AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
By selling a product for Rs. 100 how much profit was earned?
(1) \( 20 \% \) profit would have been earned if
it had been sold for Rs. 90 .
(II) The profit was one-third of the cost price
A. Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
B. Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
c. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D. EACH statement ALONE is sufficient
Subject: Maths
The differential equation of the family of straight lines which passes through the origin is
A \( \cdot y=x \frac{d y}{d x} \)
в. \( y+x \frac{d y}{d x}=0 \)
c. \( _{x+y} \frac{d y}{d x}=0 \)
D. \( \frac{d y}{d x}=m \)
Subject: Physics
toppr
Q Type your question
magnet, carrying magnetic effect, electricity, the magnitude of current deflection increases, eastwards,
southwards.
Oersted was the first to put forth the direct relation between \( _{\text {thend }} \) and
magnetism. He conducted several experiments to determine the of a current wire
The following describes the Oersted experiment conducted to establish that
a current carrying wire acts as a

A long straight wire is connected to an external battery and an electric current is passed through it. When a magnetic needle is placed below the wire such
that the wire is parallel to the axis of the
magnetic needle and the current flows in the south to north direction, a
deflection in the needle is observed. It is
observed that the north pole of the needle is deflected westwards and as
the \( _{\text {一一一一一一一 }} \) is increased, the
deflection, \( _{\text {一一一一一一一 }} \) till the north pole
of the needle turns towards exact west.
t is also observed that if instead of
placing the magnetic needle below the wire, if it was placed above the wire, the
north pole of the magnetic needle is deflected
Subject: Physics
To determine the Young's modulus of a wire, the formula is \( Y=\frac{F}{A}, \frac{L}{\triangle l} ; \) where
\( \boldsymbol{L}= \)length\( , \boldsymbol{A}=\operatorname{area~of~cross-section~} \)
of the wire, \( \triangle \boldsymbol{L}= \) Change in length of the wire when stretched with a force \( F \)
The conversion factor to change it from CGS to MKS system is
A . 1
B. 10
c. \( 0 . \)
D. 0.01
Subject: Chemistry
Arrange the following compound in decreasing order of rate of electrophilic aromatic substitution reaction.
\( (\mathbf{I I}) \)
\( (\mathrm{III}) \)
\( A \cdot(\mid)>(|| \mid)>(||)>(\mid V) \)
B. \( (\| I)>(|D>(\mid I)>(\mid V) \)
\( c \cdot(1)>(11)>(111)>(1 v) \)
Subject: Physics
The work function of a substance is
4.0eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately
A . \( 5400 A^{\circ} \)
в. \( 4000 A^{\circ} \)
c. \( 3100 A^{\circ} \)
D. 2200A \( ^{\text {0 }} \)
Subject: Chemistry
Assertion
Solids in finely divided state act as
good adsorbents
Reason
Adsorption is a surface phenomenon.
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
A ship of mass \( 3 \times 10^{7} \) kg, initially at
rest, is pulled by a force of \( 5 \times 10^{4} N \)
through a distance of 3 m. Assuming
that the resistance due to water is
negligible, the speed of the ship is
A \( .1 .5 m / s \)
в. \( 60 \mathrm{m} / \mathrm{s} \)
c. \( 0.1 m / s \)
D. \( 5 m / s \)
Subject: Chemistry
The number of oxygen atoms in 0.50 mole
of \( K H S O_{4} \) is :
A \( .1 .2 \times 10^{23} \)
B . \( 2.4 \times 10^{23} \)
c. \( 3.0 \times 10^{23} \)
D . \( 1.2 \times 10^{24} \)
E \( .2 .4 \times 10^{24} \)
Subject: Maths
The value of \( \tan \alpha+2 \tan (2 \alpha)+ \)
\( 4 \tan (4 \alpha)+\ldots+2^{n-1} \tan \left(2^{n-1} \alpha\right)+ \)
\( 2^{n} \cot \left(2^{n} \alpha\right) \) is
A \( \cdot \cot \left(2^{n} \alpha\right) \)
B \( \cdot 2^{n} \tan \left(2^{n} \alpha\right) \)
\( c \)
D. \( \cot \alpha \)
Subject: Chemistry
Which compound is obtain on
hydrolysis of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{6}} \) ?
A. \( X e O_{3} \)
в. \( X e O_{2} F_{2} \)
c. \( X e O F_{3} \)
D. \( X e O_{3} F \)
Subject: Maths
reflexive, symmetric and transitive.
This question has multiple correct options
\( A \cdot R_{3}=\{(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)\} \)
\( \mathbf{B} \cdot R_{3}= \)
\( \{(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1),(4, \)
\( \mathbf{c} \cdot R_{3}=\{(1,1),(2,2),(3,3),(4,4)\} \)
D. none of these
Subject: Physics
A circular disc of radius \( \mathrm{R} \) is removed
from a bigger circular disc of radius \( 2 \mathrm{R} \) such that the circumference of the
discs coincide. The centre of mass of
the new disc is \( \alpha R \) from the centre of
the bigger disc. The value of \( \alpha \) is
A. \( 1 / 3 \)
B. \( 1 / 2 \)
c. \( 1 / 6 \)
D. \( 1 / 4 \)
Subject: Chemistry
\( ^{87} \) Rb undergoes \( \beta \) -decay \( \left(t_{1 / 2}=4.7 \times\right. \) \( \left.10^{10} \text { year }\right) \) to form \( ^{87} \) Sr. An analysis of
the rock sample shows relative number of \( ^{87} \mathrm{Sr} \) and \( ^{87} \) Rb atoms \( 0.052: 1 . \) If all
the \( ^{87} \mathrm{Sr} \) is formed from \( \beta \) -decay of \( ^{87} \mathrm{Rb} \)
The age of the rock is :
A . \( \left[2.21 \times 10^{9} \text { year }\right] \)
B . \( \left[3.43 \times 10^{9} \text { year }\right] \)
C . \( \left[4.13 \times 10^{9} \text { year }\right] \)
D. none of these
Subject: Maths
\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{2} & \mathbf{0} & \mathbf{1} \\ \mathbf{5} & \mathbf{3} & \mathbf{8}\end{array}\right|, \) write the minor of the
elements \( a_{22} \)
Subject: Chemistry
Statement-I: Alkali metals dissolve in
liquid ammonia to give blue solutions Statement-II: Alkali metals in liquid ammonia give solvated species of the
type \( \left[M\left(N H_{3}\right)_{n}\right]^{+}(M=\text { alkali metals }) \)
A. Statement-l is true; Statement-ll is true; Statement-I is the correct explanation for Statement-
B. Statement-l is true; Statement-ll is true; Statement-1 is not the correct explanation for statement-
c. Statement-l is true; Statement-ll is false
D. Statement-I is false; Statement-II is true
Subject: Maths
\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}g(x) \cdot \cos \frac{1}{x} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right. \)
where \( g(x) \) is an even function
differentiable at \( x=0, \) passing through
the origin. Then \( \boldsymbol{f}^{\prime}(\mathbf{0}) \)
A. is equal to 1
B. is equal to 0
c. is equal to 2
D. does not exist
Subject: Physics
If a magnet of pole strength \( \mathrm{m} \) is divided into four parts such that the length and width of each part is half that of the
initial one, then the pole strength of each
part will be
\( A \cdot m / 4 \)
B. m/2
\( c \cdot m / 8 \)
D. \( 4 \mathrm{m} \)
Subject: Chemistry
Compound X has the molecular formula
\( \boldsymbol{C}_{3} \boldsymbol{H}_{\boldsymbol{6}} \boldsymbol{O}_{3} \)
Heating X under reflux with acidified
\( K_{2} C r_{2} O_{7} \) forms \( H O_{2} C C O C O_{2} H \)
Reacting \( X \) with \( N a B H_{4} \) forms
\( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}(\boldsymbol{O} \boldsymbol{H}) \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{H} \)
What is a possible structural formula
for \( X ? \)
1. \( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{2} \boldsymbol{H} \)
2. \( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C H}(\boldsymbol{O} \boldsymbol{H}) \boldsymbol{C H O} \)
3. \( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C O C H}_{2} \boldsymbol{O H} \)
A. 1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct
Subject: Maths
If \( A+B+C=\pi \) then which of the
following are true?
i. \( \tan 3 A+\tan 3 B+\tan 3 C= \)
\( \tan 3 A \tan 3 B \tan 3 C \)
ii. \( \cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}= \)
\( \cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} \)
A. only 1st statement is true
B. only 2nd statement is true
c. both statements are true
D. both statements are false
Subject: Physics
Two gases, carbon monoxide \( (C O) \) and
nitrogen \( \left(N_{2}\right) \) at the same temperature
have kinetic energies \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2} \)
respectively. Then
A \( . E_{1}=E_{2} \)
в. \( E_{1}>E_{2} \)
\( \mathbf{c} \cdot E_{1}<E_{2} \)
D. \( E_{1} \) and \( E_{2} \) cannot be compared
Subject: Chemistry
Assertion: The volume of 1 mole of an
ideal gas at 1 bar pressure at \( 25^{0} C \) is \( 24.78 \mathrm{L} \)
Reason: 1 bar \( =0.987 \) atm
A. Both Assertion and reason are correct and reason is correct explanation of Assertion
B. Both assertion and reason are correct but reason is not correct explanation of assertion
c. Assertion is correct but reason is incorrect
D. Assertion is incorrect but reason is correct
Subject: Maths
If \( f(x)=\frac{1-\tan x}{1-\sqrt{2} \sin x}, \) for \( x \neq \)
\( \frac{\pi}{4} \) is continous \( \boldsymbol{a t} \quad \boldsymbol{x}= \)
\( \frac{\pi}{4}, \quad \) find \( \quad f\left(\frac{\pi}{4}\right) \)
Subject: Physics
The displacement x of a particle varies with time \( t \) as \( x=a e^{-\alpha t}+b e^{\beta t}, \) Where \( a \)
b, \( \alpha \) and \( \beta \) are positive constants. The
velocity of the particle will:
A. Be independent of \( \alpha \) and \( \beta \)
B. Go on increasing with time
c. Drop to zero when \( \alpha=\beta \)
D. Go on decreasing with time
Subject: Maths
The graph of any Quadratic polynomial is such that the chord joining the points \( x=a \) and \( x=b \) is parallel to the
tangent line at \( \boldsymbol{x}=? \)
A. A.M. of \( a \) and \( b \)
B. G.M. of \( a \) and \( b \)
C . H.M. of \( a \) and \( b \)
D. AGP
Subject: Chemistry
The formation of the oxide ion \( O^{2-}(g) \)
requires first an exothermic and then an endothermic step as shown below.
\( \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{e}^{-} \rightarrow \boldsymbol{O}^{-}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{0}= \)
\( -142 k J m o l^{-1} \)
\( \boldsymbol{O}^{-}(\boldsymbol{g})+\boldsymbol{e}^{-} \rightarrow \boldsymbol{O}^{2-}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{0}= \)
\( 844 k J m o l^{-1} \)
The correct statement is?
A. Oxygen is more electronegative
B. \( O^{-} \) ion has comparatively larger size than oxygen atom
\( \mathrm{c} \cdot O^{-} \) ion will tend to resist the addition of another
electron
D. Oxygen has high electron affinity
Subject: Physics
Red and blue beams of light is incident
on a prism as shown in the figure.
Which of the following statements is
true?
A. The blue light bends more than the red light as the blue light has a longer wavelength.
B. The red light bends more than the blue light as the red light has a longer wavelength.
C. The blue light bends more than the red light as the blue light has a shorter wavelength.
D. The red light bends more than the blue light as the red light has a shorter wavelength.
E. The red and blue lights bend by the same amount as all colors of light refract equally.
Subject: Biology
Find the correct answers about
glomerular filtrate
1. Formed continuouslythrough ultrafiltration of blood
2. Lipid free fluid collects in the lumen
of Bowmans capsule
3. Protein free fluid collects in the
lumen of Bowmans capsule
4. Formed by process of selective reabsorption.
A .1,2,3 correct
B. 1,2 correct
c. \( 2,4, \) correct
D. 1,3 correct
Subject: Maths
Find the complement of the angle :
\( \frac{1}{4} \) of a right angle
\( \mathbf{A} \cdot 67 \cdot 5^{\circ} \)
B \( .57 \cdot 5^{\circ} \)
\( \mathbf{c} \cdot 37 \cdot 5^{\circ} \)
D. none of the above
Subject: Physics
A sound wave of wavelength \( 32 \mathrm{cm} \) enters the tube as shown in the figure.
Then the smallest radius \( r \) so that a
maximum of sound is heard at
detector is :
\( A \cdot 7 \mathrm{cm} \)
в. 14 ст
\( c \cdot 21 c m \)
D. 28 ст
Subject: Chemistry
A sample of \( C a C O_{3} \) has \( \mathrm{Ca} 40 \%, \mathrm{C} 12 \% \)
\( 048 \% \) by mass. If the law of constant proportions is true then find the mass
of \( \mathrm{Ca} \) in \( 5 \mathrm{g} \) of \( \mathrm{CaCO}_{3} \) obtained from
another source.
Subject: Maths
A conic passes through the point (2,4) and is such that the segment of any of its tangents at any point contained between the coordinate axes is bisected
at the point of tangency. Then equation of auxiliary circle of the conic is
A \( \cdot x^{2}+y^{2}=16 \)
B . \( x^{2}+y^{2}=25 \)
c. \( x^{2}+y^{2}=4 \sqrt{2} \)
D. none of these
Subject: Maths
Solution of the differential equation \( \left(x^{2}+y^{3}\right)\left(2 x^{2} d x+3 y d y\right)=12 x d x+ \)
\( 18 y^{2} d y \) is
A \( \cdot \frac{2}{3} x^{3}+\frac{3}{2} y^{2}=6 \ln \left(x^{2}+y^{3}\right)+c \)
в. \( x^{2}+y^{3}=9 \ln \left(x^{2}+y^{3}\right)+c \)
c. \( \frac{2}{3} x^{3}+\frac{3}{2} y^{2}=6 \ln \left(x^{3}+y^{2}\right)+c \)
D. \( x^{3}+y^{2}=6 \ln \left(x^{2}+y^{3}\right)+c \)
Subject: Chemistry
The Henry's law constant for helium gas
in water at \( 30^{\circ} \mathrm{C} \) is \( 3.70 \times 10^{-4} \mathrm{M} / \mathrm{atm} \)
When the partial pressure of helium above a sample of water is 0.650 at \( \mathrm{m} \) the concentration of helium in the water
is
M.
A. \( 5.69 \times 10^{-4} \)
В. \( 1.76 \times 10^{3} \)
c. 1.30
D. \( 2.41 \times 10^{-4} \)
E . \( 3.70 \times 10^{-4} \)
Subject: Chemistry
The standard electrode potential of Cu/Cu
\( ^{+2} \) electrode is \( 0.336 . \) It corresponds to
the reaction:
A. \( C u \rightarrow C u^{+2}+2 e^{-} \)
В \( \cdot \frac{1}{2} C u^{+2}+e^{-} \rightarrow \frac{1}{2} C u \)
\( \mathrm{c} \cdot \mathrm{Cu}^{+2}+2 e^{-} \rightarrow \mathrm{Cu} \)
D. \( 2 C u^{+} \rightarrow C u+2 e^{-} \)
Subject: Chemistry
The rate of formation of \( S O_{3} \) in the
following reaction \( 2 S O_{2}+O_{2} \rightarrow 2 S O_{3} \)
is \( 10 g \) sec \( ^{-1} \). The rate of disappearance
of \( \boldsymbol{O}_{2} \) will be:
A. \( 5 g \) sec \( ^{-1} \)
B. \( 100 g \) sec \( ^{-1} \)
\( \mathrm{c} .20 \mathrm{g} \) sec
D. \( 2 g \) sec \( ^{-1} \)
Subject: Physics
Find out the frequency of orange light
whose wavelength is \( 6 \times 10^{-7} \) m. The
speed of light is \( 3 \times 10^{8} m / s \)
A \( \cdot 2 \times 10^{15} \mathrm{Hz} \)
B . \( 2 \times 10^{-15} \mathrm{Hz} \)
c. \( 5 \times 10^{14} H z \)
D. \( 5 \times 10^{-14} \mathrm{Hz} \)
E . \( 2 \times 10^{14} H z \)
Subject: Chemistry
Which statements are correct about the
following compounds?

Bicyclo[2.2.1] hept-l-ene Bicyclo[4.4.0] dec-1-ene
This question has multiple correct options
A . (I) is not isolable because trans-cyclohexane is too strained.
B. (II) is isolable because trans-unit can be bridged by six C atoms. Eight-membered and larger rings can have a trans-substituted (C=C)in the ring
C. (III) is not isolable, exocyclic double bonds (double bond at the bridgehead) are unstable because of high strain (due to ring and double bond joining the two rings)
D. (IV) is isolablem, although there is a double bond at a bridgehead (joining two rings) but one of the bridgeheads has no C atom and bridgehead C atoms can flatten without ring strain.
Subject: Chemistry
\( \Delta H_{f}=-98.2 \mathrm{K} . \mathrm{Cal} / \mathrm{mole} \)
\( \boldsymbol{S}_{N a}=36 \mathrm{K.Cal} / \mathrm{mole} \)
\( \boldsymbol{I}_{N a}=118.5 \mathrm{K} . \mathrm{Cal} / \mathrm{mole} \)
\( \frac{1}{2} D_{C l_{2}}=29 \mathrm{K} . \mathrm{Cal} / \mathrm{mole} \)
\( \boldsymbol{U}_{N a C l}=-184.2 \mathrm{K} . \mathrm{Cal} / \mathrm{mole} \)
From the data given below for \( N a C l \)
the electron affinity of chlorine \( \left[-\boldsymbol{E}_{\boldsymbol{a}}\right] \) is:
A . -97.5 K.cal/ mole
B. -108 K.cal/mole
c. -75 K.cal/mole
D. -128 K.cal/mole
Subject: Maths
The area of an isosceles triangle, each of whose equal sides is \( 13 \mathrm{cm} \) and
whose base is \( 24 c m \) is
\( \mathbf{A} \cdot 60 \mathrm{cm}^{2} \)
B. \( 55 \mathrm{cm}^{2} \)
c. \( 50 \mathrm{cm}^{2} \)
D. \( 40 \mathrm{cm}^{2} \)
Subject: Maths
The value of k for which the quadratic
equation, \( k x^{2}+1=k x+3 x-11 x^{2} \)
has real and equal roots are
A. \( -11 .-3 \)
3 \( 3.31-31-3 \)
B. 5,7
c. 5,-7
D. None of these
Subject: Biology
In a given area, insects live by making burrows in the bark of a tree. These
insects are fed upon by a population of birds in the same area. The most correct
explanation for the increase in the beak size of the bird population is
A. Increased fitness of the birds, leading to speciation
B. Decreased fitness of the insects, allowing the birds to catch them more easily
c. Increased fitness of large-beaked birds, leading to evolution
D. Decreased fitness of small-beaked birds, leading to speciation
E. Random mutation and genetic recombination
Subject: Chemistry
10ml of \( N H_{4} C l, 20 \mathrm{ml} \) of \( N / 2 H_{2} S O_{4} \)
and \( 30 \mathrm{ml} \) of \( N / 3 H N O_{3} \) are mixed together and volume made to one litre.
Normality of resulting solution is:
A. \( 30 N / 100 \)
в. \( N / 10 \)
c. \( N / 20 \)
D. \( N / 40 \)
Subject: Physics
The dimensional formula for magnetic flux is
\( \mathbf{A} \cdot\left[M L^{2} T^{-2} A^{-1}\right] \)
B \( \cdot\left[M L^{3} T^{-4} A^{-2}\right] \)
c. \( \left[M^{0} L^{-2} T^{-2} A^{-2}\right] \)
D \( \cdot\left[M L^{2} T^{-1} A^{2}\right] \)
Subject: Physics
The focal length of a thin biconvex lens is \( 20 \mathrm{cm} . \) when an object is moved from a distance of \( 25 \mathrm{cm} \) in front of it to 50
\( \mathrm{cm}, \) the magnification of its image
changes from \( \boldsymbol{m}_{25} \) to \( \boldsymbol{m}_{50} . \) The ratio of
\( \boldsymbol{m}_{25} \) to \( \boldsymbol{m}_{50} \) is :
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8
Subject: Chemistry
Assertion
\( B F_{3} \) is a weaker Lewis acid than \( B C l_{3} \)
Reason

The planar \( B F_{3} \) molecule is stabilised
to a greater extent than \( B C l_{3} \) by \( B-X \)
\( \pi \) -bonding.
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: Maths
Solve the systems of equations:
\( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}=\boldsymbol{c} ; \boldsymbol{b} \boldsymbol{x}-\boldsymbol{a} \boldsymbol{y}=\boldsymbol{c} \)
A \( \cdot \frac{c(a-b)}{a^{2}+b^{2}},-\frac{c(a+b)}{a^{2}+b^{2}} \)
в. \( \frac{c(a-b)}{a^{2}+b^{2}}, \frac{c(a+b)}{a^{2}+b^{2}} \)
c. \( \frac{c(a-b)}{a^{2}+b^{2}}, \frac{c(a+b)}{a^{2}-b^{2}} \)
D. \( \frac{c(a+b)}{a^{2}+b^{2}},-\frac{c(a-b)}{a^{2}+b^{2}} \)
Subject: Maths
The values of \( a \) and \( b \) such that the
function defined as \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{ll}a x^{2}-b, & |x|<1 \\ -1 /|x|, & |x| \geq 1\end{array} \) is differentiable are \right.
\( ? \)
A \( \cdot a=1, b=-1 \)
1
B. \( a=\frac{1}{2}, b=\frac{1}{2} \)
c. \( _{a=\frac{1}{2}, b=\frac{3}{2}} \)
D. \( a=\frac{3}{2}, b=\frac{3}{2} \)
Subject: Physics
A vehicle moving on a straight road sounds a whistle of frequency \( 256 \mathrm{Hz} \) while nearing a hill with a velocity 10 ms \( -1 . \) The number of beats per second
observed by a person travelling in the vehicle is:
\( \left(V=330 m s^{-1}\right) \)
A. zero
B. 10
\( c \cdot 14 \)
D. 16
Subject: Maths
If \( a \) and \( b \) are the roots of \( x^{2}-p x+q= \)
\( 0, \) then \( a^{2}+b^{2} \) is
A \( \cdot p^{2}+q^{2} \)
B . \( p^{2}+2 q \)
c. \( p^{2}-q^{2} \)
D. \( p^{2}-2 q \)
Subject: Chemistry
Phosphine \( \left[\boldsymbol{P} \boldsymbol{H}_{3}\right] \) decomposes to
produce \( P_{4}(g) \) and \( H_{2}(g) . \) What would be the change in volume when 100 ml
of \( \boldsymbol{P} \boldsymbol{H}_{3}(\boldsymbol{g}) \) is completely decomposed \( ? \)
\( \mathbf{A} \cdot 50 m l \)
в. \( 500 \mathrm{ml} \)
c. \( 75 \mathrm{ml} \)
D. \( 250 \mathrm{ml} \)
Subject: Physics
A charged \( 30 \mu \mathrm{F} \) capacitor is connected to a \( 27 \mathrm{mH} \) inductor. The
angular frequency of free oscillations of the circuit is
A \( \cdot 1.1 \times 10^{3} r a d s^{-1} \)
B. \( 2.1 \times 10^{3} r a d s^{-1} \)
c. \( 3.1 \times 10^{3} r a d s^{-1} \)
D. \( 4.1 \times 10^{3} r a d s^{-1} \)
Subject: Maths
The work done by the force \( \overrightarrow{\boldsymbol{F}}=\mathbf{2} \hat{\mathbf{i}}- \)
\( \hat{j}-\hat{\mathbf{k}} \) in moung an object along the vector \( 3 \hat{i}+2 j-5 \hat{k} \) is
A. -9 units
B. 9 units
c. -15 units
D. None of these
Subject: Maths
Equation(s) or the straight line(s),
inclined at \( 30^{\circ} \) to the \( x \) -axis such that
the length of its (each of their) line segment(s) between the coordinate axes is 10 units is/are
This question has multiple correct options
A. \( x+\sqrt{3} y+5 \sqrt{3}=0 \)
в. \( x-\sqrt{3} y+5 \sqrt{3}=0 \)
c. \( x+\sqrt{3} y-5 \sqrt{3}=0 \)
D. \( x-\sqrt{3} y-5 \sqrt{3}=0 \)
Subject: Physics
In a potentiometer experiment, the balancing length of a cell is \( 560 \mathrm{cm} \) When an external resistance of \( 10 \Omega \) is
connected in parallel to the cell, the balancing length changes by \( 60 \mathrm{cm} . \) The internal resistance of a cell is
A . \( 1.4 \Omega \)
в. \( 1.6 \Omega \)
c. \( 0.12 \Omega \)
D. \( 1.2 \Omega \)
Subject: Physics
A jet plane having a wing-span of \( 25 \mathrm{m} \) is travelling horizontally towards east with a speed of \( 3600 \mathrm{km} / \) hour. If the Earth's magnetic field at the location is
\( 4 \times 10^{-4} \mathrm{T} \) and the angle of dip is \( 30^{\circ} \)
then, the potential difference between
the ends of the wing is?
A. \( 4 \mathrm{v} \)
B. 5 v
\( c \cdot 2 v \)
D. 2.5
Subject: Chemistry
Arrange the following compounds in increasing order of solubility in water:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{N} \boldsymbol{H}, \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \)
Subject: Maths
If \( f(x)=\ln \frac{1+x}{1-x} \) and \( g(x)=\frac{3 x+x^{3}}{1+3 x^{2}} \)
then \( \boldsymbol{f}[\boldsymbol{g}(\boldsymbol{x})] \) equals.
A. \( f(x) \)
B . \( [f(x)]^{3} \)
\( \mathbf{c} \cdot 3 f(x) \)
D. \( f(x)^{2} \)
Subject: Maths
In a non-leap year the probability of
getting 53 Sundays or 53 Tuesdays or
53 Thursdays is.
A \( \cdot \frac{1}{7} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{3}{7} \)
D. \( \frac{4}{7} \)
Subject: Physics
A lift is moving up with acceleration a. \( A \) person inside the lift throws the ball
upwards with a velocity u relative to hand. What is the time of flight of the ball?
A \( \cdot \frac{2 u}{(g+a)} \)
в. \( \frac{u}{(g+a)} \)
c. \( \frac{u}{2(g+a)} \)
D. \( \frac{2 u}{(g-a)} \)
Subject: Chemistry
Chlorine gas is passed in a medium which has \( p H=12 . \) Two products \( A \)
and \( B \) are formed with water. Now \( p H \) of
medium is changed to 1 by acidifying it Again a product \( C \) is formed with water
It is found that \( A \) is strong oxidising
agent Answer the following questions carefully: Oxidation of \( C l \) in compound \( \boldsymbol{B} \) is:
A. -1
в. +3
\( c .+5 \)
D. +7
Subject: Maths
For \( \mathbf{3} \times \mathbf{3} \) matrices \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) if \( |\boldsymbol{B}|=\mathbf{1} \)
and \( A=2 B \) then find \( |A| \)
A .
B. 4
\( c \cdot 2 \)
D. 8
Subject: Physics
An electron enters a chamber in which a
uniform magnetic field is present as
shown.
An electric feild of appropriate magnitude is also applied so that the electron travels undeviated without any
change in its speed through the
chamber. We are ignoring gravity. Then,
the direction of the electric field is
A. Opposite to the direction of the magnetic field.
B. Opposite to the direction of the electron's motion.
C. Normal to the plane of the paper and coming out of the plane of the paper.
D. Normal to the plane of the paper and into the plane of the paper.