AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The solubility in water of a sparingly soluble salt \( A B_{2} \) is \( 1.0 \times 10^{-5} \) mol \( L^{-1} \)
Its solubility product will be:
A \( \cdot 4 \times 10^{-15} \)
В. \( 4 \times 10^{-10} \)
c. \( 1 \times 10^{-15} \)
D. \( 1 \times 10^{-10} \)
Subject: Chemistry
The heat of combustion of ethanol
determined in a bomb calorimeter is
\( -670.48 k c a l m o l^{-1} \) at \( 298 K . \) What is
the \( \Delta U \) at \( 298 K \) for the reaction?
A. -760 kcal \( m o l^{-1} \)
B. -670.48 k cal mol\( ^{-1} \)
c. +760 kcal \( m o l^{-1} \)
D. +670.48 k cal mol\( ^{-1} \)
Subject: Maths
\( \cos \left(\cot ^{-1}\left(\operatorname{cosec}\left(\cos ^{-1} a\right)\right)\right)=\dots \)
(where \( 0<a<1) \)
A \( \cdot \frac{1}{\sqrt{2-a^{2}}} \)
B. \( \sqrt{3-a^{2}} \)
c. \( \sqrt{2-a^{2}} \)
D. \( \frac{1}{\sqrt{2+a^{2}}} \)
Subject: Maths
If \( \boldsymbol{a}(\boldsymbol{p}+\boldsymbol{q})^{2}+2 \boldsymbol{b} \boldsymbol{p} \boldsymbol{q}+\boldsymbol{c}=\boldsymbol{0} \) and \( \boldsymbol{a}(\boldsymbol{p}+ \)
\( r)^{2}+2 p b r+c=0(a \neq 0), \) then
A \( \cdot q r=p^{2} \)
B \( \cdot q r=p^{2}+\frac{c}{a} \)
c. \( q r=-p^{2} \)
D. None of the above
Subject: Physics
The real angle of dip, if a magnet is
suspended at an angle of \( 30^{0} \) to the
magnetic meridian and the dip needle
makes an angle of \( 45^{0} \) with horizontal is :
\( ^{A} \cdot \tan ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
B \( \cdot \tan ^{-1}(\sqrt{3}) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{1}{2}\right) \)
D \( \cdot \tan ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)
Subject: Maths
Suppose a lot of \( n \) objects having \( n_{1} \)
objects of one kind, \( n_{2} \) objects are of
second kind, \( n_{3} \) objects of third kind, \( \dots \)
\( n_{k} \) objects of \( k^{t h} \) kind satisfying the
condition \( n_{1}+n_{2} \dots+n_{k}=n, \) then the
number of possible arrangements/permutation of \( \mathrm{m} \) objects out of this lot is the coefficient
of \( x^{m} \) in the expansion of \( m ! \prod\left\{\sum_{\lambda=0}^{a_{1}} \frac{x^{\lambda}}{\lambda !}\right\} \)
The number of permutations of the letters of the word SURITI taken 4 at a
time is
A . 360
B. 240
c. 216
D. 192
Subject: Maths
If \( f(x)=\left\{\begin{array}{ll}2 x+3 & x \leq 1 \\ a^{2} x+1 & x>1\end{array}, \) then the \right.
values of \( a \) for which \( f(x) \) is injective.
A . -3
B.
c. 0
D. none of these
Subject: Maths
Find the equation of the plane through the line
\( \boldsymbol{P}=\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c} \boldsymbol{z}+\boldsymbol{d}=\mathbf{0} \)
\( \boldsymbol{Q}=\boldsymbol{a}^{\prime} \boldsymbol{x}+\boldsymbol{b}^{\prime} \boldsymbol{y}+\boldsymbol{c}^{\prime} \boldsymbol{z}+\boldsymbol{d}^{\prime}=\mathbf{0} \)
and parallel to the line \( \frac{x}{l}=\frac{y}{m}=\frac{z}{n} \)
A \( \cdot P\left(a^{\prime} l+b^{\prime} m+c^{\prime} n\right)+Q(a l+b m+c n)=0 \)
B - \( P\left(a^{\prime} l+b^{\prime} m+c^{\prime} n\right)-Q(a l+b m+c n)=0 \)
c. \( Q\left(a^{\prime} l+b^{\prime} m+c^{\prime} n\right)-P(a l+b m+c n)=0 \)
D. \( Q\left(a^{\prime} l+b^{\prime} m+c^{\prime} n\right)+P(a l+b m+c n)=0 \)
Subject: Physics
The resistance of a heating element is
\( 99 \Omega \) at room temperature. What is the temperature of the element if the
resistance is found to be \( 116 \Omega ? \)
(Temperature coefficient of the material
of the resistor is \( 1.7 \times 10^{-4} o C^{-1} \) ).
A \( \cdot 9999^{\circ} \mathrm{C} \)
B . \( 1005.3^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 1020.2^{\circ} \mathrm{C} \)
D. \( 1037.1^{\circ} \mathrm{C} \)
Subject: Chemistry
Which of the following statements, about the advantage of roasitng of sulphide ore before reduction is not
true?
A. Roasting of the sulphide to the oxide is thermodynamically feasible
B. Carbon and hydrogen are suitable reducing agents for metal sulphides
C. The \( \Delta_{f} G^{0} \) of the sulphide is greater than those for \( C S_{2} \) and \( H_{2} S \)
D. The \( \Delta_{f} G^{0} \) is negative for roasting of sulphide ore to oxide
Subject: Physics
A bus starts from rest and moves with a
uniform acceleration of \( 1 ~ m s^{-2} . A \) boy
10 \( m \) behind the bus at the start runs
at a constant speed and catches the
bus in \( 10 s . \) Speed of the boy is :
A \( \cdot 10 m s^{-1} \)
B. \( 1 m s^{-1} \)
\( \mathrm{c} \cdot 6 \mathrm{ms}^{-1} \)
D. \( 4 m s^{-1} \)
Subject: Maths
Find the matrix \( A \), such that \( \left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right] A= \) \( \left[\begin{array}{ccc}-4 & 8 & 4 \\ -1 & 2 & 1 \\ -3 & 6 & 3\end{array}\right] \)
Subject: Physics
Assertion
For each ten degree rise of temperature the specific rate constant is nearly doubled.
Reason
Energy-wise distribution of molecules in a gas is an experimental function of temperature
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
If an antiderivative of \( f(x) \) is \( e^{x} \) and
that of \( g(x) \) is \( \cos x, \) then \( \int f(x) \cos x d x+\int g(x) e^{x} d x= \)
\( \mathbf{A} \cdot f(x) g(x)+c \)
в. \( f(x)+g(x)+c \)
c. \( e^{x} \cos x+c \)
D. \( -e^{x} \cos x+c \)
Subject: Maths
Three cuboids of width \( 8 \mathrm{m} \) and joined along its width. Find surface area of resulting cuboid. \( (l=1 \mathbf{m}, h=1 \mathbf{m}) \)
\( \mathbf{A} \cdot 34 m^{2} \)
B. \( 64 m^{2} \)
\( \mathbf{c} \cdot 98 m^{2} \)
D. None of the above
Subject: Physics
Figure shows three points \( A, B \) and \( C \) in a region of uniform electric field \( \vec{E} \). The
line \( A B \) is perpendicular and \( B C \) is parallel to the field lines. Then which of
the following holds good. Here \( \boldsymbol{V}_{\boldsymbol{A}}, \boldsymbol{V}_{\boldsymbol{B}} \)
and \( V_{C} \) represents the electric potential
at point \( A, B \) and \( C \) respectively.
\( \mathbf{A} \cdot V_{A}=V_{B}=V_{C} \)
B \( \cdot V_{A}=V_{B}>V_{C} \)
\( \mathbf{c} \cdot V_{A}=V_{B}<V_{C} \)
\( \mathbf{D} \cdot V_{A}>V_{B}=V_{C} \)
Subject: Maths
f \( \boldsymbol{x}_{\boldsymbol{i}}>\mathbf{0}, \boldsymbol{i}=\mathbf{1}, \mathbf{2}, \dots, \mathbf{5 0} \) and \( \boldsymbol{x}_{\mathbf{1}}+ \)
\( \boldsymbol{x}_{2}+\ldots+\boldsymbol{x}_{50}=\mathbf{5 0} \) then the minimum
value of \( \frac{1}{x_{1}}+\frac{1}{x_{2}}+\ldots+\frac{1}{x_{50}} \) equals to
A . 50
B. \( (50)^{2} \)
\( c \cdot(50)^{3} \)
D. \( (50)^{4} \)
Subject: Maths
Let \( \boldsymbol{z}=\frac{\cos \boldsymbol{\theta}+\boldsymbol{i} \sin \boldsymbol{\theta}}{\cos \boldsymbol{\theta}-\boldsymbol{i} \sin \boldsymbol{\theta}}, \frac{\boldsymbol{\pi}}{\boldsymbol{4}}<\mathbf{0}<\frac{\boldsymbol{\pi}}{\boldsymbol{2}} \)
Then arg z is
\( A \cdot 2 \theta \)
в. \( 2 \theta-\pi \)
\( c . \pi+2 \theta \)
D. None of these
Subject: Physics
composite tube as shown in the Figure
14.24. The radius of the semicircular
portion of the tube is \( r . \) The speed of
sound in air is \( v . \) The source of sound is
capable of giving sound of varied
frequency. If \( n \) is an integer then frequency for maximum intensity is given by:
\( \mathbf{A} \cdot n v / r \)
в. \( n v / r(\pi-2) \)
c. \( n v / \pi r r \)
D. \( n v / \pi(r-2) \)
Subject: Physics
The ionisation potential of \( \boldsymbol{H} \) -atom is
\( 13.6 V . \) When it is excited from ground state by monochromatic radiations of \( \$ \$ 970.6 / \) buildrel \( _{-} \) lcirc lover \( \mathrm{~ I l m a t h r m \{ A \} 3 \$ \$ , ~ t h e ~ n u m b e r ~ o f ~} \)
emission lines will be (according to Bohr's theory)
A . 10
B. 8
c. 6
\( D \)
Subject: Maths
A vector \( \vec{B} \) which has a magnitude 8.0 is added to a vector \( \vec{A} \) which lie along
the \( x \) -axis. The sum of these two vectors
is a third vector which lie along the \( y \)
axis and has a magnitude that is twice the magnitude of \( \vec{A} . \) The magnitude of
\( \vec{A} \) is:
A. \( \frac{8}{\sqrt{5}} \)
B. \( \frac{10}{\sqrt{5}} \)
c. \( \frac{8}{\sqrt{3}} \)
D. \( \frac{8}{\sqrt{6}} \)
Subject: Maths
\( S_{1}, S_{2} \) are foci of an ellipse of major axis
of length 10 units and \( P \) is any point on the ellipse such that perimeter of
triangle \( P S_{1} S_{2} \) is \( 15 . \) Then eccentricity
of the ellipse is:
A . 0.5
B. 0.25
c. 0.28
D. 0.75
Subject: Chemistry
Oxalic acid can donate two protons to water in successive reactions:
(1) \( \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{H}_{3} \boldsymbol{O}+ \)
\( (a q)+H C_{2} O_{4}^{-}(a q) \)
(2) \( H C_{2} O_{4}^{-}(a q)+H_{2} O(l) \rightleftharpoons H_{3} O+ \)
\( (a q)+C_{2} O_{4}^{2-}(a q) \)
f \( \boldsymbol{K}_{c 1}=\mathbf{5 . 9} \times \mathbf{1 0}^{-2} \) and \( \boldsymbol{K}_{c 2}=\mathbf{6 . 4} \times \)
\( 10^{-5} \) at \( 25^{0} C, \) what is the value of \( K_{c} \)
for reaction (3)\( ? \)
(3) \( \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{H}_{3} \boldsymbol{O}+(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-}(\boldsymbol{a} \boldsymbol{q}) \)
A \( \cdot 3.8 \times 10^{-6} \)
B. \( 1.1 \times 10^{-3} \)
D. \( 9.2 \times 10^{2} \)
Subject: Chemistry
A gas mixture \( 3.67 L \) in volume contain
\( C_{2} H_{4} \) and \( C H_{4} \) is proportion of 2: 1 by
moles and is at \( 25^{\circ} \mathrm{C} \) and 1 atm. If the
\( \triangle \boldsymbol{H}_{C}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{4}\right) \) and \( \triangle \boldsymbol{H}_{C}\left(\boldsymbol{C H}_{4}\right) \) are
-1400 and \( -900 k J / \) mol. Find the heat evolved on burning this mixture.
A. \( 20.91 k J \)
В. \( 50.88 k J \)
c. \( 185 k J \)
D. 160 k
Subject: Chemistry
Benzoic acid (molecular weight \( =122 \) g
mol \( ^{-1} \) ) associates to form dimer when
dissolved in benzene and the osmotic
pressure of a solution of 5 g of benzoic acid in \( 100 \mathrm{ml} \) benzene is 5.73 atm at
\( 10^{\circ} \mathrm{C} . \) What is the percentage
association of benzoic acid?
A . \( 8 \% \)
B. \( 80 \% \)
c. \( 40 \% \)
D. \( 20 \% \)
Subject: Maths
\[
\begin{aligned}
\operatorname{Let} x &=111 \ldots 11(20 \text { digits }) \\
y &=333 \ldots 33(10 \text { digits }) \\
\text { and } z &=222 \ldots 22(10 \text { digits })
\end{aligned}
\]
The value of \( \frac{\boldsymbol{x}-\boldsymbol{y}^{2}}{\boldsymbol{z}} \)
Subject: Chemistry
Which one of the following reactions of
Xenon compounds is not feasible?
\( \mathbf{A} \cdot X e O_{3}+6 H F \rightarrow X e F_{6}+3 H_{2} O \)
B. \( 3 X e F_{4}+6 H_{2} O \rightarrow 2 X e+X e O_{3}+12 H F+1.5 O_{2} \)
\( \mathbf{c} \cdot 2 X e F_{2}+2 H_{2} O \rightarrow 2 X e+4 H F+O_{2} \)
\( \mathbf{D} \cdot X e F_{6}+R b F \rightarrow R b\left[X e F_{7}\right] \)
Subject: Maths
Divide \( \boldsymbol{x}(\boldsymbol{x}+\mathbf{1})(\boldsymbol{x}+\mathbf{2})(\boldsymbol{x}+\boldsymbol{3}) \) by
\( (x+3)(x+2) \)
A. \( x(x+3) \)
в. \( x(x+2) \)
c. \( (x+1) \)
D. \( x(x+1) \)
Subject: Chemistry
Which one of the following is an
environment related disorder with
correct main cause?
A. Black lung disease is found mainly in workers of stone quarries and crushers
B. Blue-baby disease is due to heavy use of nitrogeneous fertilizers.
C. Non-Hodgkin's Iymphoma is found mainly in worker involved in manufacture of neem-based pesticides.
D. Skin cancer occurs mainly in people exposed to benzene and methane.
Subject: Chemistry
The minimum possible angular momenturn of an election present in an orbital is \( \ldots \ldots . . . . . . \) if the magnetic quanthem number associated with this
orbinal are -1,0,+1
A \( \cdot \frac{5 h}{2 \pi} \)
в. \( \frac{3 h}{2 \pi} \)
\( c \cdot \frac{h}{2 \pi} \)
D. \( \frac{h}{\pi} \)
Subject: Physics
To reduce the light reflected by the glass surface of a camera lens, the surface is
coated with a thin layer of another material which has an index of
refraction \( (\mu=7 / 4) \) smaller than that of glass. The least thickness of the layer to ensure that light falling
perpendicularly on the surface and
having wavelengths, \( \lambda_{1}=700 \mathrm{nm} \) and \( \lambda_{2} \)
\( =420 \mathrm{nm} \) will be weekly reflected for
both wavelengths is \( 10^{-7} \mathrm{m} \). Find \( x \) ?
Subject: Maths
Show that in an arithmetical
progression \( a_{1}, a_{2}, a_{3} \)
\( \boldsymbol{S}=\boldsymbol{a}_{1}^{2}-\boldsymbol{a}_{2}^{2}+\boldsymbol{a}_{3}^{2}-\boldsymbol{a}_{4}^{2}+_{--} \)
\( \boldsymbol{a}_{2 k}^{2} \)
\( =\frac{k}{2 k-1}\left(a_{1}^{2}-a_{2 k}^{2}\right) \)
Subject: Physics
Two resistances are expressed as
\( \boldsymbol{R}_{1}(\mathbf{4} \pm \mathbf{0 . 5} \%) \boldsymbol{\Omega} \) and \( \boldsymbol{R}_{2}(\mathbf{1 2} \pm \mathbf{0 . 5} \%) \boldsymbol{\Omega} \)
The net resistance when they are
connected in series with percentage
error is:
(In series \( \left.\boldsymbol{R}=\boldsymbol{R}_{1}+\boldsymbol{R}_{2}\right) \)
A . \( (16 \pm 0.5 \%) \Omega \)
B. \( (16 \pm 6.25 \%) \Omega \)
c. \( (16 \pm 22 \%) \Omega \)
D. \( (16 \pm 2.2 \%) \Omega \)
Subject: Maths
One hundred identical coins, each with
probability \( p, \) of showing up heads are tossed. If \( 0<p<1 \) and the probability
of heads showing on 50 coins is equal to that of the heads showing in 51 coins, then the value of \( p \) is
A \( \cdot \frac{1}{2} \)
в. \( \frac{49}{101} \)
c. \( \frac{50}{101} \)
D. \( \frac{51}{101} \)
Subject: Chemistry
\( B r O_{3}^{-} \) is oxidised to \( B r O_{4}^{-} \) by \( X e F_{2} \)
\( \underset{\boldsymbol{m}_{1}}{\boldsymbol{X} \boldsymbol{F}_{2}}+\underset{\boldsymbol{m}_{2}}{\boldsymbol{B} \boldsymbol{r}} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{4}^{-}+ \)
\( \boldsymbol{X} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{H} \boldsymbol{F} \)
where,
\( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} \) are the molar masses of
\( X e F_{2} \) and \( B r O_{3}^{-}, \) respectively.

Ratio of equivalent mass of \( X e F_{2} \) and
\( B r O_{3}^{-} \) is
A \( \cdot \frac{m_{1}}{m_{2}} \)
в. \( \frac{2 m_{1}}{m_{2}} \)
c. \( \frac{m_{1}}{2 m_{2}} \)
D. \( \frac{m_{1}}{3 m_{2}} \)
Subject: Physics
What is the change in the temperature on Fahrenheit scale and on Kelvin scale,
if a iron piece is heated from \( 30^{\circ} \) to
\( 90^{\circ} \mathrm{C} ? \)
A \( \cdot 108^{\circ} F, 60 K \)
в. \( 100^{\circ} F, 55 K \)
c. \( 100^{\circ} F, 65 K \)
D. \( 60^{\circ} F, 108 K \)
Subject: Maths
If / the last term, d the common difference and 's' the sum of n terms
\( (n \neq 1) \) and 'a' the first term of an A.P.
be connected by the eqution \( 8 d s= \)
\( (d+2 l)^{2}, \) then \( d= \)
A . \( 2 a \)
в.
c. за
D. \( 4 a \)
Subject: Maths
In the figure, \( \triangle A B C \) is right angled at
\( B . D \) is any point on \( A B \)
\( \operatorname{seg} D E \perp \operatorname{sid} e A C . \) If \( A D= \)
\( 6 \mathrm{cm}, A B=12 \mathrm{cm} A C=18 \mathrm{cm} . \) Find
\( A E \)
\( A \cdot 5 c m \)
в. 3 ст
\( c .4 c m \)
\( 0.6 \mathrm{cm} \)
Subject: Physics
If \( x \) denotes displacement in time \( t \) and
\( \boldsymbol{x}=\boldsymbol{a} \cos \omega \boldsymbol{t}, \) then for \( \boldsymbol{\omega}=\mathbf{1}, \) the
acceleration will be
\( \mathbf{A} \cdot a \cos t \)
B. - a cost
\( \mathbf{c} \cdot a \sin t \)
D. - \( a \sin t \)
Subject: Chemistry
Which of the following statements are
incorrect:
This question has multiple correct options
A. Molar volume of every gas at STP is \( 22.4 \mathrm{L} \)
B. Under critical states compressibility factor is 1
C. All gases will have equal value of average \( \mathrm{KE} \) at a given temperature
D. At absolute zero, KE is 3/2 R
Subject: Maths
If \( \boldsymbol{A}=\mathbf{6 0}^{\circ} \) and \( \boldsymbol{B}=\mathbf{3 0}^{\boldsymbol{o}}, \) verify that
\( \tan (\boldsymbol{A}+\boldsymbol{B})=\frac{\tan \boldsymbol{A}+\tan \boldsymbol{B}}{1-\tan \boldsymbol{A} \tan \boldsymbol{B}} \)
Subject: Physics
A uniform aluminium wire of length \( 3 \mathrm{m} \)
and area of cross-section \( 2 m m^{2} \) is
extended through 12 mm. The energy stored in the wire is
\( \boldsymbol{Y}_{\boldsymbol{A l}}=\boldsymbol{7} \times \mathbf{1 0}^{\mathbf{1 0}} \boldsymbol{N} / \boldsymbol{m}^{2} \mathbf{)} \)
A . \( 336 J \)
B. 33.6 \( J \)
c. \( 3.36 J \)
D. 0.336 J
Subject: Chemistry
One litre of \( C O_{2} \) is passes over hot coke. After one hour volume becomes
1.4 4 Itres. Composition of product is:
A. 0.6 litre \( C O_{2} \)
B. 0.8 litre \( C O_{2} \)
c. 0.6 litre \( C O_{2} \) and 0.8 litre co
D. None of these
Subject: Chemistry
Thermal decomposition of a compound
is of first order. If 50 percent of a sample of compound is decomposed in 120 mins, how long will it take for 90 percent of compound to decompose?
\( \mathbf{A} \cdot 299 \mathrm{mins} \)
B. 399 mins.
c. 99 mins.
D. 9.9 mins.
Subject: Maths
A game has 2 spinners. Spinner \( \# 1 \) has a
probability of landing red of \( 2 / 3 . \) And, spinner#2 has a probability of landing red of \( 1 / 5 \) What is the probability spinner#1 lands red AND spinner#2 does NOT land red?
A . \( 2 / 15 \)
B. \( 8 / 15 \)
c. \( 13 / 15 \)
D. 1
E. \( 3 / 5 \)
Subject: Chemistry
Find the number of molecules(s) among
the following which is/are planar and have dipole moment.
\( \boldsymbol{S} \boldsymbol{F}_{4}, \quad \boldsymbol{P} \boldsymbol{C l}_{3} \boldsymbol{F}_{2}, \quad \boldsymbol{P C l}_{2} \boldsymbol{F}_{3}, \quad \boldsymbol{I}_{3}^{-} \)
Subject: Chemistry
Indicate the types of isomerism exhibited by the following complex and
draw the structure of this isomer.
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)
Subject: Physics
A molecule of a substance has a
permanent electric dipole moment of magnitude \( 10^{-30} \mathrm{cm} . \) A mole of this substance is polarised by applying a strong electrostatic field of magnitude \( 10^{7} V m^{-1} . \) The direction of field is
changed by an angle \( 60^{\circ} . \) The heat released by the substance in aligning its dipole along the new direction of the field is
A. -6.5
в. \( -3 . \)
\( c .3 J \)
D. 65
Subject: Physics
A car of mass \( 1000 \mathrm{kg} \) moves on a
circular track of radius \( 40 \mathrm{m} \). If the
coefficient of friction is 1.28 then the
maximum velocity with which the car can be moved is:
A. \( 22.4 \mathrm{m} / \mathrm{s} \)
B. \( 112 \mathrm{m} / \mathrm{s} \)
c. \( \frac{(0.64 \times 40)}{(1000 \times 100)} \) m/s
D. \( 1000 \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( \boldsymbol{x}-\boldsymbol{y}=-\boldsymbol{6} \) and \( \boldsymbol{x} \boldsymbol{y}=\mathbf{4}, \) find the
value of \( \boldsymbol{x}^{\mathbf{3}}-\boldsymbol{y}^{\mathbf{3}} \)
\( \mathbf{A} \cdot-288 \)
в. 288
\( c \cdot-28 \)
D. None of these
Subject: Maths
The solution of
\( \frac{3 \sin \theta-\sin 3 \theta}{1+\cos \theta}+\frac{3 \cos \theta+\cos 3 \theta}{1-\sin \theta}= \)
\( 4 \sqrt{2} \cos \left(\theta+\frac{\pi}{4}\right) \)
\( \mathbf{A} \cdot n \pi \)
В . \( n \pi+\frac{\pi}{12} \)
c. \( n \pi \pm \frac{\pi}{2} \)
D. \( 2 n \pi \)
Subject: Maths
If \( A=\left[\begin{array}{cc}-3 & 5 \\ 5 & 0 \\ -7 & 4\end{array}\right] \) and \( B=\left[\begin{array}{ccc}3 & -5 & 7 \\ -5 & 0 & -4\end{array}\right] \)
then find \( \boldsymbol{A}+\boldsymbol{B}^{\boldsymbol{T}} \)
\( A \cdot 0 \)
в. \( 2 B \)
\( c \cdot 2 A^{T} \)
D. \( 2 B^{T} \)
Subject: Chemistry
Prepare an acid salt from dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A \( \cdot 2 H_{2} S O_{4}+2 C H_{3} C O O N a \rightarrow 2 N a H S O_{4}+ \)
\( C H_{3} C O O H \)
в. \( 2 H_{2} S O_{4}+C H_{3} C O O N a \rightarrow 2 N a H S O_{4}+C H_{3} C O O H \)
c. \( H_{2} S O_{4}+C H_{3} C O O N a \rightarrow N a H S O_{4}+C H_{3} C O O H \)
D. \( H_{2} S O_{4}+2 C H_{3} C O O N a \rightarrow N a H S O_{4}+2 C H_{3} C O O H \)
Subject: Chemistry
Assertion(A): Smaller particles (size <5 microns) cause fibrosis of the lung
lining. Reason
(R): They are more likely to
penetrate into the lungs.
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not correct explanation of
c. \( A \) is true and \( R \) is false
D. A is false and R is true.
Subject: Chemistry
At \( 298 K, \) the equilibrium constant of reaction.
\( Z n^{+2}+4 N H_{3} \rightleftharpoons\left[Z n\left(N H_{3}\right)_{4}\right]^{+2} \) is
\( \mathbf{1 0}^{\mathbf{9}} \)
If \( \boldsymbol{E}_{\left[Z n\left(N H_{3}\right)_{4}\right]^{+2} / Z n+4 N H_{3}}^{o}=-1.03 V . \) The
value \( \boldsymbol{E}_{\boldsymbol{Z n} / \boldsymbol{Z} \boldsymbol{n}^{+2}} \) will be:
A. \( 0.7645 v \)
B . -1.1
\( c .+1.1 v \)
D. none of these
Subject: Chemistry
What is the IUPAC name of
\( \boldsymbol{K}\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}_{4}\right] ? \)
A. Potassium diamminetetrachlorochromate(III)
B. Potassium diamminetetrachlorochromium(III)
c. Potassium diamminetetrachlorochromate(II)
D. None of these
Subject: Chemistry
Arrange the following in decreasing
order of their boiling points.
(1) n-Butane
(II) 2-Methylbutane
(III) n-Pentane
(IV) 2,2 -Dimethylpropane
\( A \cdot|>||>|||>\mid V \)
B. ॥>॥I>IV>1
c. IV> |||>||>1
D. III > || > |V >
Subject: Physics
In a shotput event, an athlete throws the
shotput of mass \( 10 k g \) with an initial
speed of \( 1 m s^{1} \) at \( 45^{\circ} \) from a height
\( 1.5 m \) above ground. Assuming air resistance to be negligible and
acceleration due to gravity to be \( 10 m s^{2} \)
the kinetic energy of the shotput when it just reaches the ground will be:
A . 2.5 .5
в. \( 5.0 J \)
c. \( 52.5 J \)
D. \( 155.0 J \)
Subject: Biology
Assertion
The pollen tube is believed to release some stimulus for the increased growth
in the ovary wall.
Reason
The auxins can increase the activity of ovary even in the absence of pollen grain or pollen tube.
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
A circle has two equal chords \( A B \) and
\( A C, \) chord \( A D \) bisects \( B C \) in \( E . \) If \( A C=12 \)
and \( A E=8 c m, \) then the measure of \( A D \)
is ?
A \( .24 \mathrm{cm} \)
B. \( 18.5 \mathrm{cm} \)
c. \( 18 \mathrm{cm} \)
D. \( 19 \mathrm{cm} \)
Subject: Maths
Given the system of equation \( \boldsymbol{p} \boldsymbol{x}+\boldsymbol{y}+ \)
\( \boldsymbol{z}=\mathbf{1}, \boldsymbol{x}+\boldsymbol{p} \boldsymbol{y}+\boldsymbol{z}=\boldsymbol{p}, \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{p} \boldsymbol{z}=\boldsymbol{p}^{2} \)
then for what value of \( p \) does this system have no solution
A . -2
B. - 1
\( c .1 \)
D.
Subject: Chemistry
The treatment of \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C}=\boldsymbol{C H} \boldsymbol{C H}_{3} \)
with boiling \( K M n O_{4} \) produces :
A. \( C H_{3} C O C H_{3}+C H_{3} C O O H \)
B. \( C H_{3} C O C H_{3}+C H_{3} C H O \)
c. \( C H_{3} C H O+C O_{2} \)
D. \( C H_{3} C O C H_{3} \) only
Subject: Maths
if \( f(x)=\log _{x}(\ln x), \) then find \( f^{\prime}(x) \) at
\( x=e . \) Here in \( x \) means natural
logarithm of \( x, \) i.e. \( \log _{e} x \)
\( A \)
в. \( -e \)
\( c \cdot \frac{1}{e} \)
D. \( -\frac{1}{e} \)
Subject: Physics
Three forces of magnitudes 30,60 and
\( P \) Newton acting at a point are in
equilibrium. If the angle between the
first two is \( 60^{\circ} \), the value of \( P \) is:
A \( \cdot 25 \sqrt{2} \)
в. \( 30 \sqrt{3} \)
c. \( 30 \sqrt{6} \)
D. \( 30 \sqrt{7} \)
Subject: Chemistry
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N}_{2} \boldsymbol{C l} \frac{\boldsymbol{C u} C l}{\boldsymbol{H C l}} \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C l} \)
Above reaction is :
A. Gattermann's reaction
B. Sandmeyer's reaction
c. Wurtz's reaction
D. Frankland's reaction