AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Calculate the mutual conductance \( g_{m} \)
of the triode valve?
A \( .5 .33 \times 10^{-3} \mathrm{ohm}^{-1} \)
B. \( 53.3 \times 10^{-3} \) ohm \( ^{-1} \)
c. \( 4.32 \times 10^{-3} \mathrm{ohm}^{-1} \)
D. \( 5.00 \times 10^{-3} \mathrm{ohm}^{-1} \)
Subject: Physics
A drop of water detaches itself from the
exit of a tap when \( (\sigma= \) surface tension
of water. \( \rho= \) density of water, \( \boldsymbol{R}= \)
radius of the tap exit, \( r= \) radius of the
drop)
\( r>\left(\frac{2 R \sigma}{3 \rho g}\right)^{1 / 3} \)
В. \( \quad r>\frac{2}{3} \frac{\sigma}{\rho g} \)
\( ^{\mathrm{C}} \cdot \frac{2 \sigma}{r}> \) atmospheric pressure
\( r>\left(\frac{2 R \sigma}{3 \rho g}\right)^{2 / 3} \)
E. None of the above
Subject: Maths
The simplest form of the expression \( \frac{10-\sqrt{-12}}{1-\sqrt{-27}} \) is
\( A \cdot-\frac{2}{7} \)
в. \( \frac{28}{3} \)
c. \( -\frac{2}{7}+i \sqrt{3} \)
D. \( 1+i \sqrt{3} \)
Subject: Chemistry
Assertion
\( N a C l \) is not a conductor of electricity
in solid state whereas it does conduct
electricity in aqueous solution as well as in molten state.
Reason
In solid \( N a C l, \) the ions have fixed positions in the lattice structure and there are no free ions but in aqueous
solution or molten state, the ions can move freely and thus conduct electricity.
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
The domain of \( \mathbf{f}(\mathbf{x})= \) \( \cot ^{-1}\left(\frac{\mathbf{x}}{\sqrt{\mathbf{x}^{2}-\left[\mathbf{x}^{2}\right]}}\right) \) is
\( ([.] \) denotes the greatest integer function)
A. \( (0, \infty) \)
)
в. \( \mathrm{R}-\{0 \)
c. \( R-\{x: x \in Z\} \)
D. \( (-\infty, 0) \)
Subject: Physics
If \( \vec{A} \cdot \vec{B}=0, \) the angle between the
vectors \( A \) and \( B \) will be:
A \( \cdot 0^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
\( D \cdot 180^{\circ} \)
Subject: Maths
If the rate of \( V A T \) increases by \( 2 \% \) then selling price of an article goes up by
Rs. 140. Find the marked price of the article
A. \( R s .1000 \)
в. \( R s .7000 \)
c. \( R s .7500 \)
D. \( R s .9000 \)
Subject: Physics
Find the components of \( \overrightarrow{\boldsymbol{a}}=2 \hat{\boldsymbol{i}}+\boldsymbol{3} \boldsymbol{j} \)
along the directions of vectors \( \hat{i}+\hat{j} \) and
\( \hat{\mathbf{i}}-\hat{\boldsymbol{j}} \)
Subject: Maths
If \( A=\operatorname{diag}(1,-1,2) \) and \( B= \)
\( \operatorname{diag}(2,3,-1) \operatorname{then} 3 A+4 B= \)
\( \operatorname{diag}(a, b, c) . \) Then \( a-b-c= \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \in \)
\( \boldsymbol{R}, \boldsymbol{f}(\mathbf{5})=\mathbf{2}, \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{3}, \) then \( \boldsymbol{f}^{\prime}(\mathbf{5}) \)
equals:
A .4
B.
\( c \cdot \frac{1}{2} \)
\( D \)
Subject: Chemistry
A colourless salt gives a white ppt (soluble in ammonium acetate) and a
brown coloured pungent gas on reaction with conc. \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \) salt is:
\( \mathbf{A} \cdot B a\left(N O_{3}\right)_{2} \)
B. \( P b\left(N O_{3}\right)_{2} \)
c. \( \operatorname{NaNO}_{3} \)
D. \( N H_{4} N O_{3} \)
Subject: Chemistry
Nickel metal is purified by the vapour phase refining process. This process is based on the fact that:
A. nickel metal sublimes at high temperature
B. nickel reacts with carbon monoxide to form nickel carbonyl which decomposes at high temperature to form nickel
c. nickel reacts with chlorine to form nickel chloride which is volatile and decomposes easily to nickel
D. nickel can be vapourized under vacuum leaving behind impurities
Subject: Maths
Let \( [x] \) denote the greatest integer less
than or equal to \( x \). If \( f(x)=[x \sin \pi x] \)
\( \operatorname{then} f(x) \) is :
This question has multiple correct options
A. continuous at \( x=0 \)
B. continuous in (-1,0)
c. differentiable at \( x=1 \)
D. differentiable in (-1,1)
Subject: Maths
If \( \log _{\sqrt{3}} \frac{\left|z^{2}\right|-|z|+1}{2+|z|}<2, \) then locus of
\( z \) is
A \( .|z|<1 \)
В. \( 0<|z|<5 \)
c. \( |z|>1 \)
D. \( |z|>5 \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \) and
\( \boldsymbol{f}(\mathbf{5})=\mathbf{2}, \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{3} ; \) then \( \boldsymbol{f}^{\prime}(\mathbf{5}) \) is equal
to-
A .2
B. 4
\( c \cdot 6 \)
D. 8
Subject: Physics
A nail of mass \( ^{\prime} m_{1}^{\prime} \) kg is being hammered by a hammer of mass \( ^{\prime} \boldsymbol{m}_{2}^{\prime} \)
kg with a velocity of 'v' \( \mathrm{m} \mathrm{s}^{-1} \) such that the nail drives by 's' m into a wall. Find
the average resistance offered by the wall to the penetration of nail.
A. \( \left[\frac{m_{2} v}{\left(m_{1}+m_{2}\right) 2 s}\right] N \)
В \( \cdot\left[\frac{m_{2} v^{2}}{\left(m_{1}+m_{2}\right) 2 s}\right] N \)
\( ^{\mathbf{c}} \cdot\left[\frac{m_{2}^{2} v}{\left(m_{1}+m_{2}\right) 2 s}\right] N \)
D. \( \left[\frac{m_{2}^{2} v^{2}}{\left(m_{1}+m_{2}\right) 2 s}\right] N \)
Subject: Chemistry
Assertion
\( C_{P}-C_{V}=R \) for an ideal gas.
Reason
\( \left[\frac{\partial E}{\partial V}\right]_{T}=0 \) for an ideal gas.
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
There is a regular bus service between
towns \( A \) and \( B, \) with a bus leaving towns A and B every \( \boldsymbol{T} \) minutes. A cyclist
moving with a speed of \( 20 k m h^{-1} \) in the direction \( A \) to \( B \) notices that a bus goes
past him every 18 minutes in the direction of his travel and every
6 mins in the opposite direction. What is the speed with which buses travel between towns \( A \) and \( B ? \) (Assume the
speeds to be constant.)
\( \mathbf{A} \cdot 30 k m h^{-1} \)
В. \( 40 k m h^{-1} \)
\( \mathrm{c} \cdot 50 k m h^{-1} \)
D. \( 60 k m h^{-1} \)
Subject: Physics
Consider the nuclear change \( \mathbf{9 3}^{237} \boldsymbol{X} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{A} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{B} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{C} \)
Which of the following statements is
not correct?
A. Mass number of B is 233
B. Atomic number of A is 9
c. \( c \) is an isotope of
D. B is an isobar of A
Subject: Maths
The demand for different shirt sizes is
given in the table.
38 39 40 Size 4
No of
Persons 26 \( \begin{array}{lll}\text { 36 } & \text { 20 } & \text { 15 }\end{array} \)
Find the modal shirt size.
A . 39
B . 40
c. 44
D. 42
Subject: Biology
Assertion
Small leaflets are present on the
phyllode of Parkinsonia aculeata
Reason

Phyllode does not bear leaves and
flowers
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is
not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Maths
Two cubes have edge lengths in the ratio of 2: 3 respectively. The ratio of
their surface areas is
A \( \cdot \frac{4}{9} \)
в. \( \frac{8}{27} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{\sqrt{2}}{\sqrt{3}} \)
E \( \cdot \frac{\sqrt{3}}{\sqrt{2}} \)
Subject: Physics
Water drops fall at regular intervals from a roof. At an instant when a drop is
about to leave the roof, the separations
between 3 successive drops below the
roof are in the ratio
A .1: 2: 3
B. 1: 4: 9
\( \mathrm{c} \cdot 1: 3: 5 \)
D. 1: 5: 13
Subject: Physics
An electron is moving in a cyclotron at a speed of \( 3.2 \times 10^{7} m s^{-1} \) in a magnetic
field of \( 5 \times 10^{-4} \) T perpendicular to it.
What is the frequency of this electron? \( \left(\boldsymbol{q}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{C}, \boldsymbol{m}_{\boldsymbol{e}}=\mathbf{9 . 1} \times\right. \)
\( \left.10^{-31} k g\right) \)
A \( .1 .4 \times 10^{5} \mathrm{Hz} \)
B. \( 1.4 \times 10^{7} \mathrm{Hz} \)
c. \( 1.4 \times 10^{6} \mathrm{Hz} \)
D. \( 1.4 \times 10^{9} \mathrm{Hz} \)
Subject: Maths
On dividing the polynomial \( 9 x^{4}- \) \( 4 x^{2}+5 \) by another polynomial \( 3 x^{2}+ \)
\( x-1, \) the remainder comes out to be
\( a x-b, \) Find \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime} \)
Subject: Physics
An inductor of inductance \( 2.0 \mathrm{mH} \) is
connect across a charge capacitor of capacittance 5.0 uF , and the resulting LC circuit is set oscillating at natural frequency. Let \( Q \) denote the instantaneous charge on the capacitor, and I the current in the circuit. It is
found the maximum value of \( Q \) is 200
uC .When \( Q=100 u C \) the value of \( \frac{d I}{d t} \) is
found to be \( 10^{x} \) A/s. Find the value of \( x \)
is then
A. \( x=-4 \)
B. x=-
\( c \cdot x=4 \)
D. x=5
Subject: Chemistry
The ratio of \( p H \) of a solution containing
1 mole of \( \boldsymbol{C H}_{3} \boldsymbol{C O O N} \boldsymbol{a}+\mathbf{1} \) mole of
\( H C l \) per litre and of other solution
containing 1 mole of \( C H_{3} C O O N a+1 \)
mole of acetic acid per litre is:
A \( \cdot p H_{1}: p H_{2}:: 2: 5 \)
B . \( p H_{1}: p H_{2}:: 1: 2 \)
c. \( p H_{1}: p H_{2}:: 2: 3 \)
D. none of these
Subject: Maths
Consider \( \Delta A B C \) with \( A \equiv(\vec{a}), B \equiv(\vec{b}) \)
and \( C=(\vec{c}), \) ff \( \vec{b} .(\vec{a}+\vec{c})=\vec{b} \cdot \vec{b}+ \)
\( \vec{a} \cdot \vec{c} ;|\vec{b}-\vec{a}|=3 ;|\vec{c}-\vec{b}|=4 \) then the
angle between the medians \( \overline{A M} \) and
\( B D \) is
A. \( \pi-\cos ^{-1}\left(\frac{1}{5 \sqrt{13}}\right) \)
в. \( \pi-\cos ^{-1}\left(\frac{1}{13 \sqrt{5}}\right) \)
c. \( \cos ^{-1}\left(\frac{1}{5 \sqrt{13}}\right) \)
D. \( \cos ^{-1}\left(\frac{1}{13 \sqrt{5}}\right) \)
Subject: Chemistry
Which of the following arrangements represent increasing oxidation number
of the central atom?
A \( \cdot C r O_{2}^{-}, C l O_{3}^{-}, C r O_{4}^{2-}, M n O_{4} \)
B . \( C l O_{3}^{-}, C r O_{4}^{2-}, M n O_{4}^{-}, C r O_{2}^{-} \)
c. \( C r O_{2}^{-}, C l O_{3}^{-}, M n O_{4}^{-}, C r O_{4}^{2} \)
D. \( C r O_{4}^{2-}, M n O_{4}^{-}, C r O_{2}^{-}, C l O_{3} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}2 & 5 \\ 2 & 1\end{array}\right] \) and \( B=\left[\begin{array}{cc}4 & -3 \\ 2 & 5\end{array}\right], \) verify
that \( |\boldsymbol{A B}|=|\boldsymbol{A}||\boldsymbol{B}| \)
Subject: Physics
Two plane mirrors are inclined at an
angle by \( 120^{\circ}, \) as the figure shows. If a
ray strikes mirror \( M_{1} \$, \) at a \( 65^{\circ} \) angle
of incidence, at what angle \( \theta \) does it
leave mirror \( \boldsymbol{M}_{2} \)
\( A \cdot 35^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 55^{\circ} \)
\( D \cdot 65^{\circ} \)
Subject: Maths
The equation of lines parallel to \( 3 x- \)
\( 4 y-5=0 \) at a unit distance from it is
A. \( 3 x-4 y-10=0 \)
в. \( 5 x+3 y-5=0 \)
c. \( 3 x+4 y+10=0 \)
D. \( 6 x+2 y+4=0 \)
Subject: Maths
Find the Quotient and the Remainder
when the first polynomial is divided by
the second.
\( \left(x^{4}-2 x^{3}+2 x^{2}+x+4\right) \) by \( \left(x^{2}+x+\right. \)
1)
A. Quotient \( =x^{2}+3 x+4 \), Remainder \( =0 \)
B. Quotient= \( x^{2}-3 x-4 \), Remainder \( =0 \)
c. Quotient \( =-x^{2}-3 x+4 \), Remainder \( =0 \)
D. Quotient \( =x^{2}-3 x+4 \), Remainder \( =0 \)
Subject: Maths
Applying \( \boldsymbol{C}_{1} \rightarrow \boldsymbol{C}_{1}-^{8} \boldsymbol{C}_{3}, \) we
getWithout expanding the determinant, prove that \( \left|\begin{array}{ccc}\mathbf{4 1} & \mathbf{1} & \mathbf{5} \\ \mathbf{7 9} & \mathbf{7} & \mathbf{9} \\ \mathbf{2 9} & \mathbf{5} & \mathbf{3}\end{array}\right|=\mathbf{0} \)
Subject: Chemistry
How much energy is needed to convert \( 100 g \) of ice at \( 263 K \) to liquid water at
a temperature of \( 283 K ? \)
\( \boldsymbol{C}_{\boldsymbol{i c e}}=\mathbf{0 . 4 9} \boldsymbol{c a l} /\left(\boldsymbol{g}^{o} \boldsymbol{C}\right) \)
\( \boldsymbol{C}_{\boldsymbol{w} \text {ater}}=\mathbf{1 . 0 0} \boldsymbol{c a l} /\left(\boldsymbol{g}^{\boldsymbol{o}} \boldsymbol{C}\right) \)
\( \Delta H_{f u s}=79.8 \mathrm{cal} / g \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{\boldsymbol{v a p}}=\mathbf{5 4 0} \boldsymbol{c a l} / \boldsymbol{g} \)
A .9470 call \( l \)
B. 3288 cal
c. 2288 cal
D. 727.3 cal
Subject: Maths
If a ray makes angles \( \alpha, \beta, \gamma \) and \( \delta \) with the four diagonals of a cube and
\( \mathbf{A}: \cos ^{2} \boldsymbol{\alpha}+\cos ^{2} \boldsymbol{\beta}+\cos ^{2} \boldsymbol{\gamma}+\cos ^{2} \boldsymbol{\delta} \)
\( \mathbf{B}: \sin ^{2} \boldsymbol{\alpha}+\sin ^{2} \boldsymbol{\beta}+\sin ^{2} \boldsymbol{\gamma}+\sin ^{2} \boldsymbol{\delta} \)
\( \mathbf{C}: \cos 2 \boldsymbol{\alpha}+\cos 2 \boldsymbol{\beta}+\cos 2 \gamma+\cos 2 \boldsymbol{\delta} \)
Arrange \( A, B, C \) in descending order
A. \( B, A, C \)
в. \( A, B, C \)
c. \( C, A, B \)
D. \( B, C, A \)
Subject: Physics
An object and a screen are mounted on an optical bench and a converging lens is placed between them so that a sharp
image is received on the screen. The linear magnification of the image is 2.5 The lens is now moved \( 30 \mathrm{cm} \) nearer
to the screen and a sharp image is again formed on the screen. The focal length of the lens is:
A . \( 14.0 \mathrm{cm} \)
в. \( 14.3 \mathrm{cm} \)
c. \( 14.6 \mathrm{cm} \)
D. \( 14.9 \mathrm{cm} \)
Subject: Maths
Solve the following system of equations:
\( \mathbf{8} \boldsymbol{v}=\mathbf{3} \boldsymbol{u}+\mathbf{5} \boldsymbol{u} \boldsymbol{v} \)
\( \mathbf{6} \boldsymbol{v}-\mathbf{5} \boldsymbol{u}=-\mathbf{2} \boldsymbol{u} \boldsymbol{v} \)
Subject: Chemistry
Q Type your question
appropriate choice.
Column I 11
\( (A) \)
\[
\begin{array}{l}
\left.3 M g_{(} s\right)+ \\
N_{2(g)} \stackrel{\Delta}{\longrightarrow} \quad(i) \quad \text { Displacement }
\end{array}
\]
\( N_{2}(g) \longrightarrow \)
\( M g_{3} N_{2(s)} \)
\[
\begin{array}{l}
\left.N a H_{(} s\right)+ \\
\left.H_{2} O_{(} l\right) \rightarrow
\end{array}
\]
\( (B) \)
\[
N a O H_{(a q)}+
\]
\( (i i) \)
Decomposition
\( H_{2(g)} \)
\[
3 C l O_{(a q)}^{-} \rightarrow
\]
\( (C) \)
\( 2 C l_{(a q)}^{-}+ \) \( (i i i) \) Combination
\( \mathrm{ClO}^{-}_{(a q)} \)
\[
2 K C l O_{3(s)} \rightarrow
\]
\( (D) \)
\( \left.2 K C l_{(} s\right)+ \) \( (i v) \) Disproportiona
\( 3 O_{2(g)} \)
\( \mathbf{A} \cdot(A) \rightarrow(i),(B) \rightarrow(i i i),(C) \rightarrow(i i), D \rightarrow(i v) \)
B \( .(A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i i), D \rightarrow(i) \)
\( \mathbf{c} \cdot(A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i i i), D \rightarrow(i v) \)
\( \mathbf{D} \cdot(A) \rightarrow(i i i),(B) \rightarrow(i),(C) \rightarrow(i v), D \rightarrow(i i) \)
Subject: Chemistry
The value of \( \Delta G_{r}^{\circ} \) of gaseous mercury is \( 31 k J / \) mole. At what external pressure
mercury start boiling \( 25^{\circ} C \)
\( \mathbf{A} \cdot 10^{-5.44} \)
B. \( 10^{-12.5} \)
D. \( 10^{-3.12} \)
Subject: Chemistry
Which of the following statement gives the correct explanation of the fact
that solubility of alkali metal fluorides increases down the group?
A. Hydration energy increases and lattice energy decreases down the group
B. Both energy decrease down the group but decrease in hydration energy is rapid.
c. Both energy decrease down the group but decrease in lattice energy is more
D. Both energy increase down the group but increase in hydration energy is rapid.
Subject: Physics
A beam of light striking the surface of a
glass plate from the air as shown in
above figure.
If the angle between reflected beam and
refracted beam is 90 degree, Find out
the index of refraction of the glass?
\( A \cdot \sin 55^{\circ} \)
B. \( \frac{1}{\sin 55^{\circ}} \)
c. \( \frac{1}{\sin 35^{\circ}} \)
D. \( \frac{\sin 55^{\circ}}{\sin 35^{\circ}} \)
E \( \cdot \frac{\sin 35^{\circ}}{\sin 55^{\circ}} \)
Subject: Physics
For the pulley system shown in
Fig.6.317, each of the cables at \( A \) and \( B \)
is given a velocity of \( 2 m s^{-1} \) in the
direction of the arrow. Determine the
upward velocity v of the load \( m \)
A \( \cdot 1.5 m s^{-} \)
\( \mathbf{B} \cdot 3 m s^{-1} \)
\( c \cdot 63 s^{-1} \)
D. \( 4.5 m s^{-} \)
Subject: Maths
The sum of the following series \( 1+6+ \) \( \frac{\mathbf{9}\left(\mathbf{1}^{2}+\mathbf{2}^{2}+\mathbf{3}^{2}\right)}{\mathbf{7}}+ \)
\( \frac{12\left(1^{2}+2^{2}+3^{2}+4^{2}\right)}{9}+ \)
\( \frac{15\left(1^{2}+2^{2}+\ldots+5^{2}\right)}{11}+\ldots . \) up to 15
terms is:
A . 7820
в. 7830
c. 7520
D. 7510
Subject: Maths
Divide the polynomial by monomial:
\( 3 x^{5}-4 x^{4}+3 x^{3}+2 x ; x^{2}-3 \)
A \( \cdot\left(x^{2}-3\right)\left(3 x^{3}-4 x^{2}+12 x-12\right)+38 x-36 \)
B . \( \left(x^{2}-3\right)\left(x^{3}-4 x^{2}+2 x-2\right)+3 x-6 \)
C. \( \left(2 x^{2}-7\right)\left(3 x^{3}+4 x^{2}+x-1\right)+47 x-109 \)
D. \( \left(2 x^{2}+7\right)\left(3 x^{3}-4 x^{2}+12 x-12\right)+38 x-36 \)
Subject: Chemistry
Statement 1: An element that has an
electron configuration of \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{3} 4 s^{2} \) is a transition
element.
Statement 2: The transition elements
from scandium to zinc are filling the \( 3 d \)
orbitals.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.
Subject: Maths
What are the solution(s) to the system
of equations \( \boldsymbol{y}=\boldsymbol{x}^{2}-\mathbf{9} \) and \( \boldsymbol{y}-\boldsymbol{3}= \)
\( x ? \)
A. -3,0 and 4,7
в. -3,0
c. 4,7
D. 4,-3
Subject: Maths
\( \operatorname{Let} A=\{1,2,3, \dots \dots 50\} \) and \( B= \)
\( \{2,4,6 \dots \dots .100\} \). The number of
elements \( (x, y) \in A \times B \) such that \( x+ \)
\( \boldsymbol{y}=\mathbf{5 0} \)
A .24
B . 25
c. 50
D. 75
Subject: Physics
A nuclear fission is given below \( A^{240} \rightarrow B^{100}+C^{140}+Q(\text {energy}) \)
Let binding energy per nucleon \( A, B \) and \( \mathrm{C} \) is \( 7.6 \mathrm{MeV}, 8.1 \mathrm{MeV} \) and \( 8.1 \mathrm{MeV} \)
respectively. Value of \( Q \) is :
A. 20 Mev
B. 220 MeV
c. 120 Mev
D. 240 Mev
Subject: Maths
The order of the differential equation whose general solution is given by \( \boldsymbol{y}=\left(\boldsymbol{C}_{1}+\boldsymbol{C}_{2}\right) \cos \left(\boldsymbol{x}+\boldsymbol{C}_{3}\right)-\boldsymbol{C}_{4} \boldsymbol{e}^{\boldsymbol{x}+\boldsymbol{C}_{5}} \)
where, \( C_{1}, C_{2}, C_{3}, C_{4}, C_{5} \) are arbitrary constants, is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c .3 \)
D.
Subject: Physics
A circular loop of radius \( \boldsymbol{R} \), carrying
current \( I \), lies in \( x-y \) plane with its
center at the origin. The total magnetic
flux through \( x-y \) plane is
This question has multiple correct options
A. directly proportional to \( l \)
B. directly proportional to \( R \)
c. inversely proportional to \( R \)
D. zero
Subject: Maths
Let \( I \) be the purchase value of an equipment and \( v(t) \) is the value after it has been used for \( t \) years. the value \( v(t) \) depreciates at a rate \( \frac{\boldsymbol{d v}(\boldsymbol{t})}{\boldsymbol{d t}}=-\boldsymbol{k}(\boldsymbol{T}- \)
\( t) \) where \( k>0 \) is a constant and \( T \) is
the total life in years then the scrap
value \( v(T) \) of the equipment is
A \( \cdot I-\frac{k T^{2}}{2} \)
B. \( _{I-\frac{k(T-t)^{2}}{2}} \)
\( \mathbf{c} \cdot e^{-k T} \)
D. \( T^{2}-\frac{1}{T} \)
Subject: Physics
A charge \( Q \) is to be distributed on two
objects, \( A \) and \( B \). The values of the
charges on the objects are such that the force between the objects will be
maximum. The ratio \( Q_{A}: Q_{B} \) will be
A . 1: 1
B. 1: 2
c. 1: 3
D. 1: 4
Subject: Physics
A body is moving with constant acceleration from \( A \) to \( B \) in a straight line. \( C \) is the mid-point of \( A B . \) If \( u \) and \( v \) are the speeds at \( A \) and \( B \) respectively. The speed at \( C \) is
A \( \cdot \frac{u+v}{2} \)
B. \( \frac{u v}{2} \)
c. \( \sqrt{\frac{u^{2}+v^{2}}{2}} \)
D. \( \sqrt{\frac{u^{2}-v^{2}}{2}} \)
Subject: Chemistry
Select the correct statement.
\( \mathbf{A} \cdot \) The \( S-F \) bond length is longer in \( S F_{6} \) compared to
that in \( S F_{2} \)
B. In \( P C l_{5} \) axial bonds are smaller than of equatorial bonds.
C \( \cdot \ln I F_{7} \) axial bonds are longer than that of equatorial bonds
D. All are correct.
Subject: Maths
Probability of hitting a target independently of 4 persons are \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{8} . \) Then the probability that
target is hit, is?
A \( \cdot \frac{1}{192} \)
в. \( \frac{5}{192} \)
c. \( \frac{25}{32} \)
D. \( \frac{7}{32} \)
Subject: Physics
A person travels \( 6 \mathrm{m} \) towards the east
and \( 8 \mathrm{m} \) towards north from there again
he traveled \( 16 \mathrm{m} \) towards the south. What is the displacement covered by the person?
A . \( 10 \mathrm{m} \)
в. 20 m
c. \( 30 \mathrm{m} \)
D. \( 40 \mathrm{m} \)
Subject: Physics
(a) Obtain an expression for the energy stored in a solenoid of self-inductance
\( L^{\prime} \) when the current though it grows from zero to \( ^{\prime} I^{\prime} \)
(b) A square loop MNOP of side \( 20 \mathrm{cm} \) is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the figure. The loop is pulled with a constant velocity of \( 20 \mathrm{cm} s^{-1} \) till it goes out of the field
(i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist?
(ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time.
\[
x \times x \times x \times x \times x
\]
Subject: Physics
Two moles of a gas \( A \) at \( 27^{\circ} \mathrm{C} \) mixed
with a 3 moles of \( \operatorname{gas} \) at \( 37^{\circ} \mathrm{C} \). If both are monatomic ideal gases, what will be the temperature of the mixture?
\( \mathbf{A} \cdot 66^{\circ} C \)
В. \( 11^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 22^{\circ} C \)
D. \( 33^{\circ} \mathrm{C} \)
Subject: Physics
The rods of length \( L_{1} \) and \( L_{2} \) are made of materials whose coefficient of linear
expansion are \( \alpha_{1} \) and \( \alpha_{2} \) respectively.If the difference between the two length of independent of temperature, then
A \( \cdot \frac{L_{1}}{L_{2}}=\frac{\alpha_{1}}{\alpha_{2}} \)
B. \( \frac{L_{1}}{L_{2}}=\frac{\alpha_{2}}{\alpha_{1}} \)
c. \( L_{1}^{2} \alpha_{1}=L_{2}^{2} \alpha_{2} \)
D. \( \alpha_{1}^{2} L_{1}=\alpha_{2}^{2} L_{2} \)
Subject: Physics
The frequency of light in air is \( 5 \times \) \( 10^{14} H z . \) What will be the frequency of
light, when it enters in the water?
A \( .2 .5 \times 10^{14} \mathrm{Hz} \)
В. \( 5 \times 10^{14} \mathrm{Hz} \)
\( \mathbf{c} \cdot 10^{15} H z \)
D. 2.5 \( \times 10^{12} \mathrm{Hz} \)
Subject: Maths
Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( \mathbf{1}+\mathbf{3}+\mathbf{3}^{2}+\ldots+\mathbf{3}^{n-1}=\frac{\left(\mathbf{3}^{n}-\mathbf{1}\right)}{\mathbf{2}} \)
Subject: Physics
Find density when a mass of \( 9.23 \mathrm{kg} \) occupies a volume of \( 1.1 m^{3} \) with due
regard to significant figures.
\( \mathbf{A} \cdot 8.4 k g / m^{3} \)
B. \( 8.39 k g / m^{3} \)
\( \mathbf{c} \cdot 8.3 k g / m^{3} \)
D. None of the above
Subject: Maths
Find variance for following data:
\( \begin{array}{lllll}\text { Class } & 0- & 10- & 20- & 30 \\ & 10 & 20 & 30 & 40\end{array} \)
frequency ey 6 8
A. 14.75
в. 15.75
c. 17.75
D. 16.75