AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The frequency of the spectral line
obtained when the electron in \( n=3 \) of
Hydrogen atom drops to the fround
state is:
A \( \cdot 2.925 \times 10^{15} \) Hertz
B . \( 2.925 \times 10^{13} \) Hertz
C . \( 2.925 \times 10^{14} \) Hertz
D. \( 36559 \times 10^{10} \) Hertz
Subject: Physics
A circular road of radius r is banked for
a speed \( \mathbf{v}=40 \mathrm{km} / \mathrm{hr} . \) A car of mass \( \mathrm{m} \)
attempts to go on the circular road. The
friction coefficient between the tyre and
the road is negligible.
A. The car cannot make a turn without skidding
B. if the car turns at a speed less than \( 40 \mathrm{km} / \mathrm{hr} \), it will slip down.
C. If the car turns at the correct speed of \( 40 \mathrm{km} / \mathrm{hr} \), the force by the road on the car is equal to \( m v^{2} / r \)
D. If the car turns at the correct speed of \( 40 \mathrm{km} / \mathrm{hr} \), the force by the road on the car is greater than mg as well as greater than \( m v^{2} / r \)
Subject: Physics
A microscope is focused on a mark, then a glass slab of refractive index 1.5 and thickness of \( 3 \mathrm{cm} \) is placed on the mark to get the mark again in focus, the microscope should be moved
A. \( 4 \mathrm{cm} \)
B. 2cm
\( c .6 \mathrm{cm} \)
D. 8cm
Subject: Chemistry
Identify the group \( 14 A \) element that best fits each of the following descriptions:
(a) prefers the +2 oxidation state.
(b) forms the strongest \( \pi \) bonds.
(c)is the second most abundant
element in the earth's crust.
(d)forms the most acidic oxide.
A \( \cdot(a) P b ;(b) C ;(c) S i ;(d) C \)
B. (a) \( P b ; \) (b) \( C ; \) (c) \( P b ; \) (d) \( C \)
\( \mathbf{c} . \) (a) \( P b_{;} \) (b) \( C ; \) (c) \( S i ; \) (d) \( S i \)
D. \( (a) S n ;(b) C ;(c) S i ;(d) C \)
Subject: Physics
The equation of a plane progressive wave is given by \( \boldsymbol{y}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) \)
The dimension of \( (\omega / k) \) is that of
A. frequency
B. velocity
c. wavelength
D. inverse of velocity
Subject: Physics
If the dimension of a physical quantity is given by \( \left[M^{a} L^{b} T^{c}\right] \) then the physical
quantity will be
A. acceleration, if \( a=1, b=-1, c=-2 \)
B. velocity, if \( a=1, b=0, c=-1 \)
c. pressure, if \( a=1, b=-1, c=-2 \)
D. force, if \( a=0, b=-1, c=-2 \)
Subject: Physics
Electromagnetic wave of intensity \( 1400 W / m^{2} \) falls on metal surface on
area \( 1.5 m^{2} \) is completely absorbed by
it. Find out force exerted by beam.
A \( \cdot 14 \times 10^{-5} N \)
В. \( 14 \times 10^{-6} N \)
\( \mathbf{c} \cdot 7 \times 10^{-5} N \)
D. \( 7 \times 10^{-6} N \)
Subject: Physics
From the displacement-time graph
shown here, find the velocity of the body
as it moves from \( A \) to \( B \)
A. \( 0.8 \mathrm{m} / \mathrm{s} \)
B. \( 1.2 \mathrm{m} / \mathrm{s} \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. \( 20 \mathrm{m} / \mathrm{s} \)
Subject: Maths
If two of the zeros of equation \( 2 x^{4}- \) \( 3 x^{3}-3 x^{2}+6 x-2, \) are \( \sqrt{2} \) and \( -\sqrt{2} \)
and other two are \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime}, \) then \( a b= \)
0. \( P \), then the value of \( p= \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{A}+\mathbf{2} \boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{0} \\ \mathbf{6} & -\mathbf{3} & \mathbf{3} \\ -\mathbf{5} & \mathbf{3} & \mathbf{1}\end{array}\right] \) and
\( \mathbf{2} \boldsymbol{A}-\boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{2} & \mathbf{- 1} & \mathbf{5} \\ \mathbf{2} & -\mathbf{1} & \mathbf{6} \\ \mathbf{0} & \mathbf{1} & \mathbf{2}\end{array}\right], \) then \( \boldsymbol{t} \boldsymbol{r}(\boldsymbol{A}) \)
\( t r(B) \) has the value equal to
\( A \)
B.
\( c \cdot 2 \)
D. none of these
Subject: Maths
\( \frac{d}{d x} \csc ^{-1}\left(\frac{1+x^{2}}{2 x}\right) \) is equal to
A \( \cdot \frac{-2}{\left(1+x^{2}\right)}, x \neq 0 \)
в. \( \frac{2}{\left(1+x^{2}\right)}, x \neq 0 \)
c. \( \frac{2\left(1-x^{2}\right)}{\left(1+x^{2}\right)\left|1-x^{2}\right|}, x \neq\pm 1,0 \)
D. None of the above
Subject: Maths
If \( \Delta P Q R \sim \Delta X Y Z, \angle Q=50^{\circ} \) and
\( \angle R=70^{\circ}, \) then the angle \( \angle X+\angle Y \) is
equal to:
A \( .70^{\circ} \)
B. 50
\( c \cdot 120 \)
D. \( 110^{\circ} \)
Subject: Chemistry
The heat of atomization of methane and
ethane are \( 360 \mathrm{kJ} / \mathrm{mol} \) and \( 620 \mathrm{KJ} / \mathrm{mol} \)
respectively. The longest wavelength of light capable of breaking the \( C-C \)
bond is:
(Avogadro number \( =6.02 \times 10^{23}, h= \)
\( 6.62 \times 10^{-34} \mathrm{Js} \)
A \( \cdot 2.48 \times 10^{4} \mathrm{nm} \)
B . \( 1.49 \times 10^{3} \) nm
c. \( 2.48 \times 10^{3} \mathrm{nm} \)
D. \( 1.49 \times 10^{4} \) nm
Subject: Chemistry
Assertion
BaCO \( _{3} \) is more soluble in \( H N O_{3} \) than
in plain water.
Reason
Carbonate is a weak base and reacts
with the \( H^{+} \) from the strong acid causing the barium salt to dissociate.
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
Assertion
Zinc is used in the galvanization of iron.
Reason
Its coating on iron articles increases their life by protecting them from
rusting.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct
Subject: Chemistry
n the give reaction, the product(s) obtained is/are:
нн,ссн \( _{z} \) сн, о dect
\( \mathrm{CH}_{2}=\mathrm{C}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \)
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{CH}-\mathrm{CH}_{3} \)
\( \mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2} \)
Subject: Chemistry
Which among the following compounds in crystalline form is used for making Nicol's prism?
A \( \cdot \operatorname{CaSO}_{4} \)
В. \( N a_{2} A l F_{6} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \)
D. \( A l_{2} O_{3} \)
Subject: Physics
Assertion
Pascal's law is the working principle of
hydraulic lift.
Reason
Pressure \( =\frac{\text {thrust}}{\text {area}} \)
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
Assertion
\( \lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \frac{\sqrt{1-\cos 2 x}}{\boldsymbol{x}} \) does not exist.
Reason \( |\sin x|=\left\{\begin{array}{cc}\sin x ; & 0<x<\frac{\pi}{2} \\ -\sin x ; & -\frac{\pi}{2}<x<0\end{array}\right. \)
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
Which of the following is true for
Thomson's model of the atom?
A. The radius of an electron can be calculated using Thomson's model
B. In an undisturbed atom, the electrons will be at their
equilibrium positions, where the attraction between the cloud of positive charge and the electrons balances their mutual repulsion
C. When the electrons are disturbed by collision, they will vibrate around their equilibrium positions and emit electromagnetic radiation whose frequency is of the order of magnitude of the frequency of electromagnetic radiation of a vibrating electron
D. Both
(B) and (C)
Subject: Physics
A magnet makes 40 oscillations per minute at a place having magnetic field intensity of \( 0.1 \times 10^{-5} \) T. At another place, it takes 2.5 seconds to complete one vibration. The value of earth's
horizontal field at that place is
A . \( 0.25 \times 10^{-6} \mathrm{T} \)
в. 0.36 \( \times 10^{-6} \) т
c. \( 0.66 \times 10^{-8} \mathrm{T} \)
D . 1.2 \( \times 10^{-6} \) न
Subject: Physics
A reversible engine takes heat from a
reservoir at \( 527^{\circ} \mathrm{C} \) and gives out heat to
\( a \sin k \) at \( 127^{\circ} \) C. How many Joules/s must it take from the
reservoir to perform useful mechanical
work at the rate of \( 750 W ? \)
A . 257.14
B. 1500
c. 457.14
D. 557.14
Subject: Maths
\( \frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-1} \& \frac{x-1}{k}= \)
\( \frac{\boldsymbol{y}-\boldsymbol{4}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{5}}{\boldsymbol{2}} \) are coplanar then \( \mathbf{k}=? \)
A. any value
B. exactly one value
c. exactly 2 values
D. exactly 3 values
Subject: Chemistry
Which of the following are the correct
statements regarding the catalyzed and
uncatalyzed reactions at constant
temperature?
This question has multiple correct options
A. Catalyzed reaction does not alter \( \Delta H \) of the reaction
B. At constant temperature, \( \Delta G^{0} \) of the catalysed and uncatalyzed reaction is same
C. Catalyzed reaction alters equilibrium constant even at constant temperature
D. Catalysed reaction alters \( r_{f} \) and \( r_{b} \) values equally at constant temperature
Subject: Chemistry
A dilute ferrous sulphate solution was
gradually added to the beaker
containing acidified potassium
permanganate solution. The light purple colour of the solution fades and finally disappears. Which of the following is the correct explanation for the observation?
A \( \cdot K M n O_{4} \) is an oxidising agent, and it oxidies \( F e S O_{4} \)
B. \( F e S O_{4} \) acts as an oxidising agent and oxidises
\( K M n O_{4} \)
C. The colour disappear due to dilution; no reaction is involved
D. \( K M n O_{4} \) is an unstable compound and decomposes is presence of \( F e S O_{4} \) to a colourless compound
Subject: Biology
Which one of the following statements
is correct?
A. At present it is not possible to grow maize without chemical fertilizers.
B. Extensive use of chemical fertilizer may lead to eutrophication of nearby water bodies.
C. Both Azotobacter and Rhizobium fix atmospheric nitrogen in root nodules of plants.
D. Cyanobacteria such as Anabaena and Nostoc are important mobilizers of phosphates and potassium for plant nutrition in the soil.
Subject: Maths
Choose the rational number which does
not lie between rational numbers \( -\frac{2}{5} \)
and \( -\frac{1}{5} \)
\( A \cdot-\frac{1}{4} \)
B. \( -\frac{3}{10} \)
c. \( \frac{3}{10} \)
D. \( -\frac{7}{20} \)
Subject: Physics
The mean value of velocity vector projection average over \( 3 / 8 \) th of a period after the start is
A \( \cdot \frac{2 \sqrt{2} A \omega}{\pi} \)
B. \( \frac{2 A \omega}{3 \sqrt{2 \pi}} \)
c. \( \frac{A \omega}{3 \pi} \)
D. \( \frac{2 \sqrt{2} A \omega}{3 \pi} \)
Subject: Maths
If the segments joining the points \( A(a, b) \) and \( B(c, d) \) studends an angle
at the origin, prove that \( \cos \theta= \) \( \frac{\boldsymbol{a c}+\boldsymbol{b} \boldsymbol{d}}{\sqrt{\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}\right)\left(\boldsymbol{c}^{2}+\boldsymbol{d}^{2}\right)}} \)
Subject: Maths
Find the values of \( x, \) if \( \left|\begin{array}{ll}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{2}\end{array}\right|=\left|\begin{array}{cc}\mathbf{4} & \mathbf{- 1} \\ \mathbf{1} & \mathbf{3}\end{array}\right| \)
Subject: Maths
The common chord of the circles \( x^{2}+ \)
\( \boldsymbol{y}^{2}-\mathbf{4} \boldsymbol{x}-\mathbf{4} \boldsymbol{y}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{y}^{2}=\mathbf{3} \mathbf{2} \)
subtends at the origin an angle equal to
A \( \cdot \frac{\pi}{3} \)
B.
c.
D.
Subject: Maths
The domain of the function \( \mathbf{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\boldsymbol{x}^{\log \boldsymbol{x}}} \)
is
A.
B. \( (0, \infty) \)
c. \( R-\{1\} \)
D. R - \{9
Subject: Maths
The value of \( \int \frac{\sin x+\cos x}{\sqrt{1+\sin 2 x}} d x \)
\( \mathbf{A} \cdot \sin x+c \)
B. \( x+c \)
c. \( \cos x+c \)
D \( \cdot \frac{1}{2}(\sin x+\cos x) \)
Subject: Maths
Which of the following is a singleton
set?
A. \( \{x:|x|=5, x \in N\} \)
B . \( \{x:|x|=6, x \in Z\} \)
c. \( \left(x: x^{2}+2 x+1=0, x \in N\right) \)
D. \( \left\{x: x^{2}=7, x \in N\right\} \)
Subject: Physics
A force of 64 dynes is inclined to the horizontal at an angle of \( 60^{\circ} . \) Find the acceleration in a mass of 8 g, which moves in a horizontal direction.
\( A \cdot 4 \mathrm{cm} \mathrm{s}^{-2} \)
B. \( 2 \mathrm{cm} \mathrm{s}^{-2} \)
\( c \cdot 8 \mathrm{cm} \mathrm{s}^{-2} \)
\( D \cdot 6 \mathrm{cm} \mathrm{s}^{-2} \)
Subject: Physics
\( f\left(\mu_{0}=\sqrt{2} \) and the rayjust fail to \right.
emerge from the prism, refractive index
\( \mu \) of the solid will be
\( A \cdot 1.2 \)
B. \( \sqrt{2} \)
\( c \)
D. \( \sqrt{3} / 2 \)
Subject: Maths
Solve the differential equation \( \left(x^{2}+\right. \)
\( \left.\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{x}-\boldsymbol{2} \boldsymbol{x} \boldsymbol{y} \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
Subject: Physics
Three tubes \( A, B \) and \( C \) are connected to a horizontal pipe in which liquid is flowing. The radii of pipe at the joints of \( A, B \) and \( C \) are \( 2 c m, 1 c m \) and \( 2 c m \) respectively. The height of liquid:
\( A \). in A and B is equal
B. in A is maximum
\( c . \) in \( A \) and \( C \) is same
D. is same in all three
Subject: Physics
A car starts from rest and accelerates
to a speed of \( 20 \mathrm{m} / \mathrm{s} \) in a time of \( 5 \mathrm{s} \)
Find out the average acceleration of
car?
A \( \cdot 100 m / s^{2} \)
в. \( 80 m / s^{2} \)
c. \( 40 m / s^{2} \)
D. \( 20 m / s^{2} \)
E \( \cdot 4 m / s^{2} \)
Subject: Physics
Figure below shows a portion of an
electric circuit with the currents in
amperes and their directions. The
magnitude and direction of the current
in the portion \( P Q \) is
\( \mathbf{A} \cdot 0 A \)
B. \( 3 A \) from \( P \) to \( Q \)
c. \( 4 A \) from \( Q \) to \( P \)
D. \( 6 A \) from \( Q \) to \( P \)
Subject: Physics
A free particle with initial kinetic energy \( \mathrm{E} \) and de-broglie wavelength \( \lambda \) enters a region in which it has potential energy U. What is the particle's new de-
Broglie wavelength?
A \( \cdot \lambda(1-U / E)^{-1 / 2} \)
в. \( \lambda(1-U / E) \)
c. \( \lambda(1-U / E)^{-1} \)
D. \( \lambda(1-U / E)^{1 / 2} \)
Subject: Physics
The work function of a certain metal is
\( 3.31 \times 10^{-19} J . \) Then, the maximum
kinetic energy of photoelectrons emitted by incident radiation of wavelength 5000 A is \( \left(G i v e n h=6.62 \times 10^{-34} J-s, c=\right. \)
\( \left.\mathbf{3} \times \mathbf{1 0}^{-\mathbf{8}} \mathbf{m} s^{-1}, \boldsymbol{e}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{C}\right) \)
A \( .248 e V \)
B. \( 0.41 e V \)
c. \( 2.07 e V \)
D. \( 0.82 e V \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{2} \\ \mathbf{3} & \mathbf{0} & -\mathbf{2} \\ \mathbf{2} & \mathbf{0} & \mathbf{3}\end{array}\right] \) then \( (\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}) \boldsymbol{A}= \)
\( \mathbf{A} \cdot\left[\begin{array}{ccc}13 & 0 & 0 \\ 0 & 13 & 0 \\ 0 & 0 & 13\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{ccc}7 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 7\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{ccc}-7 & 0 & 0 \\ 0 & 0 & -7 \\ 0 & 0 & -7\end{array}\right] \)
D. \( \left[\begin{array}{ccc}11 & 0 & 0 \\ 0 & 11 & 0 \\ 0 & 0 & 11\end{array}\right] \)
Subject: Maths
The derivative of \( \boldsymbol{y}=(1-\boldsymbol{x})(2- \)
\( x) \ldots(n-x) \) at \( x=1 \) is equal to
A . 0
в. (-1)\( (n-1) ! \)
c. \( n !-1 \)
D \( \cdot(-1)^{n-1}(n-1) ! \)
E \( \cdot(-1)^{n}(n-1) ! \)
Subject: Chemistry
Uncertainity in position of a particle of \( 25 \mathrm{g} \) in space is \( 10^{-15} \mathrm{m} . \) Determine
uncertainity in velocity \( \left(\mathrm{m} \mathrm{sec}^{-1}\right) \) in it. (plank's constant, \( \boldsymbol{h}=\mathbf{6 . 6} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s} \) )
A . \( 2.1 \times 10^{-18} \)
В. \( 1.2 \times 10^{-18} \)
c. \( 1.8 \times 10^{-18} \)
D. \( 2.5 \times 10^{-18} \)
Subject: Physics
For the given combination of gates, if the logic states of inputs \( A, B, C \) are as
follows \( \boldsymbol{A}=\boldsymbol{B}=\boldsymbol{C}=\mathbf{0} \) and \( \boldsymbol{A}=\boldsymbol{B}= \)
\( 1, C=0 \) then the logic states of output
D are
\( A \cdot 0,0 \)
B. 0,1
c. 1,0
D. 1,1
Subject: Physics
Assertion
Two balls of different masses are
thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed.
Reason
The maximum height and downward velocity attained at the point of
projection are independent of the mass of the ball.
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
Which of the complexes will exhibit the minimum peramagnetic behavior?
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{+2} \)
B. \( \left[M n\left(H_{2} O\right)_{6}\right]^{+2} \)
\( \mathbf{c} \cdot\left[C r\left(H_{2} O\right)_{6}\right]^{+2} \)
D \( \cdot\left[N i\left(H_{2} O\right)_{6}\right]^{+2} \)
Subject: Physics
A spring is kept compressed by a toy car of mass \( 150 g . \) On releasing the car it moves with a speed of \( 0.2 m s^{-1} . \) So, the elastic potential energy of the spring is
\( A .3 m J \)
B. \( 3 J \)
c. \( 1.5 m J \)
D. \( 4 m J \)
Subject: Chemistry
Assertion
Ammonia is a base.
Reason
Ammonia when dissolved in water
takes up proton to form ammonium and
furnishes \( \boldsymbol{O H}^{-} \) 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. Both Assertion and Reason are incorrect
Subject: Maths
ff \( A=\left|\begin{array}{ccc}\boldsymbol{4} & \boldsymbol{k} & \boldsymbol{k} \\ \mathbf{0} & \boldsymbol{k} & \boldsymbol{k} \\ \mathbf{0} & \boldsymbol{0} & \boldsymbol{k}\end{array}\right| \) and \( \operatorname{det}(\boldsymbol{A})=\mathbf{2 5 6} \)
then \( |\boldsymbol{k}| \) equals
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.
Subject: Physics
State the number of significant figures in the following:
\( (a) 0.007 m^{2} \)
\( (b) 2.64 \times 10^{24} k g \)
\( (c) 0.2370 g c m^{-3} \)
\( (d) 6.320 J \)
\( (e) 6.032 N m^{-2} \)
\( (f) 0.0006032 m^{2} \)
Subject: Maths
Classify the following function as injection, surjection or bijection:
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \operatorname{given} \) by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{1} \)
Subject: Maths
Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{\sqrt{2-x}-\sqrt{2+x}}{x} \)
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( -\frac{1}{\sqrt{3}} \)
\( c \cdot-\frac{1}{2} \)
D. \( -\frac{1}{\sqrt{2}} \)
Subject: Physics
\( \boldsymbol{Y}, \boldsymbol{k}, \boldsymbol{n} \) represent respectively the
young's modulus,bulk modulus and rigidity modulus of a body. If rigidity modulus is twice the bulk
modulus, then:
A. \( Y=5 k / 18 \)
в. \( Y=5 n / 9 \)
c. \( Y=9 k / 5 \)
D. \( Y=18 k / 5 \)
Subject: Physics
A convex mirror of radius of curvature
\( 20 \mathrm{cm} \) forms an image which is half the size of the object.How far is the object from the mirror?
A. \( 5 \mathrm{cm} \)
B. 7.5 \( \mathrm{cm} \)
\( c .-30 \mathrm{cm} \)
D. 12.5 cm
Subject: Chemistry
Which of the following steps is not
correct in the mechanism of
electrophilic substitution of benzene?
A. Generation of electrophile like \( X^{+}, R^{+}, R C^{+} O, N O_{2}^{+} \) etc.
B. Attack of electrophile resulting in the formation of arenium ion in which one of the carbon is \( s p^{3} \) hybridised.
C. Addition of proton on benzene ring to give carbocation.
D. Removal of proton from \( s p^{3} \) carbon atom to restore aromatic character.
Subject: Physics
The distance of the closest approach of an alpha particle fired at a nucleus with
kinetic energy \( \boldsymbol{K} \) is \( \boldsymbol{r}_{0} . \) The distance of
the closest approach when the \( \alpha \) particle is fired at the same nucleus
with kinetic energy \( 2 K \) will be
\( ^{A} \cdot \frac{r_{0}}{2} \)
B. \( 4 r_{0} \)
c. \( \frac{r_{0}}{4} \)
D. \( 2 r_{0} \)
Subject: Physics
A body moving with uniform retardation
covers \( 3 k m \) before its speed is reduced to half of its initial value. It comes to
rest in another distance of :
A. \( 1 \mathrm{km} \)
B. \( 2 \mathrm{km} \)
\( \mathbf{c} .3 \mathrm{km} \)
D. \( \frac{1}{2} k m \)
Subject: Maths
\( \boldsymbol{V}=\boldsymbol{\pi}\left(\boldsymbol{R}^{2}-\boldsymbol{r}^{2}\right) \boldsymbol{h} ; \) make 'r' the subject
of formula.
A \( \cdot r=\sqrt{R^{2}+\frac{V}{\pi h}} \)
в. \( _{r}=\sqrt{R-\frac{V}{\pi h}} \)
\( \mathbf{c} \cdot_{r}=\sqrt{R^{2}-\frac{V}{\pi h}} \)
D. \( r=\sqrt{R^{2}-\frac{V}{\pi h^{2}}} \)
Subject: Maths
\( \mathrm{IF} \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3} \\ -\mathbf{2} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{C}=\left[\begin{array}{cc}-\mathbf{2} & \mathbf{5} \\ \mathbf{3} & \mathbf{4}\end{array}\right] \)
then find the value of \( B-4 C \)
Subject: Chemistry
Which of the following order of acidic
strength is correct:
\( \mathbf{A} \cdot R C O O H>R O H>H O H>H C \equiv C H \)
B . \( R C O O H>H O H>R O H>H C \equiv C H \)
c. \( R C O O H>H O H>H C \equiv C H>R O H \)
D . \( R C O O H>H C \equiv C H>H O H>R O H \)
Subject: Physics
1atm \( = \)
A. \( 100 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. \( 76 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 20 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 25 \mathrm{cm} \) of \( \mathrm{Hg} \)
Subject: Chemistry
Markovnikov's rule for the addition of
hydrogen halides to alkenes states that the incoming hydrogen bonds to the :
A \( \cdot s p^{2} \) carbon with the most hydrogens already
B. \( s p^{2} \) carbon with the fewest hydrogens already
c. \( s p^{3} \) carbon with the most hydrogens already
D. \( s p^{3} \) carbon with the few hydrogens already
Subject: Physics
A force of \( - \) Fk acts on \( \mathrm{O} \), the origin of the coordinate system. The torque about the point (1,-1) is :
\( \mathbf{A} \cdot-\mathrm{F}(\hat{\mathrm{i}}-\hat{\mathrm{j}}) \)
B. \( \mathrm{F}(\hat{\mathrm{i}}-\hat{\mathrm{j}}) \)
\( \mathbf{c} .-\mathrm{F}(\hat{\mathbf{i}}+\hat{\mathbf{j}}) \)
D. F(í+j)
Subject: Maths
In an isosceles triangle \( A B C \), with \( A B=A C \), the bisectors of \( \angle B \) and \( \angle C \)
interest each other at \( O \) join \( A \) to \( O \)
show that:
\( (i) O B=O C \)
(ii) \( A O \) bisects \( \angle A \)
Subject: Chemistry
Yand Zare
\( \mathbf{A} \cdot N_{2} O_{3} \) and \( H_{3} P O_{4} \)
B. \( N_{2} O_{5} \) and \( H P O_{3} \)
\( \mathbf{c} \cdot N_{2} O_{4} \) and \( H P O_{3} \)
D. \( N_{2} O_{4} \) and \( H_{3} P O_{3} \)
Subject: Physics
A simple pendulum of length \( 4 \mathrm{m} \) is
taken to a height \( R \) (radius of the earth)
from the earth's surface.The time period of small oscillations of the pendulum is
\( \left(\boldsymbol{g}_{\text {surface}}=\boldsymbol{\pi}^{2} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A . 2 s
B. 4 s
\( c \cdot 8 s \)
D. 16 s
Subject: Maths
Class \( \begin{array}{cccc}2- & 4- & 6- & 8- \\ 4 & 6 & 8 & 10\end{array} \) \( 10- \)
12 interval
frequency \( 2 \quad 4 \quad 6 \) 10 5
What is the mode for the grouped data?
A .10 .5
B. 12.5
c. 13.7
D. 9.1
Subject: Maths
If \( \theta \) is the angle between the lines
\( A B, A C \) where \( A, B, C \) are the three points with coordinates (1,2,-1),(2,0,3),(3,-1,2)
respectively, then \( \sqrt{462} \cos \theta \) is equal to
A . 20
в. 2
c. 22
D. 26