AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If the equation \( x^{2}+b x+c=0 \) and
\( \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}+\boldsymbol{b}=\mathbf{0},(\boldsymbol{b} \neq \boldsymbol{c}) \) have a
common root then
A. \( b+c=0 \)
B. \( b+c=1 \)
c. \( b+c+1=0 \)
D. None of these
Subject: Physics
The length of a wire is 4 m. Its length is
increased by \( 2 m m \) when a force acts on
it. The strain is:
A. \( 0.5 \times 10^{-3} \)
B. \( 5 \times 10^{-3} \)
\( c \cdot 2 \times 10^{-3} \)
D. 0.05
Subject: Maths
\( \cos \boldsymbol{x} \cdot \log (\cos \boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
A \( . \sin x \log (\cos x)-\log (\cos x)+c \)
B. \( \sin x \log (\cos x)+\sec x+c \)
c. \( \sin x \log (\cos x)-\sin x+\log |\sec x+\tan x|+c \)
D. \( \sin x \log (\cos x)-\sec x+c \)
Subject: Maths
Consider the cubic \( f(x)=8 x^{3}+ \)
\( 4 a x^{2}+2 b x+a, \) where \( a, b, \in R \)
For \( \boldsymbol{a}=\mathbf{1}, \) if \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) is strictly
increasing \( \forall x \in R, \) then maximum
range of values of \( b \) is
\( ^{\mathbf{A}} \cdot\left(-\infty, \frac{1}{3}\right) \)
B. \( \left(\frac{1}{3}, \infty\right) \)
\( ^{c} \cdot\left[\frac{1}{3}, \infty\right) \)
\( D \cdot(-\infty, \infty) \)
Subject: Maths
Find the product. \( \left(a^{2}\right)\left(2 a^{22}\right)\left(4 a^{26}\right) \)
\( \mathbf{A} \cdot 8 a^{40} \)
B. \( 8 a^{50} \)
\( c \cdot 8 a^{30} \)
D. \( 8^{20} \)
Subject: Maths
The distance between the origin and the tangent to the curve \( y=e^{2 x}+x^{2} \) drawn
at the point \( x=0 \) is
A \( \cdot \frac{1}{\sqrt{5}} \)
в. \( \frac{2}{\sqrt{5}} \)
c. \( \frac{-1}{\sqrt{5}} \)
D. \( \frac{2}{\sqrt{3}} \)
Subject: Maths
If \( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{1} / 2 \) and \( \boldsymbol{P}(\boldsymbol{B})=2 / 3, \) then
This question has multiple correct options
A. \( P(A \cup B) \geq 2 / 3 \)
B . \( P\left(A \cap B^{\prime}\right) \leq 2 / 3 \)
c. \( 1 / 6 \leq P(A \cap B) \leq 1 / 2 \)
D. \( 1 / 6 \leq P\left(A^{\prime} \cap B\right) \leq 1 / 2 \)
Subject: Chemistry
For the following sequential reaction \( \boldsymbol{E}^{\boldsymbol{o}} \) values in volts at \( 298 \mathrm{K} \) are given:
\( M n O_{4}^{-0.564}^{V} M n O_{4}^{-2}^{2.26 V} \)
\( M n O_{2} \stackrel{0.95}{\rightarrow} M n^{+3} \stackrel{1.51 V}{\rightarrow} M n^{+2} \)
Calculate \( \boldsymbol{E}^{o} \) for \( \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{\boldsymbol{4}}^{-} \rightarrow \boldsymbol{M} \boldsymbol{n}^{+2} \)
A. -1.81 volt
B. -1.18 volt
c. 1.51 volt
D. 1.18 volt
Subject: Chemistry
\( 14 \mathrm{g} \) of element \( \mathrm{X} \) combine with \( 16 \mathrm{g} \) of oxygen. On the basis of this information, which of the following is a correct statement?
A. The element \( x \) could have an atomic weight of 7 and its oxide is \( x 0 \)
B. The element \( x \) could have an atomic weight of 14 and its oxide is \( X_{2} O \)
c. The element \( x \) could have an atomic weight of 7 and its oxide is \( X_{2} O \)
D. The element \( x \) could have an atomic weight of 16 and its oxide is \( X_{2} O \)
Subject: Physics
A particle of mass \( m \) is made to move
with uniform speed \( v \) along the perimeter of a regular hexagon. Magnitude of impulse applied at each
corner is:
A . \( m v \)
B. \( m v \sqrt{3} \)
c. \( \frac{m v}{2} \)
D. \( \frac{m v}{\sqrt{3}} \)
Subject: Physics
A wire elongates by 1 m \( m \) when a load Wis hanged from it. If the wire goes over a pulley and two weights Weach are hung at the two ends, the elongation of the wire will be (in \( \mathrm{mm} \) ):
A . \( 1 / 2 \)
B. 1
\( c \cdot 2 \)
D. zero
Subject: Physics
The volume of an air bubble increases
by \( x \% \) as it rises from the bottom of a lake to its surface. If the height of the water barometer is \( \mathrm{H} \), the depth of the lake is
\( ^{\mathrm{A}} \cdot\left(\frac{H+x}{100}\right)^{2} \)
В. \( \frac{H x}{(100+x)} \)
c. \( \frac{H x}{100} \)
D. \( \frac{100 H}{x} \)
Subject: Maths
If \( \boldsymbol{x}=\frac{\sqrt{\mathbf{3}}+\sqrt{\mathbf{2}}}{\sqrt{\mathbf{3}}-\sqrt{\mathbf{2}}} \) find \( \boldsymbol{x}^{2}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}} \)
Subject: Chemistry
A dihaloalkane \( ^{\prime} X^{\prime} \), having formula
\( C_{3} H_{6} C l_{2}, \) on hydrolysis gives a
compound, that can reduce Tollen's
reagent. The compound' \( X^{\prime} \) is
A. 1,2 -dichloropropane
B. 1,1-dichloropropane
c. 1,3 -dichloropropane
D. 2, 2-dichloropropane
Subject: Chemistry
For the equilibrium, \( \boldsymbol{P C l}_{5} \leftrightharpoons \boldsymbol{P C l}_{3}+ \)
\( C l_{2} ; K_{c}=\frac{\alpha^{2}}{1-\alpha} V, \) temperature
remaining constant. Then:
A . \( K_{c} \) will decrease with increase in volume
B. \( K_{c} \) will increase with increase in volume
C. \( K_{c} \) will not change with the change in volume
D. \( K_{c} \) may increase or decrease with the change in volume depending upon its numerical value
Subject: Maths
If \( A \) and \( B \) are two mutually exclusive
events, then This question has multiple correct options
A \( . P(A) \leq P(\bar{B}) \)
в. \( P(A)>P(B) \)
c. \( P(B) \leq P(\bar{A}) \)
\( D(A)<P(B) \)
Subject: Biology
Assertion
Capital formation in India has been low
due to population explosion.
Reason Rising population has led to increased spending on consumption, while very little part of the national income is available for savings and investments
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: Chemistry
An element M has the electron
configuration \( [A r] 3 d^{5} 4 s^{2} . \) So, which of the following oxide cannot exist for element
M?
A. \( M O_{2} \)
B. \( M_{2} O_{3} \)
c. \( M O_{4} \)
D. \( M_{2} O_{7} \)
Subject: Chemistry
Considering \( B e C l_{2}, M g C l_{2}, C a C l_{2} \) and
\( B a C l_{2} \) predict which of the following
statement is true?
\( \mathbf{A} \cdot B e C l_{2} \) is least ionic out of the given chlorides
B. Covalent character increases as the atomic number of the metal atom increases
\( \mathrm{c} \cdot \mathrm{BeCl}_{2} \) has the lowest melting point among the given chlorides
D. All are highly ionic compounds
Subject: Maths
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\mathbf{2} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{3}} \)
Subject: Physics
A small body is thrown at an angle to
the horizontal with the initial velocity \( \vec{v}_{0} \) Neglecting the air drag, find the mean
velocity vector \( \langle\vec{v}\rangle \) averaged over the
first \( t \) sec and over the total time of
motion.
A \( \cdot(\vec{v})_{t}=\vec{v}_{0}-\frac{g t}{2},\langle\vec{v}\rangle=\vec{v}_{0}-g \frac{\left(\vec{v}_{0} g\right)}{g^{2}} \)
B \( \cdot(\vec{v})_{t}=\vec{v}_{0}-\frac{g t}{2},\langle\vec{v}\rangle=\vec{v}_{0}+g \frac{\left(\vec{v}_{0} g\right)}{g^{2}} \)
c. \( (\vec{v})_{t}=\vec{v}_{0},\langle\vec{v}\rangle=\vec{v}_{0}-g \frac{\left(\vec{v}_{0} g\right)}{g^{2}} \)
D. None of these
Subject: Chemistry
What is the relationship between thermal energy and intermolecular interaction energy of a substance in
three states in terms of \( X \) and \( Y ? \)
Gas\( \rightarrow \)Liquid\( \rightarrow \)Solid
Predominance of \( \boldsymbol{X} \)
Predominance of \( \boldsymbol{Y} \)
A. \( x \) -Thermal energy, Y- Intermolecular interactions
B. X-Thermal energy, Y-Thermal energy
c. \( x \) -Intermolecular interactions, Y-Thermal energy
D. x-ıntermolecular interactions, Y-Intermolecular interactions
Subject: Maths
The line \( (a+2 b) x+(a-3 b) y=a-b \)
for different values of \( a \) and \( b \) passes through the fixed point
\( ^{\mathrm{A}} \cdot\left(\frac{3}{5}, \frac{7}{5}\right) \)
в. \( \left(\frac{7}{2}, \frac{5}{2}\right) \)
\( ^{\mathrm{c}} \cdot\left(\frac{6}{5}, \frac{6}{5}\right) \)
D \( \cdot\left(\frac{2}{5}, \frac{3}{5}\right) \)
Subject: Physics
An atoms contains 15 protons, 15
electrons, and 16 neutrons. Which of the
following combinations of particles is
an isotope of that atom?
\( \begin{array}{llll}\text { Protons } & \text { Electrons } & \text { Neutrons } \\ \text { (A) } & 16 & 16 & 17 \\ \text { (B) } & 15 & 16 & 16 \\ \text { (C) } & 15 & 15 & 15 \\ \text { (D) } & 14 & 15 & 16 \\ \text { (E) } & 14 & 14 & 15\end{array} \)
\( A \)
B.
\( c . \)
\( D \)
\( E \)
Subject: Physics
A wire \( 2 \mathrm{m} \) in length suspended vertically stretches by \( 10 \mathrm{mm} \) when the mass of \( 10 \mathrm{kg} \) is attached to the lower end. The elastic potential energy gain by the wire is? \( \left(\operatorname{take} g=10 m / s^{2}\right) \)
A . 0.5
B. 5 J
c. 50
D. 500 J
Subject: Physics
Consider a uniform rod of mass \( \boldsymbol{M}= \)
\( 4 m \) and length \( l \) pivoted about its
centre. A mass \( m \) moving with velocity \( \boldsymbol{v} \) making angle \( \boldsymbol{\theta}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) to the rod's long
axis collides with one of the rod and
sticks to it. The angular speed of the rod-mass system just after the collision
is:
A \( \frac{3}{7 \sqrt{2}} \frac{v}{l} \)
B. \( \frac{3 \sqrt{2}}{7} \frac{v}{l} \)
c. \( \frac{4}{7} \frac{v}{l} \)
D. \( \frac{3}{7} \frac{v}{l} \)
Subject: Chemistry
A reaction:
\( \frac{1}{2} H_{2}(g)+A g C l(s) \rightleftharpoons H^{\oplus}(a q)+ \)
\( C l^{\ominus}(a q)+A g(s) \) occurs in a galvanic
cell.
The structure of the cell will be:
A \( \cdot A g, A g C l(s)|K C l(s o l)| A g N O_{3}(s o l), A g \)
B . \( P t, H_{2}(g)|H C l(s o l)| A g N O_{3}(s o l), A g \)
c. \( P t, H_{2}(g)|H C l(s o l)| A g C l(s), A g \)
D. \( P t, H_{2}(g)|K C l(s o l)| A g C l(s), A g \)
Subject: Maths
Simplify: \( \left(-3 p q^{2}+4 p q\right)- \)
\( \left(7 p q-9 p q^{2}\right) \)
\( \mathbf{A} \cdot 6 p q^{2}+3 p q \)
B. \( 6 p q^{2}-3 p q \)
c. \( -12 p q^{2}+3 p q \)
D. \( -12 p q^{2}-3 p q \)
Subject: Physics
Two identical thin rings each of radius \( r \) are coaxillary placed at a distance have equal charge q each. Work done in moving a charge \( q^{\prime} \) from the centre of one ring to that of the other is?
A . Infinity
В. \( \frac{q^{2}}{4 \pi \varepsilon_{0} r} \)
c. zero
D. \( \frac{q q^{\prime}}{4 \pi \varepsilon_{0} r} \)
Subject: Chemistry
When borax is dissolved in water:
\( \mathbf{A} \cdot B(O H)_{3} \) is formed only
\( \mathbf{B} \cdot\left[B(O H)_{4}\right]^{-} \) is formed only
\( \mathbf{c} \cdot \operatorname{both} B(O H) 3 \) and \( \left[B(O H)_{4}\right]^{-} \) are formed
D. \( \left[B_{3} O_{3}(O H)_{4}\right]^{-} \) is formed only
Subject: Physics
A plano-convex lens fits exactly into plano-concave lens as shown in figure. Their plane surfaces are parallel to each
other. If the lens are made of different
materials of refractive indices 1.6 and
1.5 respectively. If \( R \) is the radius of
curvature of curved surfaces of lenses.
Then the focal length of the combination
A \( \frac{R}{0.2} \)
в. \( \frac{R}{6.2} \)
c. \( \frac{R}{3.1} \)
D. \( \frac{R}{0.1} \)
Subject: Maths
If \( A \) is an \( n \times n \) non-singular matrix,
then \( |\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}| \) is:
\( \mathbf{A} \cdot|A|^{n} \)
B \( \cdot|A|^{n+1} \)
c. \( |A|^{n-1} \)
D. \( |A|^{n-2} \)
Subject: Maths
Which of the following sets of real numbers is such that if \( x \) and \( y \) are the
elements of the set, then the sum of \( x \)
and y is also an element of the set:
I. The set of negative integers
II. The set of rational numbers
III. The set of irrational numbers
A. None
B . I only
c. I and II only
D. Il and III only
E . I, II, and III
Subject: Maths
\( A \) and \( B \) are two independent events. The probability that both \( A \) and \( B \) occur is \( \frac{1}{6} \)
and the probability that neither of them occurs is \( \frac{1}{3} . \) The probability of
occurrence of A is?
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{5}{6} \)
D.
Subject: Physics
An electric bulb is rated \( 220 V \) and
\( 100 W, \) when it is operated on \( 110 V \)
the power consumed will be
A . \( 100 \mathrm{W} \)
в. \( 75 \mathrm{W} \)
\( \mathbf{c} .50 W \)
D. \( 25 W \)
Subject: Maths
\( A \) box \( B_{1} \) contains 1 white ball, 3 red
balls and 2 black balls. Another box \( B_{2} \)
contains 2 white balls, 3 red balls and 4
black balls. A third box \( B_{3} \) contains 3
white balls, 4 red balls and 5 black balls If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that
these 2 balls are drawn from box \( B_{2} \) is
A \( \cdot \frac{116}{181} \)
в. \( \frac{126}{181} \)
c. \( \frac{65}{181} \)
D. \( \frac{55}{181} \)
Subject: Maths
Which of the following will be the angles of a triangle?
A \( \cdot 35^{\circ}, 45^{\circ}, 90^{\circ} \)
B . \( 26^{\circ}, 58^{\circ}, 96^{\circ} \)
\( \mathbf{c} \cdot 38^{\circ}, 56^{\circ}, 96^{\circ} \)
D . \( 30^{\circ}, 55^{\circ}, 90^{\circ} \)
Subject: Maths
Solve: \( \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{y}+\boldsymbol{x} \sin \left(\frac{\boldsymbol{y}}{\boldsymbol{x}}\right)=\mathbf{0} \)
Subject: Maths
If the line passing through the origin
makes angles \( \theta_{1}, \theta_{2}, \theta_{3} \) with the planes
\( X O Y, X O Z \) and \( Z O X \) respectively
then prove that \( \cos ^{2} \theta_{1}+\cos ^{2} \theta_{2}+ \)
\( \cos ^{2} \theta_{3}=2 \)
Subject: Maths
Water poured into an inverted conical vessel of which the radius of the base is
\( 2 \mathrm{m} \) and height \( 4 \mathrm{m}, \) and the rate of 77 litres/minute. The rate at which the
water level is rising at the instant when the depth is \( 70 \mathrm{cm} \) is: (use \( \pi=22 / 7 \) )
A. \( 10 \mathrm{cm} / \mathrm{min} \)
в. \( 20 \mathrm{cm} / \mathrm{min} \)
c. \( 40 \mathrm{cm} / \mathrm{min} \)
D. None
Subject: Physics
An artificial satellite is moving in a circular orbit around the earth with a
speed equal to half the magnitude of escape velocity from the earth's surface Total energy is always constant at any orbit. (Radius of the earth is \( 6400 k m \) )
The height of the satellite above the
Earth surface
A. \( 6400 k m \)
в. \( 3200 k m \)
\( c .9600 k m \)
D. \( 4800 k m \)
Subject: Maths
Q Type your question
in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as
below:

No. of faulty \( \quad \) Number of packets devices in a packet Nun s packe 0 300
1 If 100
2
3 30
4 20
f packets 500 Total number of
If one packet is drawn from the box, what
is the probability that all the four devices in the packet are without any fault?
A . 0.3
в. 0.75
c. 0.6
D. 0.95
Subject: Physics
A ball \( A \) of mass \( 2.5 \mathrm{kg} \) moving at \( 5 \mathrm{m} / \mathrm{s} \) collides with an identical ball \( B \) at rest.
A stops and B starts moving. What is the magnitude of velocity of B after the collision?
\( A \cdot 5 m / s \)
B. 12.5 \( \mathrm{m} / \mathrm{s} \)
\( c .2 .5 \mathrm{m} / \mathrm{s} \)
D. \( 10 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
The wave function for an orbital is \( \boldsymbol{H}- \)
atom is given as:
\( \mathbf{\Psi}= \)
\( \left(\frac{\sqrt{2}}{81 \sqrt{\pi}}\right)\left(\frac{1}{a_{0}}\right)^{\frac{2}{3}}\left(6-\frac{r}{a_{0}}\right)\left(\frac{r}{a_{0}}\right)^{-\frac{r}{3 a}} \)
The orbital is:
\( A \cdot 2 s \)
в. \( 3 p \)
\( c \cdot 2 p \)
D. \( 3 d \)
Subject: Maths
Which term of the A.P.
\( \mathbf{2 1}, \mathbf{4 2}, \mathbf{6 3}, \mathbf{8 4}, \dots \dots \dots \mathbf{~ i s} \mathbf{2 1 0} \)
\( \mathbf{A} \cdot 9^{t h} \)
B. \( 10^{\text {th }} \)
c. \( 11^{\text {th }} \)
D. \( 12^{\text {th }} \)
Subject: Maths
In a parallelogram \( \mathrm{ABCD}, \angle B=(2 x+ \)
25)\( ^{0} \) and \( \angle D=(3 x-5)^{0} . \) Find:
(i) The value of \( x \)
(ii) Measure of angle.
B. \( x=32, b=91 \) degrees, de \( =89 \) degrees
c. \( x=30, b=89 \) degrees, d=91 degrees
D. \( x=32, b=89 \) degrees, d=91 degrees
Subject: Physics
A ball of mass \( 100 \mathrm{g} \) is moving with a velocity of \( 10 \mathrm{m} s^{-1} . \) The force of the
blow by the bat acts for 0.01 seconds. What is the force exerted on the ball by the bat if the ball retraces its path with same speed?
A. \( 100 \mathrm{N} \)
B. 200 N
c. 300 N
D. 400 N
Subject: Physics
The dimensional formula for pressure
gradient is :
A \( \cdot M L^{-1} T^{-2} \)
B . \( M^{1} L^{-2} T^{-2} \)
c. \( M^{1} L^{2} T^{-2} \)
D. \( M^{1} L^{-1} T^{-3} \)
Subject: Chemistry
Which of the following sets of quantum numbers is correct for an electron in \( 4 f \)
orbital?
A \( . n=4, l=3, m=+4, s=+1 / 2 \)
в. \( n=4, l=4, m=-4, s=-1 / 2 \)
c. \( n=4, l=3, m=+1, s=+1 / 2 \)
Subject: Chemistry
The correct arrangement for the ions in the increasing order of their radiiis:
\( \mathbf{A} \cdot C a^{+2}, K^{+}, S^{-2} \)
в. \( C l^{-}, F^{-}, S^{-2} \)
C. \( N a^{+}, C l^{-}, C a^{+2} \)
D. \( N a^{+}, A l^{+3}, B e^{+2} \)
Subject: Maths
If \( \cos \alpha, \cos \beta, \cos \gamma \) are the direction
\( \operatorname{cosines} \) of a vector \( \vec{a}, \) then \( \cos 2 \alpha+ \)
\( \cos 2 \beta+\cos 2 \gamma \) is equal to
A . 2
B. 3
\( c \cdot-1 \)
D. 0
Subject: Chemistry
Which of the following best describes why purely metallic mixtures are
created?
Note: These do not include metalloid
elements.
A. To reduce the damaging effects of rusting of the substance when exposed to air
B. To allow for conduction of electricity without any conduction of heat
c. To allow a solid to have high tensile strength without being ductile.
D. To easily dissolve in water that allows for very rapid decomposition in the environment reducing the amount of metals that wind up in landfills
Subject: Chemistry
If for the half-cell reactions
\( \boldsymbol{C u}^{2+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u}^{+} \boldsymbol{E}^{o}=\mathbf{0 . 1 5} \boldsymbol{V} \)
\( \boldsymbol{C u}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u} \quad \boldsymbol{E}^{o}=\mathbf{0 . 3 4} \boldsymbol{V} \)
Calculate \( E^{o} \) of the half cell reaction
\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u} \)
Also predict whether \( C u^{+} \) undergoes
disproportionation or not
Subject: Chemistry
Assertion
When ideal gas expand from \( \boldsymbol{P}_{1}, \boldsymbol{V}_{1}, \boldsymbol{T}_{1} \)
to \( P_{2}, V_{2}, T_{2} \) in two steps, and work done
is high in
which number of steps are high
Reason
Work is path function
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
\( \left|\begin{array}{ccc}1+\sin ^{2} \theta & \sin ^{2} \theta & \sin ^{2} \theta \\ \cos ^{2} \theta & 1+\cos ^{2} \theta & \cos ^{2} \theta \\ 4 \sin 4 \theta & 4 \sin 4 \theta & 1+4 \sin 4 \theta\end{array}\right|= \)
\( 0, \) then \( \sin 4 \theta \) equals to
A. \( 1 / 2 \)
B.
\( c \cdot-1 / 2 \)
D. -1
Subject: Chemistry
In a gaseous reaction of the type, \( a A+ \) \( b B \rightarrow c C+d D, \) which is wrong?
A. a litres of A combines with b litres of B to give C and
B. a mol of A combines with b mol of B to give C and
c. a g of A combines with b g of B to give C and D
D. a molecules of A combines with b molecules of B to give \( C \) and \( D \)
Subject: Maths
If \( \boldsymbol{A}=\mathbf{1} \hat{\mathbf{1}}+\mathbf{2} \hat{\boldsymbol{j}}-\boldsymbol{R} \) and \( \hat{\boldsymbol{B}}=\mathbf{3} \hat{\mathbf{1}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
then
Find unit vector along \( \overrightarrow{\boldsymbol{A}} \)
A. \( \vec{A}+\vec{B} \)
В \( \cdot|\vec{A}+\vec{B}| \)
C . Unit vector along the direction of \( |\hat{A}+\hat{B}| \)
D. None of the above
Subject: Chemistry
If the given four electronic configurations
(i) \( n=4, l=1 \)
(ii) \( n=4,1=0 \)
(iii) \( n=3,1=2 \)
\( (i v) n=3,1=1 \)
are arranged in order of increasing energy, then the order will be:
A. (iv) < (ii) < (iii) < (i)
B. (ii) < (iv) < (i) < (iii)
c. (i) < (iii) < (ii) < (iv)
D. (iii) < (i) < (iv) < (ii)
Subject: Maths
Defined \( \boldsymbol{f}:\left[-\frac{1}{2}, \infty\right) \rightarrow \boldsymbol{R} \) by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sqrt{\mathbf{1}+\mathbf{2} \boldsymbol{x}}, \boldsymbol{x} \in\left[-\frac{\mathbf{1}}{\mathbf{2}}, \infty\right) . \) Then compute
\( \lim _{\boldsymbol{x} \rightarrow\left(\frac{\mathbf{1}}{\mathbf{2}}\right)} \boldsymbol{f}(\boldsymbol{x}) \). and also find \( \lim _{\boldsymbol{x} \rightarrow \frac{-\mathbf{1}}{\mathbf{2}}} \boldsymbol{f}(\boldsymbol{x}) \)
Subject: Physics
A thin fixed ring of radius \( 1 \mathrm{m} \) has a positive charge \( 1 \times 10^{-5} \mathrm{C} \) uniformly
distributed over it. A particle of mass \( 0.9 \mathrm{g} \) and having a negative charge of
\( 1 \times 10^{-6} \mathrm{C} \) is placed on the axis at a
distance of \( 1 \mathrm{cm} \) from the centre of the ring. Calculate the time period of oscillations.
A . 0.5 secs
B. 9.28 secs
c. 0.628 secs
D. 0.1 secs
Subject: Maths
Evaluate integral of \( \int \frac{d x}{\sqrt[4]{1+x^{4}}}, \) the
ans is
\( A \)
\[
-\frac{1}{4}\left[\log \frac{\sqrt[4]{1+1 / x^{4}}-1}{\sqrt[4]{\left(1+1 / x^{4}\right)}+1}-2 \tan ^{-1}\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}\right]
\]
B.
\[
-\frac{1}{4}\left[\log \frac{\sqrt[4]{1+1 / x^{4}}-1}{\sqrt[4]{\left(1+1 / x^{4}\right)}+1}+2 \tan ^{-1}\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}\right]+C
\]
\( c \)
\[
\frac{1}{4}\left[\log \frac{\sqrt[4]{1+1 / x^{4}}-1}{\sqrt[4]{\left(1+1 / x^{4}\right)}+1}+2 \tan ^{-1}\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}\right]
\]
\( D \)
\[
\frac{1}{4}\left[\log \frac{\sqrt[4]{1+1 / x^{4}}-1}{\sqrt[4]{\left(1+1 / x^{4}\right)}+1}-2 \tan ^{-1}\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}\right]+C
\]
Subject: Physics
A massless spring of natural length of \( 0.5 m \) and spring constant \( 50 N / m \) has one end fixed and the other end
attached to a mass of 250 g. The spring mass system is on a smooth floor. The mass is pulled until the length of the
spring is 0.6 and then released from rest. The kinetic energy of the mass when the length of the spring is \( 0.5 m \) is
A. \( 0.25 J \)
B. \( 2.25 J \)
c. \( 6.25 J \)
D. \( 9 . J \)
Subject: Physics
The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position, so that the water surface in the tank is at
the same level as the top of the cylinder
as shown in the figure. The density of
the water is \( \rho \)
n equilibrium, the height H of the water column in the cylinder satisfies
A \( \cdot \rho g\left(L_{0}-H\right)^{2}+P_{0}\left(L_{0}-H\right)+L_{0} P_{0}=0 \)
B \( \cdot \rho g\left(L_{0}-H\right)^{2}-P_{0}\left(L_{0}-H\right)-L_{0} P_{0}=0 \)
\( \mathbf{c} \cdot \rho g\left(L_{0}-H\right)^{2}+P_{0}\left(L_{0}-H\right)-L_{0} P_{0}=0 \)
D \( \cdot \rho g\left(L_{0}-H\right)^{2}-P_{0}\left(L_{0}-H\right)+L_{0} P_{0}=0 \)
Subject: Maths
\( \int_{0}^{1} \tan ^{-1} x d x \)
A. \( \frac{\pi}{2}-\frac{1}{2} \log 2 \)
B. \( \frac{\pi}{4}+\frac{1}{2} \log 2 \)
c. \( \frac{\pi}{2}-\frac{1}{4} \log 2 . \)
D. \( \frac{\pi}{4}-\frac{1}{2} \log 2 \)
Subject: Physics
A work of \( 200 J \) is done in moving a charge of \( -5 C \) from infinity to a
particular point in an electrostatic field The potential of this point is...........
\( \mathbf{A} \cdot-20 V \)
в. \( -25 V \)
c. \( -30 V \)
D. \( -40 V \)
Subject: Chemistry
Assertion
Oxidation number of \( S \) in \( F e S_{2} \) is -1
Reason
\( F e S_{2} \) is made of \( F e^{+2} \) and \( (S-S)^{2-} \)
ions.
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