AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Four chargers \( q_{1}=-0.02 \mu C, q_{2}= \)
\( +0.04 \mu C, q_{3}=+0.02 \mu C, \) and \( q_{4}= \)
\( -0.04 \mu C \) are at the four corners of a
square of side \( 9 \mathrm{cm} \). Then the potential at
the centre of the square is :
A . \( 9 V \)
в. \( 3 V \)
\( \mathrm{c} .1 .2 \mathrm{V} \)
D. Zero
Subject: Chemistry
Statement \( 1: \Delta H \) for combustion of
ethane and ethyne are -341.1 and -310.0
kcal respectively.

Statement 2: Ethyne is the better gas
welder.
A. Statement 1 is True, statement 2 is True, statement 2 is a correct explanation of statement 1.
B. Statement 1 is True, statement 2 is True, statement 2 is
not a correct explanation of statement 1
C. Statement 1 is true, Statement 2 is False.
D. Statement 1 is False, Statement 2 is True.
Subject: Chemistry
In the following reaction:
\( \boldsymbol{K}_{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}+\boldsymbol{C l}_{2} \longrightarrow 2 \boldsymbol{K} \boldsymbol{C l}+ \)
\( 2 K M n O_{4} \)
2 moles \( C l_{2} \) and 2 moles \( K_{2} M n O_{4} \)
form \( \ldots \ldots . . . . . . \) moles \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
Fill in the above blank.
Subject: Maths
Suppose \( x, y, z \) are positive integers \( (\neq \)
1) if \( \Delta=\operatorname{det} \) of \( \left[\begin{array}{ccc}1 & \log _{x} y & \log _{x} z \\ \log _{y} x & 1 & \log _{y} z \\ \sin (x+y) & -\cos (x+y) & \sin ^{2} z\end{array}\right] \)
then \( \Delta \) is 1 ) Independent of \( x \) II) Independent of \( y \) IIII Independent of \( z \) The which of the above statement is
are correct
A. only land II
D. all the three I,II,III
Subject: Chemistry
An element R belongs to IVA(14) group and 3rd period in the periodic table. Arrange the elements that are placed below 'R' in increasing order of atomic size.
A. \( G e>S n>P b \)
B. \( A s>S b>B i \)
c. \( G e<S n<P b \)
D. \( A s<S b<B i \)
Subject: Physics
The driver of a train moving with a constant speed \( v_{1} \) along a straight track sights another train at a distance
d ahead of him on the same track
moving in the same direction with a
constant speed \( v_{2} . \) He at once applies
the brakes and gives his train a
constant retardation \( \mathrm{f} \). There will be a
collision of the trains if:
A \( \cdot v_{1}>v_{2} \) and \( \frac{\left(v_{1}-v_{2}\right)^{2}}{2 f}<d \)
в. \( _{v_{1}}<v_{2} \) and \( \frac{\left(v_{1}+v_{2}\right)^{2}}{2 f}>d \)
c. \( _{v_{1}>v_{2} \text { and }} \frac{\left(v_{1}-v_{2}\right)^{2}}{2 f}>d \)
D \( v_{1}>v_{2} \) and \( \frac{\left(v_{1}^{2}-v_{2}^{2}\right)}{2 f}>d \)
Subject: Physics
Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.60 seconds, then how far will he fall?
\( (\operatorname{in} m) \)
A . \( 33.1 m \)
в. \( 33 m \)
\( c .3 .1 m \)
D. \( 63.1 m \)
Subject: Maths
Let \( A B C \) be an equilateral triangle
inscribed in circle \( 0 . \) M is a point on arc
BC. Lines AM, BM and CM are drawn.
Then \( \overline{\boldsymbol{A} \boldsymbol{M}} \) is:
A. equal to \( \overline{B M}+\overline{C M} \)
B. Less than \( \overline{B M}+\overline{C M} \)
c. greater than \( \overline{B M}+\overline{C M} \)
D. equal, less than, or greater than \( \overline{B M}+\overline{C M} \) depending upon the pos
Subject: Maths
If the origin is the centroid of the
triangle \( P Q R \) with vertices \( \boldsymbol{P}(\mathbf{2} \boldsymbol{a}, \mathbf{2}, \mathbf{6}), \boldsymbol{Q}(-\mathbf{4}, \mathbf{3} \boldsymbol{b},-\mathbf{1 0}) \) and
\( \boldsymbol{R}(\mathbf{8}, \mathbf{1 4}, \mathbf{2 c}), \) then find the values of \( \boldsymbol{a}, \boldsymbol{b} \)
and \( c \)
Subject: Maths
If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{3 \times 3} \) is a square matrix so
that \( a_{i j}=i^{2}-j^{2}, \) then \( A \) is a
A. unit matrix
B. symmetric marix
c. skew symmetric matrix
D. orthogonal matrix
Subject: Chemistry
The orbital diagram which violates the aufbau principle' is:
\( A \)
\( 2 s \) \( \boldsymbol{2 p} \) \( \uparrow \downarrow \) \( \uparrow \downarrow \quad \uparrow \)
в. \( 2 s \) 一 2 \( \uparrow \) \( \uparrow \downarrow \quad \uparrow \quad \uparrow \)
\( c \)
\( 2 s \) \( 2 p \) \( \uparrow \downarrow \) \( \uparrow \quad \uparrow \quad \uparrow \)
D. \( 2 s \)
\( \prec 2 p \) Why \( \uparrow \downarrow \) \( \uparrow \downarrow|\uparrow \downarrow| \uparrow \)
Subject: Chemistry
Examine the following structures:
Which of the following statement is
correct:
\( (A) C H_{3}-C-O H \)
\( (B) C H_{3}-C-N H_{2} \)
(A) \( \mathrm{CH}_{3}-\frac{\mathrm{CH}_{3}}{\mathrm{C}}-\mathrm{OH} \)
(B) \( \mathbf{C H}_{3}-\underbrace{\mathbf{C H}_{\mathbf{3}}}_{\mathbf{C H}_{\mathbf{3}}}-\mathbf{N H}_{\mathbf{2}} \)
A. \( A \) is tertiary alcohol while \( B \) is tertiary amine
B. \( A \) is primary alcohol while \( B \) is primary amine
C. \( A \) is tertiary alcohol while \( B \) is primary amine
D. \( A \) is primary alcohol while \( B \) is tertiary amine
Subject: Maths
Let \( A, G \) and \( H \) are the A.M., G.M. and H.M. respectively of two unequal positive
integers. Then the equation \( A x^{2}- \) \( |G| x+\frac{H}{4}=0 \) has
This question has multiple correct options
A. Both roots as fractions
B. At least one root which is a negative fraction.
c. Exactly one positive root
D. At least one root which is an integer
E. None of these.
Subject: Maths
Derivative of \( (x+3)^{2}(x+4)^{3}(x+5)^{4} \)
\( \boldsymbol{w} \cdot \boldsymbol{r} \cdot \operatorname{to} \boldsymbol{x} \) is
A \( \cdot(x+3)(x+4)(x+5)^{2}\left(9 x^{2}+70 x+133\right) \)
B \cdot \( (x+3)(x+4)^{2}(x+5)^{3}\left(9 x^{2}+70 x+133\right) \)
C \( \cdot(x+3)(x+4)^{2}(x+5)\left(9 x^{2}-70 x-133\right) \)
D. none of these
Subject: Physics
A body of mass \( m \) slides down an incline and reaches the bottom with a
velocity \( v \). If the same mass was in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been:
\( A \)
B . \( (\sqrt{2}) v \)
c. \( \frac{v}{\sqrt{2}} \)
D. \( (\sqrt{\frac{2}{5}}) \)
Subject: Physics
The magnetic flux linked with a coil,in webers,is given by the equations \( \phi= \)
\( 3 t^{2}+4 t+9 . \) Then the magnitude of
induced e. \( \mathrm{m} \). \( \mathrm{f} \). at \( \mathrm{t}=2 \) second will be:
A . 2 volt
B. 4 volt
c. 8 volt
D. 16 volt
Subject: Chemistry
Allanite wanted to prepare (R) 2-
Methoxy butane using Williamson ether synthesis. He remembered that
Williamson synthesis involves a \( \boldsymbol{S}_{N} \mathbf{2} \)
displacement, which takes place with inversion of configuration. He ordered a
bottle of (S) 2-Butanol for his chiral
starting material. He also
remembered that the \( S_{N} 2 \) goes best on
primary halides so he made methyl
halide and sodium
(S) 2 -butoxide after
warming these reagents together he obtained an excellent yield of 2 -Methoxy
butane.
2-Methoxy butane \( \frac{\text {anhydrous} \boldsymbol{H} \boldsymbol{I}}{\rightarrow} \)
products
Products formed are:
\( \mathbf{A} \cdot H_{3} C-I+C H_{3}-(O H) C H-C H_{2}-C H_{3} \)
B. \( C H_{3}-I+C H_{3}-C H_{2}-C H_{2}-C H_{3} \)
\( \mathbf{c} \cdot C H_{3}-O H+C H_{3}-C H(I)-C H_{2}-C H_{3} \)
D. \( C H_{3}-C H_{2}-I+C H_{3}-(O H) C H-C H_{3} \)
Subject: Chemistry
Assertion
The metal sulphides and carbonates are
converted to metal oxides in the
process of extraction of metal from
them.
Reason
Easier to obtain metal from its oxide, as
compared from its sulphides and
carbonates.
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
Water is leaking from a conical funne
at the rate of \( 5 \mathrm{cm}^{5} / \) sec. If the radius of
base of funnel is \( 10 \mathrm{cm} \) and the altitude
is \( 20 \mathrm{cm} . \) Find the rate at which water
level is dropping when it is \( 10 \mathrm{cm} \) from
the top.
Subject: Chemistry
An open vessel containing air is heated from \( 300 \mathrm{K} \) to \( 400 \mathrm{K} \). The fraction of air
originally present which goes out of it is:
A. \( 3 / 4 \)
B. \( 1 / 4 \)
\( c \cdot 2 / 3 \)
D. 1/8
Subject: Chemistry
Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. Rhombic sulphur is stable at room temperature.
B. Monoclinic sulphur is stable at room temperature.
C. Both rhombic and monoclinic sulphur has the molecular formula \( S_{8} \)
D. Both rhombic and monoclinic sulphur are soluble in \( C S_{2} \)
Subject: Maths
The value of
\( \lim _{x \rightarrow \infty} \frac{\cot ^{-1}\left(x^{-a} \log _{a} x\right)}{\sec ^{-1}\left(a^{x} \log _{x} a\right)},(a>1) \) is equal
to
A . 1
B.
c. \( \pi / 2 \)
D. does not exist
Subject: Physics
A particle moves along the \( x \) -axis
according to the equation \( \boldsymbol{x}= \)
10 \( \sin 3(t) \). The amplitudes and
frequencies of component SHMs are
A \( \cdot \) amplitude \( \frac{30}{4}, \frac{10}{4} ; \) frequencies \( \frac{3}{2}, \frac{1}{2} \)
B. amplitude \( \frac{30}{4}, \frac{10}{4} ; \) frequencies \( \frac{1}{2}, \frac{3}{2} \)
C. amplitude 10,\( 10 ; \) frequencies \( \frac{1}{2}, \frac{1}{2} \)
D. amplitude \( \frac{30}{4}, 10 ; \) frequencies \( \frac{3}{2}, 2 \)
Subject: Physics
A hydraullic press contains \( 250 l i t \) of oil Find the decrease in volume of the oil
when its pressure increases to \( 10^{7} \) Pa.
The bulk modulus of the oil is \( \boldsymbol{K}=\mathbf{5} \times \)
\( \mathbf{1 0}^{\mathbf{5}} \boldsymbol{P a} \)
A. \( -0.8 l i t \)
B. - \( 0.5 l i t \)
c. \( -0.6 l i \)
D. - \( 0.9 l i t \)
Subject: Physics
Two coils \( A \) and \( B \) are placed parallel to
each other at a very small distance apart. The coil \( A \) is connected to an A.C.
supply. \( G \) is a very sensitive
galvanometer.When the key \( K \) is closed.
A. A constant deflection will be observed in the galvanometer for a \( 50 \mathrm{Hz} \) supply
B. Small variations will be observed in the galvanometer due to applied voltage of \( 50 \mathrm{Hz} \)
c. oscillations in the galvanometer may be observed when the input a.c. voltage has a frequency of 1 to \( 2 H z \)
D. No variations will be observed in the galvanometer even when the input a.c. voltage has a frequency of 1 to \( 2 \mathrm{H} \)
Subject: Physics
Two equal charges ' \( q \) ' of opposite sign are separated by a small distance 'd'. The electric intensity ' \( E \) ' at a point on the straight line passing through the two charges at a very large distance ' \( r \) ' from the midpoint of two charges is :
A \( \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{q d}{r^{2}} \)
В. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q d}{r^{2}} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q d}{r^{3}} \)
D. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q d}{r^{3}} \)
Subject: Maths
If three vectors along coordinate axis represents the adjacent sides of a cube of length b, then the unit vector along its diagonal passing through the origin will be
\( \mathbf{A} \cdot \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{2}} \)
B. \( \frac{i+3+\hat{k}}{\sqrt{36}} \)
\( \mathbf{c} \cdot \hat{i}+\hat{j}+\hat{k} \)
D. \( \frac{i+\vec{j}+\hat{k}}{\sqrt{3}} \)
Subject: Chemistry
(a) Complete the following chemical equations:
(i) \( \underset{(\text {hot and conc.})}{N a O H}+C l_{2} \rightarrow \)
(ii) \( \boldsymbol{X}_{e} \boldsymbol{F}_{4}+\boldsymbol{O}_{2} \boldsymbol{F}_{2} \rightarrow \)
(b) Draw the structures of the following molecules:
(i) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7} \)
(iii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4} \)
Subject: Maths
Find the absolute maximum and the
absolute minimum values of the
following function in the given intervals. \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\mathbf{2}) \sqrt{\boldsymbol{x}-\mathbf{1}} \) in \( [\mathbf{1}, \boldsymbol{9}] \)
Subject: Physics
A large cylindrical vessel contains water to a height of \( 10 m \). It is found that
the thrust acting on the curved surface is equal to that at the bottom. if
atmospheric pressure can support a water column of \( 10 m, \) the radius of the
vessel is :
A . \( 10 m \)
B. \( 15 \mathrm{m} \)
\( c .5 m \)
D. 25
Subject: Physics
Four pieces of wooden sticks \( P, Q, R \) and S are placed along the length of \( 15 \mathrm{cm} \) long scale as shown in figure. What is the average length of these sticks?
A . 2.0
B. 2.5 \( \mathrm{cm} \)
c. \( 2.6 \mathrm{cm} \)
D. 2.9 \( \mathrm{cm} \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{I} \rightarrow \boldsymbol{I}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+1, \) then \( \boldsymbol{f} \) is
A. one-one but not onto
B. onto but not one-one
c. one-one onto
D. none of these
Subject: Physics
If six persons are at the corners of a regular hexagon of side \( X \) move at a
constant speed \( V . \) Each person
maintains a direction towards the
person at the next corner. The time, the persons will take to meet each other is
A \( \cdot \frac{2 X}{3 V} \)
в. \( \frac{2 X}{V} \)
\( c \cdot \frac{X}{V} \)
D. \( \frac{5 X}{6 V} \)
Subject: Chemistry
The correct increasing order of 10 Dq. value for the given chromium complexes is :
(1) \( \left[\boldsymbol{C r}(\boldsymbol{e n})_{3}\right]^{3+} \)
(2)\( \left[\boldsymbol{C r}(\boldsymbol{o x})_{3}\right]^{3-} \)
(3) \( \left[\boldsymbol{C r} \boldsymbol{F}_{\mathbf{6}}\right]^{3-} \)
(4) \( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \)
A. \( 4<3<1<2 \)
в. \( 3<2<4<1 \)
c. \( 4<3<2<1 \)
D. \( 3<4<1<2 \)
Subject: Maths
ff \( \left(x^{2}+\frac{1}{x}\right)^{n} \) has exactly one middle term which is equal to \( \alpha . x^{3} \) then the
value of \( (\boldsymbol{\alpha}+\boldsymbol{n}) \) is- \( \quad(\boldsymbol{n} \in \boldsymbol{N}) \)
A . 18
B . 21
c. 24
D. 26
Subject: Chemistry
Identify the order in which the spin only magnetic moment (in BM) increases for the following four ions:
(।) \( \boldsymbol{F} \boldsymbol{e}^{2+}(\|) \boldsymbol{T} \boldsymbol{i}^{2+}(\| \boldsymbol{l}) \boldsymbol{C} \boldsymbol{u}^{2+}(\mid V) \boldsymbol{V}^{2+} \)
A \( . I, I I, I V, I I I \)
в. \( I V, I, I I, I I I \)
с. \( I I I, I V, I, I I \)
D. III, II, IV,
Subject: Physics
Assertion
We can live very happily if the friction is
not present in nature.
Reason
Aeroplane shape is stream lined to
reduce the effort of frictional force.
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
Find the solution of system of
equations:
\( -24-8 j=12 k \) and \( 3+\frac{5}{3} k=-\frac{7}{6} j \)
A. (6,-6)
в. (3,0)
c. (0,2)
(年. \( 0,2,2) \)
D. (-4,1)
Subject: Chemistry
The time for half-life period of a certain reacting \( \boldsymbol{A} \rightarrow \) product is an hour. How
much time does it take for its
concentration to come from 0.50 to 0.25
\( \operatorname{mol} L^{-1} \) if it is a zero order reaction?
A . \( 0.25 h \)
B. 1h
\( c \cdot 4 h \)
D. 0.5h
Subject: Physics
At a given instant, four particle having
masses and acceleration as shown in
the figure lie at vertices of a square.
Acceleration of the center of mass of the
system is:
A \( \cdot \frac{1}{5}(\hat{i}+\hat{j}) \)
B \( \cdot \frac{1}{5}(\hat{j}-\hat{i}) \)
c. \( \frac{1}{5}(\hat{i}-\hat{j}) \)
D. \( -\frac{1}{5}(\hat{i}+\hat{j}) \)
Subject: Physics
Two charges \( q_{1} \) and \( q_{2} \) are placed \( 30 c m \)
a part as shown. A third charge \( q_{3} \) is
moved along the circle of radius \( 40 \mathrm{cm} \)
from \( C \) to \( D \). The change in the potential energy of the system is \( \frac{q_{3} K}{4 \pi \epsilon_{0}} \)
Find K?
\( \mathbf{A} \cdot 8 q_{2} \)
B. \( 8 q \)
\( c \cdot 6 q_{2} \)
D. \( 6 q \)
Subject: Chemistry
Which of the following is correct about
\( (A),(B) \) and \( (C) ? \)
A. \( A, B \) and \( C \) are anomers
B. A and C are anomers
\( \mathrm{c} \cdot \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) are metamers
D. None of the above
Subject: Chemistry
Assertion
During covalent bonding the electro negativity difference between two
atoms is greater than 1.7
Reason
Covalent bond is formed by sharing of
electrons between atoms that have
same size
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 short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the
axis of the magnet at \( 14 \mathrm{cm} \) from the
centre of the magnet. The earth's
magnetic field at the place is \( 0.36 \mathrm{G} \) and the angle of dip is zero.What is the
total magnetic field on the normal
bisector of the magnet at the same distance as the null-point (i.e., \( 14 \mathrm{cm} \) )
from the centre of the magnet? (At null points, field due to a magnet is
equal and opposite to the horizontal component of earth's magnetic field.)
Subject: Maths
The value of \( 60^{g} \) in circular measure is
A \( \cdot \frac{\pi^{c}}{10} \)
в. \( \frac{3 \pi^{c}}{10} \)
c. \( \frac{2 \pi^{c}}{5} \)
D. \( \frac{\pi^{c}}{2} \)
Subject: Physics
The displacement x of a particle moving in one dimension under the action of a
constant force is related to time t by the
equation \( t=\sqrt{x}+3, \) where \( x \) is in meter and \( t \) is in second. Find the
displacement of the particle when its velocity is zero.
A. zero
в. \( 12 m \)
\( c .6 m \)
D. 18 т
Subject: Physics
In the above circuit, \( C=\frac{\sqrt{3}}{2} \mu F, R_{2}= \) \( 20 \Omega, L=\frac{\sqrt{3}}{10} H \) and \( R_{1}=10 \Omega . \) Current
\( \operatorname{in} L-R_{1} \) path is \( I_{1} \) and in \( C-R_{2} \) path
it is \( I_{2} \). The voltage of \( A . C \) source is \( \operatorname{given} \operatorname{by} V=200 \sqrt{2} \sin (100 t) \) volts.
The phase difference between \( I_{1} \) and \( I_{2} \)
is
A \( \cdot 30 \)
B . \( 0^{\circ} \)
\( c \cdot 150 \)
D. 60
Subject: Maths
In the figure, ABCD is a parallelogram.
\( \boldsymbol{A} \boldsymbol{E} \perp \boldsymbol{D} \boldsymbol{C}, \boldsymbol{C} \boldsymbol{F} \perp \boldsymbol{A} \boldsymbol{D} . \) If \( \boldsymbol{A} \boldsymbol{B}=\mathbf{1 6} \mathrm{cm} \)
\( A E=8 \mathrm{cm} \)
and \( C F=10 \mathrm{cm} \) then \( A D \) is equal to
\( A \cdot 12 c m \)
B. \( 15 \mathrm{cm} \)
c. \( 12.8 \mathrm{cm} \)
D. \( 15.5 \mathrm{cm} \)
Subject: Chemistry
Assertion(A): Atmosphere plays an important role in maintaining the heat balance on earth.

Reason(R): Atmosphere absorbs a portion of electromagnetic
radiation coming from the sun
and transmits near UV, visible
and near IR radiation.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not correct explanation of Assertion
c. Assertion is true and Reason is false
D. Assertion is false and Reason is true
Subject: Maths
If the two straight lines \( \boldsymbol{y}=\boldsymbol{m}_{1} \boldsymbol{x}+\boldsymbol{c}_{1} \)
and \( y=m_{2} x+c_{2} \) are perpendicular to
each other then \( \boldsymbol{m}_{1} \boldsymbol{m}_{2}= \)
A . -
B.
\( c \cdot 1 / 2 \)
D.
Subject: Maths
If \( 2 x^{2}+x y-3 y^{2}+x+a y-10= \)
\( (2 x+3 y+b)(x-y-2), \) the value of a
and b are
A. 11 and 5
B. 1 and -5
c. -1 and -5
D. -11 and 5
Subject: Maths
In triangle \( A B C, P \) is the mid-point of side BC.A line through P and parallel to CA meets \( A B \) at point \( Q ; \) and a line through \( Q \) meets at \( S . Q S \) parallel to BC
meets median AP at point R. prove that:
(i) \( A P=2 A R \)
(ii) \( \mathrm{BC}=4 \mathrm{QR} \)
Subject: Chemistry
Consider the following statements:
1. Rate of a process is directly proportional to its free energy change.
2. The order of an elementary reaction
step can be determined by examining the stoichiometry.
3. The first order reaction describes
exponential time course. Of these statements:
A. 1,2 and 3 are correct
B. 1 and 2 are correct
\( c .2 \) and 3 are correct
D. 1 and 3 are correct
Subject: Maths
A spherical balloon is being inflated so that its volume increases uniformly at
the rate of \( 40 \mathrm{cm}^{3} / \) min. When \( r=8 \)
then the increase in radius in the next
\( 1 / 2 m i n \) is
A \( .0 .025 \mathrm{cm} \)
B . \( 0.050 \mathrm{cm} \)
c. \( 0.075 \mathrm{cm} \)
D. \( 0.01 \mathrm{cm} \)
Subject: Chemistry
Assertion
\( \boldsymbol{S O}_{3} \) has a planar structure
Reason
\( \boldsymbol{S} \operatorname{atom} \operatorname{in} \boldsymbol{S} \boldsymbol{O}_{3} \) is \( \boldsymbol{s} \boldsymbol{p}^{2} \) hybridized
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
If \( \frac{4 z_{1}}{9 z_{2}}+\frac{4 \overline{z_{1}}}{9 \overline{z_{2}}}=0, \) then the value of
\( \left|\frac{z_{1}-z_{2}}{z_{1}+z_{2}}\right| \) is
A \( \cdot \frac{4}{9} \)
в. \( \frac{9}{4} \)
\( c \cdot 1 \)
\( D \)
Subject: Physics
The value of 1 amu is equal to:
A \( \cdot 1.66 \times 10^{-8} g \)
в. \( 1.66 \times 10^{-4} g \)
c. \( 1.66 \times 10^{-16} g \)
D. \( 1.66 \times 10^{-24} g \)
Subject: Maths
The perpendicular distance from the
point (3,1,1) on the plane passing through the point (1,2,3) and containing the line, \( \vec{r}=\hat{i}+\hat{j}+ \) \( \lambda(2 \hat{i}+\hat{j}+4 \hat{k}), \) is:
\( ^{A} \cdot \frac{1}{\sqrt{11}} \)
в. \( \frac{4}{\sqrt{41}} \)
\( c .0 \)
D. \( \frac{3}{\sqrt{11}} \)
Subject: Physics
A voltmeter is connected in parallel with a variable resistance are which is in
series and an ammeter and call. For one
value of \( R, \) metres read \( 0.3 \mathrm{A} \) and 0.9
volt. For another value of \( R \) the readings are 0.25 ampere and 1.0 volt. What is the internal resistance of the cell?
A . \( 0.5 \Omega \)
B. 2\Omega
c. \( 1.2 \Omega \)
D. 12
Subject: Physics
The steel wire can withstand a load up
to \( 2940 \mathrm{N} \). A load of \( 150 \mathrm{kg} \) is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position so that the wire does not break
A . 30
B. 60
\( c .80 \)
D. \( 85^{\circ} \)
Subject: Physics
toppr
Q Type your question
an electric field that decreases with
altitude. Near the surface of the earth,
the field is about \( 100 V m^{-1} . \) Why then
do we not get an electric shock as we
step out of our house into the open?
(Assume the house to be a steel cage so
there is no field inside!)
(b) A man fixes outside his house one evening a two metre high insulating slab
carrying on its top a large aluminium sheet
of area \( 1 m^{2} \). Will he get an electric shock if
he touches the metal sheet next morning?
(c) The discharging current in the atmosphere due to the small conductivity of
air is known to be 1800 A on an average
Over the globe. Why then does the atmosphere not discharge itself completely
in due course and become electrically
neutral? In other words, what keeps the atmosphere charged?
(d) What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning?
(Hint: The earth has an electric field of
about \( 100 \mathrm{Vm}^{-1} \) at its surface in the
downward direction, corresponding to a Surface charge density \( =-10^{-9} \mathrm{Cm}^{-2} \). Due
to the slight conductivity of the atmosphere
up to about \( 50 \mathrm{km} \) (beyond which it is
good conductor), about \( +1800 \mathrm{C} \) is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually allover the globe pump an equal amount of negative charge on the earth.)