AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The length of the shortest face diagonal of a cuboid of dimensions \( 5 \mathrm{cm} \times 4 \mathrm{cm} \times \)
\( 3 \mathrm{cm} \) is \( _{--}-_{-}(\text {in } \mathrm{cm}) \)
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.
Subject: Physics
A block B of mass \( 4 \mathrm{kg} \) is placed on a
rough horizontal plane. A time dependent horizontal plane. A time
dependent horizontal force \( \boldsymbol{f}=\boldsymbol{k} \boldsymbol{t}^{2} \) acts
on the block, \( k=2 N / s^{2} . \) The frictional
force between the block and the plane at
\( \boldsymbol{t}=2 \sec \) is \( \boldsymbol{\mu}=\mathbf{0 . 2} \)
A . 4 N
B. 8N
c. 12 N
D. zero
Subject: Maths
A point on the parabola \( y^{2}=18 x \) at
which the ordinate increase at twice the
rate of the abscissa is
\( \mathbf{A} \cdot(9 / 8,9 / 2) \)
в. (2,-4)
c. \( (-9 / 8,9 / 2) \)
D. (2,4)
Subject: Maths
If \( \frac{x+y-8}{2}=\frac{x+2 y-14}{3}=\frac{3 x-y}{4} \)
then the values of \( x \) and \( y \) is
A \( . x=1, y=3 \)
B. \( x=5, y=2 \)
c. \( x=3, y=3 \)
D. \( x=2, y=6 \)
Subject: Maths
Find the midpoint of the segment connecting the points \( (a,-b) \) and
\( (5 a, 7 b) \)
A \( \cdot(3 a,-3 b) \)
в. \( (2 a,-3 b) \)
c. \( (3 a,-4 b) \)
D. \( (-2 a, 4 b) \)
E. none of these
Subject: Physics
A concave mirror produces 2 times magnified real image of an object
placed at \( 5 \mathrm{cm} \) in front of it. Where is
image located?
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( -5 c m \)
c. \( -10 c m \)
D. \( 2.5 \mathrm{cm} \)
Subject: Maths
Let the function \( f \) be defined by \( f(x)= \) \( 5 x-2 a, \) where \( a \) is a constant. If
\( \boldsymbol{f}(\mathbf{1 0})+\boldsymbol{f}(\mathbf{5})=\mathbf{5 5}, \) what is the value of
\( \boldsymbol{a} ? \)
A . -
B. 0
\( c \cdot 5 \)
D. 10
E. 20
Subject: Maths
If \( l=\lim _{x \rightarrow 0} \frac{\sin a x-\sin x-x}{x^{3}} \) exists, and
is finite, then the values of ' \( l \) ' and 'a' are
respectively equal to
A \( \cdot \frac{7}{6}, 2 \)
в. \( -\frac{4}{3}, 2 \)
c. \( -\frac{7}{6},-2 \)
D. \( -\frac{7}{6}, 2 \)
Subject: Maths
Consider the points \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}+\boldsymbol{c}) \)
\( B(b, c+a), \) and \( C(c, a+b) \) be the
vertices of \( \triangle \mathrm{ABC} \). The area of \( \triangle \mathrm{ABC} \) is:
A \( \cdot 2\left(a^{2}+b^{2}+c^{2}\right) \)
B . \( a^{2}+b^{2}+c^{2} \)
c. \( 2(a b+b c+c a) \)
D. None of these
Subject: Physics
The distance between the ends of the
wings of an airplane is \( 50 m \). It is flying in a horizontal plane at a speed of \( 360 K m / \)hour. The vertical component
of earth's magnetic field at that place is \( 2.0 \times 10^{-4} W b / m^{2}, \) then the potential
difference induced between the ends of
the wings will be
A . \( 0.1 v o l t \)
B. \( 1.0 v o l t \)
c. \( 0.2 v o l t \)
D. \( 0.01 v \) volt
Subject: Chemistry
The radius of \( H e^{+} \) ion is \( x \dot{A} \) in its
ground state. The radius of \( L i^{2+} \) ion in the ground state \( (\boldsymbol{A}) \) is:
A \( \cdot \frac{2 x}{3} \)
в. \( \frac{3 x}{2} \)
c. \( \frac{2}{3 x} \)
D. \( \frac{3}{2 x} \)
Subject: Physics
Three resistances of \( 8 \Omega, 16 \Omega \) and \( 4 \Omega \)
are joined in parallel. If each resistor is
rated \( 0.5 W, \) what is the maximum
voltage that may be applied to the combination?
A . \( 1 V \)
в. \( 1.5 V \)
\( c \cdot 2 V \)
D. 2.5V
Subject: Maths
The number of ways in which 20
different white balls and 19 different
black balls be arranged in a row. So that no two balls of the same colour come
together is
A \( \cdot 20 !^{2} 1 P_{19} \)
B . \( 20 ! \times 19 ! \)
c. \( (20 !)^{2} \)
D. \( (21) !^{120} C_{19} \)
Subject: Maths
\( A B C D \) is a trapezium with \( A B / / D C \) A line parallel to \( A C \) intersects \( A B \) at
point \( M \) and \( B C \) at point \( N . \) Prove that area of \( \triangle A D M= \) area of \( \triangle \)
\( A C N \)
Subject: Physics
A moving coil ammeter requires a potential difference of \( 0.4 V \) across it for
full scale deflection. It has fixed shunt
resistance of 0.01 ohm with a coil
circuit resistance of \( \boldsymbol{R}=\mathbf{1} \boldsymbol{k} \) ohm. The
value of shunt required to give full scale deflection when the total current is \( 10 A \)
is equal to
A. 0.02 ohm
B. 0.04 ohm
c. 0.05 ohm
D. 0.06 ohm
Subject: Physics
A object of mass \( 40 k g \) having velocity
\( 4 m / s \) collides with another object \( m= \)
\( 60 k g \) having velocity \( 2 m / s . \) The
collision is perfectly inelastic. The loss in energy is
A . \( 110 J \)
в. \( 48 J \)
\( \mathrm{c} .3925 \)
D. \( 440 J \)
Subject: Maths
Let a relation \( \boldsymbol{R} \) be defined by \( \boldsymbol{R}= \)
\( \{(4,5),(1,4),(4,6),(7,6),(3,7)\} . \) The
relation \( R^{-1} \circ R \) is given by
A \( \cdot\{(1,1),(4,4),(7,4),(4,7),(7,7)\} \)
B - \{(1,1),(4,4),(4,7),(7,4),(7,7),(3,3)\}
c. \{(1,5),(1,6),(3,6)\}
D. None of these
Subject: Physics
A uniform of rod of length \( l \) is placed
symmetrically on two walls as shown in the figure. The rod is in equilibrium. If
\( N_{1} \) and \( N_{2} \) are the normal forces
exerted by the walls on the rod, then :
A. \( N_{1}>N_{2} \)
B. \( N_{1}<N_{2} \)
\( \mathbf{c} \cdot N_{1}=N_{2} \)
D. \( N_{1} \) and \( N_{2} \) would be in the vertical directions \( N_{1} N_{2} \)
Subject: Chemistry
Sodium hydroxide is manufacture by the electrolysis of brine solution. The
reaction by-products are:
A. \( C l_{2} \) and \( H_{2} \)
B. \( C l_{2} \) and \( \mathrm{Na}-\mathrm{Hg} \)
c. \( C l_{2} \) and \( \mathrm{NaC} \)
D. \( C l_{2} \) and \( O_{2} \)
Subject: Physics
A rope ladder of length L is attached to a balloon of mass \( \mathrm{M} \). As the man of mass
m climbs the ladder into the balloon
basket, the balloon comes down by a
vertical distance s. Then the increase in
potential energy of man divided by the increase in potential energy of balloon
is
A \( \cdot \frac{L-s}{s} \)
B. \( \underline{L} \)
c. \( \frac{s}{L-s} \)
D. L- s
Subject: Physics
The value due regard to significant figure \( 4.0 \times 10^{-4}-2.5 \times 10^{-6} \)
A \( \cdot 4.0 \times 10^{-4} \)
B. \( 3.975 \times 10^{-4} \)
c. \( 3.9 \times 10^{-4} \)
D. none of the above
Subject: Maths
Let \( \boldsymbol{R} \) be a relation in \( \boldsymbol{N} \) defined by \( \boldsymbol{R}= \)
\( \{(x, y): x+2 y=8, x, y \epsilon N\} . \) The
range of \( \boldsymbol{R} \) is
A \( \cdot\{2,4,6\} \)
в. \{1,2,3\}
\( \mathbf{c} \cdot\{1,2,3,4,5,6\} \)
D. None of these
Subject: Physics
The focal length of a symmetric biconvex lens is \( 20 \mathrm{cm} \). If the refractive
index of the material of the prism is 1.5
the radius of curvature of one of two
surfaces is
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
c. \( 40 \mathrm{cm} \)
D. 80 cm
Subject: Chemistry
\( \mathrm{CO}_{2} \) is gas, while \( \mathrm{SiO}_{2} \) is solid
because:
\( \mathbf{A} \cdot C O_{2} \) is a linear molecule, while \( S i O_{2} \) is angular.
B. van der Waals' forces are very strong in \( S i O_{2} \)
\( \mathrm{C} \cdot \mathrm{CO}_{2} \) is covalent, while \( \mathrm{SiO}_{2} \) is ionic.
D. \( S i \) cannot form stable bonds with \( O \), hence \( S i \) has to form a \( 3 D \) lattice
Subject: Physics
Needles \( N_{1}, N_{2} \) and \( N_{3} \) are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A
magnet when brought close to them will
A. attract all three of them.
B. attract \( \mathrm{N}_{1} \) and \( \mathrm{N}_{2} \) strongly but repel \( \mathrm{N}_{3} \)
C. attract \( \mathrm{N}_{1} \) strongly, \( \mathrm{N}_{2} \) weakly and repel \( \mathrm{N}_{3} \) weakly
D. attract \( \mathrm{N}_{1} \) strongly, but repel \( \mathrm{N}_{2} \) and \( \mathrm{N}_{3} \) weakly
Subject: Chemistry
Which of the following statements is
correct?
rhis question has multiple correct options
A. Dipole moment
B. Stability of free radical
c. Basic strength: \( C H_{3} O^{\ominus}>\stackrel{\delta}{O} H>R \) S
D. Basic and nucleophilic strength: \( I^{\ominus}>B r^{\ominus}>C l^{\ominus} \) >
\( F^{c} \)
Subject: Biology
Pick the correct match.
A. Helicase
(i) To join nucleotides on DNA
B. Gyrase
(ii) To open DNA
C. Primase
(iii) Unwind DNA
D. DNA
(iv) For RNA printing polymerase III
A. A-ii, B-iii, C-iv, D-i
B. A-i, B-ii, C-iii, D-iv
c. A-ii, B-iv, C-iii, D-i
D. A-iv, B-iii, C-i, D-ii
Subject: Maths
If \( \vec{a} \) and \( \vec{b} \) are non-collinear vectors and
\( \boldsymbol{A}=(\boldsymbol{p}+\mathbf{4} \boldsymbol{q}) \boldsymbol{a}+(\boldsymbol{2} \boldsymbol{p}+\boldsymbol{q}+\mathbf{1}) \boldsymbol{b} \)
\( \boldsymbol{B}=(-\mathbf{2} \boldsymbol{p}+\boldsymbol{q}+\mathbf{2}) \boldsymbol{a}+(\mathbf{2} \boldsymbol{p}-\boldsymbol{3} \boldsymbol{q}-\mathbf{1}) \boldsymbol{b} \)
then determine \( p \) and \( q, \) so that \( 3 A= \)
\( 2 B \)
A. \( p=1 \) and \( q=-0.3 \)
B. \( p=-1 \) and \( q=1.1 \)
C. \( p=2 \) and \( q=-1 \)
D. \( p=-2 \) and \( q=1.8 \)
Subject: Chemistry
Which of the following is maximum
stable?
A . Conjugated alkadiene \( \left(C H_{2}=C H-C H=C H_{2}\right) \)
B. Isolated alkadiene \( \left(C H_{2}=C H-C H_{2}-C H=C H_{2}\right) \)
c. cumulated alkadiene \( \left(C H_{2}=C=C H_{2}\right) \)
D. All are equal
Subject: Maths
\( \int \frac{2 x-1}{2 x^{2}+2 x+1} d x= \)
\( \mathbf{A} \cdot \frac{1}{2} \ln \left|2 x^{2}+2 x+1\right|+2 \tan ^{-1}(2 x+1)+c \)
B \( \cdot-\frac{1}{2} \ln \left|2 x^{2}+2 x+1\right|-2 \tan ^{-1}(2 x+1)+c \)
C \( -\frac{1}{2} \ln \left|2 x^{2}+2 x+1\right|+2 \tan ^{-1}(2 x+1)+c \)
D \( \cdot \frac{1}{2} \ln \left|2 x^{2}+2 x+1\right|-2 \tan ^{-1}(2 x+1)+c \)
Subject: Maths
Consider the determinant \( \Delta= \) \( \left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3}\end{array}\right| \)
\( M_{i j}= \) Minor of the element of \( i^{t h} \) row \( \& \) \( j^{t h} \) column \( C_{i j}= \) Cofactor of element of \( i^{t h} \) row \( \& \) \( j^{t h} \) column
\( a_{2} \cdot C_{12}+b_{2} \cdot C_{22}+c_{2} \cdot C_{32} \) is equal to
A.
B. \( \Delta \)
\( c \cdot 2 \Delta \)
D. \( \Delta^{2} \)
Subject: Maths
For any two sets \( A \) and \( B \), show that the
following statements are equivalent.
(i) \( \boldsymbol{A} \subset \boldsymbol{B} \)
(ii) \( \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{\phi} \)
(iii) \( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{B} \)
(iv) \( \boldsymbol{A} \cap \boldsymbol{B}=\boldsymbol{A} \)
Subject: Physics
A rectangular tube of uniform cross section has three liquids of densities
\( \rho_{1}, \rho_{2} \) and \( \rho_{3} . \) Each liquid column has
length I equal to length of sides of the equilateral triangle. Find the length \( x \) of
the liquid of density \( \rho_{1} \) in the horizontal
limb of the tube, if the triangular tube is kept in the vertical plane
Subject: Physics
\( A B \) and \( C D \) are two parallel conductors
kept \( 1 \mathrm{m} \) apart and connected by a resistance \( R \) of \( 6 \Omega \) as shown in figure.
They are placed in a magnetic field \( B= \)
\( 3 \times 10^{-2} \mathrm{T} \) which is perpendicular to the
plane of the conductors and directed
into the paper. A wire MN is placed over
\( A B \) and \( C D \) and then made to slide with
velocity \( 2 m s^{-1} . \) (Neglect the resistance of \( A B, C D, \) and \( M N \) ). Calculate the induced current flowing through the resistor R.
Subject: Physics
A particle starts from rest with constant acceleration for 20 sec. If it travels a
distance \( y_{1} \) in the first 10 sec and a
distance \( y_{2} \) in the next 10 sec then?
A \( \cdot y_{2}=2 y_{1} \)
в. \( y_{2}=3 y_{1} \)
\( \mathbf{c} \cdot y_{2}=4 y_{1} \)
D. \( y_{2}=5 y_{1} \)
Subject: Maths
In a certain shop, which stocks four types of caps, there are \( \frac{1}{3} \) as many red caps as blue and \( \frac{1}{2} \) as many green caps
as red caps. There are equal number of
green caps and yellow caps. If there are
42 blue caps, then what percent of the total caps in the shop are blue?
A. \( 70 \% \)
в. \( 28 \% \)
c. \( 60 \% \)
D. \( 14 \% \)
Subject: Biology
Assertion
Bacteria and Protista do not have
circulatory system.
Reason
These organisms live in moist and
watery environment.
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 man walks 12 steps in Northern direction and turns left to walk 5 steps, then returns to the initial point by the
shortest path. Find the distance
travelled given each step is \( 0.3 \mathrm{m} \)
A . \( 5.1 \mathrm{m} \)
B. \( 9 \mathrm{m} \)
\( c \cdot o m \)
D. 3.6 m
Subject: Chemistry
The tarnishing of silver ornaments in the atmosphere is due to the formation
of:
\( \mathbf{A} \cdot A g_{2} O, A g_{2} S \)
B. \( A g N O_{3}, A g_{2} S \)
c. \( A g O H, A g_{2} C O_{3} \)
D. \( A g \)
Subject: Physics
Charge \( Q, 2 Q \) and \( 4 Q \) are uniformly
distributed in three dielectric solid
spheres 1,2 and 3 of \( \operatorname{radii} R / 2, R \) and
\( 2 R \) respectively, as shown in figure. If
magnitudes of the electric field at point
\( P \) at a distance \( R \) from the centre of
spheres 1,2 and 3 are \( E_{1}, E_{2} \) and \( E_{3} \)
respectively, then
\( \mathbf{A} \cdot E_{1}>E_{2}>E_{3} \)
B \( \cdot E_{3}>E_{1}>E_{2} \)
\( \mathbf{c} \cdot E_{2}>E_{1}>E_{3} \)
\( \mathbf{D} \cdot E_{3}>E_{2}>E_{1} \)
Subject: Maths
Sum of 4 numbers in GP is \( 60 . \) And the
AM of first and last no. is 18 find the
first term and common difference of the
\( \mathrm{GP} \)
This question has multiple correct options
A \( . a=4, r=2 \)
B. \( a=32, r=\frac{1}{2} \)
c. \( a=3, r=1 \)
D. \( a=6, r=3 \)
Subject: Maths
Coefficient of \( \boldsymbol{x}^{\mathbf{5 0}} \)
\( (x>0), \) in \( (1+x)^{1000}+2 x(1+ \)
\( \boldsymbol{x})^{999}+\mathbf{3} \boldsymbol{x}^{2}(\mathbf{1}+\boldsymbol{x})^{998}+\ldots \) is
A. \( 1000 C_{50} \)
B. \( ^{1000} C_{50} \)
c. \( ^{1002} 250 \)
D. \( ^{1000} C_{49} \)
Subject: Chemistry
Which of the following shapes of \( S F_{4} \) is
more stable and why?
(i)
A. (i) Lone pair at axial position is stable
B. (ii) Lone pair at equatorial position is stable
c. Both are equally stable due to \( l p \) -bp repulsion
D. Both are unstable since \( S F_{4} \) has tetrahedral shape
Subject: Chemistry
Draw the Lewis structures for the
following molecules and ions:
\( \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{S} \boldsymbol{i} \boldsymbol{C l}_{4}, \boldsymbol{B} \boldsymbol{e} \boldsymbol{F}_{2}, \boldsymbol{C} \boldsymbol{O}_{3}^{2-} \) and
HCOOH
Subject: Physics
A resistance \( (\boldsymbol{R})=12 \Omega ; \) inductance
\( (L)=2 \) henry and capacitive reactance \( C=5 m F \) are connected in series to an
ac generator, then:
A. at resonance, the circuit impedance is zero
B. at resonance, the circuit impedance is \( 12 \Omega \)
c. the resonance frequency of the circuit is \( 1 / 2 \pi \)
D. at resonance, the inductive reactance is less than the capacitive reactance
Subject: Physics
A hollow cylindrical box of length 1 m
and area of cross-section \( 25 \mathrm{cm}^{2} \) is
placed in a three dimensional coordinate system as shown in the
figure. The electric field in the region is \( \operatorname{given} \) by \( \vec{E}=50 x \hat{i}, \) where \( E \) is in \( N C^{-1} \)
and \( x \) is in metres.
Find
(i) Net flux through the cylinder
(ii) Charge enclosed by the cylinder.
Subject: Chemistry
What is the molarity of \( 0.2 \mathrm{N} \mathrm{Na}_{2} \mathrm{CO}_{3} \)
solution?
A. \( 0.1 \mathrm{m} \)
B. O M
c. \( 0.4 \mathrm{M} \)
D. 0.2 M
Subject: Chemistry
Assertion
Copper is used to make hot water tanks
and not steel (an alloy of iron)
Reason
Copper does not react with cold water, hot water or steam. However, iron reacts
with steam. If the hot water tanks are
made of steel (an alloy of iron), then iron would react vigorously with the steam formed from hot water.
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
Dashrath and Naresh are friends
,Naresh is 2 years younger than Dashrath.If the sum of their age is 56
years, find their present age.
A. Naresh=27 years, Dashrath =29 years
B. Naresh=37 years, Dashrath =29 years
c. Naresh=27 years, Dashrath =39 years
D. Naresh=47 years, Dashrath =29 years
Subject: Chemistry
Energy barrier between staggered and eclipsed ethane is :
A. \( 6.0 \mathrm{kcal} / \mathrm{mole} \)
B. 3.0 kcal/mole
c. \( 2.0 \mathrm{kcal} / \mathrm{mol} \)
D. \( 4.0 \mathrm{cal} / \mathrm{mole} \)
Subject: Physics
The angular frequency of an AC source is 10 radian/sec. The reactance of \( 1 \mu F \) capacitor will be
A \( \cdot 10^{4} \Omega \)
B . \( 10^{2} \Omega \)
\( \mathbf{c} \cdot 10^{1} \Omega \)
D. \( 10^{5} \Omega \)
Subject: Chemistry
The heat capacity for aluminium, iron,
and for zinc are \( 0.89 \mathrm{J} . \mathrm{g}^{-10} \mathrm{C}^{-1}, 0.45 \mathrm{J} \)
\( \boldsymbol{g}^{-10} \boldsymbol{C}^{-1}, 0.39 \mathrm{J} . \boldsymbol{g}^{-10} \boldsymbol{C}^{-1} \) respectively. If
\( 100 \mathrm{J} \) of heat energy was added to \( 10.0 \mathrm{g} \) sample of each of the metals, which of the following would be true?
A. \( A l \) would have the largest temperature increase
B. Fe would have the largest temperature increase
c. \( Z n \) would have the largest temperature increase
D. \( F e \) and \( Z n \) would have the same temperature increase
E. All three metals would have the same temperature increase.
Subject: Maths
Given that \( A+B+C=0 . \) Out of three
vectors, two are equal in magnitude and the magnitude of third vector is \( \sqrt{2} \) times that of either of the two having equal magnitude. Then, the angles between the vectors are given by.
A . \( 30^{\circ}, 60^{\circ}, 90^{\circ} \)
в. \( 45^{\circ}, 45^{\circ} \), \( 90^{\circ} \)
c. \( 45^{\circ}, 60^{\circ}, 90^{\circ} \)
D. \( 90^{\circ}, 135^{\circ}, 135^{\circ} \)
Subject: Physics
If \( i_{1}=3 \sin \omega t \) and \( i_{2}=4 \cos \omega t, \) then \( i_{3} \)
is
\( \mathbf{A} \cdot 5 \sin \left(\omega t+53^{\circ}\right) \)
\( \mathbf{B} \cdot 5 \sin \left(\omega t+37^{\circ}\right) \)
\( \mathbf{c} \cdot 5 \sin \left(\omega t+45^{\circ}\right) \)
\( \mathbf{D} \cdot 5 \cos \left(\omega t+53^{\circ}\right. \)
Subject: Chemistry
Oxidation number of three elements
\( A, B \) and \( C \) are +2,+3 and -2 respectively. What is the formula of the compound formed from these three elements?
A. \( A_{2} B C_{3} \)
в. \( A B_{2} C_{4} \)
\( \mathrm{c} \cdot A_{3} B C_{3} \)
D. \( A_{2} B_{2} C_{4} \)
Subject: Maths
Assertion(A): \( \cos ^{-1} x \) and \( \tan ^{-1} x \) are
positive for all positive real values of \( x \)
in their domain.
Reason(R): The domain of \( f(x)= \)
\( \cos ^{-1} x+\tan ^{-1} x \) is [-1,1]
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not correct explanation of
c. A is true but R is false
D. A is false but R is true
Subject: Maths
Yesterday's closing prices of 2420 different stocks listed on a certain
stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price than yesterday?
A .484
в. 726
\( c .1100 \)
D. 1320
E . 1694
Subject: Chemistry
The decomposition of certain mass of
\( \mathrm{CaCO}_{3} \) gave \( 11.2 \mathrm{dm}^{3} \) of \( \mathrm{CO}_{2} \) gas at
STP. The mass of KOH required to completely neutralise the gas is :
A. \( 56 g \)
в. 28 \( g \)
c. 42 g
D. 20
Subject: Chemistry
Calculate the partial pressure of \( B \) at equilibrium in the following equilibrium. \( \boldsymbol{A}(s) \rightleftharpoons \boldsymbol{B}(\boldsymbol{g})+\mathbf{2} \boldsymbol{C}(\boldsymbol{g}) ; \quad \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{3} 2 \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}^{3} \)
Subject: Physics
A particle is dropped on Earth from
height \( \mathbf{R}(\text { radius of Earth }) \) and it
bounces back to a height \( \mathbf{R} / \mathbf{2} \)
coefficient of restitution for collision is
(ignore air resistance and rotation of Earth)
\( A \cdot \frac{2}{3} \)
B. \( \sqrt{\frac{2}{3}} \)
\( c \cdot \sqrt{\frac{1}{3}} \)
D. \( \sqrt{\frac{1}{2}} \)
Subject: Physics
The reactance of inductance at \( 10^{4} H z \)
is \( 10^{4} \Omega . \) Its reactance at \( 2 \times 10^{4} H z \) will
be:
A \( \cdot 10^{4} \Omega \)
B \( \cdot 2 \times 10^{4} \Omega \)
\( \mathbf{c} \cdot 3 \times 10^{4} \Omega \)
D. \( 4 \times 10^{4} \Omega \)
Subject: Chemistry
An organic compound \( (X) \) with
molecular formula \( C_{3} H_{6} O \) is not
readily oxidised. On reduction, it gives
\( C_{3} H_{8} O(Y) \) which react with \( H B r \) to
give a bromide \( (Z) \) which is converted
to Grignard's reagent. Grignard's
reagent reacts with \( (X) \) to give 2,3
dimethylbutan-2-ol. \( (X),(Y) \) and \( (Z) \) respectively are:
A \( \cdot C H_{3} C O C H_{3}, C H_{3} C H_{2} C H_{2} O H, C H_{3} C H(B r) C H_{3} \)
B. \( C H_{3} C H_{2} C H O, C H_{3} C H=C H_{2}, C H_{3} C H(B r) C H_{3} \)
c. \( C H_{3} C O C H_{3}, C H_{3} C H(O H) C H_{3}, C H_{3} C H(B r) C H_{3} \)
D. \( C H_{3} C H_{2} C H O, C H_{3} C H_{2} C H_{2} O H, C H_{3} C H_{2} C H_{2} B r \)
Subject: Chemistry
Which of the following element is represented by electronic configuration \( \mathbf{1} \boldsymbol{s}^{2} \mathbf{2} \boldsymbol{s}^{2} \mathbf{2} \boldsymbol{p}_{\boldsymbol{x}}^{1} \mathbf{2} \boldsymbol{p}_{\boldsymbol{y}}^{\mathbf{1}} \boldsymbol{2} \boldsymbol{p}_{z}^{1} \)
A. Nitrogen
B. Oxygen
c. Fluorine
D. sulphur
Subject: Maths
Calculate the average income of workers using direct method.
\begin{tabular}{|l|l|l|l|l|l|}
\hline Workers & 4 & 6 & 8 & 10 & 12 \\
\hline Weekly income & 300 & 500 & 700 & 800 & 900 \\
\hline
\end{tabular}
A. 10 rupees
B. 9 rupees
c. 8 rupees
D. 7 rupees
Subject: Physics
The Young's modulus of the material of a wire of length L and radius r is \( Y \)
newton per \( m^{2} \). If the length of the wire
is reduced to \( L / 2 \) and the radius to \( r / 2 \) then its Young's modulus will be.
A. \( Y / 2 \)
B.
\( c .2 Y \)
D. \( 4 Y \)
Subject: Physics
A ball of mass \( 2 k g \) is connected to a
string of length \( 1 m \) and made to move
in a horizontal circle on a smooth
frictionless table with a constant speed
of \( 2 m / s . \) The other end of the string is connected to a fixed peg on the table. Find the magnitude of the average impulse exerted by the string on the
ball in half a revolution:
A. 0
в. \( 8 N-s \)
c. \( 4 N-s \)
D. \( 2 \sqrt{2} N-s \)
Subject: Physics
The temperature coefficient of a wire is \( 0.00125^{0} C^{-1} . \) At \( 300 \mathrm{K} \) its resistance is
one ohm.The resistance of the wire will
be \( 2 \Omega \) at
\( \mathbf{A} \cdot \) 1154 \( \mathbf{K} \)
B. \( 1100 \mathrm{k} \)
\( c \cdot 1400 k \)
D. 1127 K
Subject: Physics
Three capacitors of capacitance 1.0,2.0
and \( 5.0 \mu F \) are connected in series to a
\( 10 V \) source. The potential difference
across the \( 2.0 \mu F \) capacitor is
A \( \cdot \frac{100}{17} \)
в. \( \frac{20}{17} v \)
c. \( \frac{50}{17} v \)
D. \( 10 V \)
Subject: Physics
A concave lens of focal length produces an image equal to \( \frac{1}{n} \) of the size of the object, the distance of the object from the lens is:
A \( \cdot(n-1) f \)
в. \( (n+1) f \)
c. \( \left(\frac{n-1}{n}\right) f \)
D. \( \left(\frac{n+1}{n}\right) f \)