AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \mathbf{f} \mathbf{P}=\left\{\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right\} \mathbf{A}=\left\{\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right\} \)
and \( \mathbf{Q}=\mathbf{P} \mathbf{A} \mathbf{P}^{\mathbf{T}} \) and \( \mathbf{x}=\mathbf{P}^{\mathbf{T}} \mathbf{Q}^{2005} \mathbf{P} \)
then \( x \) is equal to
A. \( \left\{\begin{array}{ll}1 & 2005 \\ 0 & 1\end{array}\right\} \)
в. \( \left\{\begin{array}{ll}4+2005 \sqrt{3} & 6015 \\ 2005 & 4-2005 \sqrt{3}\end{array}\right\} \)
c. \( _{\frac{1}{4}}\left[\begin{array}{cc}2+\sqrt{3} & 1 \\ -1 & 2-\sqrt{3}\end{array}\right] \)
D. \( \frac{1}{4}\left\{\begin{array}{ll}2005 & 2-\sqrt{3} \\ 2+\sqrt{3} & 2005\end{array}\right\} \)
Subject: Chemistry
Which of the following is/are not
correctly matched?

This question has multiple correct options
A. Basic strength of oxides: \( C s_{2} O<R b_{2} O<K_{2} O<N a_{2} O< \)
\( L i_{2} O \)
B. Stability of peroxides: \( N a_{2} O_{2}<K_{2} O_{2}<R b_{2} O_{2}<C s_{2} O_{2} \)
C . Stability of bicarbonates: \( L i H C O_{3}<N a H C O_{3}< \)
\( K H C O_{3}<R b H C O_{3}<C s H C O_{3} \)
D. Melting point: \( N a F<N a C l<N a B r<N a I \)
Subject: Maths
If \( \lim _{x \rightarrow 0} \frac{x^{a} \sin ^{b} x}{\left(\sin ^{c} x\right)}, \) where \( a, b, c \in R-\{0\} \)
exists \& has non zero value then \( a+ \)
\( \boldsymbol{b}=\boldsymbol{c} \)
If true enter 1 else enter 0
Subject: Physics
Match the physical quantities given in
Column I with suitable dimensions
expressed in Column II.
Column Column I II
a) Angular momentum
g) \( M L^{2} T^{-2} \)
Latent heat
h) \( M L^{2} Q^{-2} \)
b)
Torque \( M L^{2} T^{-1} \)
c)
i)
d) Capacitane
j) \( M L^{3} T^{-1} Q^{-2} \)
Inductance
k)
e) \( M^{-1} L^{-2} T^{2} Q^{2} \) \( L^{-2} T^{2} Q^{2} \)
\( f) \)
Resistivity ।) \( L^{2} T^{-2} \) \( T \)
A. a-i, b-l, c-g, d-k, e-h, f-j
B. a-l, b-i, c-k, d-g, e-j, f-h
c. a-i, b-l, c-h, d-j, e-g, f-k
D. a-h, b-j, c-g, d-k, e-i \( f- \)
Subject: Physics
What will be the ratio of temperatures of sun and moon if the wavelengths of their maximum emission radiations
rates are \( 140 A^{\circ} \) and \( 4200 A^{\circ} \)
respectively:
\( \mathbf{A} \cdot 1: 30 \)
B. 30: 1
c. 42: 14
D. 14: 42
Subject: Chemistry
Assertion
Elementary phosphorus exists in three principal allotropic forms, i.e., white (or yellow), red (or violet) and black.
Reason
Of the three forms, white phosphorus is the most important and most reactive.
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
What is the median for the following
data?
\( \begin{array}{lllll} & 2- & 4- & 6- & 8- \\ x & 4 & 6 & 8 & 10\end{array} \)
4 frequency \( \quad 1 \quad 3 \quad 2 \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 6.5
c. 7
D. 7.5
Subject: Chemistry
Difference between \( \Delta H \) and \( \Delta E \) for the
combustion of liquid benzene at \( 27^{\circ} \mathrm{C} \)
is:
A \( .7 .48 k J \)
в. \( 3.47 k J \)
c. \( 14.86 k J \)
D. \( 5.73 k J \)
Subject: Maths
The equation of tangent to the curve
\( \boldsymbol{y}=3 x^{2}-x+1 \) at the point (1,3) is
A. \( y=5 x+2 \)
в. \( y=5 x-2 \)
c. \( _{y=\frac{1}{5} x+2} \)
D. \( _{y=\frac{1}{5} x-2} \)
Subject: Physics
A ball is dropped from the roof of a tower of height h. The total distance covered it in the last seconds of its motion is
equal to the distance covered by it in first three seconds. The value of h in
meters is \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A . 125
B. 200
\( c \cdot 100 \)
\( D \cdot 80 \)
Subject: Physics
An \( n \) sided regular polygon is inscribed
in a circular region of radius \( \boldsymbol{R} \) using a
wire of cross sectional radius \( r \) and
resistivity \( \rho . \) If the magnetic field in the
circular region has a time rate of
change given by \( B \) then the current in
the wire loop at any time is given by
\( ^{\mathbf{A}} \cdot \frac{\pi R B r^{2} \cos (\pi / n)}{2 \rho} \)
\( ^{\mathbf{B}} \cdot \frac{\pi R B r^{2} \cos (\pi / n)}{\sqrt{2} \rho} \)
\( \frac{\pi R B r^{2} \sin (\pi / n)}{2 \rho} \)
D. \( \frac{\pi R B r^{2} \cos (\pi / n)}{3 \rho} \)
Subject: Maths
The following sets are equal. \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{N} ; \mathbf{1}<\boldsymbol{x}<\mathbf{4}\} \) and
\( B=\left\{x: x \text { is a solution of } x^{2}+5 x+\right. \)
\( \mathbf{6}=\mathbf{0}\} \)
A . True
B. False
Subject: Physics
A man who is \( 1.40 \mathrm{m} \) tall stands in front
of a mirror and can just see himself from head to top. Assuming that his eyes are \( 0.14 \mathrm{m} \) below the top of his head, the minimum height of the mirror is:
\( A \cdot 1.4 \mathrm{m} \)
B. \( 1.26 \mathrm{m} \)
c. \( 0.70 \mathrm{m} \)
D. 0.63 \( m \)
Subject: Chemistry
Charge on electron of mass \( 9.109 \times \)
\( 10^{-31} \mathrm{Kg} \) is:
A \( \cdot 1.603 \times 10^{-19} \mathrm{C} \)
В. \( -1.603 \times 10^{-19} \mathrm{C} \)
c. \( 9.109 \times 10^{-31} \mathrm{C} \)
D. \( -9.109 \times 10^{-31} \mathrm{C} \)
Subject: Maths
If \( m \) arithmetic means are inserted
between 1 and 31 so that the ratio of the
\( 7 t h \) and \( (m-1) t h \) means is \( 5: 9, \) then
the value of \( m \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 11
c. 13
D. 14
Subject: Maths
If the function \( f: R \rightarrow R \) be such that
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}], \) where \( [\boldsymbol{x}] \) denotes the
greatest integer less than or equal to \( x \)
then \( \boldsymbol{f}^{-1}(\boldsymbol{x}) \) is
\( ^{\mathrm{A}} \cdot \frac{1}{x-[x]} \)
B \cdot \( [x]-x \)
c. not defined
D. none of these
Subject: Chemistry
Match List I with List II and select the
answer from the given codes.
List I
List II
A. \( C(s)+O_{2}(g) \longrightarrow C O_{2}(g) \)
\( \mathbf{1} \mathbf{\Delta} \boldsymbol{H}=\mathbf{\Delta} \boldsymbol{U}+\boldsymbol{R} \boldsymbol{T} \)
B. \( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
2. \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U} \)
C. \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{H} \boldsymbol{S}(\boldsymbol{s}) \longrightarrow \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
3. \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U}-\boldsymbol{2} \boldsymbol{R} \boldsymbol{T} \)
D. \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \longrightarrow \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
4. \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U}+\boldsymbol{2} \boldsymbol{R} \boldsymbol{T} \)
E. \( 2 S O_{2}(g)+O_{2}(g) \longrightarrow 2 S O_{3}(g) \)
5. \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U}-\boldsymbol{R} \boldsymbol{T} \)
A. \( A-1, B-2, C-3, D-4, E-5 \)
B. \( A-5, B-2, C-3, D-4, E-1 \)
c. \( A-1, B-3, C-4, D-2, D-5 \)
D. \( A-2, B-3, C-4, D-1, E-5 \)
Subject: Biology
Assertion
Humans are considered advanced from
all its primates relatives, because of the large cranial capacity and high intelligence
Reason
A lumbar curve is present in man, which is also present in apes.
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
Evaluate
\( \lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^{2}}\right)\left(1+\frac{2^{2}}{n^{2}}\right)\left(1+\frac{3^{2}}{n^{2}}\right)\right. \)
A \( \cdot\left(\frac{\pi-4}{2}\right) \)
в. \( _{2 e}\left(\frac{\pi-2}{2}\right) \)
c. \( _{2 e}\left(\frac{\pi-4}{4}\right) \)
D. \( _{2 e}\left(\frac{\pi-4}{3}\right) \)
Subject: Maths
\( \mathbf{1 f} \mathbf{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{5} & \mathbf{- 6} \\ \mathbf{- 8} & \mathbf{0} & \mathbf{4} \\ \mathbf{3} & \mathbf{- 7} & \mathbf{2}\end{array}\right] \) then the
cofactors of the elements 3,-7,2 are
p,q,r respectively their ascending order
is
\( \mathbf{A} \cdot \mathbf{p}, \mathbf{r}, \mathbf{q} \)
B. \( \mathrm{q}, \mathrm{r}, \mathrm{p} \)
\( c \cdot p, q, r \)
\( D \cdot r, p, q \)
Subject: Maths
If radii of two concentric circles are 4
\( \mathrm{cm} \) and \( 5 \mathrm{cm}, \) then the length of each chord of one circle which is tangent to
the other circle is
A. \( 3 \mathrm{cm} \)
B. 6 \( \mathrm{cm} \)
\( c \cdot 9 \mathrm{cm} \)
D. \( 1 \mathrm{cm} \)
Subject: Physics
A body projected vertically up with a
velocity of \( 10 \mathrm{m} \mathrm{s}^{-1} \) reaches a height of \( 20 \mathrm{m} . \) If it is projected with a velocity of \( 20 \mathrm{m} \mathrm{s}^{-1}, \) then the maximum height reached by the body is :
A . 20
B. 10 \( m \)
c. \( 80 \mathrm{m} \)
D. \( 40 \mathrm{m} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{f}(\boldsymbol{x})=\log _{e} \boldsymbol{x}, \boldsymbol{R} \)
being the set of real numbers then which of the following is not correct?
A. \( f \) is onto
B. \( f \) is one-one
c. \( f \) is invertible
D. \( f \) is into
Subject: Chemistry
Heat of hydrogenation of ethene is \( x_{1} \)
and that of Benzene is \( x_{2} \) Hence
resonance energy is ?
A \( \cdot x_{1}-x_{2} \)
В. \( x_{1}+x_{2} \)
\( \mathbf{c} \cdot 3 x_{1}-x_{2} \)
D. \( x_{1}-3 x_{2} \)
Subject: Maths
\( (x, y) \) and \( (p, q) \) are two ordered pairs. Find the values of \( p \) and \( y, \) if \( (4 y+ \)
\( \mathbf{5}, \mathbf{3} \boldsymbol{p}-\mathbf{1})=(\mathbf{2 5}, \boldsymbol{p}+\mathbf{1}) \)
A. \( p=0, y=5 \)
В. \( p=1, y=5 \)
c. \( p=0, y=1 \)
D. \( p=1, y=1 \)
Subject: Physics
Two particles 1 and 2 are projected
simultaneously with velocities \( v_{1} \) and
\( v_{2}, \) respectively. Particle 1 is projected vertically up from the top of a cliff of height h and particle 2 is projected vertically up from the bottom of the cliff Find the time of meeting of particles, if the bodies meet (a) Above the top of the
cliff,
(b) Between the top and bottom of the cliff, and (c) below the bottom of the
cliff, find the time of the meeting of the particles.
Subject: Chemistry
The above electron-dot formulas for
carbon dioxide both satisfy the octet
rule for all of the atoms. Which of these
structures is the better structure and
why is this the case?
\[
\begin{array}{cc}
: \mathrm{O}=\mathrm{C}=\mathrm{o} & : \mathrm{O} \equiv \mathrm{C}-\ddot{\mathrm{O}}: \\
\mathbf{A} & \mathbf{B}
\end{array}
\]
A. "A" is the better structure because there is no formal charge on any of the atoms.
B. "B" is the better structure because the bond energies of a single bond and a triple bond are higher than the bond energies of two double bonds.
C. "A" is the better structure because all the bonds and non-bonding electron pairs are arranged in a symmetrical pattern.
D. "B" is the better structure because there are opposite formal charges on the two oxygen atoms which attract each other and give the molecule a lower energy.
Subject: Chemistry
At \( 25^{\circ} \mathrm{C} \), the dissociation constant for
pure water is given by :-
\( \mathbf{A} \cdot\left(55.4 \times 10^{14}\right)^{-1} \)
B . \( 1 \times 10^{-14} \)
c. \( \frac{1 \times 10^{-14}}{18} \)
D. none of these
Subject: Physics
A large sheet of uniform charge passes
through a hypothetical spherical
surface. The figure shows principle
section of situation. The electric flux
through the spherical surface is given
by
\( ^{\mathbf{A}} \cdot \frac{\pi R^{2} \sigma}{\epsilon_{0}} \)
B. \( \frac{2 \pi\left(R^{2}-x^{2}\right) \sigma}{\epsilon_{0}} \)
\( c \)
\( D \)
Subject: Physics
A coil has an inductance of \( 0.7 \mathrm{H} \) and is
joined in series with a resistance of 220
\Omega. When an alternating e.m.f. of \( 220 \mathrm{V} \) at 50 c.p.s. is applied to it, then the wattless component of the current in the circuit is
A. 5 ampere
B. 0.5 ampere
c. 0.7 ampere
D. 7 ampere
Subject: Maths
Let \( \mathbf{x}=\mathbf{3}^{\mathbf{n}} . \) The index 'n' is given a
positive integral value at random. The
probability that the value of 'x' will have
3 in the units place is
A . \( 1 / 4 \)
B. \( 1 / 2 \)
c. \( 1 / 3 \)
D. \( 1 / 5 \)
Subject: Maths
f \( \sum_{i=1}^{2 n} \sin ^{-1} x_{i}=n \pi, \) then \( \sum_{i=1}^{2 n} x_{i} \) is
equal to
\( \mathbf{A} \cdot n / 2 \)
B. \( 2 n \)
c. \( \frac{n(n+1)}{2} \)
D. none of these
Subject: Physics
One of the two slits in YDSE is painted over, so that it transmits only light
waves having intensity half of the intensity of the light waves having half of the intensity of the light waves through the other slit. As a result of this
A. fringe pattern disappears
B. bright fringes become brighten and dark ones become darker
c. dark and bright fringes get fainter
D. dark fringes get brighter and bright fringes get darker
Subject: Physics
If a ball of steel (density \( \rho=7.8 g c m^{-3} \)
attains a terminal velocity of \( 10 \mathrm{cm} s^{-1} \) when falling in a tank of water (coefficient of viscosity \( \eta_{w a t e r}= \)
\( \left.8.5 \times 10^{-4} \text {Pa.s }\right) \) then its terminal
velocity in glycerine \( (\rho= \) \( \left.12 g c m^{-3}, \eta=13.2 \text { pa.s }\right) \) would be
nearly:-
A. \( 1.6 \times 10^{-5} \mathrm{cm} \mathrm{s}^{-1} \)
в. \( 6.25 \times 10^{-4} \mathrm{cm} \mathrm{s}^{-1} \)
c. \( 6.45 \times 10^{-4} \mathrm{cm} s^{-1} \)
D. \( 1.5 \times 10^{-5} \mathrm{cm} \mathrm{s}^{-1} \)
Subject: Chemistry
For a first order reaction, \( (A) \rightarrow \) product
the concentration of A changes from 0.1 M to \( 0.025 \mathrm{M} \) in 40 minutes. The rate of
reaction when the concentration of A is
\( 0.01 \mathrm{M}, \) is:
A \( \cdot 1.73 \times 10^{-5} \mathrm{Mmin}^{-1} \)
В. \( 3.47 \times 10^{-4} \) М \( \min ^{-1} \)
\( \mathbf{c} \cdot 3.47 \times 10^{-5} \mathrm{Mmin}^{-1} \)
D. \( 1.73 \times 10^{-4} \mathrm{M} \min ^{-1} \)
Subject: Physics
\( A . \) another positively charged particle of
mass \( m \) and charge \( +q \) is projected
from a point \( B \) with velocity \( u \) as shown
in figure. The point \( B \) is at the lage distance from \( A \) and at distance \( d \) from
the line \( A C . \) The initial velocity is
parallel to the line \( A C . \) The point \( C \) is at
very large distance from \( A \). The minimum distance (in meter) of \( +\boldsymbol{q} \)
from \( +Q \) during the motion is \( d(1+ \) \( \sqrt{A}) . \) Find the value of \( A \)
(Take \( \boldsymbol{Q} \boldsymbol{q}=\boldsymbol{4} \boldsymbol{\pi} \varepsilon_{0} \boldsymbol{m} \boldsymbol{u}^{2} \boldsymbol{d} \) and \( \boldsymbol{d}=(\sqrt{\mathbf{2}}- \)
1) meter)
A . 3
B. 2
\( c \cdot 4 \)
\( D \)
Subject: Physics
A uniform elastic plank moves over a smooth horizontal plane due to a
constant force \( \boldsymbol{F}_{0} \) distributed uniformly over the end face. The surface of the end
face is equal to \( S \) and Young's
modulus of the material is \( E . \) If the
compressive strain of the plank in
the direction of the acting force is \( \sigma= \) \( \frac{\boldsymbol{F}_{0}}{\boldsymbol{x} \boldsymbol{S} \boldsymbol{E}}, \) find the value of \( ^{\prime} \boldsymbol{x}^{\prime} \)
Subject: Chemistry
Which of the following is most reactive
towards aqueous \( N a O H ? \)
A \( \cdot C_{6} H_{5} C l \)
в. \( C_{6} H_{5} C H_{2} C l \)
\( \mathbf{c} \cdot C_{6} H_{5} B r \)
D. \( B r C_{6} H_{4} B r \)
Subject: Chemistry
Write the IUPAC names of following ketone or aldehyde. If possible, give common name(s) also.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H} \)
Subject: Chemistry
The empirical formula of natural rubber
is:
\( \mathbf{A} \cdot\left(C_{3} H_{5}\right)_{n} \)
B \( \cdot\left(C_{5} H_{8}\right)_{n} \)
\( \mathbf{c} \cdot\left(C_{5} H_{3}\right)_{n} \)
D. \( \left(C_{8} H_{5}\right)_{n} \)
Subject: Maths
Which of the following matrix is inverse of itself
A. \( \left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right] \)
В. \( \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \)
C. \( \left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 1 & 1 \\ 0 & 1 & 0\end{array}\right] \)
Subject: Physics
If the mass of a planet is \( 10 \% \) less than that of the earth and the radius is \( 20 \% \)
greater than that of the earth, the
acceleration due to gravity on the planet will be.
A. \( 5 / 8 \) times that on the surface of the earth
B. \( 3 / 4 \) times that on the surface of the earth
c. \( 1 / 2 \) times that on the surface of the earth
D. \( 9 / 10 \) times that on the surface of the earth
Subject: Physics
The uranium nucleus \( _{92} \mathrm{U}^{238} \) emits an \( \alpha \)
-particle and resulting nucleus emits one \( \beta \) -particle. The atomic number and
mass number of the final nucleus will
be respectively
\( \mathbf{A} .91,234 \)
B. 90,234
c. 91,238
D. 92,234
Subject: Physics
On a photosensitive material, when frequency of incident radiation is increased by \( 30 \% \) kinetic energy of emitted photo electrons increases from
\( 0.4 e V \) to \( 0.9 e V . \) The work function of
the surface is :
A. \( 1 e V \)
B. 1.267 eV
c. \( 1.4 e V \)
D. 1.8 eV
Subject: Physics
A container is filled with 20 moles of an
ideal diatomic gas at absolute
temperature \( T . \) When heat is supplied
to gas, temperature remains constant but 8 moles dissociate into atoms. Heat
energy given to gas is
A \( .4 R T \)
в. \( 6 R T \)
\( c .3 R T \)
D. \( 5 R T \)
Subject: Maths
Let two vectors \( \vec{x} \) and \( \vec{y} \) satisfy the following conditions \( : \vec{x}+\vec{y}=\vec{a} ; \vec{x} \times \)
\( \vec{y}=\vec{b} \times \vec{a}, \vec{x} \cdot \vec{a}=1 \) where \( \vec{a} \) and \( \vec{b} \)
are non-zero perpendicular vectors,
then
\( ^{\mathrm{A}} \cdot_{\vec{x}}=\frac{|\vec{a}|^{2} \vec{b}+\vec{a}}{|\vec{a}|^{2}} \)
\( ^{\mathrm{B}} \cdot_{\vec{x}}=\frac{|\vec{a}|^{2} \vec{b}-\vec{a}}{|\vec{a}|^{2}} \)
\( \stackrel{\mathrm{C}}{*} \vec{y}=\frac{|\vec{a}|^{2}(\vec{a}-\vec{b})-\vec{a}}{|\vec{a}|^{2}} \)
\( \vec{y}=\frac{\vec{a}(\vec{a} \cdot \vec{y})-|\vec{a}|^{2} \vec{b}}{|\vec{a}|^{2}} \)
Subject: Maths
Which one of the following is correct?
\( \mathbf{A} \cdot \sin 45^{0} \cos 45^{0}=1 \)
B \( \cdot \sin ^{2} 45^{0}-\cos ^{2} 45^{0}=1 \)
\( \mathbf{C} \cdot \sin 30^{0}+\cos 60^{0}=1 \)
D \( \cdot \cos ^{2} 30^{0}-\cos ^{2} 60^{0}=1 \)
Subject: Chemistry
Assertion
Divalent compounds of alkaline earth metals are diamagnetic.
Reason
\( M^{2+} \) ions of group 2 have noble gas conguration.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Find the maximum value of current
when inductance of two henry is connected to \( 150 V, 50 \) cycle supply
\( ^{\mathrm{A}} \cdot \frac{3}{2 \sqrt{2} A} \)
B. \( \frac{5}{2 \sqrt{2} A} \)
c. \( \frac{6}{2 \sqrt{2} A} \)
D. \( \frac{7}{2 \sqrt{2} A} \)
Subject: Physics
A bullet is fired vertically upwards with velocity \( v \) from the surface of a
spherical planet. When it reaches its maximum heights, its acceleration due
to the planet's gravity is \( 1 / 4 \) th of its value at the surface of the planet. If the
escape velocity from the planet is \( \boldsymbol{v}_{e s c}=\boldsymbol{v} \sqrt{\boldsymbol{N}}, \) then the value of \( \mathrm{N} \) is
(ignore energy loss due to atmosphere)
Subject: Physics
In the relation \( \frac{d y}{d x}=2 \omega \sin \left(\omega t+\phi_{0}\right) \) the
dimensional formula for \( \omega t+\phi_{0} \) is
A . MLT
в. мLт
c. мL \( ^{0} \neg^{0} \)
D. M^ \( ^{0} \) L \( ^{0} \) Т \( ^{0} \)
Subject: Chemistry
What is the final product? \( \boldsymbol{C H} \)
The compound \( \boldsymbol{C H}_{3}-\boldsymbol{C}=\boldsymbol{C H}- \)
\( C H_{3} \) on reaction with \( N a l O_{4} \) in the
presence of \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{\boldsymbol{4}} \)
A. \( C H_{3} C O C H_{3} \)
в. \( C H_{3} C O C H_{3}+C H_{3} C O O H \)
c. \( C H_{3} C O C H_{3}+C H_{3} C H O \)
D. \( C H_{3} C H O+C O_{2} \)
Subject: Physics
Two identical parallel plate capacitance
C each are connected in series with a
battery of emf, \( E \) as shown, If one of the
capacitors is now filled with a dielectric of dielectric constant \( \mathrm{k} \), the amount of
charge which will flow through the
battery is ?(neglect internal resistance of the battery)
A \( \cdot \frac{k+1}{2(k-1)} C E \)
В \( \cdot \frac{k-1}{2(k+1)} C E \)
c. \( \frac{k-2}{k+2} C E \)
D. \( \frac{k+2}{k-2} C E \)
Subject: Chemistry
In which addition to alkene, syn
addition takes place?
A \( \cdot H_{2}(P d) \)
в. \( M n O_{4}^{-} / O H^{-} \)
\( \mathrm{c} \cdot O s O_{4}, \mathrm{NaH} \mathrm{SO}_{3} \)
D. All
Subject: Physics
Two masses \( m_{1}=10 \mathrm{kg} \) and \( m_{2}= \)
\( 5 k g \) are connected by an ideal string as
shown in the figure. The coefficient of
friction between \( m_{1} \) and the surface is
\( \mu=0.2 . \) Assuming that the system is
released from rest. The velocity of
blocks when \( m_{2} \) has descended by \( 4 m \)
is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A. \( 4 \mathrm{m} / \mathrm{s} \)
в. \( 8 \mathrm{m} / \mathrm{s} \)
c. \( 2 m / s \)
D. \( 12 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
The standard Gibbs energy change at \( 300 K \) for the reaction \( 2 A \rightleftharpoons B+C \) is
\( 2494.2 J . \) At a given time, the composition of the reaction mixture is
\( [\boldsymbol{A}]=\frac{1}{2},[\boldsymbol{B}]=\mathbf{2},[\boldsymbol{C}]=\frac{1}{2} . \) The reaction
proceeds in the:
\( [\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} / \boldsymbol{K} / \boldsymbol{m o l}, \boldsymbol{e}=\mathbf{2 . 7 1 8}] \)
A. Reverse direction because \( Q<K_{c} \)
B. Forward direction because \( Q>K_{c} \)
c. Reverse direction because \( Q>K_{c} \)
D. Forward direction because \( Q<K_{c} \)
Subject: Maths
When \( x^{3}-2 x^{2}+a x-b \) is divided by
\( x^{2}-2 x-3, \) the remainder is \( x-6 . \) The
values of \( a \) and \( b \) are respectively:
\( A \cdot-2 \) and -6
B. 2 and -6
c. -2 and 6
D. 2 and 6
Subject: Physics
At \( t=0, \) fringe width is \( \beta_{1}, \) and \( a t t= \)
\( 2 s, \) fringe width of figure is \( \beta_{2} . \) Then
\( A \cdot \beta_{1}>\beta_{2} \)
в. \( \beta_{2}>\beta_{1} \)
c. \( \beta_{1}=\beta_{2} \)
D. data is insufficient
Subject: Chemistry
Which is not a buffer solution:
A \( . N H_{4} C l+N H_{4} O H \)
в. \( C H_{3} \)СООН\( + \)СН\( _{3} \)СОО Na
c. \( C H_{3} C O O N H_{4} \)
D. \( N H_{4} N O_{3} \)
Subject: Maths
If \( A B C D \) is a rhombus such that
\( \angle A C B=40^{\circ}, \) then \( \angle A D B \) is
A \( \cdot 40^{\circ} \)
B . \( 45^{\circ} \)
\( c .50^{\circ} \)
D. \( 60^{\circ} \)
Subject: Physics
Show that the rate of change of the speed is \( \frac{\boldsymbol{d} \boldsymbol{v}}{\boldsymbol{d} \boldsymbol{t}}=\frac{\left(\boldsymbol{v}_{\boldsymbol{x}} \boldsymbol{a}_{\boldsymbol{x}}+\boldsymbol{v}_{\boldsymbol{y}} \boldsymbol{a}_{\boldsymbol{y}}\right)}{\sqrt{\boldsymbol{v}_{\boldsymbol{x}}^{2}+\boldsymbol{v}_{\boldsymbol{y}}^{2}}} \)
Subject: Chemistry
The rate of a reaction expressed in terms of change in concentration of
reactants at two different times, that is
the average rate in terms of reactants, can be written as ?
This question has multiple correct options
A \( \cdot \frac{x_{2}-x_{1}}{t_{2}-t_{1}} \)
B. \( +\Delta x / \Delta t \)
c. \( -\frac{x_{2}-x_{1}}{t_{2}-t_{1}} \)
D. \( -\Delta x / \Delta t \)
Subject: Maths
Define a relation \( \mathrm{R} \) on the set \( \mathrm{N} \) of
natural numbers by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{y}= \)
\( x+5, x \) is a natural number less than
\( \mathbf{4}, \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{N}\} \)
Depict this relationship using
(i) roster
form (ii) an arrow diagram. Write down the domain and range or \( \mathrm{R} \)