AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
Statement \( -1: P O F_{3} \) exist but \( N O F_{3} \)
does not exist.
Reason
Statement - 2 : 'P' can form five bonds by
expanding its octet while 'N' can not expand its octet to form five bonds.
A. Statement-1 is true, statement- - 2 is true and statement - 2 is correct explanation for statement-1
B. Statement-1 is true, statement - 2 is true and statement - 2 is NOT the correct explanation for statement - 1.
c. statement- 1 is true, statement- 2 is false.
D. Statement- -1 is false, statement - 2 is true
Subject: Chemistry
Find out the major product in given reaction.
\( \boldsymbol{H}_{5} \boldsymbol{C}_{6} \boldsymbol{C H O}+ \)
\( \boldsymbol{H}_{3} \boldsymbol{C C H}_{2} \boldsymbol{C H O} \stackrel{\text {dil.NaOH}}{\longrightarrow} ? \)
Subject: Physics
A ray of light is incident on a
rectangular plate at an angle of
incidence \( 60^{\circ} . \) The light ray suffers a
deviation which is \( 25 \% \) of the angle of incidence. The refractive index of the
glass will be
A \( \cdot \sqrt{3} \)
B. \( \sqrt{2} \)
c. \( \sqrt{\frac{3}{2}} \)
D. 1.5
Subject: Chemistry
Which statements are correct for CO
and \( N_{2} \) according to molecular orbital theory?
(I) Bond order of \( \mathrm{CO} \) and \( N_{2} \) are 3 and 3
(II) Bond order of \( \mathrm{CO} \) and \( N_{2} \) are same
(III) During the formation of \( N_{2}^{+} \) from
\( N_{2} \) bond length increases
(IV) During the formation of \( C O^{+} \) from
CO, the bond length decreases.
\( \mathbf{A} \cdot \|, 1 \vee, \)
в. ।, и, II, Iv
\( c \cdot \) ।, ॥
D. ।, и, II
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{7}, \mathbf{9}\}, \boldsymbol{B}= \)
\( \{\mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}\} \) then \( \boldsymbol{B}-\boldsymbol{A}= \)
Subject: Chemistry
What is \( p K \) value of the complex
\( \left[\boldsymbol{P t C l}_{4}\right] \) if
\( \boldsymbol{P t}^{4+}+\boldsymbol{C l}^{-} \rightarrow[\boldsymbol{P t C l}]^{3+} \)
\( \boldsymbol{K}_{\mathbf{1}}=\mathbf{1 0}^{-\mathbf{2}} \)
\( [\boldsymbol{P t C l}]^{3+}+\boldsymbol{C l}^{-} \rightarrow\left[\boldsymbol{P t} C l_{2}\right]^{2+} \)
\( \boldsymbol{K}_{2}=\mathbf{1 0}^{-3} \)
\( \left[\boldsymbol{P t C l}_{2}\right]^{2+}+\boldsymbol{C l}^{-} \rightarrow\left[\boldsymbol{P t C l}_{3}\right]^{+} \)
\( \boldsymbol{K}_{3}=\mathbf{1 0}^{-4} \)
\( \left[\boldsymbol{P t C l}_{3}\right]^{+}+\boldsymbol{C l}^{-} \rightarrow\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] \)
\( \boldsymbol{K}_{4}=\mathbf{1 0}^{-4} \)
Subject: Maths
Let \( \boldsymbol{A}=\{1,2,3, \dots, 10\} \) and \( B= \)
\( \{101,102,103, \dots, 1000\} . \) Then set \( A \)
and \( B \) are
A. Both finite sets
B. Infinite and finite set respectively
c. Both Infinite sets
D. Finite and infinite set respectively
Subject: Physics
Kinetic energy of a particle moving in a straight line is proportional to the time
\( t . \) The magnitude of the force acting on the particle is:
This question has multiple correct options
A. directly proportional to the speed of the particle
B. inversely propotional to \( \sqrt{t} \)
c. inversely proportional to the speed of the particle
D. directly proportional to \( \sqrt{t} \)
Subject: Physics
A person standing on the floor of an elevator drops a coin. The coin reaches the floor of the elevator-
a) in a time \( t_{1} \) if the elevator is
stationary and
b) in time \( t_{2} \) if it is moving uniformly,
then
A \( \cdot t_{1}=t_{2} \)
в. \( t_{1}>t_{2} \)
c \( \cdot t_{1}<t_{2} \)
D. \( t_{1}<t_{2} \) or \( t_{1}>t_{2} \) depending on whether the lift is going
up or down
Subject: Physics
A screw gauge has positive error of 4 divisions. When the screw gauge holds a sphere the main scale reading is 4 \( \mathrm{mm} \) and the head scale coinciding division is \( 24 . \) If its least count is 0.01
\( \mathrm{mm}, \) the volume of the sphere is \( m m^{3} \)
A . 24.456
B. 38.808
c. 62.378
D. 40.567
Subject: Chemistry
Assertion: The standard potential of
hydrogen half-cell is zero at all conditions of temperature and
pressure. Reason: Standard conditions require 298 K temperature and 1 atm pressure.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Physics
Figure below shows pressure (P) versus volume(V) graphs for a certain mass of
a gas at two constant temperatures \( T_{1} \)
and \( T_{2} . \) Which of the inferences given
below is correct?
\( A \cdot T_{1}=T_{2} \)
в. \( T_{1}>T_{2} \)
\( c \cdot T_{1}<T_{2} \)
D. none of the above
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{\sqrt{x+6}-\sqrt{6}}{x}= \)
А. \( \frac{1}{\sqrt{6}} \)
в. \( -\frac{1}{\sqrt{6}} \)
с. \( \frac{1}{2 \sqrt{6}} \)
D. \( -\frac{1}{2 \sqrt{6}} \)
Subject: Chemistry
Which of the following statement (s) is/are true regarding the change:
\( \boldsymbol{C N}^{-} \rightarrow \boldsymbol{C N O}^{-} ? \)
This question has multiple correct options
A. Carbon is losing two electrons per atom.
B. The oxidation state of carbon change from +2 to +4
c. oxidation state of nitrogen is not changing
D. oxidation state of nitrogen changes from - 3 to -
Subject: Maths
Sum of all integral values of \( \boldsymbol{a} \in[\mathbf{1}, \mathbf{5 0 0}] \)
for which the equation \( [x]^{3}+x-a=0 \)
has a solution ( \( [.] \) denotes the greatest integer function) is
A .1342
в. 512
c. 784
D. 812
Subject: Physics
The least count of a stop watch is \( 1 / 5 \) sec. The time of 20 oscillations of a
pendulum is measured to be 25 sec. The
minimum percentage error in the measurement of time will be:
\( A \cdot 0.1 \% \)
B. \( 0.8 \% \)
c. \( 1.8 \% \)
D. 8\%
Subject: Chemistry
A compound \( M X_{2} \) has observed
and normal molar masses 65.6 and 164
respectively. The apparent degree of
ionization of \( M X_{2} \) is:
A . \( 75 \% \)
B. \( 85 \% \)
c. \( 65 \% \)
D. \( 25 \% \)
Subject: Maths
Find the simple interest and the
amount when
Principal= \( \boldsymbol{R s} . \boldsymbol{6 4 0 0}, \boldsymbol{r a t e}=\boldsymbol{6} \% \boldsymbol{p} \boldsymbol{a} \)
and \( \operatorname{tim} e=2 \) years
Subject: Maths
If \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x}) \) for \( \boldsymbol{a} \leq \boldsymbol{x} \leq \boldsymbol{b}, \) then
\( \int_{a}^{b} f(x) g(x) d x \) equals to:
A. \( f(2)-f(1) \)
В. \( g(2)-g(1) \)
c. \( \frac{[f(b)]^{2}-[f(a)]^{2}}{2} \)
D. \( \frac{[g(b)]^{2}-[g(a)]^{2}}{2} \)
Subject: Physics
X-rays are incident on a target metal atom having 30neutrons. The ratio of radii of nucleus to that of Helium
nucleus is \( 14^{1 / 3} \)
(a) Find the atomic number of target
atom.
(b) Find the frequency of \( \boldsymbol{K}_{\boldsymbol{\alpha}} \) line
emitted by this metal.
\( \boldsymbol{R}=\mathbf{1 . 1} \times \mathbf{1 0}^{\mathbf{7}} \mathbf{m}^{-1}, \boldsymbol{c}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{8}} \mathbf{m} / \mathbf{s} \)
A \( .20,1.546 \times 10^{4} \mathrm{Hz} \)
В . 24. \( 1.546 \times 10^{1} 0 H z \)
\( \mathbf{c} \cdot 26,1.546 \times 10^{1} 8 H z \)
D. None of these
Subject: Maths
\( \sim p \wedge q \) is logically equivalent to
\( \mathbf{A} \cdot p \rightarrow q \)
в. \( q \rightarrow p \)
\( \mathbf{c} \cdot \sim(p \rightarrow q) \)
\( \mathbf{D} \cdot \sim(q \rightarrow p) \)
Subject: Physics
A car moving at \( 2.5 m s^{-1} \) doubles its velocity with an acceleration of
\( 0.5 m s^{-2} \) in some time. If the same car
travels at \( 1.5 m s^{-1}, \) what will be its final
velocity if same acceleration acts on it for same time?
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. \( 3 m s^{-1} \)
\( \mathbf{c} \cdot 4 m s^{-1} \)
\( \mathrm{D} \cdot 5 \mathrm{ms}^{-1} \)
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{O}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \) react
with hot and excess HI the product formed is:
A. \( C H_{3} C H_{2} I \) and \( C H_{3} C H_{2} O H \)
в. \( C H_{3} C H_{2} \) ОН
c. \( C H_{3} C H_{2} I \)
D. None of these
Subject: Maths
For \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \in \boldsymbol{R}, \) let \( \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{\alpha}^{2} & \boldsymbol{6} & \boldsymbol{8} \\ \boldsymbol{3} & \boldsymbol{\beta}^{2} & \boldsymbol{9} \\ \boldsymbol{4} & \boldsymbol{5} & \boldsymbol{\gamma}^{2}\end{array}\right] \)
and \( \boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{2} \boldsymbol{\alpha} & \boldsymbol{3} & \boldsymbol{5} \\ \boldsymbol{2} & \boldsymbol{2} \boldsymbol{\beta} & \boldsymbol{6} \\ \boldsymbol{1} & \boldsymbol{4} & \boldsymbol{2} \boldsymbol{\gamma}-\boldsymbol{3}\end{array}\right] \)
\( \boldsymbol{T}_{\boldsymbol{r}}(\boldsymbol{A})=\boldsymbol{T}_{\boldsymbol{r}}(\boldsymbol{B}) \) then the value of
\( \left(\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}\right) \) is
\( \boldsymbol{T}_{r}(\boldsymbol{A}) \) is a Trace \( (\boldsymbol{A}) \) of a matrix
\( A \)
B. 2
\( c .3 \)
D.
Subject: Physics
If \( \vec{A} \times \vec{B}=0, \vec{B} \times \vec{C}=0, \) then \( \vec{A} \times \)
\( \vec{C}= \)
A. \( A C \)
в. \( \frac{A B^{2}}{C} \)
c. \( Z \) ero
D. Noneofthese
Subject: Chemistry
Assertion
White phosphorus is more reactive than
red phosphorus.
Reason
It readily catches fire in air to give
dense white fumes of \( \boldsymbol{P}_{4} \boldsymbol{O}_{10} \)
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
When 2 g of gas \( A \) is introduced into an evacuated flask kept at \( 25^{\circ} \mathrm{C} \), the pressure was found to be 1 atm. If 3 g of another gas B is then added to the same flask containing A, the pressure
becomes 1.5 atm. Assuming ideal behaviour, the ratio of molecular
weights \( \left(M_{A}: M_{B}\right) \) is :
A . 1: 3
B. 3:
\( c \cdot 2: 3 \)
D. 3:
Subject: Maths
\( \left(\begin{array}{lll}\mathbf{7} & \mathbf{1} & \mathbf{5} \\ \mathbf{8} & \mathbf{0} & \mathbf{0}\end{array}\right)\left(\begin{array}{l}\mathbf{2} \\ \mathbf{3} \\ \mathbf{1}\end{array}\right)+\mathbf{5}\left(\begin{array}{l}\mathbf{1} \\ \mathbf{0}\end{array}\right) \) is equal to
A \( \cdot\left(\begin{array}{l}16 \\ 27\end{array}\right. \)
B. \( \left(\begin{array}{l}27 \\ 16\end{array}\right. \)
c. \( \left(\begin{array}{l}15 \\ 16\end{array}\right. \)
D. \( \left(\begin{array}{l}16 \\ 15\end{array}\right. \)
Subject: Maths
f \( \boldsymbol{y}=\boldsymbol{f}\left(\boldsymbol{a}^{\boldsymbol{x}}\right) \) and \( \boldsymbol{f}^{\prime}(\sin \boldsymbol{x})=\log _{e} \boldsymbol{x}, \) then
find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) if it exists, where \( \frac{\boldsymbol{\pi}}{\boldsymbol{2}}<\boldsymbol{x}<\boldsymbol{\pi} \)
Subject: Physics
A charged particle \( \left(Q=10^{-4} C\right) \) is
released from rest at \( z=0 \) in magnetic field given as \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{B}_{0} \cos (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{z}) \hat{\boldsymbol{i}}+ \)
\( B_{1} \cos (\omega t+k z) \hat{j} \) where \( B_{0}=3 x \)
\( 10^{-5} T \) and \( B_{1}=2 \times 10^{-6} T . \) Then the
rms value of force acting on particle is?
A. \( 3 \times 10^{-2} \)
B. 0.6
c. 0.9
D. \( 0 . \)
Subject: Physics
The refractive index of water with
respect to air is \( 1.33 . \) Calculate the critical angle for water air interface
A \( \cdot 26^{\circ} \)
В \( \cdot 22^{\circ} 6^{1} \)
\( \mathbf{c} \cdot 48^{\circ} 45 \)
D. \( 76^{\circ} 5^{1} \)
Subject: Chemistry
The most appropriate reagent for the
following stereoselective reduction is:
\( \mathbf{A} \cdot \mathrm{NaBH}_{4} \)
\( \mathbf{B} \cdot \mathrm{Et}_{2} \mathrm{BOMe}, \mathrm{NaBH}_{4}, \mathrm{H}_{2} \mathrm{O}_{2} \)
\( \mathbf{C} \cdot \mathrm{LiAlH}_{4} \)
\( \mathrm{D} \cdot \mathrm{Me}_{4} \mathrm{NBH}(\mathrm{OAc})_{3} \)
Subject: Physics
A simple pendulum with bob of mass \( m \)
and conducting wire of length \( L \) swings
under gravity through an angle \( 2 \theta \). The
earth's magnetic field component in the direction perpendicular to swing is \( B \) The maximum potential difference
induced across the pendulum is:
\( ^{\mathrm{A}} \cdot_{2 B L} \sin \left(\frac{\theta}{2}\right) \sqrt{g L} \)
B. \( \quad B L \sin \left(\frac{\theta}{2}\right) \sqrt{g L} \)
\( ^{\mathrm{c}} \cdot_{B L \sin }\left(\frac{\theta}{2}\right)(g L)^{3 / 2} \)
D. \( \quad B L \sin \left(\frac{\theta}{2}\right)(g L)^{2} \)
Subject: Chemistry
\( \boldsymbol{A}(\boldsymbol{a} \boldsymbol{q}) \longrightarrow \boldsymbol{B}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C}(\boldsymbol{a} \boldsymbol{q}) \) is a first
order reaction.
Time
moles of reagent
Reaction progress is measure with help of titration ' \( R \) '. If all \( A, B \) and \( C \) reacted
with reagent and have 'n' factors \( [n \)
factor; \( \left.e q . w t=\frac{\text { mol.wt. }}{n}\right] \) in the ratio of
1: 2: 3 with the reagent. The \( k \) in terms
of \( t, n_{1} \) and \( n_{2} \) is :
A \( \cdot k=\frac{1}{t} \ln \left(\frac{n_{2}}{n_{2}-n_{1}}\right) \)
в. \( \quad k=\frac{1}{t} \ln \left(\frac{2 n_{2}}{n_{2}-n_{1}}\right) \)
c. \( _{k}=\frac{1}{t} \ln \left(\frac{4 n_{2}}{n_{2}-n_{1}}\right) \)
D.
\[
k=\frac{1}{t} \ln \left(\frac{4 n_{2}}{5\left(n_{2}-n_{1}\right)}\right)
\]
Subject: Chemistry
Assertion
Hydrogen resembles both, alkali metals
as well as halogens.
Reason
Hydrogen forms oxides, halides and sulphides, and exists as diatomic
molecule.
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
The IUPAC name for the compound
\( \boldsymbol{C H}_{3}-\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)=\boldsymbol{C H}-\boldsymbol{C O O H} \) is:
A. 2-Methyl-2-butenoic acid
B. 3-Methyl-3-butenoic acid
c. 3-Methyl-2-butenoic acid
D. 2-Methyl-3-butenoic acid
Subject: Physics
A geostationary satellite is orbiting the earth at a height of \( 5 R \) above the
surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of \( 2 \mathrm{R} \) from
the surface of the earth is:
A \( \cdot \frac{6}{\sqrt{2}} \)
B. 5
c. 10
D. \( 6 \sqrt{2} \)
Subject: Physics
The increase in the internal energy of
\( 10 g \) of water when it is heated from
\( 0^{\circ} \) to \( 100^{\circ} \) and converted into steam at
\( 100 k P a \) is given as \( x \times 10^{2} J . \) Find \( x \)
The density of steam \( =\mathbf{0 . 6} k g / m^{3} \)
Specific heat capacity of water \( = \) \( 4200 J / k g-^{\circ} C \) and the latent heat of
vaporization of water \( =2.5 \times \)
\( \mathbf{1 0}^{\mathbf{6}} \boldsymbol{J} / \boldsymbol{k} \boldsymbol{g} \)
Subject: Maths
If the line \( a x+b y+c=0 \) is a normal
to the rectangular hyperbola \( \boldsymbol{x} \boldsymbol{y}=\mathbf{1} \)
then
This question has multiple correct options
A \( . a>0, b>0 \)
в. \( a>0, b<0 \)
c. \( a<0, b>0 \)
D. \( a<0, b<0 \)
Subject: Chemistry
\( R H_{2} \) (ion exchange resin ) can replace
\( C a^{2+} \) in hard water as:
\( \boldsymbol{R} \boldsymbol{H}_{2}+\boldsymbol{C} \boldsymbol{a}^{2+} \rightarrow \boldsymbol{R} \boldsymbol{C} \boldsymbol{a}+\boldsymbol{2} \boldsymbol{H}^{+} \)
One litre of hard water after passing
through \( R H_{2} \) has \( \mathrm{pH}=2 . \) Hence,
hardness in ppm of \( C a^{2+} \) is:
A . 200
B. 100
\( c .50 \)
D. 125
Subject: Chemistry
The rate of the reaction, \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C} \longrightarrow \)
Products, is given by, \( -\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} t}= \)
\( \boldsymbol{k}[\boldsymbol{A}]^{1 / 2}[\boldsymbol{B}]^{1 / 3}[\boldsymbol{C}]^{1 / 4} \)
The order of the reaction is:
A \( \cdot \frac{1}{2} \)
в. \( \frac{13}{12} \)
c. 1
D. 2
Subject: Physics
A shell of mass \( 200 g m \) is ejected from a gun of mass \( 4 k g \) by an explosion that
generates \( 1.05 k J \) of energy. The initial velocity of the shell is:
A \( \cdot 40 \mathrm{ms}^{-1} \)
B . \( 120 \mathrm{ms}^{-1} \)
c. \( 100 \mathrm{ms}^{-1} \)
D. \( 80 \mathrm{ms}^{-1} \)
Subject: Physics
Which of the following are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) If \( R \) is the radius of a planet, \( g \) is the acceleration due to gravity, the mean density of the planet is \( 3 g / 4 \pi G R \)
B. Acceleration due to gravity is a universal constant.
C. The escape velocity of a body from earth is \( 11.2 \mathrm{km} \mathrm{s}^{-1} \) The escape velocity from a planet which has double the mass of earth and half its radius is \( 22.4 \mathrm{km} \mathrm{s}^{-1} \)
D. The ratio of gravitational mass and inertial mass of a body at the surface of earth is 1
Subject: Physics
A uniform disc of mass \( m \), radius \( r \) and
a point mass \( m \) are arranged as shown
in the figure. The acceleration of point
mass is : (Assume there is no slipping
between pulley and thread and the disc
can rotate smoothly about a fixed
horizontal axis passing through its
centre and perpendicular to its plane).
A \( \cdot \frac{g}{2} \)
B. \( \frac{g}{3} \)
\( c \cdot \frac{2 g}{3} \)
D. None of these
Subject: Maths
If \( \cos (A-B)=\frac{3}{5} \& \tan A \tan B=2 \)
then
This question has multiple correct options
A \( \cdot \cos A \cos B=\frac{1}{5} \)
B. \( \sin A \sin B=-\frac{2}{5} \)
\( c \cdot \cos (A+B)=-\frac{1}{5} \)
D. \( \sin A \sin B=\frac{2}{5} \)
Subject: Maths
The roots of the equation \( 2 y^{2}+y- \)
\( \mathbf{2}=\mathbf{0} \) are
A. \( \frac{-1-\sqrt{17}}{2}, \frac{-1-\sqrt{17}}{2} \)
B. \( \frac{-1-\sqrt{17}}{4}, \frac{-1+\sqrt{17}}{4} \)
c. \( -1-\sqrt{17},-1+\sqrt{17} \)
D. None
Subject: Maths
Given, \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}-|\boldsymbol{x}-\mathbf{2}| \) for \( \mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3} \)
and \( f(3 x)=a f(x) \) for all other values
of \( x . \) If \( a=3 \), then \( \lim _{x \rightarrow 10^{+}} f(x)=? \) and \( \lim _{x \rightarrow 10^{-}} f(x)=? \)
Subject: Maths
Let
\( f(x)=\left|\begin{array}{ccc}\sec ^{2} x & 1 & 1 \\ \cos ^{2} x & \cos ^{2} x & \operatorname{cosec}^{2} x \\ 1 & \cos ^{2} x & \cot ^{2} x\end{array}\right| \)
then
Subject: Maths
\( \int_{0}^{1} \frac{x\left(2 x^{2}+1\right)}{x^{8}+2 x^{6}-x^{2}+1} d x= \)
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{\pi}{2 \sqrt{3}} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{\pi}{6} \)
Subject: Physics
Potential Energy \( (U) \) of a body of unit mass moving in a one-dimension conservative force field is given by \( U= \)
\( \left(x^{2}-4 x+3\right) . \) All units are in S.I.
(i) Find the equilibrium position of the body
(ii) Show that oscillations of the body
about this equilibrium position is simple harmonic motion and find its time period.
(iii) Find the amplitude of oscillations if the speed of the body at equilibrium position is \( 2 \sqrt{6} m / s \)
Subject: Physics
The Poisson's ratio of the material of a
wire is0.25. If it is stretched by a force \( F \) the longitudinal strain produced in the
wire is \( 5 \times 10^{-4} \). What is the
percentage increase in its volume?
A . 0.2
B. \( 2.5 \times 10^{-2} \)
c. zero
D . \( 1.25 \times 10^{-6} \)
Subject: Maths
Let \( _{y}-y(x) \) be the solution of the
differential equation \( \sin x \frac{d y}{d x}-y \cos x- \)
\( 4 x,_{x} \epsilon(0, \pi) . i f y\left(\frac{\pi}{2}\right)=0 \)
then \( y\left(\frac{\pi}{6}\right) \) is equal to
A \( \cdot-\frac{4}{9} \pi^{2} \)
B. \( -\frac{4}{9 \sqrt{3}} \pi^{2} \)
c. \( -\frac{-8}{9 \sqrt{3}} \pi^{2} \)
D. None of these
Subject: Chemistry
The vapour pressure of a solution
having \( 2.0 g \) of solute \( X \) (gram atomic
\( \left.\operatorname{mass}=32 g \operatorname{mol}^{-1}\right) \operatorname{in} 100 g \) of \( C S_{2} \)
(vapour pressure \( =854 \text { torr }) \) is 848.9 torr. The molecular formula of the solute
is:
\( \mathbf{A} \cdot X \)
в. \( X_{2} \)
\( c \cdot X_{4} \)
D. \( X_{8} \)
Subject: Maths
Sum the series \( 1^{3}+3^{3}+5^{3}+\dots \dots \dots \)
to \( n \) terms is
A \( \cdot n^{2}\left(2 n^{2}-1\right) \)
В \( \cdot n\left(2 n^{2}-1\right) \)
c. \( n\left(2 n^{2}+1\right) \)
D \cdot \( n^{2}\left(2 n^{2}+1\right) \)
Subject: Chemistry
Detergents are less or non bio-
degradable when compare with soaps. For detergents to be bio-degradable in
nature, the non-polar part of the
molecule should:
A. consist of a hydrocarbon with more branching
B. consist of a hydrocarbon with more number of branches and unsaturation
C. have straight or open chain hydrocarbons
D. be replaced by aromatic rings substituted by alkyl groups
Subject: Maths
In measuring the sides of a rectangle errors of \( 5 \% \) and \( 3 \% \) in excess are made. The error per cent in the calculated area
is
A . \( 8.35 \% \)
B . \( 7.15 \% \)
c. \( 8.15 \% \)
D. \( 6.25 \% \) \%
Subject: Chemistry
The compounds \( (A) \) and \( (B) \) in the
equation given above are:
\( \mathbf{A} \cdot C H_{3} C O O H \quad C H_{3} C H_{3} \)
B. \( D C H_{2}-C O O D \quad C H_{4} \)
\( \mathbf{c} \cdot D C H_{2}-C O O H \quad C H_{2} D_{2} \)
\( \mathbf{D} \cdot C h_{3}-C O O D \quad C H_{3} D \)
Subject: Chemistry
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -286 k J \)
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g})+\boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \longrightarrow \)
\( 2 H_{2} O(l) \dots \dots \dots J(\pm ?) \)
A \( \cdot 2 H_{2}(g)+O_{2}(g) \longrightarrow 2 H_{2} O(l)+572 k J \)
В \( \cdot 2 H_{2}(g)+O_{2}(g) \rightarrow 2 H_{2} O(l)-572 k J \)
C. \( 2 H_{2}(g)+O_{2}(g) \longrightarrow 2 H_{2} O(l)+0 k J \)
D. None of these
Subject: Maths
Evaluate: \( \lim _{\boldsymbol{\pi}} \frac{\boldsymbol{c o t}^{3} \boldsymbol{x}-\boldsymbol{t a n} \boldsymbol{x}}{\cos (\boldsymbol{x}+\boldsymbol{\pi} / \mathbf{4})} \)
\( \boldsymbol{x} \rightarrow \boldsymbol{\boldsymbol { 4 }} \)
\( A \)
B. \( 8 \sqrt{2} \)
\( c \cdot 4 \)
D. \( 4 \sqrt{2} \)
Subject: Maths
The equation of the normal to the curve
\( \boldsymbol{y}=(1+\boldsymbol{x})^{y}+\sin ^{-1}\left(\sin ^{2} \boldsymbol{x}\right) \boldsymbol{a t} \quad \boldsymbol{x}=\mathbf{0} \)
is
A. \( x+y=1 \)
B. x-y+1=0
c. \( 2 x+y=2 \)
D. 2x-y+
Subject: Physics
A vector \( \vec{A} \) has magnitude of 3 units and it points towards east while another vector \( \vec{B} \) has magnitude of 4 units and it points towards north.The ratio between \( \vec{A} \cdot \vec{B} \) and \( |\vec{A} \times \vec{B}| \) is:
A . 1:
B. 1:
c. 0: 12
D. 12:0
Subject: Maths
If the range for \( \boldsymbol{y}= \)
\( \left(\cot ^{-1} x\right)\left(\cot ^{-1}(-x)\right) \) is
\( \mathbf{0}<\boldsymbol{y} \leq \frac{\boldsymbol{\pi}^{\boldsymbol{a}}}{\boldsymbol{b}} \)
Find the value of \( a+b \)
A . 2
в. 4
c. 5
D. 6
Subject: Maths
If the number of function from the set
\( A=\{0,1,2\} \) and \( B= \)
\{0,1,2,3,4,5,6,7\} such that \( f(i), \leq \)
\( \boldsymbol{f}(\boldsymbol{j}), \boldsymbol{i}<\boldsymbol{j} ; \boldsymbol{i}, \boldsymbol{j} \epsilon \boldsymbol{A} \mathbf{2 0} \boldsymbol{k}, \) then the value of
\( k \) is
Subject: Physics
Assertion
The smaller the orbit of a planet around
the Sun, the shorter is the time it takes
to complete.
Reason
According to Kepler's third law of planetary motion, square of time period is proportional to cube of mean distance from Sun.
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 and Reason is correct