2}\right. \)
Subject: Physics
Consider a ring performing pure rolling when on a fixed rough surface. There is
a point 'A' marked on the circumference of it. If velocity of centre of ring is uniform, then this point will move in cycloidal path as shown. Now, if the ring is performing pure rolling with uniform acceleration what will be the
path followed by this point?
A. increasing size of cycloid
B. decreasing size of cycloid
c. It will depend on direction of acceleration whether it is in the direction of velocity of centre or opposite.
D. No change in path will occur
Subject: Physics
One atomic mass unit (a.m.u) is equal
to:
A \( .2 .67377 \times 10^{-27} \)
В. \( 1.67377 \times 10^{-22} \)
c. \( 0.67377 \times 10^{-27} \)
D. \( 1.67377 \times 10^{-27} \)
Subject: Maths
If the lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and
\( \frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{1}}=\frac{\boldsymbol{y}-\boldsymbol{k}}{\mathbf{2}}=\frac{\boldsymbol{z}}{\mathbf{1}} \) intersect, then \( \boldsymbol{k}= \)
A. 0
B. 3
\( c \cdot \frac{7}{2} \)
D. -
Subject: Physics
A point object is placed \( 33 \mathrm{cm} \) from a
convex mirror of curvature radius \( =40 \)
\( \mathrm{cm} . \) A glass plate of thickness \( 6 \mathrm{cm} \) and index 2.0 is placed between the object and mirror, close to the mirror. The distance of final image from the object is
\( \mathbf{A} \cdot 90 \mathrm{cm} \)
B. \( 35 \mathrm{cm} \)
\( \mathrm{c} .36 \mathrm{cm} \)
D. \( 45 \mathrm{cm} \)
E. None of these
Subject: Chemistry
If \( 1.0 \mathrm{k} \) cal of heat is added to \( 1.2 \mathrm{L} \) of \( \mathrm{O}_{2} \)
in a cylinder of constant pressure of 1 atm, the volume increases to 1.5 L.
Calculate \( \Delta H \) and \( \Delta U \) of the process.
Subject: Physics
If a car is moving forward, what is the
direction of the moment of the moment
caused by the rotation of the tires
A. It is heading inwards, i.e. the direction is towards inside of the car
B. It is heading outwards, i.e. the direction is towards outside of the car
c. It is heading forward, i.e. the direction is towards the forward direction of the motion of the car
D. It is heading backward, i.e. the direction is towards back side of the motion of the car
Subject: Chemistry
Choose the correct reason(s) for the
stability of the Iyophobic colloidal
particles.
This question has multiple correct options
A. Preferential adsorption of ions on their surface from the solution
B. Preferential adsorption of solvent on their surface from the solution
C. The attraction between different particles having opposite charges on their surface
D. The potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles
Subject: Maths
Examine the graph of \( y=f(x) \) as
shown and evaluate the following limits
(i) \( \lim _{x \rightarrow 1} f(x) \)
(ii) \( \lim _{x \rightarrow 2} f(x) \)
(iii) \( \lim _{x \rightarrow 3} f(x) \)
(iv) \( \lim _{x \rightarrow 199} f(x) \)
\( (v) \lim _{x \rightarrow 3^{+}} f(x) \)
Subject: Chemistry
12.2 \( g \) of benzoic acid \( (M=122) \) in 100 g water has elevation in the boiling point of \( 0.27 \mathrm{K} . K_{b}=0.54 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1} . \) If there is
\( 100 \% \) polymerisation, the number of molecules of benzoic acid in the
associated state is:
A.
B. 2
\( c \cdot 3 \)
\( D \)
Subject: Maths
The distribution of sale of shirts sold in
a month in a departmental store is as under. Calculate the model size of shirts
sold.
\( \begin{array}{llll}\text { 80- } & \text { 85- } & \text { 90- } & \text { 95- }\end{array} \)
\[
\begin{array}{lll}
\text { Size } & \text { 80- } & \text { 85- } \\
\text { (in } & \text { 85 } & \text { 90 }
\end{array}
\]
\( 95 \quad 100 \)
\( \mathrm{cm} \)
No
of 3
85
155
shirts sold
Subject: Physics
Why do humans have two eyes?
a. The view field is increased up to \( 180^{\circ} \)
b. Better detection of faint objects
c. 3 dimensional view
d. More accurate estimation of distance
\( A \cdot a, b \) and \( d \)
B. c and d
\( c \cdot a, c \) and \( d \)
D. All of the above
Subject: Physics
The displacement of a particle varies with time as \( \boldsymbol{x}=\boldsymbol{a} e^{-\boldsymbol{\alpha} \boldsymbol{t}}+\boldsymbol{b} \boldsymbol{e}^{\boldsymbol{\beta} \boldsymbol{t}} \) where
\( a, \alpha, b, \beta \) are positive constants. The
velocity of the particle will
A. be independent of \( \alpha \) and \( \beta \)
B. drop to zero when \( \alpha=\beta \)
c. go on decreasing with time
D. go on increasing with time
Subject: Physics
Color of the four strips of carbon
resistor are respectively orange, green golden, silver. Then its resistance is :
\( \mathbf{A} \cdot 2.5 \pm 10 \% \) ohm
B. \( 3.5 \pm 5 \% \) ohm
c. \( 3.5 \pm 10 \% \) ohm
\( \mathbf{D} \cdot 350 \pm 10 \% \) ohm
Subject: Physics
Two bodies, \( A(\text { of } \operatorname{mass} 1 \mathrm{kg}) \) and \( \mathrm{B} \) (of mass \( 3 \mathrm{kg} \) ), are dropped from heights of
\( 16 \mathrm{m} \) and \( 25 \mathrm{m} \) respectively. The ratio of
the time taken by them to reach the ground is:-
A \( \cdot \frac{5}{4} \)
в. \( \frac{12}{5} \)
c. \( \frac{5}{12} \)
D. \( \frac{4}{5} \)
Subject: Physics
A uniform thin rod of length L is moving
in a uniform magnetic field \( B_{0} \) such
that velocity of its centre of mass is \( \mathbf{v} \) and angular velocity is \( \omega=\frac{4 v}{L} \) Then
A. e.m.f. between end \( \mathrm{P} \) and \( \mathrm{Q} \) of the rod is \( B_{0} l v \)
B. end P of the rod is at higher potential than end Q of the rod
C. end \( Q \) of the rod is at higher potential than end P of the rod
D. the electrostatic field induced in the rod has same direction at all points along the length of rod
Subject: Physics
Show that the expression of the time period \( T \) of a simple pendulum of length
\( l \) given by \( T=2 \pi \sqrt{\frac{l}{g}} \) is dimensionally
correct.
A. As in the above equation, the dimensions of both sides are same. The given formula is dimensionally correct
B. The dimension of LHS and RHS are not same
c. It cannot be solved
D. None of these
Subject: Chemistry
Assuming that water vapour is an ideal
gas, the internal energy change \( (\Delta U) \) when 1 mol of water is vaporised at 1
bar pressure and \( 100^{\circ} \mathrm{C} \) will be:
(Given: Molar enthalpy of vapourisation of water at 1 bar and \( 373 K= \)
\( 41 k J . m o l^{-1} \) and \( R=8.3 J m o l^{-1} K^{-1} \)
A \( \cdot 4.100 k J \) mol \( ^{-1} \)
В. 3.7904 k J \( \mathrm{mol}^{-1} \)
c. \( 37.904 k J \) mol \( ^{-1} \)
D. \( 41.00 \mathrm{kJ} \mathrm{mol}^{-1} \)
Subject: Maths
\( \cos ^{-1}\left\{\frac{1}{2} x^{2}+\sqrt{1-x^{2}} \cdot \sqrt{1-\frac{x^{2}}{4}}\right\}= \)
\( \cos ^{-1} \frac{x}{2}-\cos ^{-1} x \) holds for
A \( \cdot|x| \leq 1 \)
В. \( x \in R \)
c. \( 0 \leq x \leq 1 \)
D. \( -1 \leq x \leq 0 \)
Subject: Maths
If linear function \( f(x) \) and \( g(x) \) satisfy \( \int[(3 x-1) \cos x+(1-2 x) \sin x] d x= \)
\( \boldsymbol{f}(\boldsymbol{x}) \cos \boldsymbol{x}+\boldsymbol{g}(\boldsymbol{x}) \sin \boldsymbol{x}+\boldsymbol{C}, \) then
A. \( f(x)=3 x-3 \)
B. \( g(x)=3+x \)
C. \( f(x)=3(x-1) \)
D. \( g(x)=3(x-1) \)
Subject: Maths
The unit vector which is orthogonal to the vector \( \vec{a}=3 \vec{i}+2 \vec{j}+6 \vec{k} \) and is coplanar with the vectors \( \overrightarrow{\boldsymbol{b}}=\mathbf{2} \overrightarrow{\mathbf{i}}+\overrightarrow{\boldsymbol{j}}+ \)
\( \vec{k} \) and \( \vec{c}=\vec{i}-\vec{j}+\vec{k} \) is
A \( \cdot \frac{1}{\sqrt{41}}(2 \vec{i}-6 \vec{j}+\vec{k}) \)
B. \( \frac{2 \vec{i}-3 \vec{j}}{\sqrt{13}} \)
c. \( \frac{3 \vec{j}-\vec{k}}{\sqrt{10}} \)
D. \( \frac{4 \vec{i}+3 \vec{j}-3 \vec{k}}{\sqrt{14}} \)
Subject: Physics
A wheel with 8 metallic spokes each 50
\( \mathrm{cm} \) long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the place is \( 0.4 \mathrm{G} \) and the angle
of \( 60^{\circ} \).Calculate the emf induced
between the axle and the rim of the
wheel.How will the value of emf be
affected if the number of spokes were increased?
Subject: Chemistry
Assertion
Cryolite is used in electrolytic
extraction of \( A l \) from alumina.
Reason
It dissolves alumina.
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 and Reason is correct
Subject: Chemistry
which of the following statements is true about effective nuclear charge?
This question has multiple correct options
A. \( Z_{\text {eff}} \) decreases from top to bottom
B. \( Z_{\text {eff}} \) increases from top to bottom
C. \( Z_{\text {eff}} \) increases as we move from left to right in periodic table
D. \( Z_{e f f}=Z \times \sigma \) (here \( \sigma \) is screening constant
Subject: Physics
A student measures the thickness of a
copper wire using standard instruments and reports it as \( 0.1 \mathrm{cm} \)
\( 0.15 \mathrm{cm} \) and \( 0.157 \mathrm{cm} . \) The instruments
used to find these measurements are
and
respectively.
A. vernier calipers, ordinary scale, screw gauge
B. ordinary scale,vernier calipers, screw gauge
C. screw gauge, vernier calipers, ordinary scale,
D. ordinary scale, screw gauge, vernier calipers
Subject: Maths
Choose the correct answer from the
alternatives given A tree is broken by the wind. If the top of the tree struck the ground at an angle of
\( 30^{\circ} \) and at a distance of \( 30 \mathrm{m} \) from the
root, then the height of the tree is
B. \( 20 \sqrt{3} m \)
\( \mathbf{c} \cdot 25 \sqrt{3} m \)
D. \( 30 \sqrt{3} m \)
Subject: Chemistry
The total energy of the electron of \( \boldsymbol{H} \) atom in the second quantum state is
\( -\boldsymbol{E}_{2} . \) The total energy of the \( \boldsymbol{H} \boldsymbol{e}^{+} \) atom in the third quantum state is:
\( ^{\mathrm{A}} \cdot-\left(\frac{3}{2}\right) E_{2} \)
в. \( -\left(\frac{2}{3}\right) E_{2} \)
c. \( -\left(\frac{4}{9}\right) E_{2} \)
D. \( -\left(\frac{16}{9}\right) E_{2} \)
Subject: Maths
\( \left|\frac{1}{2}\left(z_{1}+z_{2}\right)+\sqrt{z_{1} z_{2}}\right|+ \)
\( \left|\frac{1}{2}\left(z_{1}+z_{2}\right)-\sqrt{z_{1} z_{2}}\right|= \)
A \( \cdot \mid z_{1}+z_{2} \)
B . \( \left|z_{1}-z_{2}\right| \)
\( \mathbf{c} \cdot\left|z_{1}\right|+\left|z_{2}\right| \)
D. \( \left|z_{1}\right|-\mid z_{2} \)
Subject: Chemistry
In cyamide extraction process of silver from argentite ore, the oxidising and
reducing agents are respectively.
\( A \cdot O_{2} \) and \( C O_{2} \)
B. \( O_{2} \) and \( Z n \) dust
\( \mathrm{c} . H N O_{3} \) and \( Z n \) dust
D. \( H N O_{3} \) and \( C O \)
Subject: Chemistry
An industrial method of preparation of
methanol is:
A. catalytic reduction of carbon monoxide in presence of \( Z n o-C r_{2} O_{3} \)
B. by reacting methane with steam at \( 900^{\circ} \mathrm{C} \) with a nickel catalyst
C. by reducing formaldehyde with lithium aluminium hydride
D. by reacting formaldehyde with aqueous sodium hydroxide solution
Subject: Physics
Find the minimum wavelength of \( X \) -ray produced if \( 10 \mathrm{kV} \) potential difference is applied across the anode and cathode of the tube.
A \( \cdot 12.4 \mathrm{A}^{\circ} \)
B. 12.4 nm
\( c \cdot 1.24 \mathrm{nm} \)
D. \( 1.24 \mathrm{A}^{\circ} \)
Subject: Physics
One mole of an ideal gas undergoes a process \( P=\frac{P_{o}}{1+\left(\frac{V}{V_{o}}\right)^{2}}, \) where \( P_{o} \) and
\( V_{o} \) are constants. Find the temperature
of the gas when \( V=V_{o} \)
A \( \cdot \frac{P_{o} V_{o}}{R} \)
в. \( \frac{2 P_{o} V_{o}}{3 R} \)
c. \( \frac{2 P_{o} V_{o}}{R} \)
D. \( \frac{P_{o} V_{o}}{2 R} \)
Subject: Physics
A charge \( Q \) is placed at each of the opposite corners of a sequare. A charge \( q \) is placed at each of the other two
corners. If the net electric force on \( Q \) is
zero, then \( Q / q \) equals:
A . -1
B. 1
c. \( -\frac{1}{2} \)
D. \( -2 \sqrt{2} \)
Subject: Maths
A seven-digit number without repetition
and divisible by 9 is to be formed by using seven digits out of
\( \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9} . \) The number of ways
in which this can be done is
A . 9
в. \( 2(7 !) \)
c. \( 4(7 !) \)
D. None of these
Subject: Maths
The distance between (0,1,-1) and the point of intersection of the line \( \frac{x}{2}= \) \( \frac{\boldsymbol{y}-\mathbf{1}}{\mathbf{3}}=\frac{\boldsymbol{z}+\mathbf{1}}{\mathbf{4}} \) and the plane \( \boldsymbol{x}+\boldsymbol{y}+ \)
\( z=9 \) is
A. \( \sqrt{29} \)
в. \( \frac{1}{2} \sqrt{29} \)
\( c \cdot \frac{4}{9} \)
D. \( \frac{2}{9} \sqrt{29} \)
Subject: Chemistry
Chlorine exists in two isotopic forms, \( C l-37 \) and \( C l-35 \) but its atomic
mass is \( 35.5 . \) This indicates the ratio of
\( C l-37 \) and \( C l-35 \) is approximately:
A .1: 2
B. 1: 1
c. 1: 3
D. 3: 1
Subject: Maths
If \( \boldsymbol{a}_{\boldsymbol{i}}>\mathbf{1} \) for all \( \boldsymbol{i} \boldsymbol{\epsilon} \boldsymbol{N}, \) then \( \log _{\boldsymbol{a}_{2}} \boldsymbol{a}_{\boldsymbol{1}}+ \)
\( \log _{a_{3}} a_{2}+\ldots+\log _{a_{n}} a_{n-1}+\log _{a_{1}} a_{n} \)
has the minimum value
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 0 \)
D. none of these
Subject: Maths
If \( \vec{a}=x \vec{i}-y \vec{j}, \vec{b}=y \vec{i}+x \vec{j} \) and \( \mid \vec{a} \times \)
\( \vec{b} \mid=5, \) then locus of \( (x, y) \) is
A. Hyperbola
B. Parabola
c. Ellipse
D. Circle
Subject: Physics
Sl unit of \( G \) is \( N m^{2} k g^{-2} . \) Which of the
following can also be used as the Sl unit
of G?
A \( \cdot m^{3} k g^{-1} s^{-2} \)
B . \( m^{2} k g^{-2} s^{-1} \)
\( \mathbf{c} \cdot m k g^{-3} s^{-1} \)
D. \( m^{2} k g^{-3} s^{-2} \)
Subject: Maths
\( \int \frac{1}{\left(1+x^{2}\right) \sqrt{p^{2}+q^{2}\left(\tan ^{-1} x\right)^{2}}} d x \) is
equal to
A \( \cdot \frac{1}{p} \log \left|p\left(\tan ^{-1} x\right)+\sqrt{p^{2}+\left(q \tan ^{-1} x\right)^{2}}\right|+C \)
B. \( \frac{1}{p} \log \left|\left(p \cot ^{-1} x\right)+\sqrt{p^{2}+\left(p \cot ^{-1} x\right)^{2}}\right|+C \)
c. \( \frac{1}{q} \log \left|q\left(\cot ^{-1} x\right)+\sqrt{p^{2}+\left(q \cot ^{-1} x\right)^{2}}\right|+C \)
D \( \cdot \frac{1}{q} \log \left|q\left(\tan ^{-1} x\right)+\sqrt{p^{2}+\left(q \tan ^{-1} x\right)^{2}}\right|+C \)
Subject: Chemistry
Calculate the mean free path in \( C O_{2} \) at
\( 27^{\circ} \mathrm{C} \) and a pressure of \( 10^{-9} \) bar.

Molecular diameter of \( C O_{2} \) is 500 pm. Given \( : \mathrm{R}=\frac{25}{3} J . m o l^{-1} K^{-1}, \sqrt{2}= \)
\( \mathbf{1} . \mathbf{4}, \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}, \boldsymbol{N}_{\boldsymbol{A}}=\mathbf{6} \times \mathbf{1 0}^{\mathbf{2 3}} \mathbf{j} \)
A \( \cdot 3.788 \times 10^{3} \mathrm{cm} \)
В . \( 7.47 \times 10^{3} \mathrm{cm} \)
\( \mathbf{c} \cdot 6.43 \times 10^{5} \mathrm{cm} \)
D. None of these
Subject: Physics
Determine the magnetic flux through
the smaller loop as a function of \( x \)
A \( \cdot \frac{\mu_{0} i R^{2} \pi r^{2}}{x^{3}} \)
B. \( \frac{\mu_{0} i R^{2} \pi r^{2}}{2 x^{3}} \)
c. \( \frac{2 \mu_{0} i R^{2} \pi r^{2}}{x^{3}} \)
D. \( \frac{\sqrt{2} \mu_{0} i R^{2} \pi r^{2}}{x^{3}} \)
Subject: Physics
A slide projector gives a magnification
10. If a slide of dimensions \( 3 \mathrm{cm} \times 2 \mathrm{cm} \)
is projected on the screen the area of image screen is
A \( .6000 \mathrm{cm}^{2} \)
в. \( 600 \mathrm{cm}^{2} \)
\( c \cdot 60^{2} \mathrm{cm}^{2} \)
D. \( 6 \mathrm{cm}^{2} \)
Subject: Chemistry
Which of the following would not have a dipole moment?
(i) \( \boldsymbol{C C l}_{\mathbf{4}} \)
\( (i i i) 1,2- \)
dichloroacetylene
(ii) trans-1, 2-dichloroethene
\( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2} \)
\( A \cdot \) (i) and (iv)
B. (i), (ii) and (iv)
C . (i), (ii) and (iii)
D. (ii) and (iii)
Subject: Physics
the \( x y \) -plane along the lines \( x=\pm R \)
The wire located at \( x=+R \) carries a
constant current \( I_{1} \) and the wire located
at \( x=-R \) carries a constant current \( \boldsymbol{I}_{2} \)
A circular loop of radius \( \boldsymbol{R} \) is
suspended with its centre at \( (0,0, \sqrt{3} R) \) and in a plane parallel to the
\( \boldsymbol{x} \boldsymbol{y} \) -plane. This loop carries a constant
current \( I \) in the clockwise direction as
seen from above the loop. The current in the wire is taken to be positive if it is in the \( +\hat{\boldsymbol{j}} \) direction. Which of the following statements regarding the magnetic field \( \vec{B} \) is (are) true?
This question has multiple correct options
A \( \cdot \) If \( I_{1}=I_{2} \), then \( \vec{B} \) cannot be equal to zero at the origin
(0,0,0)
B. If \( I_{1}>0 \) and \( I_{2}<0 \), then \( \vec{B} \) can be equal to zero at the origin (0,0,0)
C \( \cdot \) If \( I_{1}<0 \) and \( I_{2}>0, \) then \( \vec{B} \) can be equal to zero at the origin (0,0,0)
D. If \( I_{1}=I_{2} \), then the \( z \) -component of the magnetic field at the centre of the loop is \( \left(-\frac{\mu_{0} I}{2 R}\right) \)
Subject: Maths
PQRS is a parallelogram and PA, SB, RC,
QD are angle bisectors. If \( P Q=Q D=6 \)
units, find \( \boldsymbol{m} \angle \boldsymbol{P Q R} \)
\( A \cdot 30^{\circ} \)
B. 60
\( c \cdot 120 \)
D. Indeterminate
Subject: Physics
Assertion
Current in wire-1 is in the direction as
shown in figure.The bottom wire is fixed.To keep the upper wire stationary current in it should be in opposite direction.
Reason
Under the above condition,equilibrium
of upper wire is stable.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
In a N-P-N transistor about \( 10^{10} \)
electrons enter the emitter in \( 2 \mu s, \) when
it is connected to a battery. Then \( \boldsymbol{I}_{\boldsymbol{E}}= \)
\( \boldsymbol{\mu} \boldsymbol{A} \)
A . 200
в. 400
c. 800
D. 1600
Subject: Chemistry
Correct order of stability of group IIA
metal carbonates is :
\( \mathbf{A} \cdot M g C O_{3}>C a C O_{3}>S r C O_{3}>B a C O_{3} \)
B. \( B a C O_{3}>S r C O_{3}>C a C O_{3}>M g C O_{3} \)
\( \mathbf{c} \cdot \operatorname{Sr} C O_{3}>B a C O_{3}>C a C O_{3}>M g C O_{3} \)
\( \mathrm{D} \cdot \mathrm{CaCO}_{3}>\mathrm{MgCO}_{3}>\mathrm{BaCO}_{3}>\mathrm{SrCO}_{3} \)
Subject: Chemistry
A light whose frequency is equal to \( 6 x \) \( 10^{14} H z \) is incident on a metal whose
work function is \( 2 e V \)
\( \left(h=6.63 \times 10^{-34} J s, 1 e V=1.6 \times 10^{-}\right. \)
The maximum energy of electrons emitted will be:
A \( .2 .49 e V \)
в. \( 4.49 e V \)
c. \( 0.49 e V \)
D. \( 5.49 e V \)
Subject: Maths
For a polynomial, dividend is \( x^{4}+4 x- \)
\( 2 x^{2}+x^{3}-10, \) quotient is \( x^{2}+3 x- \)
\( 3 x^{2}+4 x+12 \) and remainder is 14
then divisor is equal to
A. \( x^{2}+2 \)
B . \( x^{2}-2 \)
c. \( x+2 \)
D. None of these
Subject: Physics
A \( 5 m \) long cylindrical steel wire with
radius \( 2 \times 10^{-3} \mathrm{m} \) is suspended
vertically from a rigid support and carrics a bob of mass \( 100 \mathrm{kg} \) at the
other end. If the bob gets snapped,
calculate the change in temperature of the wire ignoring radiation losses. \( \left(\text { Take } g=10 m / s^{2}\right) \) (For the steel wire:
Young's modulus \( =2.1 \times 10^{11} N / m^{2} \)
Density \( =7860 k g / m^{3} \) Specific heat \( = \)
\( 420 J / k g C) \)
Subject: Chemistry
Assertion
Decrease in free energy causes
Spontaneous reaction.
Reason
Spontaneous reactions are invariably
exothermic.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A toy car travels in a horizontal circle of
radius \( 2 a, \) kept on the track by a radial elastic string of unstretched length a. The period of rotation is T. Now the car
is speeded up until it is moving in a circle of radius 3 a. Assuming that the string obeys Hooke's law then the new period will be
A \( \cdot \sqrt{\frac{4}{3}} T \)
B \( \cdot \frac{3^{2}}{3^{3}} T \)
c. \( \sqrt{\frac{3}{2}} T \)
D. \( \frac{3}{4} T \)
Subject: Physics
Given two vectors \( \vec{A}=\hat{i}-2 \hat{j}-3 \hat{k} \) and \( \vec{B}=4 \hat{i}-2 \hat{j}+6 \hat{k}, \) the angle made by
\( (\vec{A}+\vec{B}) \) with \( x \) -axis is:
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)
Subject: Chemistry
The order of stability of the alkenes is:
\( \mathrm{R}_{2} \mathrm{C}=\mathrm{CR}_{2}, \mathrm{R}_{2} \mathrm{C}=\mathrm{CHR}, \mathrm{R}_{2} \mathrm{C}=\mathrm{CH}_{2}, \mathrm{RCH}=\mathrm{CHR} \)
and \( \mathrm{RCH}=\mathrm{CH}_{2} \)
1
\( \| \)
\( \mathbf{V} \)
\( A \cdot|>||>|||>\mid V>V \)
B. \( |=||>|||>\mid V>v \)
c. \( \|>|>| V>\|>v \)
D. \( v>|V>|||>|>| \mid \)
Subject: Physics
\( \mathrm{m} / \mathrm{s} \) at an angle of \( 60^{\circ}, \) with
the positive \( x \) direction taken along
horizontal. At that instant, an
observer moves past the football in a
car that moves with a constant speed
of \( 11 \mathrm{m} / \mathrm{s} \) in the positive \( \mathrm{x} \) direction. Take
+ve y direction vertically upwards. \( (\boldsymbol{g}= \)
\( \left.10 m / s^{2}\right) \)
ball
Observer
This question has multiple correct options
A. The initial velocity of the ball relative to the observer in the car is \( 11 \sqrt{3} \mathrm{m} / \mathrm{s} \) in the \( +\mathrm{y} \) direction
B. The initial velocity of the ball relative to the observer in the car is \( 17 \mathrm{m} / \mathrm{s} \) at 60 to the \( +x \) direction
c. According to the observer in the car, the ball will follow a path that is straight up and down in the y direction.
D. According to the observer in the car, the ball will follow straight line that is angled (less than 90 ) with respect to the observer.