AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Find the focus of the parabola \( \boldsymbol{y}= \)
\( -2(x+4)^{2}-1 \)
\( \mathbf{A} \cdot(-4,-1) \)
в. \( \left(-4, \frac{9}{8}\right) \)
c. (-4,1)
D. \( \left(-4,-\frac{9}{8}\right) \)
Subject: Chemistry
Using IUPAC norms, write the systematic names of the following.
(i) \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
(ii) \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right] \boldsymbol{S} \boldsymbol{O}_{4} \)
Subject: Chemistry
The correct match between Item(l) and
Item(II)
is :
\( \begin{array}{ll}\text { Item-I } & \text { Item-II } \\ \text { Nortehindrone } & \text { Anti-biotic } \\ \text { Ofloxacin } & \text { Anti-fertility } \\ \text { Equanil } & \text { Hypertension } \\ & \text { Analgesics }\end{array} \)
A. A-R, B-P, C-S
B. A-Q, B-P, C-R
c. \( A-R, B-P, C-R \)
D. A-Q, B-R, C-S
Subject: Maths
The adjoint of the matrix \( \boldsymbol{A}= \)
\[
\left[\begin{array}{ccc}
1 & 1 & 1 \\
2 & 1 & -3 \\
-1 & 2 & 3
\end{array}\right] \text { is }
\]
\( A \)
\[
\left.\begin{array}{l|lcc} 
& 9 & -1 & -4 \\
\frac{1}{11} & -3 & 4 & 5 \\
& 5 & -3 & -1
\end{array}\right]
\]
B.
\[
\left[\begin{array}{ccc}
9 & 1 & -4 \\
3 & 4 & -5 \\
5 & 3 & -1
\end{array}\right]
\]
\( c \)
\[
\left[\begin{array}{ccc}
9 & -3 & 5 \\
-1 & 4 & -3 \\
-4 & 5 & -1
\end{array}\right]
\]
D.
\[
\left[\begin{array}{ccc}
9 & -1 & -4 \\
-3 & 4 & 5 \\
5 & -3 & -1
\end{array}\right]
\]
Subject: Maths
Solve:
\( \operatorname{Tan}(\boldsymbol{A}-\boldsymbol{B})+\boldsymbol{\operatorname { T a n }}(\boldsymbol{B}-\boldsymbol{C})+ \)
\( \operatorname{Tan}(C-A) \) is equal to
A. \( \operatorname{TanA} \) TanB \( \operatorname{TanC} \)
B. CotA CotB CotC
c. \( \operatorname{Tan}(A-B) \operatorname{Tan}(B-C) \operatorname{Tan}(C-A) \)
D.
Subject: Physics
A closed coil having 100 turns is rotated
in a uniform magnetic field \( B=4.0 \times \)
\( 10^{-4} T \) about a diameter which is
perpendicular to the field. The angular velocity of rotation is 300 revolution per minute. The area of the coil is \( 25 \mathrm{cm}^{2} \)
and its resistance is \( 4.0 \Omega . \) Find (a) the average emf developed in half a turn from a position where the coil is perpendicular to the magnetic field,
(b)the average emf in full turn and the net charge displaced in part (a).
Subject: Maths
A square hole of cross - sectional area
\( 4 c m^{2} \) is drilled across a cube with its
length parallel to a side of the cube. If
edge of the cube measures \( 5 c m, \) what is the total surface area of the body so formed?
A \( \cdot 140 \mathrm{cm}^{2} \)
В. \( 142 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 162 \mathrm{cm}^{2} \)
D. \( 182 \mathrm{cm}^{2} \)
Subject: Maths
The distance between the lines \( 3 x+ \)
\( \mathbf{4} \boldsymbol{y}=\mathbf{9} \) and \( \mathbf{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}+\mathbf{1 5}=\mathbf{0} \) is
\( A \cdot \frac{3}{10} \)
в. \( \frac{33}{10} \)
\( c \cdot \frac{33}{5} \)
D. none of these
Subject: Chemistry
The order of basic strength of
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\mathbf{2}}(\mathbf{1}), \boldsymbol{C}_{2} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{2}(\boldsymbol{2}) \)
\( \left(C_{2} H_{5}\right)_{2} N H(3), \) and \( N H_{3}(4) \) is:
A. \( 1<4<2<3 \)
в. \( 1<2<3<4 \)
c. \( 4<3<2<1 \)
D. \( 3<2<4<1 \)
Subject: Physics
A travelling acoustic wave of frequency \( 500 \mathrm{Hz} \) is moving along the positive \( x \)
direction with a velocity of \( 300 m s^{-1} \)
The phase difference between two
points \( x_{1} \) and \( x_{2} \) is \( 60^{\circ} . \) Then the minimum separation between the two pints is
\( \mathbf{A} \cdot 1 \mathrm{mm} \)
B. \( 1 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 1 \mathrm{m} \)
Subject: Physics
The stress-strain curves for three wires
of different materials are shown in
figure, where \( P, Q \) and \( R \) are the elastic
limits of the wires. The figure shows
that
A. Elasticity of wire \( P \) is maximum
B. Elasticity of wire \( Q \) is maximum
C. Elasticity of wire \( R \) is maximum
D. None of the above is true
Subject: Physics
Calculate the mass loss in the
following:
\( _{1}^{2} \boldsymbol{H}+_{1}^{3} \boldsymbol{H} \longrightarrow_{2}^{4} \boldsymbol{H} \boldsymbol{e}+_{0}^{1} \boldsymbol{n} \)
Given the masses: \( _{1}^{2} H=2.014 \) amu, \( _{1}^{3} \boldsymbol{H}=\mathbf{3 . 0 1 6} \boldsymbol{a m u} ;_{2}^{4} \boldsymbol{H e}=\mathbf{4 . 0 0 4} \boldsymbol{a m u} \)
\( \mathbf{0}_{\mathbf{n}}=\mathbf{1 . 0 0 8} \) amu.
\( \mathbf{A} \cdot 0.018 a m u \)
B. 0.18 amu
c. 0.0018 amu
D. 1.8 amu
E . 18 amu
Subject: Maths
The annual maintenance cost of a
machine in a factory over a seven years
period is represented in the histogram.
In which year the maintenance cost is
\( 2500 ? \)
A . \( 1998-1999 \)
в. \( 2000-2001 \)
c. \( 2001-2002 \)
D. \( 1995-1996 \)
Subject: Chemistry
A student was carrying out a Grignard reaction between \( P h M g B r \) and ethyl
benzoate. She ran out of anhydrous ether just after the Grignard reagent was made. Which of the following solvents can still used to dissolve the
ethyl benzoate for its reaction with
already formed \( \boldsymbol{P h} M \boldsymbol{g} \boldsymbol{B r} \)
A. acetone
B. ethyl acetate
c. absolute alcohol
D. benzene
Subject: Maths
If \( \boldsymbol{P}(\boldsymbol{B})=\frac{\boldsymbol{3}}{\boldsymbol{4}}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \overline{\boldsymbol{C}})=\frac{1}{3} \) and
\( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B} \cap \overline{\boldsymbol{C}})=\frac{1}{3} \operatorname{then} \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C}) \) is
A \( \cdot \frac{1}{12} \)
B.
c. \( \frac{1}{15} \)
\( D \)
Subject: Chemistry
In a first order reaction, the concentration of product 'x' at time 't' is given by the expression:
(where,a = initial concentration, \( \mathbf{k}= \)
rate constant, \( n=\text { order }) \)
A \( \cdot x=a\left(1-e^{-k t}\right) \)
в. \( x=\frac{1}{(a-x)} \)
c. \( _{x}=\frac{1}{2^{n-1}} \)
D. \( x=\frac{a}{(a-x)} \)
Subject: Chemistry
Assertion: Atoms are not electrically
neutral
Reason: Number of protons and
electrons are different.
A. Both assertion and reason are true and the reason is a correct explanation of the assertion.
B. Both assertion and reason are true but reason is not a correct explanation of the assertion.
c. Assertion is true but reason is false
D. Both the assertion and reason are false.
E. Assertion is false but reason is true
Subject: Chemistry
Select the correct I.U.P.A.C. name
for \( \mathrm{Mn}(\mathrm{CO})_{5}\left(\sigma-\mathrm{C}_{3} \mathrm{H}_{5}\right) \)
This question has multiple correct options
A. Allylpentacarbonylmanganese (I)
B. Cyclopropylpentacarbonylmanganese (I)
c. Pentacarbonylcyclopropylmanganese (।)
D. Pentacarbonyl allylmanganese (I)
Subject: Maths
The coefficient of \( t^{24} \) in the expansion of
\( \left(1+t^{2}\right)^{12}\left(1+t^{12}\right)\left(1+t^{24}\right) \) is
A. \( ^{12} C_{6}+2 \)
B. \( ^{12} C_{5} \)
\( \mathbf{c} \cdot^{12} C_{6} \)
D. \( ^{12} C_{7} \)
Subject: Chemistry
A student places a strip of solid magnesium metal into a beaker full of
\( 100 . m L \) of \( 3.0 \mathrm{M} \) hydrochloric acid
solution. The student observes bubbling and the disappearance of the magnesium metal.
Which species is being oxidized and which species is being reduced in this
reaction?
A. Magnesium being oxidized and the chloride ion is being reduced.
B. Magnesium being oxidized and the hydrogen ion is being reduced.
c. Magnesium being reduced and the chloride ion is being oxidized.
D. Magnesium being reduced and the hydrogen ion is being oxidized.
Subject: Physics
Choose the correct statements from the
following:
This question has multiple correct options
A. Steel is more elastic than rubber.
B. The stretching of a coil spring is determined by the young's modulus of the wire of the spring.
C. The frequency of a tuning fork is determined by the shear modulus of the material of the fork.
D. When a material is subjected to a tensile (stretching) stress the restoring forces are caused by interatomic attraction.
Subject: Physics
A magnetic needle lying parallel to a magnetic field requires W units of work
to turn it through \( 60^{0} \). The torque needed to maintain the needle in this
position will be:
A \( \cdot \sqrt{3} \mathrm{W} \)
B. \( W \)
c. \( \sqrt{3 / 2} \mathrm{W} \)
D. 2w
Subject: Maths
Which of the following is a factor of the
polynomial \( -2 x^{2}+7 x-6 ? \)
A. \( -2 x-3 \)
B. \( 2 x+2 \)
c. \( x-6 \)
D. \( 2 x-2 \)
E . \( -2 x+3 \)
Subject: Physics
Select the output \( Y \) of the combination
of gates shown in figure for inputs \( \boldsymbol{A}= \)
\( \mathbf{1}, \boldsymbol{B}=\mathbf{0} ; \boldsymbol{A}=\mathbf{1}, \boldsymbol{B}=\mathbf{1} \) and \( \boldsymbol{A}=\mathbf{0}, \boldsymbol{B}= \)
respectively.
A \( .(0,1,1) \)
в. (1,0,1)
c. (1,1,1)
D. (1,0,0)
Subject: Physics
A spherical body of diameter D is falling in viscous medium. Its terminal velocity is proportional to:
\( \mathbf{A} \cdot V_{1} \propto D^{1 / 2} \)
B. \( V_{1} \propto D^{3 / 2} \)
\( \mathbf{c} \cdot V_{1} \propto D^{2} \)
D. \( V_{1} \propto D^{5 / 2} \)
Subject: Physics
A ball is projected from level ground with a velocity of \( 40 \mathrm{m} / \mathrm{s} \) at an angle of
\( 30^{\circ} \) from the ground. Calculate the vertical component of the projectile's velocityjust before it strikes the ground?
(Take \( \left.\sin 30^{\circ}=0.5, \cos 30^{\circ}=0.87\right) \)
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c .30 \mathrm{m} / \mathrm{s} \)
D. 35 m/s
E. \( 40 \mathrm{m} / \mathrm{s} \)
Subject: Maths
A random variable \( \boldsymbol{X} \) is binomially
distributed with mean 12 and variance
8. The parameters of the distribution
are \( \ldots . . \& \ldots . \)
A \( \cdot_{36, \frac{2}{3}} \)
в. \( _{36, \frac{1}{3}} \)
c. \( _{24, \frac{1}{3}} \)
D. \( 24, \frac{2}{3} \)
Subject: Physics
A particle is moving with a constant acceleration. Its velocity is reduced to zero in 5 s and it covered a distance of
\( 100 \mathrm{m} \) in this direction. The distance covered by the particle in the next 5 s is
A. Zero
B. 250 m
c. \( 100 \mathrm{m} \)
D. 500 \( \mathrm{m} \)
Subject: Chemistry
\( H_{2} S \) is acidic in nature while \( H_{2} O \) is
neutral in nature. Give reason.
A. Oxygen is more electronegative than sulphur
B. \( H-S \) bond is weaker than \( O-H \) bond
c. Bond angle in \( H_{2} \) S is less than that in \( H_{2} \) O
D. \( H-S \) bond is stronger than \( O-H \) bond.
Subject: Physics
Q Type your question
charges along the \( x-, y- \) and z-axes,
respectively. The charge density, i.e.,
charge per unit length of each wire is \( \lambda: \)
A \( \cdot \frac{\lambda}{3 \pi \varepsilon_{0} a}(\hat{i}+\hat{j}+\widehat{k}) \)
В \( \cdot \frac{\lambda}{2 \pi \varepsilon_{0} a}(\hat{i}+\hat{j}+\widehat{k}) \)
c. \( \frac{\lambda}{2 \sqrt{2} \pi \varepsilon_{0} a}(\hat{i}+\widehat{j}+\widehat{k}) \)
D. \( \frac{\sqrt{2} \lambda}{(\hat{i}+\hat{j}+\widehat{k})} \)
Subject: Maths
The base of a right prism is a Trapezium whose lengths of two Parallel sides are
\( 10 c m \) and \( 6 \mathrm{cm} \) and distance between
them is \( 5 \mathrm{cm} . \) If the height of the prism
is \( 8 \mathrm{cm}, \) its volume is
A \( \cdot 320 \mathrm{cm}^{3} \)
B. \( 300.5 \mathrm{cm}^{3} \)
\( c \cdot 310 c m^{3} \)
D. \( 300 \mathrm{cm}^{3} \)
Subject: Maths
Prove that the points \( \boldsymbol{A}= \) \( (1,2,3), B(3,4,7), C(-3,-2,-5) \) are
collinear \( \& \) find the ratio in which \( B \)
divides \( \boldsymbol{A C} \)
A .2: 5
B . 2: 3
c. 2: 8
D. 2: 7
Subject: Maths
Find the mode of the following:
\( \mathbf{1 8}, \mathbf{1 4}, \mathbf{2 2}, \mathbf{2 3}, \mathbf{1 4}, \mathbf{1 8}, \mathbf{1 7}, \mathbf{2 8}, \mathbf{2 8}, \mathbf{1 4}, \mathbf{2 5}, \mathbf{1} \)
A . 12
B. 13
c. 14
D. 15
Subject: Physics
A circular racket of radius \( 300 \mathrm{m} \) is
backed at an angle of \( 15^{0} \). The
coefficient of friction between the
wheels of a race car and the road is 0.2
the maximum permissible speed to avoid slipping is ( Take \( \left.\tan 15^{0}=0.27, g=10 m s^{-2}\right) \)
\( \mathbf{A} \cdot 18.6 \mathrm{ms}^{-1} \)
B. 28.6 \( m s^{-1} \)
c. \( 38.6 \mathrm{ms}^{-1} \)
D. \( 48.6 \mathrm{ms}^{-1} \)
Subject: Maths
Distinguish which one is initial valued
ordinary differential equation and
boundary valued ordinary differentia equation:
\( \mathbf{y}^{\prime \prime}+\mathbf{2} \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}}, \boldsymbol{y}(\boldsymbol{\pi})=\mathbf{1} ; \boldsymbol{y}^{\prime}(\boldsymbol{\pi})=\mathbf{2} \)
¡) \( \boldsymbol{y}^{\prime \prime}+\mathbf{2} \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}}, \boldsymbol{y}(\mathbf{0})=\mathbf{1} ; \boldsymbol{y}^{\prime}(\mathbf{1})=\mathbf{1} \)
Subject: Physics
An object \( 5 \mathrm{cm} \) tall is placed \( 1 \mathrm{m} \) from a concave spherical mirror which has a
radius of curvature of \( 20 \mathrm{cm} . \) The size of the image is:
A. \( 0.11 \mathrm{cm} \)
B. \( 0.50 \mathrm{cm} \)
c. \( 0.55 \mathrm{cm} \)
D. \( 0.60 \mathrm{cm} \)
Subject: Physics
The Jupiter's period of revolution around
the Sun is 12 times that of the

Earth. Assuming the planetary orbits to be circular, find the acceleration of Jupiter in the heliocentric reference frame.
A \( \cdot 2 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
B. \( 4.2 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
C \( .2 .2 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
D. \( 4 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
Subject: Chemistry
Which is expected to be more stable, (I)
\( \boldsymbol{O}_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O}^{-} \) or \( (\|) \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O} \)
and why?
A. (I) due to resonance
B. (II) due to resonance
c. (I) due to inductive effect
D. (II) due to inductive effect
Subject: Chemistry
\( \Delta S^{\ominus} \) for the cell reaction assuming
that these quantities remain
unchanged in the range \( 15^{\circ} C \) to \( 35^{\circ} C \) is:
A \( \cdot 193 J K^{-1} \)
B. -193 Л \( K^{-1} \)
\( \mathbf{c} \cdot 1930 J K^{-1} \)
D. \( -1930 J K^{-1} \)
Subject: Physics
toppr
Q Type your question
OB are resistanceless and rotating with
constant angular velocity \( \omega \) in the same
plane as that ring, about hinge point '0
and the separation between 0 and
\( \mathrm{C} \) (centre of ring) is' \( 2 \ell \) as shown in the
figure. Find the current in the rod 'OA' when the both rod becomes tangent
to the ring.
A. Zero
B.
\[
\frac{B a V}{R} e \frac{-3 t}{2 C R}
\]
\( c \)
\[
\frac{B a V}{R} e \frac{3 t}{2 C R}
\]
D.
\[
\frac{B a V}{R} e \frac{-4 t}{2 C R}
\]
E. None of the above
Subject: Maths
If \( \bar{a} \) and \( \bar{b} \) are any two non-zero and non-
collinear vectors, then prove that any vector \( \bar{r} \) coplanar with \( \bar{a} \) and \( \bar{b} \) can be
uniquely expressed as \( \overline{\boldsymbol{r}}=\boldsymbol{t}_{1} \boldsymbol{a}+\boldsymbol{t}_{2} \boldsymbol{b} \)
where \( t_{1} \) and \( t_{2} \) are scalars.
Subject: Maths
\( \mathbf{f} \mathbf{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{5} & \mathbf{- 6} \\ \mathbf{- 8} & \mathbf{0} & \mathbf{4} \\ \mathbf{3} & \mathbf{- 7} & \mathbf{2}\end{array}\right], \) then the
cofactor of \( -7= \)
A . 44
B. 43
\( c \cdot 40 \)
D. 39
Subject: Maths
The value of \( \tan ^{-1}\left(\frac{x}{y}\right)- \)
\( \tan ^{-1}\left(\frac{x-y}{x+y}\right), x, y>0 \) is
\( A \cdot \frac{\pi}{4} \)
B. \( -\frac{\pi}{4} \)
\( c \cdot \frac{\pi}{2} \)
D. \( -\frac{\pi}{2} \)
Subject: Maths
Negation of the statement:
\( \sqrt{5} \) is an integer or 5 is irrational is?
A. \( \sqrt{5} \) is not an integer or 5 is not irrational
B. \( \sqrt{5} \) is not an integer and 5 is not irrational
c. \( \sqrt{5} \) is irrational or 5 is an integer
D. \( \sqrt{5} \) is an integer and 5 is irrational
Subject: Physics
A stone falls freely under gravity. It
covers distances \( h_{1}, h_{2} \) and \( h_{3} \) in the
first 5 second, the next \( 5 s \) and next
5 second respectively. The relation
between \( h_{1}, h_{2} \) and \( h_{3} \) is :
A \( \cdot h_{1}=2 h_{2}=3 h_{3} \)
B. \( h_{1}=\frac{h_{2}}{3}=\frac{h_{3}}{5} \)
c. \( h_{2}=3 h_{1} \) and \( h_{3}=3 h_{2} \)
D. \( h_{1}=h_{2}=h_{3} \)
Subject: Physics
Surface charge density of the plate is
equal to
\( \mathbf{A} \cdot 8.85 \times 10^{-10} \mathrm{C} / \mathrm{m}^{2} \)
B . \( -8.85 \times 10^{-10} C / m^{2} \)
C \( \cdot 17.7 \times 10^{-10} \mathrm{C} / \mathrm{m}^{2} \)
D. \( -17.7 \times 10^{-10} C / m^{2} \)
Subject: Chemistry
Assertion
Specific gravity is dimensionless
quantity.
Reason
Specific gravity is relative density of a substance, measured with respect to
density of water at \( 4^{\circ} \mathrm{C} \)
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
The direction cosine of a line equally inclined to the axes are
A \( \cdot \frac{1}{3}, \frac{1}{3}, \frac{1}{3} \)
B. \( -\frac{1}{3},-\frac{1}{3},-\frac{1}{3} \)
c. \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \)
D. none of these
Subject: Chemistry
A lead storage battery containing 5.0 Lof
(1N) \( H_{2} S O_{4} \) solution is operated for
\( 9.65 \times 10^{5} \mathrm{s} \) with a steady current of 100
mA. Assuming volume of the solution
remaining constant, normality of \( H_{2} S O_{4} \)
will:
A. remain unchanged
B. increases by 0.20
c. increase by unity
D. decrease by 0.40
Subject: Physics
On applying brakes the angular velocity of a flywheel reduces from 900
cycles/min to 720 cycles/min in 6 seconds. Its angular retardation in rad
\( / s^{2} \) will be?
A . \( \pi / 3 \)
в. \( \pi \)
c. \( 2 \pi / 3 \)
D. \( 2 \pi \)
Subject: Chemistry
Which of the following molecule doesn't have \( d \pi-p \pi \) bonding?
\( A \cdot S O_{2} \)
В. \( P_{4} O_{10} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{4} \)
D. \( B_{3} N_{3} H_{6} \)
Subject: Maths
The velocity \( v \) of a particle is given by the equation \( v=6 t^{2}-6 t^{3}, \) where \( v \) is in
the \( m s^{-1}, t \) is the instant of time in
seconds while 6 and 6 are suitable
dimensional constants. At what values
of \( t \) will the velocity be maximum and minimum? Determine these maximum
and minimum values of the velocity.
Subject: Maths
If a curve passes through the point \( \left(2, \frac{7}{2}\right) \) and has slope \( \left(1-\frac{1}{x^{2}}\right) \) at any
point \( (x, y) \) on it, then the abscissa of the point on the curve whose ordinate is
\( \frac{-3}{2} \) is
\( A \cdot 2 \)
B. -2
c. 1
D. -
Subject: Physics
A beam of cathode rays moves from left
to right in a plane of the paper and it enters into a uniform magnetic field acting perpendicular to the plane of the paper and inwards. Now, the cathode rays are deflected:
A. Downwards
B. Upwards
c. In a direction perpendicular to the plane of the paper and inwards
D. In a direction perpendicular to the plane of the paper and outwards
Subject: Physics
A thermally insulated vessel is divided
into two parts by a heat-insulating piston which can move in the vessel without friction. The left part of the
vessel contain one mole of an ideal
monoatomic gas, \( \& \) the right part is
vacuum. The piston is connected to the right wall of the vessel through a spring whose length in free state is equal to the length of the vessel as shown in the
figure. Determine the heat capacity \( C \) of the system, neglecting the heat capacities of the vessel, piston and
spring.
Subject: Physics
Visible light of wavelength \( 6000 \times \)
\( 10^{-8} \mathrm{cm} \) falls normally on a single slit
and produces a diffraction pattern. It is found that the second diffraction
minimum is at \( 60^{0} \) from the central
maximum. if the first minimum is
produced at \( \theta_{1} \) then \( \theta_{1} \) is close to :
A \( \cdot 25^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 20^{0} \)
D. \( 45^{\circ} \)
Subject: Chemistry
One molecule of a substance absorbs
one quantum of energy. The energy involved when 1.5 moles of the
substance absorb red light of frequency
\( 7.5 \times 10^{14} s e c^{-1} \) will be?
A \( \cdot 4.49 \times 10^{5} J \)
B . \( 2.24 \times 10^{5} J \)
c. \( 9.23 \times 10^{7} J \)
D. \( 2.24 \times 10^{7} J \)
Subject: Physics
toppr
Q Type your question.
cnargea partıcies. wıth a rıela b resia,
is found that the filter transmits \( \alpha \) -
particles each of energy \( 5.3 \mathrm{MeV} \). The magnetic field is increased to \( 2.3 \mathrm{B} \)
Tesla and deuterons are passed into the filter. The energy of each deuteron
transmitted by the filter is MeV.
A . 28 Mev
B. 14Mev
c. 7 Mev
D. 18Me
Subject: Physics
The vertical height of an almirah is \( 2 m \)
its base is a square of side length \( 0.4 m \)
and its mass is \( 200 k g . \) The maximum height from the floor at which a
horizontal force \( 490 N \) should be
applied on the almirah so that it does not tilt is:
A. \( 0.6 m \)
в. \( 0.8 m \)
\( c .1 m \)
D. \( 1.2 m \)
Subject: Physics
Three equal resistors connected in
series across a source of e.m.f.
dissipate 10 watts of power. What will be the power dissipated in watts if the same resistors are connected in paralle
across the same source of e.m.f.?
A. \( 10 W \)
в. \( 30 W \)
c. \( 90 W \)
D. \( \frac{10}{3} W \)
Subject: Maths
If \( \sin A=x, \cos B=y \) and \( A+B+ \)
\( C=0, \) then \( x^{2}+2 x y \sin C+y^{2} \) is
equal to
\( \mathbf{A} \cdot \sin ^{2} C \)
B. \( \cos ^{2} C \)
c. \( 1+\sin ^{2} C \)
D. \( 1+\cos ^{2} C \)
Subject: Chemistry
The conversion of \( -\operatorname{coch}_{2}-t o- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \) using Hg/ Zn and HCl is
known as
A. Clemmensen reduction
B. Birch reduction
c. Wolf kishner reduction
D. Rosenmund reduction
Subject: Physics
For a cube and a sphere made of same material, what should be the ratio of the
side of the cube to the radius of the
sphere such that both of them have the
same thermal capacity?
A \( \cdot \sqrt[3]{\frac{4}{3} \pi} \)
B. \( \sqrt[3]{\frac{5}{3} \pi} \)
c. \( \sqrt[3]{\frac{3}{4} \pi} \)
D. \( \sqrt[3]{\frac{2}{3} \pi} \)
Subject: Maths
\( f\left(\begin{array}{ccc}2 & -1 & 3 \\ -5 & 3 & 1 \\ -3 & 2 & 3\end{array}\right], \) then
\( A .(A d j A)= \)
A \( \cdot\left(A d j \cdot A^{T}\right) \)
B. \( (\text {Adj.A}) . A \)
c. \( |A| . A \)
D. None of these
Subject: Chemistry
Which of the following alkaline earth metal sulphates has hydration enthalpy higher than the lattice enthalpy?
A \( \cdot \operatorname{CaSO}_{4} \)
в. \( B e S O_{4} \)
c. \( B a S O_{4} \)
D. \( \operatorname{sr} \operatorname{sO} 4 \)
Subject: Chemistry
The molecular formula of ammonia is
\( N H_{3} . \) Therefore, the number of
hydrogen atoms in 34 g of ammonia will
be:
A. \( 3 \times 6.023 \times 10^{23} \)
В. \( 6.023 \times 10^{23} \)
c. \( 34 \times 6.023 \times 10^{23} \)
D. \( 6 \times 6.023 \times 10^{23} \)
Subject: Chemistry
Assertion
The formation of \( N H_{3} \rightarrow B F_{3} \) is
neutralization according to Lewis acid base theory.
Reason
Formation of Co-ordinate covalent bond
is neutralization.
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 kind of isomerism is exhibited
by octahedral \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{B r}_{2}\right] \boldsymbol{C l} ? \)
A. Geometrical and ionization
B. Geometrical and optical
c. optical and ionization
D. Geometrical only