AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The volume of \( 20 V-H_{2} O_{2} \) solution
required to prepare 5 litres of oxygen at
STP is:
A . \( 125 \mathrm{ml} \)
B. 250 m1
c. \( 100 \mathrm{ml} \)
D. \( 50 \mathrm{m} \)
Subject: Chemistry
\( 0.24 \mathrm{g} \) of a volatile gas upon vaporization gives 45 mL vapour at \( \mathrm{NTP} \) What will be the vapour density of the
substances? (density of \( \boldsymbol{H}_{2}=\mathbf{1} \) )
(a) 95.39
(b) 5.973
(c) 95.93
(d) 59.73
Subject: Physics
\( \mathbf{1} \boldsymbol{k} \boldsymbol{m} / \boldsymbol{h} \boldsymbol{r}=\dots \dots \dots \dots \dots \)
A \( \cdot \frac{18}{5} \)
в. \( \frac{5}{18} \)
c. \( \frac{15}{18} \)
D. \( \frac{18}{15} \)
Subject: Chemistry
Ramesh mixed some iron filings with
sulphur powder in a China dish. In
another dish, he mixed iron filings and
sulphur powder and heated the mixture.
Which of his observations is not
correct?
A. Dish \( X \) shows a physical change while dish \( Y \) shows chemical change.
B. In dish \( X \) sulphur powder and iron filings can be seen separately.
C. In dish \( Y \) a new substance is formed on heating the mixture.
D. The change which has taken place in dish \( Y \) is reversible
Subject: Maths
et \( \frac{\boldsymbol{d} \boldsymbol{f}(\boldsymbol{x})}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{e}^{\sin \boldsymbol{x}}}{\boldsymbol{x}}, \boldsymbol{x}>\mathbf{0} \)
\( \int_{1}^{4} \frac{3 e^{\sin x^{3}}}{x} d x=f(k)-f(1) \) then one
of the possible values of \( k \) is
A . 16
B. 63
c. 64
D. 15
Subject: Physics
A magnetic field \( B=2 t+4 t^{2} \) (where
\( t=\text { time }) \) is applied perpendicular to
the plane of a circular wire of radius \( r \)
and resistance \( R \). If all the units are in
\( S I, \) the electric charge that flows
through the circular wire during \( t=0 s \)
to \( t=2 s \) is:
\( \mathbf{A} \cdot \frac{6 \pi r^{2}}{R} \)
В. \( \frac{20 \pi r^{2}}{R} \)
\( ^{\mathrm{c}} \cdot \frac{32 \pi r^{2}}{R} \)
D. \( \frac{48 \pi r^{2}}{R} \)
Subject: Maths
Divide the following and write your answer in lowest terms: \( \frac{x}{x+1} \div \) \( \frac{x^{2}}{x^{2}-1} \)
A \( \cdot \frac{x-1}{x} \)
в. \( \frac{x+1}{x} \)
c. \( \frac{x-1}{x^{2}} \)
D. None of these
Subject: Chemistry
(a) How would you account for the following:
(i) Actinoid contraction is greater than lanthaniod contraction.
(ii) Transition metals form coloured
compounds.
(b) Complete the following equation:
\( \mathbf{2} M \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{6} \boldsymbol{H}^{+}+\mathbf{5} \boldsymbol{N} \boldsymbol{O}_{2}^{-} \rightarrow \)
Subject: Physics
A condenser of \( 250 \mu F \) is connected in parallel to a coil of inductance \( 0.16 \mathrm{mH} \) while its effective resistance is \( 20 \Omega \)
Determine the resonant frequency.
A \( \cdot 9 \times 10^{4} H z \)
B . \( 16 \times 10^{7} \mathrm{Hz} \)
c. \( 8 \times 10^{5} H z \)
\( \mathbf{D} \cdot 9 \times 10^{3} H z \)
Subject: Physics
A satellite is orbiting the earth. Its speed is more at point \( \mathrm{B} \) as compared to point A. Which of the following statements are true?
I. The gravitational force is greater at \( \mathrm{B} \)
than at \( \mathbf{A} \)
II. The speed is greater at \( \mathrm{B} \) than at \( \mathrm{A} \)
III. The kinetic energy is greater at \( \mathrm{B} \) than at \( A \)
IV. The angular momentum is greater at
\( B \) than at \( A \)
A. I only
B. I and II only
c. ॥ only
D. I, II and III only
E . ।, ॥।, ॥I।, IV
Subject: Biology
Assertion
In short day plant, day length should be less than critical day length.
Reason
Long night should be continuous.
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
:For the reaction
\( C_{2} H_{4}(g)+3 O_{2}(g) \rightarrow 2 C O_{2}(g)+2 H_{2} O(l) \)
\( \Delta E=-1415 k J . \) The \( \Delta \mathrm{H} \) at \( 27^{0} \mathrm{C} \) is
\( \mathbf{A} \cdot-1410 k J \)
в. \( -1420 k J \)
\( \mathbf{c} .+1420 k J \)
D. \( +1410 k J \)
Subject: Chemistry
\( H_{2} S \) is acidic in nature while \( H_{2} O \) is
neutral in nature. Give reason.
A. Oxygen is more electro negative than sulphur
B. \( H-S \) bond is weaker than \( O-H \) bond
c. Bond angle in \( H_{2} S \) is less than that in \( H_{2} O O \)
D. \( H-S \) bond is stronger than \( O-H \) bond
Subject: Physics
Two trains, each \( 50 m \) long, are travelling in opposite directions with velocity \( 10 m / s \) and \( 15 m / s . \) The time of crossing is-
\( \mathbf{A} \cdot 2 s \)
B . \( 4 s \)
c. \( 2 \sqrt{3} s \)
D. \( 4 \sqrt{3} s \)
Subject: Physics
In the series LCR circuit (figure), the
voltmeter and ammeter readings are:
A. \( V=100 V, I=2 A \)
B. \( V=100 V, I=5 A \)
\( \mathbf{c} . V=1000 V, I=2 A \)
D. \( V=300 V, I=1 A \)
Subject: Chemistry
Assertion
On reacting \( M g \) with \( C l_{2}, M g C l_{2} \) is
formed and not \( M g C l \)
Reason
\( M g^{2+} \) ion has stable octet
configuration and not \( M g^{+} \)
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
Electron density studies have revealed that \( X \) and \( Y \) have an equal number of
electrons.What are \( X \) and \( Y ? \)
\( \mathbf{A} \cdot C a^{+} \) and \( \mathbf{K} \)
B. \( H^{+} \) and \( \mathrm{He} \)
c. \( \mathrm{cl} \) and \( \mathrm{F} \)
D. \( O^{-} \) and \( S^{+} \)
E. None of the above
Subject: Maths
Prove the following:
\( \left|\begin{array}{ccc}\boldsymbol{a}^{2}+\boldsymbol{b}^{2} & \boldsymbol{c} & \boldsymbol{c} \\ \boldsymbol{c} & \frac{\boldsymbol{b}^{2}+\boldsymbol{c}^{2}}{\boldsymbol{a}} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{b} & \frac{\boldsymbol{c}^{2}+\boldsymbol{a}^{2}}{\boldsymbol{b}}\end{array}\right|=\boldsymbol{4 a b c} \)
Subject: Physics
at opposite sides of an infinitely long straight conducting wire as shown in the figure. If current in the wire is slowly
decreased, then the direction of the
nduced current will be :
A. clockwise in \( A \) and anticlockwise in \( B \)
3. anticlockwise in \( A \) and clockwise in \( B \)
c. clockwise in both \( A \) and \( B \)
D. anticlockwise in both \( A \) and \( B \)
Subject: Maths
In right angle \( \triangle A B C, \angle B=90^{\circ}, \angle A= \)
\( 45^{\circ}=\angle C, \) then \( \operatorname{cosec} 45^{\circ}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \sqrt{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. None of above
Subject: Physics
rest on a rough horizontal table. A
horizontal force \( F \) is applied normal to one of the face at a point, at a height \( 3 b / 4 \) above the base. What should be
the coefficient of friction \( (\mu) \) between
cube and table so that it will tip about
an edge before it starts slipping?
' \( \mu>\frac{2}{3} \)
3. \( \mu>\frac{1}{3} \)
\( c_{\mu>\frac{3}{2}} \)
\( D \)
Subject: Physics
Two identical thin rings, each of radius
10cm carrying charges \( 10 C \) and \( 5 C \) are
coaxially placed at a distance \( 10 \mathrm{cm} \) a part. The work done in moving a charge
\( q \) from the centre of the first ring to that
of the second is
A \( \cdot \frac{q}{8 \pi \varepsilon_{0}}\left(\frac{\sqrt{2}+1}{\sqrt{2}}\right) \)
В. \( \frac{q}{8 \pi \varepsilon_{0}}\left(\frac{\sqrt{2}-1}{\sqrt{2}}\right) \)
c. \( \frac{q}{4 \pi \varepsilon_{0}}\left(\frac{\sqrt{2}+1}{\sqrt{2}}\right) \)
D. \( \frac{q}{4 \pi \varepsilon_{0}}\left(\frac{\sqrt{2}-1}{\sqrt{2}}\right) \)
E \( \cdot \frac{q}{4 \pi \varepsilon_{0}}\left(\frac{\sqrt{3}+1}{\sqrt{2}}\right) \)
Subject: Physics
The moment of a force of \( 10 N \) about a
fixed point \( \boldsymbol{O} \) is \( \mathbf{5} \boldsymbol{N} \boldsymbol{m} . \) Calculate the
distance of the point \( O \) from the line of action of the force.
A. \( 5 m \)
в. \( 1 m \)
\( c .50 m \)
D. \( 0.5 m \)
Subject: Chemistry
According to the ideal gas law, what is the approximate volume that will be occupied by 0.5 mole of an ideal gas at
\( 30^{\circ} \mathrm{C} \) and 3 atm pressure (gas constant \( \boldsymbol{R}=\mathbf{0 . 0 8 2 1} \boldsymbol{L} . \boldsymbol{a t m} /(\boldsymbol{m o l . K})) ? \)
A. Less than 1 L
в. 5 L
\( c .10 L \)
D. 15 L
Subject: Physics
If acceleration \( (A), \operatorname{mass}(M), \) velocity
\( V \) ), time \( (T) \) are the fundamental units,
then the dimensions of height will be
A \( \cdot V T^{-1} M^{2} \)
в. \( A M T^{-1} \)
c. \( A^{-1} M^{3} V^{-1} \)
D. \( A T^{2} \)
Subject: Maths
A retired person wants to invest an
amount of Rs. \( 50,000 . \) His broker
recommends investing in two type of bonds A and B yielding 10\% and 9\% return respectively on the invested
amount. He decides to invest at least
Rs.20, 000 in bond A and at least

Rs. 10,000 in bond \( B . \) He also wants to
invest at least as much in bond \( A \) as in
bond B. Solve this linear programming problem graphically to maximize his
returns.
A. 4900
B. 2900
\( c .5400 \)
D. 4000
Subject: Maths
Let \( A \) and \( B \) are two matrices of same
order \( 3 \times 3 \) given by \( A= \) \( \left[\begin{array}{ccc}1 & 3 & \lambda+2 \\ 2 & 4 & 6 \\ 3 & 5 & 8\end{array}\right] B=\left[\begin{array}{ccc}3 & 2 & 4 \\ 3 & 2 & 5 \\ 2 & 1 & 4\end{array}\right] \) If \( \lambda=4 \)
\( \operatorname{then} \frac{1}{6}\{\operatorname{tr}(A B)+\operatorname{tr}(B A)\} \) is equal to
\( A \cdot 42 \)
B. 37
\( c .35 \)
D. None of thes
Subject: Physics
Value of planck's constant is
\( \mathbf{A} \cdot 6.6 \times 10^{-34} J s \)
B . \( 6.4 \times 10^{-26} \mathrm{Js} \)
C \( \cdot 6.8 \times 10^{-27} \mathrm{Js} \)
D. \( 6.6 \times 10^{-28} \mathrm{Js} \)
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{S} \) a toxic gas with rottenegg like smell is used for the qualetative
analysis, if the solubility of \( H_{2} S \) in
water,at STP is 0.195mole.kg \( ^{-1} \), the Henry's law constant is:
A. 282 bar
B. 324.8 bar
c. 462.9 bar
D. 534.8 bar
Subject: Physics
In a house, individual powers of two elements are \( \$ \$ 1001 \mathrm{W} 11001 \mathrm{W} \$ \$ . \) The effective power of their series combination will be :
A . \( 120 \mathrm{W} \)
B. \( 75 W \)
\( \mathbf{c} .50 W \)
D. \( 60 W \)
Subject: Physics
A thin \( 1 \mathrm{m} \) long rod has a radius of 5
mm.1 A force of 50 \( \pi k N \) is applied at
one end to determine its Young's modulus. Assume that the force is
exactly known. If the least count in the measurement of all lengths is \( 0.01 \mathrm{mm} \) which of the following statements is false?
A. The maximum value of \( Y \) that can be determined is \( 10^{14} N / m^{2} \)
B. \( \frac{\Delta Y}{Y} \) gets minimum contribution. from the uncertainty in the length.
c. \( \frac{\Delta Y}{Y} \) gets its maximum contribution from the uncertainty in strain
D. The figure of merit is the largest for the length of the rod
Subject: Physics
Four cells, each of emf \( E \) and internal
resistance \( r, \) are connected in series
across an external resistance \( \boldsymbol{R} \). By
mistake one of the cells is connected in
reverse. Then the current in the external
circuit is:
A \( \cdot \frac{2 E}{4 r+R} \)
в. \( \frac{3 E}{4 r+R} \)
c. \( \frac{3 E}{3 r+R} \)
D. \( \frac{2 E}{3 r+R} \)
Subject: Physics
A ball of mass \( 50 \mathrm{g} \) is dropped from a height of 20 m.A boy on the ground hits the ball vertically upwards with a bat with an average force of \( 200 \mathrm{N}, \) so that it attains a vertical height of 45 m.The time foe which the ball remains in
contact with the bat is
A \( \cdot 1 / 20^{\operatorname{th}} \) of a second
B . \( 1 / 40^{\text {th }} \) of a second
c. \( 1 / 80^{\text {th }} \) of a second
D. \( 1 / 20^{\text {th }} \) of a second
Subject: Biology
Consider the following feature of tissues.
A. They are similar and dissimilar cells.
B. They are performing a common function.
C. They have a common origin.
D. They are characterized by the distinct
cell wall.
The correct ones are grouped in
\( A \cdot A, B \) and \( D \)
B. B, C and D
c. \( A, B \) and \( c \)
D. \( A, C \) and \( D \)
Subject: Physics
A circular track of radius \( 300 \mathrm{m} \) is banked at an angle \( \frac{\pi}{12} \) radian. If the coefficient of friction between wheel of a
vehicle and road is \( 0.2, \) the maximum safe speed of vehicle is :
A \( \cdot 28 m s^{-1} \)
B . 38 \( m s^{-1} \)
\( \mathrm{c} \cdot 18 \mathrm{ms}^{-1} \)
D. \( 48 \mathrm{ms}^{-1} \)
Subject: Chemistry
Assertion
\( P H_{3} \) exists but \( P H_{5} \) does not exist
while both \( P C l_{3} \) and \( P C l_{5} \) exist.
Reason
\( P H_{3} \) has \( s p^{3} \) -hybridization.
A. The Assertion is true, Reason is true and Reason is the
correct explanation for Assertion
B. The Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion
C. The Assertion is true, Reason is false.
D. The Assertion is false, Reason is true.
Subject: Physics
If \( n_{p} \) and \( n_{e} \) are the number of holes and
conduction electrons in an intrinsic
semiconductor then
A \( \cdot n_{p}>n_{e} \)
в. \( n_{p}=n_{e} \)
c. \( n_{p}<n_{e} \)
D \( \cdot n_{p} \neq n_{e} \)
Subject: Chemistry
Which of the following contain \( \boldsymbol{P}-\boldsymbol{P} \)
bond?
A \( \cdot P_{2} O_{7}^{4} \)
B. \( P_{2} O_{6}^{2-} \)
\( \mathrm{c} \cdot P_{3} O_{9}^{3-} \)
D. \( P_{2} O_{6}^{4-} \)
Subject: Physics
A particle of mass \( m=5 \) unit is
moving with a uniform speed \( \boldsymbol{v}=\mathbf{3} \sqrt{\mathbf{2}} \)
unit in the \( X \) OY plane along the line \( y= \) \( x+4 . \) The magnitude of the angular
momentum of the particle about the origin is :
A. 60 unit
B. \( 40 \sqrt{2} \) unit
c. zero
D. 7.5 unit
Subject: Maths
A square \( A B C D \) and a circle are drawn
a graph sheet such that the vertices of the square \( A B C D \) are
\( \boldsymbol{A}(-\mathbf{2}, \mathbf{2}), \boldsymbol{B}(\mathbf{2}, \mathbf{2}), \boldsymbol{C}(\mathbf{2},-\mathbf{2}), \boldsymbol{D}(-\mathbf{2},- \)
and the circle with centre (0,0) and
radius \( 2 \mathrm{cm} \) is cut off from the above
square \( A B C D . \) Find the area of the
remaining region in the square \( A B C D \).
Subject: Physics
A thin straight vertical conductor has
10amp current flows vertically upwards. It is present at a place where \( B_{H}=4 \times 10^{-6} T . \) At which point
magnetic feild will be maximum
A. \( 0.5 m \) on south of conductor
B. \( 0.5 m \) on west of conductor
\( \mathrm{c} .0 .5 \mathrm{m} \) on east of conductor
D. \( 0.5 m \) on north-east of conductor
Subject: Chemistry
10 g of an organic compound on complete combustion gives \( 17.6 \mathrm{g} \mathrm{CO}_{2} \)
\( 3.6 \mathrm{g} \) water and \( 6.4 \mathrm{g} \mathrm{SO}_{2 .} \) The
empirical formula of the compound is :
A. \( C_{4} H_{4} S O \)
в. \( C_{3} H_{4} \) SO
\( \mathbf{c} \cdot C_{4} H_{8} S O \)
D. \( C_{2} H_{4} S O \)
Subject: Chemistry
The octahedral complex ions \( \left[\boldsymbol{F e C l}_{6}\right]^{3-} \)
and \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{6}\right]^{3-} \) are both
paramagnetic but the former is high spin and the latter is low spin. In the low
spin complex, \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{3-} \) has the d-
configuration as:
\( \mathbf{A} \cdot t_{2 g}^{3} e_{g}^{2} \)
B . \( t_{2}^{5} \)
\( \mathbf{c} \cdot t_{2}^{2} \)
D. \( e^{5} \)
Subject: Physics
An astronaut is approaching the moon.
He sends a radio wave of frequency \( 5 \times \) \( 10^{9} H z \) towards the moon. The
frequency of the radio echo received by him has a frequency \( 9 \times 10^{4} H z \) more
than that of the real frequency. The velocity of the astronaut relative to the
moon is
A. \( 5.40 \mathrm{m} / \mathrm{s} \)
B. \( 4.05 k m / s \)
c. \( 2.70 k m / s \)
D. \( 1.35 k m / s \)
Subject: Physics
An electron is shot in a steady electric and magnetic field such that its velocity is \( V \). Electric field \( E \) and
magnetic field \( \boldsymbol{B} \) are
mutually perpendicular. The magnitude
of \( \boldsymbol{E} \) is 1 volt \( / \mathrm{cm} \) and that of \( \boldsymbol{B} \) is
2 tesla. Now it happens that the Lorentz (Magnetic) force cancels with the
electrostatic force on the electron, then
the velocity of the electron is:
A. \( 50 \mathrm{ms}^{-1} \)
B. \( 2 \mathrm{cms}^{-1} \)
c. \( 0.5 \mathrm{cms}^{-1} \)
D. \( 200 m s^{-1} \)
Subject: Chemistry
\( \boldsymbol{E}_{\boldsymbol{n}}=-\frac{\mathbf{3 1 3 . 6}}{\boldsymbol{n}^{2}}, \) if the value of \( \boldsymbol{E}_{\boldsymbol{i}}= \)
-34.84 to which value ' \( n \) ' corresponds:
A . 2
B. 4
c. 1
D. 3
Subject: Physics
a conducting sphere \( A \) of radius a, with
charge \( Q, \) is placed concentrically
inside a conducting shell \( B \) of radius \( b \)
B is earthed. \( C \) is the common centre of
A and B:
This question has multiple correct options
A \( \cdot \) The field at a distance r from \( \mathrm{C} \), where \( a \leq r \leq b \), is \( k \frac{Q}{r^{2}} \)
B. The potential at a distance r from C, where \( a \leq r \leq b \), is
\( k \frac{Q}{r} \)
C. The potential difference between A and B is, \( k Q\left(\frac{1}{a}-\frac{1}{b}\right) \)
D. The potential difference between r and C, where \( a \leq \) \( r \leq b, \) is \( k Q\left(\frac{1}{a}-\frac{1}{b}\right) \)
Subject: Physics
A stone is dropped freely from the top of a tower and it reaches the ground in \( 4 s \)
taking \( g=10 m s^{-2} \), calculate the height of the tower.
\( A \cdot 80 m \)
B. \( 40 \mathrm{m} \)
\( c \cdot 4 m \)
D. 20 \( m \)
Subject: Physics
Analyse the following observation table showing variation of image - distance
(v) with object - distance
(u) in case of a
convex lens and answer the questions that follow without doing any calculations:
(a) what is the focal length
of the convex lease? Give reason to
justify your answer
(b) Write serial number of the
observation which is not correct. On
what basis have you arrived at this conclusion?
(c) Select an appropriate scale and draw a ray diagram for the observation
at S.No. 2. Also the approximate value of magnification.
Subject: Physics
A small sphere of mass \( m \) and having charge \( q \) is suspended by a silk thread of length \( l \) in a uniform horizontal
electric filed. If it stands at a distance \( x \)
from the vertical line from point of suspension, then magnitude of electric field is :
A. \( \frac{m g}{q} \)
в. \( \frac{m g}{q} \)
c. \( \frac{m g x}{q \sqrt{l^{2}-x^{2}}} \)
D. \( \frac{m g l}{q \sqrt{x^{2}-l^{2}}} \)
Subject: Physics
A rod of length 1 m and mass 0.5 kg
hinged at one end, is initially hanging vertical. The other end is now raised
slowly until it makes an angle \( 60^{\circ} \) with the vertical. The required work is (use
\( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A \( \cdot \frac{5}{2} J \)
в. \( \frac{5}{4} J \)
c. \( \frac{17}{8} J \)
D. \( \frac{5 \sqrt{3}}{4} J \)
Subject: Maths
If the points \( (k, 2-2 k)(1-k, 2 k) \) and \( (-k \) \( -4,6-2 x) \) be collinear the possible values of k are
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{2} \)
\( c \)
D. - -
Subject: Maths
f \( \boldsymbol{I}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{x}^{3} \sqrt{\boldsymbol{x}^{2}-1}}, \) then I equals
A \( \cdot \frac{1}{2}\left(\frac{\sqrt{x^{2}-1}}{x^{3}}+\tan ^{-1} \sqrt{x^{2}-1}\right)+C \)
B. \( \frac{1}{2}\left(\frac{\sqrt{x^{2}-1}}{x^{2}}+x \tan ^{-1} \sqrt{x^{2}-1}\right)+C \)
\( ^{c} \cdot \frac{1}{2}\left(\frac{\sqrt{x^{2}-1}}{x}+\tan ^{-1} \sqrt{x^{2}-1}\right)+C \)
D \( -\frac{1}{2}\left(\frac{\sqrt{x^{2}-1}}{x^{2}}+\tan ^{-1} \sqrt{x^{2}-1}\right)+C \)
Subject: Maths
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows \( R s 200 \) for the
first day, \( \boldsymbol{R} \boldsymbol{s} \) 250 for the second day
Rs 300 for the third day, etc. the penalty
for each succeeding day being \( R s 50 \)
more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by
30 days?
Subject: Chemistry
Write the electronic configuration of
Sr \( ^{2+} \) in absence of Aufbau Principle.
\( \mathbf{A} \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{5} 4 d^{1} \)
B. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{3} 4 d^{3} \)
C \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{6} \)
D. None of these
Subject: Maths
If \( A \) and \( B \) mutually exclusive events associated with a random experiment such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \)
then find \( \boldsymbol{P}(\boldsymbol{A} \cap \overline{\boldsymbol{B}}) \)
Subject: Maths
Solve for \( \boldsymbol{x}: \cos ^{-1}\left(\frac{\boldsymbol{x}^{2}-\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{1}}\right)+ \)
\( \frac{\mathbf{1}}{\mathbf{2}} \tan ^{-1} \frac{\mathbf{2} \boldsymbol{x}}{\mathbf{1}-\boldsymbol{x}^{2}}=\frac{\mathbf{2} \boldsymbol{\pi}}{\mathbf{3}} \)
Subject: Physics
Assertion
Specific heat of any substance remains constant at all temperatures.
Reason
It is given by \( \boldsymbol{S}=\frac{\mathbf{1}}{\boldsymbol{m}} \cdot \frac{\boldsymbol{d} \boldsymbol{Q}}{\boldsymbol{d T}} \)
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: Physics
A proton when accelerated through a potential difference of \( V \) volt has a wavelength \( \lambda \) associated with it. An \( \alpha \)
particle in order to have the same
wavelength \( \lambda \) must be accelerated
through a p.d. of
A. \( \vee / 8 \) volt
B. V/4 volt
c. v volt
D. 2v volt
Subject: Maths
\( A B C D \) is a rectangle with \( A(-1,2) \) \( B(3,7) \) and \( A B: B C=4: 3 . \) If \( P \) is
the centre of the rectangle then the distance of \( P \) from each corner is equal
to
A \( \cdot \frac{\sqrt{41}}{2} \)
B. \( \frac{3 \sqrt{41}}{4} \)
c. \( \frac{2 \sqrt{41}}{3} \)
D. \( \frac{5 \sqrt{41}}{8} \)
Subject: Physics
A particle of mass \( 0.3 \mathrm{kg} \) is subjected to a force \( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \) with \( \mathbf{k}=15 \mathrm{N} / \mathrm{m} . \) What
will be its initial acceleration if it is
released from a point \( x=20 \mathrm{cm} ? \)
Subject: Physics
Balmer gives an equation for wavelength of visible radiation of \( \mathrm{H} \) spectrum as \( \lambda=\frac{k n^{2}}{n^{2}-4} . \) The value of
in terms of Rydberg's constant R is
\( A \cdot R \)
B. 4R
c. \( \frac{R}{4} \)
D. \( \frac{4}{R} \)
Subject: Maths
The table below gives the distance, \( d \)
feet, the cart was from a reference point
at 1 second intervals while it moves
from \( t=0 \) seconds to \( t=5 \) seconds.
\[
\begin{array}{cccccc}
t & 0 & 1 & 2 & 3 & 4 \\
d & 14 & 20 & 26 & 32 & 38 \\
88 & & & & \\
& & & & \\
& 20 & 26 & 32 & 38 & 38 & 3
\end{array}
\]
Find the correct relationship between \( d \)
and \( t \)
A. \( d=t+14 \)
B. \( d=6 t+8 \)
c. \( d=6 t+14 \)
D. \( d=14 t+6 \)
E \( . d=34 t \)
Subject: Maths
The following table shows the number of students and the time they utilized daily for their studies. Find the mean
time spent by students for their studies by direct method.
\( \begin{array}{lllll}\text { Time } & \mathbf{0}- & \mathbf{2}- & \mathbf{4}- & \mathbf{6}- \\ \text { (hrs.) } & \mathbf{2} & \mathbf{4} & \mathbf{6} & \mathbf{8}\end{array} \)
No. of
12
students
A. 4 hrs
B. 5 hrs
c. 4.36 hrs
D. 5.36 hrs
Subject: Physics
If \( \boldsymbol{A}=\boldsymbol{B}=\mathbf{1}, \) then in terms of Boolean
algebra the value of \( \boldsymbol{A} . \boldsymbol{B}+\boldsymbol{A} \) is not
equal to
\( \mathbf{A} \cdot B \cdot A+B \)
в. \( B+A \)
\( c . B \)
D. \( \bar{A} . B \)