AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A solid insulating sphere of radius \( \boldsymbol{R} \) is
given a charge \( Q \). If at a point inside the
sphere the potential is 1.5 times the potential at the surface, this point will
be:
A. at a distance of \( 2 R / 3 \) form the centre
B. at the centre
c. at a distance of \( 2 R / 3 \) form the surface
D. data insufficient
Subject: Physics
Which of the following are correct?
This question has multiple correct options
A. The product of bulk modulus of elasticity and compressibility is 1
B. A rope 1cm in diameter breaks if the tension in it exceeds \( 500 N \). The maximum tension that may be
given to a similar rope of diameter \( 2 \mathrm{cm} \) is \( 2000 \mathrm{N} \)
C. According to Hooke's law, the ratio of the stress and strain remains constant
D. None of the above
Subject: Physics
A police jeep is chasing with velocity of \( 45 k m / h \) a thief in another jeep moving with velocity \( 153 k m / h . \) Police fires a
bullet with muzzle velocity of \( 180 m / s \) The velocity it will strike the car of the
thief is?
A. \( 150 \mathrm{m} / \mathrm{s} \)
в. \( 27 \mathrm{m} / \mathrm{s} \)
c. \( 450 m / s \)
D. \( 250 \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( A \) is a square matrix of order 3
then \( \left|\mathbf{A} \mathbf{d} \mathbf{j}\left(A d j A^{2}\right)\right|= \)
\( \mathbf{A} \cdot|A|^{2} \)
B . \( |A|^{4} \)
c. \( \left.|A|^{8}\right|^{8} \mid \)
D. \( |A|^{16} \)
Subject: Biology
Assertion
Peroxisomes alone can carry the
photorespiration.
Reason
Peroxisome contain all enzymes to
carry out photorespiration.
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
The number of \( \alpha \) and \( \beta \) -particles
emitted in the conversion of \( g_{0} T h^{232} \) to
\( 82 P b^{208} \) are :
\( \mathbf{A} \cdot 6,4 \)
в. 4,6
\( c \cdot 8,6 \)
D. 6,8
Subject: Physics
Assertion
For an observer looking out through the window of a fast moving train, the
nearby objects appear to move in the opposite direction to the train, while the
distant objects appear to be stationary.
Reason
If the observer and the object are
moving at velocities \( \bar{V}_{1} \) and \( \bar{V}_{2} \)
respectively with reference to a laboratory frame the velocity of the
object with respect to the observer is \( \bar{V}_{2}-\bar{V}_{1} \)
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 \( \boldsymbol{a} \boldsymbol{x}_{1}^{2}+\boldsymbol{b} \boldsymbol{y}_{1}^{2}+\boldsymbol{c} \boldsymbol{z}_{1}^{2}=\boldsymbol{a} \boldsymbol{x}_{2}^{2}+\boldsymbol{b} \boldsymbol{y}_{2}^{2}+ \)
\( \boldsymbol{c} \boldsymbol{z}_{2}^{2}=\boldsymbol{a} \boldsymbol{x}_{3}^{2}+\boldsymbol{b} \boldsymbol{y}_{3}^{2}+\boldsymbol{c} \boldsymbol{z}_{3}^{2}=\boldsymbol{d} \) and
\( \boldsymbol{a} \boldsymbol{x}_{2} \boldsymbol{x}_{3}+\boldsymbol{b} \boldsymbol{y}_{2} \boldsymbol{y}_{3}+\boldsymbol{c} \boldsymbol{z}_{2} \boldsymbol{z}_{3}=\boldsymbol{a} \boldsymbol{x}_{3} \boldsymbol{x}_{1}+ \)
\( \boldsymbol{b} \boldsymbol{y}_{3} \boldsymbol{y}_{1}+\boldsymbol{c} \boldsymbol{z}_{3} \boldsymbol{z}_{1}=\boldsymbol{a} \boldsymbol{x}_{1} \boldsymbol{x}_{2}+\boldsymbol{b} \boldsymbol{y}_{1} \boldsymbol{y}_{2}+ \)
\( \boldsymbol{c} \boldsymbol{z}_{1} \boldsymbol{z}_{2}=\boldsymbol{f}, \) then prove that
\( \left|\begin{array}{lll}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \boldsymbol{z}_{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \boldsymbol{z}_{2} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & \boldsymbol{z}_{3}\end{array}\right|=(\boldsymbol{d}- \)
\( f)\left[\frac{d+2 f}{a b c}\right]^{1 / 2}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \neq \mathbf{0}) \)
Subject: Physics
Which of the following is correct for the efficiency of a heat engine:
A \( \cdot \eta=\frac{W}{Q_{1}} \)
в. \( \eta=\frac{W}{Q_{2}-Q_{1}} \)
c. \( _{\eta}=\frac{W}{Q_{2}} \)
D. \( \eta=\frac{Q_{2}}{Q_{1}} \)
Subject: Physics
\( P \) and \( Q \) are two unlike magnetic poles
Induction due to \( P \) at the location of \( Q \) is
B, and induction due to \( Q \) at the location
of \( \mathrm{P} \) is \( \frac{B}{2} \). The ratio of pole strengths of \( \mathrm{P} \) and \( Q \) is
A . 1:
B. 1: 2
c. 2: 1
D. \( 1: \sqrt{2} \)
Subject: Chemistry
Given below is the cascade of events
following deforestation. Select the option which arrange them in the
correct sequence.
\( P: \) Erosion of top soil
Q: River channel become shallow.
R : Eroded soil gets deposited on the river bed as silt
S : Destruction of crops leads to starvation.
T : Shallow channels cannot hold excess
water during rain and hence cause
flood
U: Floods damage agricultural crops.
A. \( P \rightarrow Q \rightarrow R \rightarrow S \rightarrow T \rightarrow U \)
в. \( P \rightarrow R \rightarrow Q \rightarrow T \rightarrow U \rightarrow S \)
\( c \cdot Q \rightarrow R \rightarrow P \rightarrow S \rightarrow T \rightarrow U \)
D. \( P \rightarrow T \rightarrow U \rightarrow Q \rightarrow R \rightarrow S \)
Subject: Chemistry
Structure of \( A \) and the type of
isomerism in the above reaction are respectively:
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C H} \frac{40 \% \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{1 \% \boldsymbol{H g S O}_{4}} \)
\( \boldsymbol{A} \stackrel{\text {Isomerisation}}{\longrightarrow} \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
A. prop-1-en-2-ol, metamerism
B. prop-1-en-2-ol, tautomerism
c. prop-z-en-2-ol, cis and trans isomerism
D. prop-2-en-1-ol, tautomerism
Subject: Chemistry
Consider the following equation for a
cell
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} \)
\( \boldsymbol{E}^{o}= \)
\( \boldsymbol{X} \boldsymbol{v o l t}, \quad \boldsymbol{K}_{e q}=\boldsymbol{K}_{1} \)
\( \mathbf{2 A}+\mathbf{2 B} \rightleftharpoons \mathbf{2 C}+\mathbf{2 D} ; \quad \boldsymbol{E}^{\boldsymbol{o}}= \)
\( \boldsymbol{y} \) volt, \( \quad \boldsymbol{K}_{e q}=\boldsymbol{k}_{2} \)
A. \( X=y, K_{1}=K_{2} \)
B . \( X=2 y, K_{1}^{2}=K_{2} \)
C . \( X=y, K_{1}^{2}=K_{2} \)
D. \( X^{2}=y, K_{1}^{2}=K_{2} \)
Subject: Chemistry
For a reaction \( \boldsymbol{R} \rightarrow \boldsymbol{P} \), the concentration
of a reactant changes from \( 0.05 M \) to
\( 0.04 M \) in 30 minutes. What will be the
average rate of reaction in minutes?
A \( \cdot 4 \times 10^{-4} \mathrm{M} \min ^{-1} \)
В. \( 8 \times 10^{-4} \mathrm{M} \min ^{-1} \)
\( \mathrm{c} \cdot 3.3 \times 10^{-4} \mathrm{M} \min ^{-1} \)
D. 2.2 \( \times 10^{-4} \mathrm{M} \) min\( ^{-1} \)
Subject: Chemistry
During the kinetic study of the reaction,
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \) following results
were obtained.
\( \begin{array}{lll} & {[\mathrm{A}]} & {[\mathrm{B}]} \\ & \text { Run } & \text { in } & \text { in } \\ & \text { M } & \text { M }\end{array} \) Iniitial rate of
formation of D in
\( \boldsymbol{m} \boldsymbol{s}^{-1} \)
0.1
\( 0 . \)
\( 6.0 \times 10^{-3} \)
\( \begin{array}{ll}0.2 & 7.2 \times 10^{-2}\end{array} \)
0.3
\( 2.88 \times 10^{-1} \) 0.3
0.4
0.4
\( \begin{array}{ll}0.1 & 2.40 \times 10^{-2}\end{array} \)
On the basis of above data which one is
correct?
A \( \cdot r=k[A]^{2}[B] \)
B. \( r=k \) (A)[B]
C \( \cdot r=k[A]^{2}[B]^{2} \)
D . \( r=k[A][B]^{2} \)
Subject: Chemistry
Which of the following statement is not
correct?
A. Atomic no.of A,B,C are 40,57,105 respectively
3. Group no of \( A, B, C \) are IV \( B \), III \( B \) and \( V B \) respectively
c. Period no of \( A, B, C \) are 4 th \( , 5 \) th and 6 th respectively
D. \( \mathrm{C} \) is a radioactive element
Subject: Maths
If \( 1+\sin x+\sin ^{2} x+\sin ^{3} x+\ldots \infty \) is
equal to \( 4+2 \sqrt{3}, 0 \leq x<\pi \) then \( x \) is
equal to
A.
в.
c. \( \frac{\pi}{3} \) or \( \frac{\pi}{6} \)
D. \( \frac{\pi}{3} \) or \( \frac{2 \pi}{3} \)
Subject: Chemistry
Which of the following is(are) Dobereiner's triads?
(a) \( P, A s, S b \)
(b) \( \mathrm{Cu}, \mathrm{Ag}, \mathrm{Au} \)
(c) \( \mathrm{Fe}, \mathrm{Co}, \mathrm{Ni} \)
\( (d) S, S e, T e \)
\( A \cdot \) a and \( b \)
B. b and c
\( c . \) a and d
D. all of the above
Subject: Physics
A conducting shell \( S_{1} \) having a charge \( Q \)
is surrounded by an uncharged concentric conducting spherical shell \( S_{2} \). Let the potential difference between
\( S_{1} \) and that \( S_{2} \) be \( V \). If the shell \( S_{2} \) is now
given a charge \( -3 Q, \) the new potential difference between the same two shells
is :
\( A \cdot 1 v \)
B. 2
\( c \cdot 4 v \)
D. -2 v
Subject: Physics
A body is moving with a velocity 1 ms \( ^{-1} \)
a force \( F \) is needed to stop it within a
distance \( x \). If the speed of the body is
\( 3 m s^{-1}, \) the force needed to stop it with
in the same distance \( (x) \) will be:
A \( .9 F \)
в. \( 6 F \)
\( c .3 F \)
D. \( 1.5 F \)
Subject: Chemistry
The solubility of \( C a C O_{3} \) is \( 7 m g / \)litre. Calculate the solubility product of
\( B a C O_{3} \) from this information and from
the fact that when \( N a_{2} C O_{3} \) is added
slowly to a sloution containing equimolar concentration of \( C a^{2+} \) and
\( B a^{2+}, \) no precipitate is formed until 90
\( \% \) of \( B a^{2+} \) has been precipitated as
\( B a C O_{3} . \) The solubility product of \( B a C O_{3} \) is \( X \times 10^{-10} \) mol \( ^{2} l i t r e^{-2}, \) the
value of integer nearest to \( \boldsymbol{X} \) is:
Subject: Chemistry
The dissociation of \( C a C O_{3} \) takes place
as per the equation,
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \Leftrightarrow \boldsymbol{C a O}(\boldsymbol{s})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta} \boldsymbol{H}=\mathbf{1 1 0} \boldsymbol{k} \boldsymbol{J} \)
If the reaction is carried out in a closed
vessel, the pressure of \( C O_{2} \) is increased
and reaches a constant value when:
A. Temperature is increased
B. Temperature is decreased
c. volume of vessel is increased
D. Amount of \( C a C O_{3} \) is decreased
Subject: Biology
The correct floral formula of soyabean is
\( A \)
\( \% \oplus \mathbf{K}_{5} \mathbf{C}_{\mathbf{1}+(2)+2} \mathbf{A}_{(9)+\mathbf{1}} \mathbf{G}_{\underline{\mathbf{1}}} \)
B. \( \% \oplus \mathbf{K}_{(5)} \mathbf{C}_{1+2+(2)} \mathbf{A}_{(9)+1} \mathbf{G}_{\underline{1}} \)
c. \( \% \oplus \mathbf{K}_{(5)} \mathbf{C}_{\mathbf{1}+2+(\mathbf{2})} \mathbf{A}_{\mathbf{1}+(\mathbf{9})} \mathbf{G}_{\underline{\mathbf{l}}} \)
D. \( \% \oplus \mathbf{K}_{(5)} \mathbf{C}_{\mathbf{1}+(2)+2} \mathbf{A}_{(9)+\mathbf{1}} \mathbf{G}_{\mathbf{1}} \)
Subject: Physics
A particle performing linear simple
harmonic motion has maximum
velocity \( 25 \mathrm{cm} / \mathrm{s} \) and maximum
acceleration of \( 100 \mathrm{cm} / \mathrm{s}^{2} \). Find the amplitude and period of oscillation. \( (\boldsymbol{\pi}=\mathbf{3 . 1 4 2}) \)
Subject: Chemistry
The correct order of the spin-only magnetic moment of metal ions in the
following low spin complexes, \( \left[\boldsymbol{V}(\boldsymbol{C N})_{6}\right]^{4-},\left[\boldsymbol{F e}(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{4-} \)
\( \left.\left[\boldsymbol{R u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{3+}, \text { and }\left[\boldsymbol{C r}(\boldsymbol{N} \boldsymbol{H})_{3}\right)_{6}\right]^{2+}, \) is:
A \( \cdot V^{2+}>C r^{2+}>R u^{3+}>F e^{2+} \)
B . \( V^{2+}>R u^{3+}>C r^{2+}>F e^{2+} \)
c. \( C r^{2+}>V^{2+}>R u^{3+}>F e^{2+} \)
D. \( C r^{2+}>R u^{3+}>F e^{2+}>V^{2}+ \)
Subject: Physics
From the centre of the earth to the
surface of the earth, the relation between the value of \( g \) and distance \( (r) \) represented as a proportionality, is given by
A \( \cdot g \propto \frac{1}{r^{2}} \)
В . \( g \propto r \)
c. \( g \propto r^{2} \)
D \( \cdot g \propto r^{o} \)
Subject: Chemistry
In the electrochemical cell
\( H_{2}(g), 1 a t m\left|H^{+}(1 M)\right|\left|C u^{2+}(1 M)\right| C u(s) \)
which one of the following is the correct value of reduction potential?
A . \( 1.10 \mathrm{V} \)
B. 0.110
c. \( 1.50 \mathrm{v} \)
D. 0.220
Subject: Physics
Two current-carrying parallel conductors are shown in the figure. The
magnitude and nature of force acting between them per unit length will be :
A \( \cdot 8 \times 10^{-8} N / m, \) attractive
B. \( 3.2 \times 10^{-5} N / m \), repulsive
c. \( 3.2 \times 10^{-5} N / m \), attractive
D. \( 8 \times 10^{-8} N / m \), repulsive
Subject: Maths
The D.E whose solution is \( y=a x^{3}+b x^{2} \)
is
A \( \cdot x^{2} y_{2}-4 x y_{1}+6 y=0 \)
B . \( x^{2} y_{2}-4 y_{1}+6 y=0 \)
c. \( x^{2} y_{2}+4 x y_{1}-6 y=0 \)
D. \( x^{2} y_{2}-2 x y_{1}+6 y=0 \)
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\frac{\boldsymbol{\operatorname} \boldsymbol{\operatorname { a n } \boldsymbol { x }}-\boldsymbol{\operatorname { c o t } \boldsymbol { x }}}{\boldsymbol{\operatorname { t a n } \boldsymbol { x }}+\boldsymbol{\operatorname { c o t } \boldsymbol { x }}}\right]= \)
\( A \cdot 2 \sin 2 x \)
B. - -2 \( \sin 2 x \)
\( c \cdot 2 \cos 2 x \)
D. \( -2 \cos 2 x \)
Subject: Chemistry
Match the Lists I and II and pick the
correct matching from the codes given
below.
List I
(i) Peroxy acetyl nitrate
1. Carcinogens
(ii) Polycyclic aromatic \( \quad \) 2. Global warming hydrocarbons
3. Photochemical
(iii) IR active molecules
4. Waste
(iv) Dioxins \( \quad \) incineration
A. \( (i)-3, \) (ii) \( -1, \) (iii) \( -4, \) (iv) -2
B. (i) - 3, (ii) - 2, (iii) - 4, (iv) - 1
C. (i) - 3, (ii) - 1, (iii) - 2, (iv) - 4
D. (i) - 4, (ii) - 2, (iii) - 1, (iv) - 3
Subject: Maths
The circumference of a circle is \( 100 \mathrm{cm} \)
Then the side of a square inscribed in the circle is:
A \( \cdot \frac{100 \sqrt{2}}{\pi} \mathrm{cm} \)
B. \( \frac{50 \sqrt{2}}{\pi} \mathrm{cm} \)
c. \( \frac{100}{\pi} \mathrm{cm} \)
D. \( 50 \sqrt{2} \mathrm{cm} \)
Subject: Maths
If \( \vec{a}=i+2 j+k, \vec{b}=i-j+k \) and \( \vec{c}= \)
\( i+j-k . \) A vector in the plane of \( \vec{a} \) and \( \vec{b} \) whose projection on \( \vec{c} \) is \( 1 / \sqrt{3}, \) is
A \( .4 i-j+4 k \)
в. \( 3 i+j-3 k \)
c. \( 2 i+j-2 k \)
D. \( 4 i+j-4 k \)
Subject: Maths
In a business venture a man can make
a profit of Rs. \( 2000 /- \) with probability of 0.4 or have a loss of Rs. \( 1000 /- \) with probability 0.6. His expected profit is
A. Rs. \( 800 /- \)
B. Rs. \( 600 /- \)
c. Rs. \( 200 /- \)
D. Rs. 400/-
Subject: Maths
\( \frac{\mathbf{3}}{\mathbf{1}+\boldsymbol{i}}-\frac{\mathbf{2}}{\mathbf{2}-\boldsymbol{i}}+\frac{\mathbf{2}}{\mathbf{1}-\boldsymbol{i}} \)
A \( \cdot \frac{1}{10}(17+9 i) \)
в \( \cdot \frac{1}{5}(17-9 i) \)
c \( \cdot \frac{1}{10}(17-9 i) \)
D \( \cdot \frac{1}{5}(17+9 i) \)
Subject: Physics
Consider a hypothetical hydrogen like
atom. The wavelength in \( A \) for the
spectral lines for transition from \( \boldsymbol{n}=\boldsymbol{p} \)
\( \operatorname{ton}=1 \) are given by- \( \lambda=\frac{1500}{p^{2}-1} \)
Where \( \boldsymbol{p}=\mathbf{2}, \mathbf{3}, \mathbf{4}, \) (given \( \boldsymbol{h} \boldsymbol{c}= \)
\( 12400 e V / A) \)
This question has multiple correct options
A. The wavelength of the least energetic and the most energetic photons in this series is 2000 A, 1500 A
B. Difference between energies of fourth and this orbit is \( 0.40 \mathrm{eV} \)
C. Energy of second orbit is 6.2 eV
D. The ionization potential of this element is \( 8.27 V \)
Subject: Chemistry
Using the data given below, establish that the vaporization of \( C C l_{4}(l) \) at 298K to produce \( C C l_{4}(g) \) at 1 atm
pressure does not occur spontaneously. Given
\( \boldsymbol{C C l}_{4}(\boldsymbol{l}, \mathbf{1 a t m}) \rightarrow \boldsymbol{C C l}_{4}(\boldsymbol{g}, \mathbf{1 a t m}) \)
\( \boldsymbol{\Delta} \boldsymbol{S}^{o}=\boldsymbol{9} \boldsymbol{4} . \boldsymbol{9} \boldsymbol{8} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m} \boldsymbol{o l}^{-1} \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{f}^{o}\left(\boldsymbol{C} \boldsymbol{C l}_{4}, \boldsymbol{g}\right)=\mathbf{1 0 6 . 7} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{z} \)
\( \Delta H_{f}^{o}\left(C C l_{4}, l\right)=139.3 k J m o l^{-1} \)
A \( \cdot \Delta G^{o}=4.3 k J / m o l \)
в. \( \Delta G^{o}=-4.3 k J / \) mol
c. \( \Delta G^{o}=2.15 k J / \) mol
D. None of these
Subject: Maths
If \( f(x)=\log \left(\frac{x^{2}+a b}{x(a+b)}\right), \) then the
value of \( ^{\prime} C^{\prime} \) for which \( f^{\prime}(c)=0 \) in \( [a, b] \)
\( \mathbf{A} \cdot C=\pm \sqrt{\frac{a}{b}} \)
B. \( C=\pm \sqrt{a b} \)
\( ^{c} \cdot c=\pm \sqrt{\frac{b}{a}} \)
D. none of these
Subject: Maths
The population of a is town is \( 64,000 . \) If the annual birth rate is \( 10.7 \% \) and the
annual death rate is \( 3.2 . \) Calculate the
population after three years.
\( \mathbf{A} \cdot 79507 \)
B. 79000
c. 79500
D. 79510
Subject: Maths
If \( \boldsymbol{A}=\left\{4^{n}-3 n-1: n \in N\right\} \) and \( B= \)
\( \{9(n-1): n \in N\}, \) then?
\( \mathbf{A} \cdot B \subset A \)
B. \( A \cup B=N \)
c. \( A \subset B \)
D. None of these
Subject: Physics
Mean free time of electrons are
expressed in picosecond\( (\boldsymbol{p s}) . \) 1ps \( =? \)
\( \mathbf{A} \cdot 10^{-12} s \)
B \( \cdot 10^{-9} s \)
\( \mathbf{c} \cdot 10^{-3} s \)
D. None of these
Subject: Physics
When the temperature of an iron sphere
of mass \( 1 k g \) falls from \( 30^{\circ} C \) to \( 25^{\circ} C \)
then 550 cal of heat is released. The
heat capacity of the iron sphere will be
in \( \left.\operatorname{cal}^{\circ} C^{-1}\right) \)
A . 440
в. 330
\( c \cdot 220 \)
D. 110
Subject: Chemistry
The heat of combustion of benzene at
\( 27^{\circ} \mathrm{C} \) found by bomb calorimeter i.e. for
the reaction \( C_{6} H_{6(l)}+7 \frac{1}{2} O_{2(g)} \rightarrow \)
\( \mathbf{6} C O_{2(g)}+\mathbf{3} H_{2} O_{(l)} \) is 780 K.Cal \( m o l^{-1} \)
The heat evolved on burning 39 g of benzene in an open vessel will be
A. 390 K.Cal I
B. 780.9 K.Cal
c. 390.45 K.Cal
D. 780 K.Cal
Subject: Physics
The plane side of a plano-convex lens is silvered and the lens then acts as a
concave mirror of \( 30 \mathrm{cm} \) focal length. The refractive Index of the lens is \( \frac{3}{2} \)
Find the radius of the curvature of the
lens.
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathbf{c} \cdot 40 \mathrm{cm} \)
D. \( 25 \mathrm{cm} \)
Subject: Chemistry
Assertion
Bond angle of \( \boldsymbol{P} \boldsymbol{F}_{3}>\boldsymbol{P} \boldsymbol{C l}_{3} \) but bond
angle of \( \boldsymbol{P C l}_{3}<\boldsymbol{P B r}_{3} \)
Reason
The bond angles show an increase on decreasing electronegativity of attached other atom on central atom
but in \( P F_{3} p \pi-d \pi \) bonding results in
an increase in bond angle.
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
If \( \int \frac{x^{4}+1}{x^{6}+1} d x=\tan ^{-1}(f(x)) \)
\( \frac{2}{3} \tan ^{-1}(g(x))+C, \) then
A. Both \( f(x) \& g(x) \) are odd functions
B. \( g(x) \) is monotonic function
c. none of these
D. None
Subject: Physics
A ball thrown up vertically returns to the thrower after 6 s Find it's initial velocity.
A. 20 \( \mathrm{m} / \mathrm{s} \)
B. 40 \( \mathrm{m} / \mathrm{s} \)
\( c .35 \mathrm{m} / \mathrm{s} \)
D. 30 \( \mathrm{m} / \mathrm{s} \)
Subject: Biology
Assertion
Ernst Haeckal developed binomial system of nomenclature
Reason
Vernacular names are chosen for
nomenclature.
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
Mark the CORRECT statements(s)
This question has multiple correct options
A. Direction of wave propagation is along the normal to wavefront.
B. For a point source of light, the shape of wavefront can be considered to be plane at very large
distance from the source.
C. A point source of light is placed at the focus of a thin spherical lens, then the shape of the wavefront for emerged light may be plane.
D. The shape of the wavefront for the light incident on a thin spherical lens (kept in vacuum) is plane, the shape of the wavefront corresponding to emergent light would be always spherical
Subject: Chemistry
An organic compound (A) of molecular
formula \( C_{2} H_{6} O \) on oxidation with
alkaline \( K M n O_{4} \) solution gives an acid (B) with the same number of
carbon atoms. Compound A is used as an antiseptic to sterilize wounds, in hospitals. Identify A and
B. Write the
chemical equation involved in the formation of B from A.
Subject: Chemistry
An electric charge of 5 Faraday's is passed through three electrolytes
\( A g N O_{3}, C u S O_{4} \) and \( F e C l_{3} \) solution
The grams of each metal liberated at cathode will be:
A. \( A g=10.8 g, C u=12.7 g, F e=1.11 g \)
в. \( A g=540 g, C u=367.5 g, F e=325 g \)
c. \( A g=108 g, C u=63.5 g, F e=56 g \)
D. \( A g=540 g, C u=158.8 g, F e=93.3 g \)
Subject: Chemistry
Assertion
\( C s \) and \( F_{2} \) reacts violently.
Reason
Cs is most electropositive and \( \boldsymbol{F}_{2} \) is
most electronegative.

Read the above assertion and reason
and choose the correct option regarding
¡t.
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
The middle term in the expansion of \( \left(1-3 x+3 x^{2}-x^{3}\right)^{2 n} \) is
\( \mathbf{A} \cdot 6 n_{C_{3 n}}(-x)^{3 n} \)
B . \( 6 n_{C_{2 \text { n }}}(-x)^{2 n+1} \)
\( \mathbf{c} \cdot 4 n_{C_{S n}}(-x)^{3 n} \)
D. \( 6 n_{C_{3 n}}(-x)^{3 n-1} \)
Subject: Physics
Potential due to an electric dipole is represented by:
(where \( p \) is the dipole moment, \( r(>> \)
2a) is the distance at which the
potential \( V \) of the dipole is calculated
and \( \theta \) is the angle between the distance
vector and the dipole.)
A \( \cdot V=\frac{p \cos \theta}{4 \pi \epsilon_{c} r^{4}} \)
B. \( V=\frac{p \sin \theta}{4 \pi \epsilon_{o} r^{2}} \)
c. \( V=\frac{p \sin \theta}{4 \pi \epsilon_{o} r^{4}} \)
D. \( V=\frac{p \cos \theta}{4 \pi \epsilon_{o} r^{2}} \)
Subject: Chemistry
To what temperature should water be
heated so that its vapor pressure
equals the vapor pressure chloroform at
\( 40^{\circ} \mathrm{C} ? \)
\( \mathbf{A} \cdot 40^{\circ} C \)
\( \mathbf{B} \cdot 50^{\circ} C \)
\( \mathbf{c} \cdot 60^{\circ} C \)
D. \( 70^{\circ} \mathrm{C} \)
\( E \cdot 80^{\circ} C \)
Subject: Maths
A point \( P \) on the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 \) has the eccentric angle \( \frac{\pi}{8} . \) The sum of the distance of \( P \) from the two foci is
A . 5
B. 6
c. 10
D. 3
Subject: Physics
Two capillary tubes of diameters 3.0 \( \mathrm{mm} \) and \( 6.0 \mathrm{mm} \) are joined together to form a U-tube open at both ends. If the U-tube is filled with water, what is the
difference in its levels in the two limbs
of the tube? Surface tension of water at
the temperature of the experiment is \( \mathbf{7 . 3} \times \mathbf{1 0}^{-\mathbf{2}} \mathbf{N} / \mathbf{m} . \) Take the angle of
contact to be zero and density of water to be \( 10^{3} k g / m^{3}\left(g=9.8 m / s^{2}\right) \)
\( A \cdot 5 \mathrm{mm} \)
B. 10 \( \mathrm{mm} \)
c. \( 15 \mathrm{mm} \)
D. 20 mm