AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A nut is opened by a wrench of length \( 10 \mathrm{cm} . \) If the least force required is
\( 5.0 N, \) find the moment of force needed
to turn the nut.
\( A .50 N m \)
в. \( 0.5 N \mathrm{cm} \)
c. \( 5 N m \)
D. \( 0.5 N \) m
Subject: Biology
Pick up the correct statement for Gibberellins.
1) Abnormal growth of plants is due to
\( \mathrm{G} \mathrm{A} \)
II) GA is more in concentration in tall
varieties than dwarf
III) Gibberellins have the ability to
induce flowering.
IV) GA generally inhibits flowering.
A. I and II are correct.
B. II and III are correct
c. I and III are correct
D. III and IV are correct
Subject: Maths
If the solution of the differential
equation \( x \frac{d y}{d x}+y=x e^{x} \) be, \( x y= \)
\( e^{x} \varphi(x)+c \) then \( \varphi(x) \) is equal to:
A. \( x+1 \)
B. \( x-1 \)
c. \( 1-x \)
D.
Subject: Chemistry
Which of the following statements is/are true?
1) \( P H_{5} \) and \( B i C l_{5} \) do not exist.
2) \( p \pi-d \pi \) bond is present in \( S O_{2} \)
3) \( I_{3}^{+} \) has bent geometry.
4) \( \operatorname{Se} F_{4} \) and \( C H_{4} \) have same shape
\( A \cdot 1,2,3 \)
в. 1, 3
\( c \cdot 1 \) and 2
D. 1,2,4
Subject: Physics
Q Type your question
the shape of track is defined by equation \( y=\frac{x^{2}}{a} \) where \( a \) is a constant.
A ring of mass \( m \) which can slide freely
on wire track, is placed at the position
\( (a, a) . \) The track is rotated
with constant angular speed \( \omega \) such
that there is no relative slipping
between the ring and the track then \( \omega \) is
equal to
A. \( \sqrt{\frac{2 g}{a}} \)
B. \( \sqrt{\frac{g}{a}} \)
c. \( \sqrt{\frac{g}{2 a}} \)
D. None of these
Subject: Maths
Solve the following systems of linear equations
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{5} \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{3} \)
\( \boldsymbol{x}+\boldsymbol{z}=\boldsymbol{4} \)
Subject: Maths
The value of \( \frac{1}{i}+\frac{1}{i^{2}}+\frac{1}{i^{3}}+\ldots+\frac{1}{i^{102}} \) is
equal to
A \( .-1-i \)
в. \( -1+i \)
\( \mathrm{c} \cdot 1-i \)
D. \( 1+i \)
Subject: Physics
In a rocket of mass \( 1000 k g \) fuel is consumed at a rate of \( 40 k g / s . \) The velocity of the gases ejected from the rocket is \( 5000 m / s \). the thrust on the rocket is
A. \( 2 \times 10^{4} \) N
B . \( 2 \times 10^{6} \mathrm{N} \)
c. \( 4 \times 10^{2} \) N
D \( .4 \times 10^{6} \mathrm{N} \)
Subject: Chemistry
The equilibrium constant for the reaction
\( \boldsymbol{S} \boldsymbol{r}(\boldsymbol{s})+\boldsymbol{M} \boldsymbol{g}^{+2}(\boldsymbol{a} \boldsymbol{q}) \rightleftharpoons \boldsymbol{S} \boldsymbol{r}^{+2}(\boldsymbol{a} \boldsymbol{q})+ \)
\( M g(s) \) is \( 4 \times 10^{12} \) at \( 25^{\circ} C \)
The \( E^{o} \) for a cell made up of the
\( \boldsymbol{S} \boldsymbol{r} \mid \boldsymbol{S} \boldsymbol{r}^{+2} \) and \( \boldsymbol{M} \boldsymbol{g}^{+2} \mid \boldsymbol{M} \boldsymbol{g} \) half cells \( (\log \)
\( \mathbf{2}=\mathbf{0 . 3}) \)
A. \( 0.3717 V \)
в. \( 0.7434 \mathrm{V} \)
c. \( 0.1858 V \)
D. \( 0.135 V \)
Subject: Chemistry
If \( \eta_{2} \) and \( \eta_{2} \) are the coefficients of
viscosity of two liquids, \( d_{1} \) and \( d_{2} \) their
densities and \( t_{1} \) and \( t_{2} \) the flow times in Ostwald viscometer, then
A \( \cdot \frac{\eta_{1}}{\eta_{2}}=\frac{d_{1} t_{2}}{d_{2} t_{1}} \)
В. \( \frac{\eta_{1}}{\eta_{2}}=\frac{d_{2} t_{2}}{d_{1} t_{1}} \)
c. \( \frac{\eta_{1}}{\eta_{2}}=\frac{d_{1} t_{1}}{d_{2} t_{2}} \)
D. \( \frac{\eta_{1}}{\eta_{2}}=\frac{d_{2} t_{1}}{d_{1} t_{2}} \)
Subject: Maths
The direction cosines of a vector \( \hat{\boldsymbol{i}}+ \) \( \hat{\boldsymbol{j}}+\sqrt{\mathbf{2}} \hat{\boldsymbol{k}} \) are
A \( \cdot \frac{1}{2}, \frac{1}{2}, 1 \)
B. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{2} \)
c. \( \frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)
Subject: Physics
If a planet consists of a satellite whose
mass and radius were both half that of
the earth, then the acceleration due to
gravity at the surface of the planet would be
A. \( 5.0 \mathrm{ms}^{-2} \)
B. \( 6.5 \mathrm{ms}^{-2} \)
c. \( 7.9 \mathrm{ms}^{-2} \)
D. \( 19.6 \mathrm{ms}^{-2} \)
Subject: Physics
A ball is thrown vertically up with a velocity of \( 14.7 m / s \) from the top of a
tower of height \( 49 \mathrm{m} . \) On its return, it misses the tower and finally strikes the ground. The time that elapsed from the instant the ball was thrown until it
passes the edge of the tower is
A . \( 1.5 s \)
B . \( 3 s \)
\( c \cdot 6 s \)
D. \( 0.5 s \)
Subject: Maths
If the system of equations \( : x-k y-z= \)
\( \mathbf{0}, \boldsymbol{k} \boldsymbol{x}-\boldsymbol{y}-\boldsymbol{z}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{z}=\mathbf{0} \) has a non
zero solutions then find the possible
value of \( k \)
Subject: Chemistry
\( \begin{array}{ll}\text { Appearance } & \begin{array}{l}\text { Reaction } \\ \text { with } \\ \text { dilute }\end{array} \\ & \boldsymbol{H C l}\end{array} \)
Unknown
metal #1 Dissolved
with
bubbles
of clear
gas Dull gray
solid with
white oxide
coating of
\( D \)
Unknow \( _{1 \# 2}^{\text {าown }} \) metal Solid;
lustrous,
smooth
silver-gray
surface No
reaction bub
of
gas
Identify the orange gas produced on the
addition of dilute \( H N O_{3} \) to unknown
metal #2.
\( \mathbf{A} \cdot C l_{2} \)
B. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( C O_{2} \)
E \( . N O_{2} \)
Subject: Chemistry
Which of the following is not correct?
This question has multiple correct options
A. Hydrolysis of \( 4 \mathrm{NC}_{3} \) gives \( \mathrm{NH}_{3} \) and \( \mathrm{HOC} \)
B. \( \mathrm{NH}_{3} \) is less stable than \( \mathrm{PH}_{3} \)
\( \mathrm{C} \cdot \mathrm{NH}_{3} \) is weak reducing agent compared to \( \mathrm{PH}_{3} \)
D. Nitric Oxide in solid state exhibitsdiamagnetic property.
Subject: Physics
A train travels at a speed \( 50 \mathrm{km} / \mathrm{hr} \) for \( 0.5 \mathrm{hr}, \) at \( 30 \mathrm{km} / \mathrm{hr} \) for next \( 0.26 \mathrm{hr} \) and
then \( 70 \mathrm{km} / \mathrm{hr} \) for next \( 0.76 \mathrm{hr} \)
Determine the average speed of the train.
Subject: Physics
An inductive coil has a resistance of 100
\( \Omega . \) When an \( A C \) signal of frequency 1000 \( \mathrm{Hz} \) is applied to the coil, the voltage
leads the current by \( 45^{\circ} . \) The inductance of the coil is
A \( \cdot \frac{1}{100 \pi} \) #
в. \( \frac{1}{20 \pi} \) н
c. \( \frac{1}{40 \pi} \) н
D. \( \frac{1}{60 \pi} \) н
Subject: Physics
toppr
Q Type your question-
\( A \)
\begin{tabular}{cc|c}
\( \boldsymbol{x} \) & \( \boldsymbol{y} \) & \( \boldsymbol{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \boldsymbol{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \boldsymbol{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{0} \)
\end{tabular}
B. \begin{tabular}{cc|c}
\( \boldsymbol{x} \) & \( \boldsymbol{y} \) & \( \boldsymbol{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{0} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
\( c \)
\begin{tabular}{cc|c}
\( \boldsymbol{x} \) & \( \boldsymbol{y} \) & \( \boldsymbol{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
\( D \)
\begin{tabular}{cc|c}
\( \boldsymbol{x} \) & \( \boldsymbol{y} \) & \( \boldsymbol{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
Subject: Maths
The length of the latus rectum of the
parabola \( \boldsymbol{x}^{2}-\mathbf{4} \boldsymbol{x}-\mathbf{8} \boldsymbol{y}+\mathbf{1 2}=\mathbf{0} \) is-
\( \mathbf{A} \cdot \mathbf{4} \)
B. 6
\( c \cdot 8 \)
D. 10
Subject: Physics
A body is projected with velocity \( 24 m s^{-1} \) making an angle \( 30^{\circ} \) with the horizontal. The vertical component of its
velocity after \( 2 s \) is \( \left(g=10 m s^{-2}\right) \)
A. \( 8 m s^{-1} \) upward
B. \( -8 m s^{-1} \) downward
c. \( 32 m s^{-1} \) upward
D. \( 32 m s^{-1} \) downward
Subject: Chemistry
Radiation of wavelength 242 nm is
sufficient to ionize the sodium atom.
Calculate the ionization energy in
\( \boldsymbol{k J} \boldsymbol{m o l}^{-1} \cdot\left(\boldsymbol{n}=\mathbf{6 . 6 2 5} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s}\right) \)
A. \( 493.6 k J \)
\( J \)
B . \( 6.625 \times 10^{3} J \)
c. \( 242 k J \)
D. \( 1324 k J \)
Subject: Maths
\( \ln \operatorname{an} A . P, \) if \( m^{t h} \) term is \( n \) and \( n^{t h} \) term
is \( \mathrm{m} . \) Then find \( p^{t h} \) term \( (\boldsymbol{m} \neq \boldsymbol{n}) \)
Subject: Chemistry
If 50.0 milliters of \( 3.50 \mathrm{M} H_{2} S O_{4} \mathrm{be} \)
diluted in order to make \( 2.00 \mathrm{M} H_{2} S O_{4} \)
what should be the final volume in
mililiters?
A . 25.0
B. \( 60 . \)
c. 87.5
D. 93.2
E . 101
Subject: Chemistry
Select the correct statement.
This question has multiple correct options
A. At radioactive equilibrium, the number of atoms of \( A \) and \( B \) are in the inverse ratio of their average life.
B. In beta decay, all the emitted electrons have altogether different energy.
C. If \( n / p \) is lower than required for the belt of stability, either positron emission or \( \mathrm{K} \) -electron capture must be shown.
D. Like electrons energy level in atoms, nuclear energy level also exist.
Subject: Chemistry
In the reversible reaction \( 2 N H_{3}(g) \Leftrightarrow \)
\( N_{2}(g)+3 H_{2}(g) \) when 1 mol of \( N H_{3} \) is
taken initially in a litre flask and 0.2
moles of \( N_{2} \) are formed at equilibrium.
Its equilibrium constant \( \boldsymbol{K}_{c} \) is:
A . 72
B. \( 12 \times 10^{-2} \)
\( c \cdot 0.3 \)
D. 0.27
Subject: Chemistry
The Henry's law constant for the
solubility of \( N_{2} \) gas in water at \( 298 K \) is
\( 1.0 \times 105 \) atm. The mole fraction of \( N_{2} \)
in air is \( 0.8 . \) The number of moles of \( N_{2} \)
from air dissolved in 10 moles of water
at \( 298 K \) and 5 atm pressure is
A \( \cdot 4 \times 10^{-4} \)
B . \( 4 \times 10^{-5} \)
\( \mathbf{c} \cdot 5 \times 10^{-4} \)
D. \( 4 \times 10^{-6} \)
Subject: Maths
The monthly income (in rupees) of 7 households in village are
\( \mathbf{1 2 0 0}, \mathbf{1 5 0 0}, \mathbf{1 4 0 0}, \mathbf{1 0 0 0}, \mathbf{1 0 0 0}, \mathbf{1 6 0 0}, \mathbf{1 0 0} \)
(i) Find the median income of the house
holds.
(ii) If one more household with monthly
income of Rs. 1500 is added, what will
the median income be?
\( \begin{array}{ll} \text { A }. i) 1400 & \text { i) } 1450\end{array} \)
B. \( i \) ) 1450 ii) 1400
c. \( i) 1200 \) ii) 1450
D. \( i \) ) 1000 ii) 1250
Subject: Chemistry
Acid hydrolysis of ester is first order reaction and rate constant is given by \( \boldsymbol{k}=\frac{\mathbf{2 . 3 0 3}}{\boldsymbol{t}} \log \frac{\boldsymbol{V}_{\infty}-\boldsymbol{V}_{\mathbf{0}}}{\boldsymbol{V}_{\infty}-\boldsymbol{V}_{\boldsymbol{t}}} \) where, \( \boldsymbol{V}_{0}, \boldsymbol{V}_{\boldsymbol{t}} \)
and \( V_{\infty} \) are the volume of standard
NaOH required to neutralise acid
present at a given time, if ester is \( 50 \% \) neutralised then:
\( \mathbf{A} \cdot V_{\infty}=V_{t} \)
В \( \cdot V_{\infty}=\left(V_{t}-V_{0}\right) \)
C \( . V_{\infty}=2 V_{t}-V_{0} \)
D. \( V_{\infty}=2 V_{t}+V_{0} \)
Subject: Chemistry
Among the following which has the highest boiling point?
A \( \cdot C H_{3} C H_{2} \) OH
в. \( C H_{3} C H_{2} C H_{3} \)
\( \mathbf{c} \cdot C H_{2}=C H C H_{3} \)
D. \( C H_{3} O C H_{3} \)
Subject: Chemistry
Two elements \( A \) and \( B \) form
compounds having molecular formulae
\( A B_{2} \) and \( A B_{4} . \) When dissolved in 20.0 g
of benzene, 1.0 g of \( A B_{2} \) lowers the freezing point by \( 2.3^{\circ} \mathrm{C} \), whereas \( 1.0 \mathrm{g} \)
of \( A B_{4} \) lowers the freezing point by
\( 1.3^{\circ} \mathrm{C} . \) The molal depression constant for benzene in 1000 g is \( 5.1 . \) Calculate the atomic masses of \( A \) and \( B \)
Subject: Maths
\( \int_{1}^{2} \frac{1-x}{1+x} d x \) equals
\( \left(\frac{1}{2}\right) \log \left(\frac{3}{2}\right)-1 \)
B \( \cdot 2 \log \left(\frac{3}{2}\right)-1 \)
\( ^{\mathbf{C}} \cdot \log \left(\frac{3}{2}\right)-1 \)
D. None of these
Subject: Physics
Two trains \( A \) and \( B \) each of length 400 m are moving on two parallel tracks with a uniform speed \( 72 \mathrm{km} h^{-1} \) in the same
direction with \( A \) ahead of \( B \). The driver of
B decides to overtake \( A \) and accelerates
by \( 1 \mathrm{m} s^{-2} \). If after 50 s, the guard of \( B \) just brushes past \( A, \) what was the original distance between them?
A. \( 450 \mathrm{m} \)
B. 1000 \( \mathrm{m} \)
\( c . \) 1250 \( m \)
D. 2250 \( \mathrm{m} \)
Subject: Maths
The weight of a cubic meter of a certain
metal is 480 kg. It is melted and then rolled into a square bar \( 4 m \) long. Now, an exact cube is cut from it. Find the
weight of the cube
A. \( 240 \mathrm{kg} \)
в. \( 80 \mathrm{kg} \)
c. \( 120 \mathrm{kg} \)
D. \( 60 \mathrm{kg} \)
Subject: Chemistry
Arrange benzene, n-hexane and ethyne in decreasing order of acidic behaviour. Also give reason for this behaviour.
\[
\begin{array}{c}
\text { Ethyne }>\text { Benzene }>\quad n \text { -Hexane } \\
\mathrm{H}-\mathrm{C}=\mathrm{C}-\mathrm{H} \\
s p
\end{array}
\]
Subject: Maths
Given that \( \boldsymbol{P}(\boldsymbol{3}, \boldsymbol{2},-\boldsymbol{4}), \boldsymbol{Q}(\boldsymbol{5}, \boldsymbol{4},-\boldsymbol{6}) \) and
\( R(9,8,-10) \) are collinear. Find the ratio in which \( Q \) divides \( P R \)
Subject: Chemistry
In which of the compound given below contains more than one kind of
hybridization \( \left(s p, s p^{2}, s p^{3}\right) \) for carbon:
A \( \cdot C H_{3} C H_{2} C H_{2} C H_{3} \)
в. \( C H_{3}-C H=C H-C H_{3} \)
\( \mathrm{c} \cdot C H_{2}=C H-C H=C H_{2} \)
D. \( H-C \equiv C-H \)
Subject: Chemistry
Two atoms of elements \( X \) and \( Y \)
contribute an electron each during the bond formation and both \( X \) and \( Y \) have
equal tendency to attract the shared electron pair. The type of bond formed between \( X \) and \( Y \)
is
A. polar covalent bond
B. ionic bond
c. coordinate covalent bond
D. non-polar covalent bond
Subject: Physics
Four equal charges q each are placed at four corners of a square of side a each. Work done in carrying a charge q from its centre to infinity is:
A. zero
В. \( \frac{2 q^{2}}{\pi \varepsilon_{0} a} \)
c. \( \frac{\sqrt{2} q^{2}}{\pi \varepsilon_{0} a} \)
D. \( \frac{q^{2}}{2 \pi \varepsilon_{0} a} \)
Subject: Physics
An electric dipole of momentum \( \vec{p} \) is placed in a uniform electric field. The dipole is rotated through a very smal angle from equilibrium and is released. Prove that it executes simple harmonic motion with frequency \( f=\frac{1}{2 \pi} \sqrt{\frac{p E}{1}} \)
Where, \( I= \) moment of inertia of the
dipole.
Subject: Chemistry
Which one of the following is the correct
statement?
\( \mathbf{A} \cdot H C O_{3}^{-} \) is the conjugate base of \( C O_{3}^{2-} \)
B. \( N H_{2}^{-} \) is the conjugate acid of \( N H_{3} \)
\( \mathrm{C} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \) is the conjugate acid of \( \mathrm{HSO}_{4}^{-} \)
D. \( N H_{3} \) is the conjugate base of \( N H_{2}^{-} \)
\( \mathrm{E} \cdot \mathrm{H}_{2} \mathrm{CO}_{3} \) is the conjugate base of \( \mathrm{HCO}_{3}^{-} \)
Subject: Physics
Two capillary tubes of the same material but of different radii are
dipped in a liquid. The heights to which the liquid rises in the two tubes are
\( 2.2 c m \) and \( 6.6 c m . \) The ratio of radii of
the tubes will be
A . 1: 9
B. 1: 3
c. 9: 1
D. 3: 1
Subject: Physics
The power (P) of a wave, whose amplitude (A) and area of cross section
of the medium is \( \mathrm{S} \), is related to its time period (T) by:
A \( \cdot P / T^{2}= \) constant
B. \( P T^{2}= \) constant
c. \( P T= \) constant
D. \( P / T= \) constant
Subject: Chemistry
In a 0.25 -liter tube dissociation of 4
moles of NO is took place. If its degree of
dissociation is \( 10 \% . \) The value of \( \boldsymbol{K}_{\boldsymbol{p}} \) for
reaction \( 2 N O \rightleftharpoons N_{2}+O_{2} \) is:
A \( \cdot \frac{1}{(18)^{2}} \)
в. \( \frac{1}{(8)^{2}} \)
c. \( \frac{1}{(16)} \)
D. \( \frac{1}{(32)} \)
Subject: Physics
A harmonic oscillator vibrates with
amplitude of \( 4 \mathrm{cm} \) and performs 150 oscillations in one minute. If the initial
phase is 450 and it starts moving away from the equation of motion is
A \( \cdot 0.04 \sin \left(5 \pi t+\frac{\pi}{4}\right) \)
B. \( 0.04 \sin \left(5 \pi t-\frac{\pi}{4}\right) \)
c. \( 0.04 \sin \left(4 \pi t+\frac{\pi}{4}\right) \)
D. \( 0.04 \sin \left(4 \pi t-\frac{\pi}{4}\right) \)
Subject: Chemistry
For the reaction; \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \mathbf{3} \boldsymbol{C}, \) at \( \mathbf{2 5}^{\boldsymbol{o}} \boldsymbol{C} \)
a 3 litres vessel contains 1,2 and 4
moles of \( A, B \) and \( C \) respectively. If \( K_{c} \)
for the reaction is \( 10, \) the reaction will
proceed in :
A. forward reaction
B. backward direction
C. either direction
D. equilibrium
Subject: Maths
For any two events \( A \) and \( B \)
This question has multiple correct options
\( \mathbf{A} \cdot P(A \cap B) \geq P(A)+P(B)-1 \)
B \( \cdot P(A \cap B) \geq P(A)+P(B) \)
\( \mathbf{c} \cdot P(A \cap B)=P(A)+P(B)-P(A \cup B) \)
D \( \cdot P(A \cap B)=P(A)+P(B)+P(A \cup B) \)
Subject: Chemistry
Which of the following species are formed by Lewis acid-base interaction? This question has multiple correct options
A \( \cdot C H_{4} \)
в. \( N a B F_{4} \)
\( \mathbf{c} \cdot P C l_{4}^{+} \)
\( \mathbf{D} \cdot A l(O H)_{4}^{-} \)
Subject: Maths
If \( f(x)=x+\int_{0}^{1}\left[x y^{2}+s^{2} y\right] f(y) d y \)
where \( x \) and \( y \) are independent varibles. Find \( f(x) \)
A \( \quad f(x)=x+\frac{61}{119} x+\frac{80}{119} x^{2} \)
в. \( f(x)=\frac{80 x^{2}+180 x}{119} \)
c. \( f(x)=\frac{80 x+180 x}{119} \)
D. \( f(x)=\frac{80 x^{2}+180 x}{19} \)
Subject: Physics
An electron is projected so that it crosses three different regions of space
as shown. if \( B_{1}, B_{2} \) and \( B_{3} \) are the
magnetic field in the region,then:
\( A \cdot B_{1} \) is inward
B. \( B_{2} \) is outward
\( c \cdot B_{3} \) is inward
D. All of these
Subject: Chemistry
Which statement correctly completes
the statement?
Except for glycerine, which is achiral, all
the amino acids present in proteins.:
\( \mathbf{A} \)
\( H_{3}^{+} N H C O_{2} H \)
are chiral, but racemic
B. \( H_{2} N C H C O_{2} H \)
have the L configuration at their \( \alpha \) carbon
\( c \)
\( H_{3}^{+} \stackrel{R}{N C}_{H C O_{2}^{-}} \)
have the \( R \) configuration at their \( \alpha \) carbon
D. \( R \)
\( H_{2} N C H C O_{2}^{-} \)
have the S configuration at their \( \alpha \) carbon
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) then \( \boldsymbol{A}^{-\mathbf{1}}= \)
A \( \cdot \frac{-1}{2}\left[\begin{array}{cc}4 & -2 \\ -3 & 1\end{array}\right] \)
в. \( \frac{1}{2}\left[\begin{array}{cc}4 & -2 \\ -3 & 1\end{array}\right] \)
c. \( \left[\begin{array}{cc}-2 & 4 \\ 1 & 3\end{array}\right] \)
D. \( \left[\begin{array}{ll}2 & 4 \\ 1 & 3\end{array}\right] \)
Subject: Physics
The equipotential surface of an electric
dipole is:
A. A sphere whose centre coincides with the centre of the electric dipole
B. A plane surface inclined at an angle of \( 45^{\circ} \) with the axis of the electric dipole
C. A plane surface passing through the centre of the electric dipole and perpendicular to the axis of the electric dipole
D. Any plane surface parallel to the axis of the electric dipole
Subject: Physics
The diagram shown above represents the applied force per unit area with the
corresponding change \( \boldsymbol{X} \) (per unit length) produced in a thin wire of uniform cross-section in the curve
shown. The region in which the wire behaves like a liquid is :
\( A \cdot a \)
в. \( b c \)
\( c \cdot c d \)
D. \( O a \)
Subject: Maths
The solution of the differential equation \( \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{2} \boldsymbol{y}=\boldsymbol{x}^{2}(\boldsymbol{x} \neq \mathbf{0}) \) with \( \boldsymbol{y}(\mathbf{1})=\mathbf{1} \)
is?
A \( \cdot y=\frac{x^{3}}{5}+\frac{1}{5 x^{2}} \)
B. \( y=\frac{4}{5} x^{3}+\frac{1}{5 x^{2}} \)
c. \( y=\frac{3}{4} x^{2}+\frac{1}{4 x^{2}} \)
D. \( y=\frac{x^{2}}{4}+\frac{3}{4 x^{2}} \)
Subject: Maths
An airplane is heading north east at a speed of \( 141 m s^{-1} \). The northward
component of its velocity is:
A. \( 141.4 m s^{-1} \)
B. \( 100 \mathrm{ms}^{-1} \)
c. zero
D. \( 50 m s^{-1} \)
Subject: Maths
At \( x=\frac{3}{2}, \) the value is real for
This question has multiple correct options
\( \mathbf{A} \cdot \tan ^{-1} x \)
B. \( \cos ^{-1} 2 x \)
\( \mathbf{c} \cdot \operatorname{cosec}^{-1} x \)
D. none of these
Subject: Maths
If coefficients \( a, b, c \) of quadratic equation \( a x^{2}+b x+c=0 \) are chosen
at random with replacement from the \( \operatorname{set} S=1,2,3,4,5,6, \) find out the
probability that roots of quadratic are real and distinct.
A \( \frac{20}{108} \)
в. \( \frac{19}{108} \)
c. \( \frac{21}{108} \)
D. \( \frac{22}{108} \)
Subject: Maths
Which one of the following is correct in
respect of the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}^{2}}{|\boldsymbol{x}|} \) for
\( \boldsymbol{x} \neq \mathbf{0} \) and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} ? \)
A. \( f(x) \) is discontinuous everywhere
B. \( f(x) \) is continuous everywhere
c. \( f(x) \) is continues at \( x=0 \) only
D. \( f(x) \) is discontinuous at \( x=0 \) only
Subject: Physics
Two condensers of capacitance \( 4 \mu F \) and \( 5 \mu F \) are joined in series. If the potential difference across \( 5 \mu F \) is \( 10 V \), then the
potential difference across \( 4 \mu F \)
condenser is :
\( \mathbf{A} \cdot 22.5 V \)
B. \( 10 V \)
c. \( 12.5 V \)
D. \( 25 V \)
Subject: Maths
Let \( N \) denote the set of all natural
numbers and \( R \) be the relation on \( N \times \)
\( N \) defined by \( (a, b) R(c, d), \) if \( a d(b+ \)
\( c)=b c(a+d), \) then show that \( R \) is an
equivalence relation.
Subject: Physics
The breakdown field strength for dry air
is \( 3 \times 10^{6} \mathrm{V} / \mathrm{m} \). Each of the plates of the
parallel plate capacitor has an area of
\( 0.2 m^{2} . \) The maximum charge that can be
collected is : (Given permittivity of air \( \left.\epsilon_{\circ}=8.85 \times 10^{-12} C^{2} / N m^{2}\right) \)
A. \( 5.3 \mu \) С
в. \( 0.6 \mu \mathrm{c} \)
c. \( 1.5 \mu \) С
D. \( 4.56 \mu \) С
Subject: Maths
ff \( \left[\begin{array}{cc}2 & -1 \\ 2 & 0\end{array}\right]+2 A=\left[\begin{array}{cc}-3 & 5 \\ 4 & 3\end{array}\right], \) then the
matrix A equals
A. \( \left[\begin{array}{ll}-5 & 6 \\ 2 & 3\end{array}\right] \)
B. \( \left[\begin{array}{cc}-\frac{5}{2} & 3 \\ 1 & \frac{3}{2}\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-\frac{5}{2} & 6 \\ 2 & 3\end{array}\right] \)
D. \( \left[\begin{array}{cc}-5 & 8 \\ 1 & 3\end{array}\right] \)
Subject: Maths
A 5 m \( 60 \mathrm{cm} \) high vertical pole casts a
shadow \( 3 m 20 \mathrm{cm} \) long. Find at the
same time (i) the length of the shadow cast by another pole 10 m \( 50 \mathrm{cm} \) high
(ii) the height of a pole which casts a shadow 5 m long.
Subject: Maths
The shortest distance between z-axis
and the line
\( \boldsymbol{x}+\boldsymbol{y}+\mathbf{2} \boldsymbol{z}-\mathbf{3}=\mathbf{0}=\mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{4} \boldsymbol{z} \)
\( 4, \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D. 3