AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The resistance of an iron wire is \( 10 \Omega \)
and its temperature coefficient of
resistance is \( 5 \times 10^{-3} /^{o} C . \) A current of
\( 30 \mathrm{mA} \) is flowing in it at \( 20^{\circ} \mathrm{C} \). Keeping potential difference across its ends constant, if its temperature is
increased to \( 120^{\circ} \mathrm{C} \) then the current
flowing in the wire will be (in \( \mathrm{mA} \) )
A . 20
B . 35
c. 10
D. 40
Subject: Chemistry
In which of the following reactions, the product obtained is chiral?
A. \( C H_{3} C O C H_{3} \stackrel{N a B H_{4}}{\longrightarrow} \)
B. \( C H_{3} \) COCl Rosenmund's reduction
c. \( C H_{3} C H_{2} C O_{2} C H_{2} C H_{3} \stackrel{S n, H C l}{\longrightarrow} \)
D. \( C H_{3} C H_{2} C O C H_{3} \stackrel{L i A H H_{4}}{\longrightarrow} \)
Subject: Physics
Assertion
A capacitor can be given only a limited
quantity of charge
Reason
A capacitor is an arrangement which can store sufficient quantity of charge
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 is correct
Subject: Maths
In the given figure, \( \angle \mathbf{1}=\mathbf{7 0}^{\circ} . \) Find
\( 180^{\circ}-2 \angle x \)
\( A \cdot 50^{\circ} \)
B . \( 40^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Physics
Mercury boils at \( 356^{\circ} \mathrm{C} \). However mercury thermometers are made such
that they can measure temperatures up to \( 500^{\circ} \mathrm{C} \). This is done by :
A. maintaining vacuum above the mercury column in the steam of the thermometer
B. filling nitrogen gas at high pressure above the mercury column
C. filling nitrogen gas at low pressure above the mercury column
D. filling oxygen gas at high pressure above the mercury column
Subject: Maths
Four digit numbers are formed using
each of the digits \( 1,2, \ldots \ldots ., 8 \) only once One number from them is picked at random then the probability that the selected number contains unity is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{8} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{3} \)
Subject: Physics
In a Young's double slit experiment, let
\( \beta \) is the fringe width, and let \( I_{o} \) be the intensity at the central bright fringe. At a distance \( x \) from the central bright
fringe, the intensity will be:
A \( \cdot I_{o} \cos \left(\frac{x}{\beta}\right) \)
B \( \cdot I_{o} \cos ^{2}\left(\frac{x}{\beta}\right) \)
\( \mathbf{c} \cdot_{I_{o} \cos ^{2}\left(\frac{\pi x}{\beta}\right)} \)
D. \( \left(\frac{I_{o}}{4}\right) \cos ^{2}\left(\frac{\pi x}{\beta}\right) \)
Subject: Maths
\( * \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{1-\sin x}{(\pi-2 x)^{2}} \cdot \frac{\log \sin x}{\log \left(1+\pi^{2}-4 \pi x+4 x^{2}\right)}, x \)
\( \pi / 2 \) The assigned to function at \( x= \)
\( \pi / 2 \) in order that it may be continuous
at \( x=\pi / 2 \) is \( -\frac{1}{m} . \) Find \( m \)
Subject: Maths
The coefficient of \( x^{4} \) in the expansion of
\( \{\sqrt{1+x^{2}}-x\}^{-1} \) in ascending powers
of \( x, \) when \( |x|<1 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D. \( -\frac{1}{8} \)
Subject: Maths
f 0 is a point on the circle and \( P \) is a
point in the exterior of the circle. Length
of \( \boldsymbol{O} \boldsymbol{P}=7.5 \mathrm{cm} \) and radius of the circle
is \( 5.5 \mathrm{cm} . \) What will be the length of \( Q P \) if \( Q \) is the centre?
A. \( 5.5 \mathrm{cm} \)
B. \( 13 \mathrm{cm} \)
\( c .7 .5 \mathrm{cm} \)
D. \( 13.5 \mathrm{cm} \)
Subject: Maths
Prove the converse of the mid-point theorem following the guidelines given below: Consider a triangle \( A B C \) with \( D \) as the mid-point of \( A B . \) Draw \( D E \| B C \)
to intersect \( A C \) in \( E . \) Let \( E_{1} \) be the mid-
point of \( A C . \) Use mid-point theorem to
\( \operatorname{get} D E_{1} \| B C \) and \( D E_{1}=B C / 2 \)
Conclude \( E=E_{1} \) and hence \( E \) is the
mid-point of \( \boldsymbol{A C} \)
Subject: Maths
Find the square of \( 3 a+7 b \)
\( \mathbf{A} \cdot 9 a^{2}+42 a b+49 b^{2} \)
B \( \cdot 9 a^{2}+40 a b+49 b^{2} \)
C \( \cdot 18 a^{2}+42 a b+98 b^{2} \)
D. \( 18 a^{2}+40 a b+98 b^{2} \)
Subject: Physics
The area of cross section of the wider
tube shown in figure is \( 900 \mathrm{cm}^{2} \). If the
boy standing on the piston weighs 45
kg, the difference in the levels of water
in the two tubes.
A. \( 50 \mathrm{cm} \)
B. 25cm
c. \( 75 \mathrm{cm} \)
D. 100 \( \mathrm{cm} \)
Subject: Chemistry
Which of the following statements
is/are true?
This question has multiple correct options
A. It is impossible to satisfy the octet rule for all atoms in \( X e F_{2} \)
B. \( M g S O_{4} \) is soluble in water because hydration energy of \( M g S O_{4} \) is higher in comparison to its lattice energy.
C. The bond in \( N O^{+} \) should be stronger than the bond in
\( N O^{-} \)
D. For ozone molecule, one oxygen-oxygen bond is stronger than the other oxygen-oxygen bond.
Subject: Physics
Figures \( (a),(b),(c) \) and \( (d) \) respectively
correspond to
A. The short-sighted eye, the correction of long-sight, the long-sighted eye and the correction of short-sight
B. The short-sighted eye, the correction of short-sight, the long-sighted eye and the correction of long-sight
c. The long-sighted eye, correction of short-sight, the short-sighted eye and the correction of long-sight
D. The long-sighted eye, the correction of long-sight, the long-sighted eye and the correction of short-sight
Subject: Physics
A \( 2.0 m \) diameter propeller is rotating at
\( 2500 r p m \)
Which of the following values best represents the tangential velocity of the tip of the propeller blade?
A \( .262 m / s \)
в. \( 524 m / s \)
c. \( 1,050 m / s \)
D. \( 15,700 \mathrm{m} / \mathrm{s} \)
E . \( 2500 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
\( 56 \mathrm{g} \) of nitrogen and \( 96 \mathrm{g} \) of oxygen are mixed isothermally and at a total pressure of 10 atm. The partial pressures of oxygen and nitrogen (in atm) are \( _{\text {- - }} \) -respectively
\( A \cdot 4,6 \)
B. 5,5
c. 2,8
\( D \cdot 6,4 \)
Subject: Physics
A soap bubble of radius \( 3 \mathrm{cm} \) is charged with surface charge density \( \sigma \) such that \( \frac{\sigma^{2}}{\epsilon_{0}}=0.4 S I \) units. The excess
pressure inside the bubble in SI unit
(surface tension of soap solution \( =3 \times \)
\( 10^{-3} \mathrm{N} / \mathrm{m} \) ) is:
A . \( 0 . \)
B. 0.2
c. 0.5
D. 0.25
Subject: Chemistry
toppr OG
Q Type your question_
-
carried out slowly and reversibly.
Starting at state a, where its volume
and pressure are \( \left(V_{0}, p_{0}\right), \) the gas
undergoes an isothermal expansion
until it reaches state b where its
volume and pressure are \( \left(8 V_{0}, p_{0} / 8\right) . \) In
process \( b \rightarrow c \) the gas is cooled at
constant volume to \( \left(8 V_{0}, p_{0} / 32\right) \)
Process \( c \rightarrow a \) is an adiabatic
compression back to state a.
Select incorrect statement:
This question has multiple correct options
\( \mathbf{A} \cdot a \rightarrow b, \) there is no change in internal energy of gas
B. \( c \rightarrow a \), there is no change in entropy of gas
c. \( b \rightarrow c \), there is no work done by gas
D. \( a \rightarrow b \rightarrow c \rightarrow a \), there is work done by gas in cyclic
process
Subject: Physics
The critical angle of a certain medium is \( \sin -1(35) \sin -1(35) \) The polarizing
angle of the medium is:
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left(\frac{4}{5}\right) \)
B. \( \tan ^{-1}\left(\frac{5}{3}\right) \)
\( ^{\mathbf{c}} \cdot \sin ^{-1}\left(\frac{3}{4}\right) \)
D. \( \tan ^{-1}\left(\frac{4}{3}\right) \)
Subject: Chemistry
The structure of Nylon-6 is:
\( \left[\begin{array}{rr}0 & \mathrm{H} \\ -\mathrm{c} \mathrm{H}_{2} & -\mathrm{C}-\mathrm{N}\end{array}\right] \)
B. \( \left[\begin{array}{rr}0 & H \\ \| & I \\ \left(C H_{2}\right)_{4}-C-N & -\end{array}\right] \)
\( \left[\begin{array}{cc}0 & H \\ \| & I \\ -C-\left(C H_{2}\right)_{5}-N & -\end{array}\right] \)
\( D \)
\( \left[\begin{array}{cc}\mathbf{o} & \mathbf{H} \\ \| & \mathbf{I} \\ -\mathbf{c}-\left(\mathbf{C H}_{2}\right)_{\mathbf{6}}-\mathbf{N} & \mathbf{-}_{\mathbf{n}}\end{array}\right. \)
Subject: Maths
Assertion \( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a}_{11} & \boldsymbol{a}_{12} \\ \boldsymbol{a}_{21} & \boldsymbol{a}_{22}\end{array}\right], \boldsymbol{X}=\left[\begin{array}{l}\boldsymbol{x}_{1} \\ \boldsymbol{x}_{2}\end{array}\right], \boldsymbol{y}= \)
\( \left[\begin{array}{l}\boldsymbol{y}_{1} \\ \boldsymbol{y}_{2}\end{array}\right. \)
If \( A \) is symmetric, then \( X^{\prime} A Y=Y^{\prime} A X \)
for each pair of \( X \) and \( Y \)
Reason
If \( \boldsymbol{X}^{\prime} \boldsymbol{A} \boldsymbol{Y}=\boldsymbol{Y}^{\prime} \boldsymbol{A} \boldsymbol{X} \) for each pair of \( \boldsymbol{X} \)
and \( Y, \) then \( A \) is symmetric.
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 is correct
Subject: Chemistry
The unit of ebullioscopic constant is:
A \( \cdot K \) Kg mol\( ^{-1} \) or \( K(\text { molality })^{-1} \)
B . mol Kg \( K^{-1} \) or \( K^{-1} \) (molality)
C \( \cdot k g \) mol \( ^{-1} K^{-1} \) or \( K^{-1}(\text {molality })^{-1} \)
D \cdot K mol kg \( ^{-1} \) or \( K(\text { molality }) \)
Subject: Physics
A \( 20 k g \) load is suspended from the
lower end of a wire \( 10 \mathrm{cm} \) long and \( 1 \mathrm{mm} \)
\( ^{2} \) in cross sectional area. The upper half of the wire is made of iron and the lower
half with aluminium. The total
elongation in the wire is
\( \left(Y_{i r o n}=20 \times 10^{10} \mathrm{N} / \mathrm{m}^{2}, Y_{A l}=7 \times 10^{10}\right. \)
\( \left.\mathrm{N} / \mathrm{m}^{2}\right) \)
A \( \cdot 1.92 \times 10^{-4} \mathrm{m} \)
B. 17.8 \( \times 10^{-3} \mathrm{m} \)
c. \( 1.78 \times 10^{-3} \mathrm{m} \)
D. \( 1.92 \times 10^{-3} \mathrm{m} \)
Subject: Chemistry
Considering the state of hybridization of carbon atoms, the molecule among the following which is linear is :
A \( \cdot C H_{3}-C H \equiv C H-C H_{3} \)
в. \( C H_{3}-C H=C H-C H_{3} \)
c. \( C H_{2}=C H-C H_{2}-C \equiv C H \)
D. \( C H_{3}-C H_{2}-C H_{2}-C H_{3} \)
Subject: Maths
The position vector of the foci of an ellipse are \( \vec{b} \) and \( -\vec{b}, \) and the length of
major axis is \( 2 a \), then the equation of
ellipse
A \( \cdot a^{4}-a^{2}\left(\vec{r}^{2}+\vec{b}^{2}\right)+\left(\vec{b}^{2} \times \vec{r}^{2}\right)=0 \)
\( ^{\text {В }} a^{4}-a^{2}\left(|\vec{r}|^{2}+|\vec{b}|^{2}\right)+\left(|\vec{b}|^{2} \cdot \vec{r}^{2}\right)=0 \)
c. \( a^{4}+\vec{a}^{2}\left(\vec{r}^{2}+\vec{b}^{2}\right)+\left(\vec{b}^{2} \cdot \vec{r}^{2}\right)=0 \)
D・ \( a^{4}-a^{2}\left(\vec{r}^{2}-\vec{b}^{2}\right)+\left(\vec{b}^{2} \cdot \vec{r}^{2}\right)=0 \)
Subject: Maths
If \( \boldsymbol{a}>\mathbf{0}, \lim _{x \rightarrow \infty} \frac{[\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b}]}{\boldsymbol{x}} \) is where [
denotes G.I.F.
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( [a] \)
\( D \cdot[b] \)
Subject: Chemistry
The freezing point of a solution containing 0.2 g of acetic acid in 20.0 g benzene is lowered by \( 0.45^{\circ} \mathrm{C} \). The degree of association of acetic acid in benzene is:
[Assume acetic acid dimerizes in
benzene and \( K_{f} \) for benzene \( =\mathbf{5 . 1 2} \mathbf{K} \)
\( \left.\mathrm{kg} \mathrm{mol}^{-1}\right] \)
A. \( 94.5 \% \)
B . \( 54.9 \% \)
c. \( 78.2 \% \)
D. 100\%
Subject: Maths
The H.C.F. of two expressions is \( x \) and their L.C.M is \( x^{3}-9 x \) IF one of the
expression is \( x^{2}+3 x \) then,the other
expression is
A \( \cdot x^{2}-3 x \)
B. \( x^{3}-3 x \)
c. \( x^{2}+9 x \)
D. \( x^{2}-9 x \)
Subject: Physics
The \( P E \) of a \( 2 k g \) particle, free to move along \( x \) -axis is given by \( V(x)= \) \( \left(\frac{x^{3}}{3}-\frac{x^{2}}{2}\right) J . \) The total mechanical energy of the particle is \( 4 J . \) Maximum
speed \( \left(\operatorname{in} m s^{-1}\right) \) is
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{2} \)
c. \( \frac{3}{\sqrt{2}} \)
D. \( \frac{5}{\sqrt{6}} \)
Subject: Physics
Two inductors \( L_{1} \) and \( L_{2} \) are connected
in parallel and a time varying current i flows as shown. The ratio of currents
\( \mathbf{i}_{i} / \mathrm{l}_{2} \) at any time \( \mathrm{t} \) is
\( A \cdot L_{1} / L_{2} \)
B . \( L_{2} / L_{1} \)
\( \mathbf{C} \cdot \frac{L_{1}^{2}}{\left(L_{1}+L_{2}\right)^{2}} \)
\( D \)
Subject: Chemistry
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C r}(\boldsymbol{S C} \boldsymbol{N})_{6}\right] \) and
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}(\boldsymbol{S C N})_{4}\right]\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}(\boldsymbol{S C N}\right. \)
are the examples of what type of isomerism?
A. lonisation isomerism
B. Linkage isomerism
c. coordination isomerism
D. Solvate isomerism
Subject: Physics
A projectile of mass \( m \) is fired with
velocity \( v \) from a point as shown in
figure, neglecting air resistance, what
is the change in momentum when
leaving \( P \) and arriving at \( Q ? \)
\( A \cdot 0 \)
\( \mathbf{B} \cdot m v \)
\( \mathbf{c} \cdot 4 m v \)
D. \( \frac{2 m v}{\sqrt{3}} \)
Subject: Physics
A \( 10 W \) electric heater is used to heat a
container filled with \( 0.5 \mathrm{kg} \) of water. It is
found that the temperature of water and
the container rises by \( 3 K \) in 15 min. The container is then emptied, dried
and filled with \( 2 k g \) of oil. The same heater now raises the temperature of
container-oil system by \( 2 K \) in 20 min. Assuming that there is no heat loss in the process and the specific heat of water is \( 4200 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \), the specific
heat of oil in the same unit is equal to:
A. \( 1.50 \times 10^{3} \)
В. \( 2.55 \times 10^{3} \)
c. \( 3.00 \times 10^{3} \)
D. \( 5.10 \times 10^{3} \)
Subject: Chemistry
One mole of \( H N O_{3} \) absorbs 5 moles of
electrons in a redox reaction. The
reduced product of this reaction is :
A. 1 mole \( N_{2} \)
B. 1 mole \( N_{2} \) O
c. 1 mole \( N O_{2} \)
D. 1 mole \( N H_{3} \)
Subject: Maths
A chord of length \( 30 \mathrm{cm} \) is drawn at a
distance of \( 8 \mathrm{cm} \) from the centre of
a circle. The radius of the circle (in cm.)
is
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 21 \mathrm{cm} \)
c. \( 18 \mathrm{cm} \)
D. \( 17 \mathrm{cm} \)
Subject: Maths
Solve:
\( \operatorname{cosec}^{-1}(\cos x) \) is real \( , \) if
A. \( x \in[-1,1] \)
в. \( x \in R \)
c. \( x \) is an odd multiple of \( \frac{\pi}{2} \)
D. x is a multiple of \( \pi \)
Subject: Physics
There is an infinite straight chain
of alternating charges \( q \) and \( -q \)
The distance between the two
neighbouring charges is equal to a. Find the interaction energy of any charge with all the other charges.
A \( \cdot \frac{2 q^{2}}{4 \pi \varepsilon_{0} a} \)
B \( \cdot \frac{2 q^{2} \log _{e} 2}{4 \pi \varepsilon_{0} a} \)
\( ^{\mathbf{C}}-\frac{2 q^{2} \log _{e} 2}{4 \pi \varepsilon_{0} a} \)
D. none of these
Subject: Maths
At some point \( \mathbf{P} \) on the ellipse, the segment \( \mathbf{S S}^{1} \) subtends a right angle,
then its eccentricity is
\( ^{A} \cdot_{e}=\frac{\sqrt{2}}{2} \)
в. \( e<\frac{1}{\sqrt{2}} \)
c. \( e>\frac{1}{\sqrt{2}} \)
D. \( \frac{\sqrt{3}}{2} \)
Subject: Maths
If \( 1, \log _{3}\left(3^{x}-2\right), 2 \log _{9}\left(3^{x}-8 / 3\right) \) are
in A.P., then the value of \( x \) can be-
\( \mathbf{A} \cdot \log \left(\frac{4}{3}\right) \)
B. \( \frac{\log 4}{\log 3} 4 \)
c.
\( \mathbf{D} \cdot \log _{3} 4 \)
Subject: Physics
Assertion
Electromotive force is a force which
help the electrons to flow and produce
current.
Reason
Electromotive force is independent of
the voltage across the cell
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
Three point charges of \( 2 q,-q \) and \( -q \) are placed at the corner of an equilateral triangle of side a. Then:
This question has multiple correct options
A. the potential at the centroid of the triangle is zero
B. the electric field at the centroid of triangle is zero
c. the dipole moment of the system is \( \sqrt{2} q a \hat{j} \)
D. the dipole moment of the system is \( \sqrt{3} q a \hat{j} \)
Subject: Physics
Assertion
nm is not same as mN
Reason
\( \ln m=10^{-9} m \operatorname{and} 1 m N=10^{-3} N \)
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 is correct
Subject: Physics
Two convex lenses have focal lengths 10
\( \mathrm{cm} \) and \( 40 \mathrm{cm} . \) If a telescope has to be
made by using these two lenses
1. The distance between the lenses
should be \( 50 \mathrm{cm} \)
2. The distance between the lenses
should be \( 30 \mathrm{cm} \)
3. The magnifying power of this
telescope will be 5
4. An inverted image will be produced in this telescope Which two of the give are correct?
A. 1 and 4
B. 2 and 4
c. 1 and 3
D. 3 and 4
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{g}^{\prime}(1)+\boldsymbol{g}^{\prime \prime}(2) \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(1) \cdot \boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{f}^{\prime}(\boldsymbol{x})+\boldsymbol{f}^{\prime \prime}(\boldsymbol{x}) \) then
This question has multiple correct options
A \( \cdot f^{\prime}(1)+f^{\prime}(2)=0 \)
B . \( g^{\prime}(2)=g^{\prime}(1) \)
c. \( g^{\prime \prime}(2)+f^{\prime \prime}(3)=6 \)
D. none of these
Subject: Chemistry
The decomposition of an equal mole of two reactants \( P \) and \( Q \) obey 1 st order kinetics with half-life 54 and 18
minutes respectively. If both are allowed to run for 54 minutes. The ratio of mole of \( Q \) and \( P \) left after decomposition will
be:
A . 3
B. \( \frac{1}{4} \)
\( c \cdot 4 \)
D. 16
Subject: Chemistry
The given figure depicts the change in
concentration of species \( X \) and \( Y \) as a
function of time. The point of
ntersection of the two curves
represents:
\( A \cdot t_{1 / 2} \)
в. \( t_{3 / 4} \)
\( c \cdot t_{2 / 3} \)
D. data insufficient to predict
Subject: Maths
Out of the following matrices, choose that matrix which is a scalar matrix.
\( A \cdot\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \)
В. \( \left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right] \)
c. \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0 \\ 0 & 0\end{array}\right] \)
D. \( \left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \)
Subject: Maths
The value of \( \left|\begin{array}{ccc}\boldsymbol{a}+\boldsymbol{p} \boldsymbol{d} & \boldsymbol{a}+\boldsymbol{q} \boldsymbol{d} \boldsymbol{a}+\boldsymbol{r} \boldsymbol{d} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r} \\ \boldsymbol{d} & \boldsymbol{f} & \boldsymbol{d}\end{array}\right| \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot 1 \)
D. \( p+q+r \)
Subject: Chemistry
Calculate the pH of \( 1.0 \times 10^{-3} \mathrm{M} \)
sodium phenolate, \( N a O C_{6} H_{5} \cdot K_{a} \) for
\( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C}_{6} \boldsymbol{H}_{5} \) is \( \boldsymbol{0 . 6} \times \mathbf{1 0}^{-10} \)
Subject: Chemistry
Complete the following reaction:
\( N a N O_{3}+N H_{4} C l \longrightarrow ? \)
\( \mathbf{A} \cdot N a N O_{3}+N H_{4} C l \longrightarrow N H_{4} N O_{3}+N a C l \stackrel{\Delta}{\rightarrow} N_{2} O+ \)
\( 2 H_{2} O \)
B \( \cdot N a N O_{3}+3 N H_{4} C l \longrightarrow 2 N H_{4} N O_{3}+N a C l \triangleq N_{2} O+ \)
\( 2 H_{2} O \)
\( \mathbf{c} \cdot 2 N a N O_{3}+3 N H_{4} C l \longrightarrow 2 N H_{4} N O_{3}+2 N a C l \triangleq \)
\( N_{2} O+2 H_{2} O \)
D. None of these
Subject: Chemistry
2 moles of \( P C l_{5} \) when heated in a
closed vessels of 2 litre capacity at
equilibrium \( 40 \% \) of \( P C l_{5} \) dissociated
in \( P C l_{3} \) and \( C l_{2} . \) What is the value of the equilibrium constant?
A. 0.267
B. 0.786
c. 0.345
D. 1.879
Subject: Maths
The formula for the coefficient of range is \( \frac{\text { Range }}{\boldsymbol{a}+\boldsymbol{b}} . \) Here, \( \boldsymbol{a} \) and \( \boldsymbol{b} \) denote
A. the mean and median of the data set
B. the maximum and the minimum value of the data set
c. the mean and mode value of the data set
D. the minimum and mean value of the data set
Subject: Chemistry
The correct order of decreasing polarity
¡s:
\( \mathbf{A} \cdot H F>S O_{2}>H_{2} O>N H_{3} \)
B \( \cdot H F>H_{2} O>S O_{2}>N H_{3} \)
\( \mathbf{c} \cdot H F>N H_{3}>S O_{2}>H_{2} O \)
\( \mathbf{D} \cdot H_{2} O>N H_{3}>S O_{2}>H F \)
Subject: Physics
An electron accelerated by \( 200 \mathrm{V} \) enters a magnetic field .If its velocity is \( 100 \mathrm{m} / \mathrm{sec} \). then \( (\mathrm{e} / \mathrm{m}) \) for it will be:
\( (\mathrm{C} / \mathrm{Kg}) \)
A. \( 1.75 \times 10^{10} \)
B. \( 1.75 \times 10^{11} \)
c. \( 1.75 \times 10^{9} \)
D. \( 1.75 \times 10^{6} \)
Subject: Maths
If the first, second and last terms of an
A.P be \( a, b, 2 a \) respectively, then its sum will be
A \( \cdot \frac{a b}{-a+b} \)
В. \( \frac{a b}{2(b-a)} \)
c. \( \frac{3 a b}{2(b-a)} \)
D. \( \frac{3 a b}{4(b-a)} \)
Subject: Maths
Show that the three lines with direction
\( \operatorname{cosines} \)
\( \frac{12}{13}, \frac{-3}{13}, \frac{-4}{13}: \frac{4}{13}, \frac{12}{13}, \frac{3}{13} ; \frac{-4}{13}, \frac{12}{13} \) are mutually
perpendicular
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}-\boldsymbol{i} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{i}\end{array}\right], \) then \( \boldsymbol{A}^{\prime} \boldsymbol{A} \) is equal to
A . \( I \)
B. \( -i A \)
\( c .-I \)
D. \( i A \)
Subject: Physics
A motor car moving at a speed of
\( 72 k m / h \) can not come to a stop in less
than \( 3.0 s \) while for a truck this time
interval is \( 5.0 s . \) On a higway the car is behind the truck both moving at
\( 72 k m / h . \) The truck gives a signal that
it is going to stop at emergency. At what
distance the car should be from the
truck so that it does not bump onto (collide with) the truck. Human
response time is \( 0.5 s \)
\( \mathbf{A} \cdot 1.25 m \)
в. \( 1.5 m \)
c. \( 1 m \)
D. \( 0.5 m \)
Subject: Chemistry
For the first order reaction, \( \boldsymbol{A}(\boldsymbol{g}) \rightarrow \)
\( 2 B(g)+C(g), \) the initial pressure is
\( \boldsymbol{P}_{\boldsymbol{A}}=\mathbf{9 0} \) mm Hg. Then pressure after 10
minutes is found to be 180 mm Hg. The
half-life period of the reaction is:
A \( \cdot 1.15 \times 10^{-3} \mathrm{sec}^{-1} \)
в. 600 sec
c. \( 3.45 \times 10^{-3} s e c^{-1} \)
D. 200 sec
Subject: Chemistry
An electron in the hydrogen atom is excited from \( 1^{s t} \) orbit to \( 5^{t h} \) orbit. Find
the change in energy of the electron in
\( e V: \)
A. (13.6 \( \times 24) / 25 \)
B. (13.6 \( \times 4) / 5 \)
\( c \cdot(0.529 \times 4) / 5 \)
D. (13.6 \( \times 4) / 9 \)
Subject: Physics
The apparent depth of water in a
cylindrical water tank of diameter \( 2 R \)
\( \mathrm{cm} \) is reducing at the rate of \( x \mathrm{cm} / \mathrm{min} \)
when water is being drained out at a
constant rate. The amount of water
drained in \( c c / \) minute is: \( \left(n_{1}=\right. \)
refractive index of air, \( n_{2}= \) refractive
index of water)
A \( \cdot \frac{x \pi R^{2} n_{1}}{n_{2}} \)
В \( \cdot \frac{x \pi R^{2} n_{2}}{n_{1}} \)
\( \mathbf{c} \cdot \frac{2 \pi R n_{1}}{n_{2}} \)
D. \( \pi R^{2} x \)