AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A circular coil connected to a cell of
e.m.f \( \boldsymbol{E} \) produced a magnetic field. The
coil is unwound, stretched to double its length, rewound into a coil of \( \frac{1}{3} \) of the original radius and connected to a cell
of e.m.f \( \boldsymbol{E}_{1} \) to produce the same field at
the centre. Then \( \boldsymbol{E}_{\mathbf{1}} \) is :
\( \mathbf{A} \cdot \frac{E}{2} \)
B. \( \frac{2 E}{3} \)
c. \( \frac{9 E}{4} \)
D. \( \frac{E}{6} \)
Subject: Physics
In L-C oscillation the maximum charge on the capacitor can be \( Q \). If at any instant, electric energy and magnetic energy associated with the current is
equal, then the charge on the capacitor at that instant is :
A \( \cdot \frac{Q}{\sqrt{2}} \)
в. \( \frac{Q}{2} \)
c. \( \frac{3 Q}{\sqrt{2}} \)
D. \( \frac{3 Q}{2} \)
Subject: Chemistry
The structure of glycine (amino acid) is
\( H_{2} N-C H_{2} C O O^{-}(z \text { witter ion }) \)
Select the correct statement:-
A. Glycine as well as other amino acids are amphoteric
B. The acidic functional group in amino acids is \( N H_{3} \)
C. The basic functional group in amino acids is \( -C O O \)
D. All are correct
Subject: Chemistry
The reaction is balanced if \( 5 H_{2} O_{2}+ \)
\( \boldsymbol{x} \boldsymbol{C l} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{x} \boldsymbol{C l}^{-}+\boldsymbol{y} \boldsymbol{O}_{2}+ \)
\( 6 H_{2} O \)
The value of \( y \) is :
Subject: Physics
If a water falls from a dam into a turbine
wheel \( 19.6 m \) below, then the velocity of
water at the turbines is ( take \( g= \)
\( \left.9.8 m / s^{2}\right) \)
A \( .9 .8 m / s \)
в. \( 19.6 \mathrm{m} / \mathrm{s} \)
c. \( 39.2 \mathrm{m} / \mathrm{s} \)
D. \( 98.0 m / s \)
Subject: Maths
\( \lim _{\mathbf{n} \rightarrow \infty} \sum_{\mathbf{r}=\mathbf{1}}^{\mathbf{n}} \frac{\mathbf{1}}{\mathbf{n}} \mathbf{e}^{\mathbf{r} / \mathbf{n}} \mathbf{i} \mathbf{s} \)
\( \mathbf{A} \cdot \mathbf{e} \)
B. e -1
\( c \cdot 1-e \)
D. e +1
Subject: Maths
The unit vector orthogonal to \( -\hat{\mathbf{i}}+ \) \( \hat{k}, 2 \hat{j}-\hat{k} \) and forming a right handed
system with them is
\( \mathbf{A} \cdot 2 \hat{i}+\hat{j}+2 \hat{k} \)
B. \( \frac{2 \hat{i}+\hat{j}+2 \hat{k}}{3} \)
c. \( -\frac{2 \hat{i}+\hat{j}+2 \hat{k}}{3} \)
D. \( -\frac{2 \hat{i}+\hat{j}+2 \hat{k}}{9} \)
Subject: Physics
A dancer demonstrating dance steps
along a straight line. The position time
\( \operatorname{graph}(x-t) \) is as shown in the given
figure. Find the average speed for the
dance step depicted by CD.
A. \( 1 \mathrm{ms}^{-1} \)
B. \( 2.66 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 3 m s^{-1} \)
D. \( 0.89 \mathrm{ms}^{-1} \)
Subject: Physics
If the focal length of a convex mirror is
\( 16 \mathrm{cm}, \) what is its radius of curvature?
\( A \cdot 8 \mathrm{cm} \)
B. \( 16 \mathrm{cm} \)
c. \( 32 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Physics
Two rods of different materials having coefficients of thermal expansion and
Young's moduli \( Y_{1}, Y_{2}, \) respectively are
fixed between two rigid massive walls. The rods are heated such that undergo the same increase in temperature.
There is no bending of the rods. If \( \boldsymbol{\alpha}_{1}: \)
\( \boldsymbol{\alpha}_{2}=\boldsymbol{2}: \boldsymbol{3}, \) the thermal stresses
developed in the two rods are equal
provided \( Y_{1}: Y_{2} \) is equal to:
A .2: 3
B. 1: 1
c. 3: 2
D. 4: 9
Subject: Chemistry
Assertion
O \( _{2} \) is paramagenetic in nature.
Reason
Bond-order of oxygen is two.
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
Using the information, given in each of the following figures, find the valuesof
\( a \)
\( [\text { Given }: \boldsymbol{C} \boldsymbol{E}=\boldsymbol{A C}] \)
A . \( 136^{\circ} \)
B. \( 124^{\circ} \)
\( c \cdot 110^{\circ} \)
D. none of the above
Subject: Physics
The coil in a MCG has an area of \( 4 \mathrm{cm}^{2} \)
and 500 turns. The intensity of magnetic induction is 2T. When a
current of \( 10^{-4} \) A is passed through it,
the deflection is \( 20^{0} \). The couple per
unit twist is (N-m)
A. \( 3 \times 10^{-6} \)
B. \( 2 \times 10^{-6} \)
\( \mathbf{c} \cdot 4 \times 10^{-6} \)
D. \( 5 \times 10^{-6} \)
Subject: Physics
Three rings, each of mass \( m \) and radius
\( r, \) are so placed that they touch each
other. Find the moment of inertia about
the axis as shown in the figure:
\( A \cdot 5 m r^{2} \)
B. \( \frac{5}{7} m r^{2} \)
\( c \cdot 7 m r^{2} \)
Subject: Maths
If \( \cos ^{2} x+\cos ^{2} 2 x+\cos ^{2} 3 x=1 \) then
A \( \cdot x=(2 n+1) \frac{\pi}{4}, n \epsilon I \)
B. \( x=(4 n+1) \frac{\pi}{4}, n \in I \)
c. \( x=n \pi \frac{\pi}{4}, n \epsilon I \)
D. none of these
Subject: Maths
The length \( x \) of a rectangle is decreasing at a rate of \( 3 \mathrm{cm} / \mathrm{min} \) and
width \( y \) is increasing at a rate of \( 2 c m / m i n . \) When \( x=10 c m \) and \( y= \)
\( 6 c m, \) find the rates of change of (i) the
perimeter
(ii) the area of the rectangle.
Subject: Chemistry
Assertion
Hydrogen is a diatomic molecule.
Reason
Hydrogen atom has a single electron in
its outermost shell
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
\( (a) C H_{3} C O N H_{2}+K O H \longrightarrow \)
\( (b) C H_{3} C O O H+s o d a l i m e \longrightarrow \)
\( (c) C H_{3} C O O A g+B r_{2} \longrightarrow \)
All the three reactions show similarity
in:
A. Descending of carbon atoms
B. Ascending of carbon atoms
c. Both the above
D. None of above
Subject: Physics
A car starts from rest, moves with an
acceleration \( a \) and then decelerates at \( b \)
for some time to come to rest. If the
total time taken is \( t, \) the maximum
velocity is
A \( \cdot \frac{a b t}{a+b} \)
B. \( \frac{a^{2}}{a+b} \)
c. \( \frac{a t}{a+b} \)
D. \( \frac{b^{2}}{a+b} \)
Subject: Physics
Five identical plates are connected
across a battery as in figure. If the
charge on plate 1 be \( +q \), then the
charges on the plates 2,3,4 and 5 are:
\( \mathbf{A} .-q,+q,-q,+q \)
в. \( -2 q,+2 q,-2 q,+q \)
c. \( -q,+2 q,-2 q,+q \)
D. none of the above.
Subject: Maths
\( \frac{x^{-1}}{x^{-1}+y^{-1}}+\frac{x^{-1}}{x^{-1}-y^{-1}} \) is equal to
A. \( \frac{2 y^{2}}{y^{2}-x^{2}} \)
в. \( \frac{2 x^{2}}{y^{2}-x^{2}} \)
c. \( \frac{2 y^{2}}{y^{2}+x^{2}} \)
D. none
Subject: Chemistry
Write IUPAC names of the following compounds and classify them into primary, secondary and tertiary amines.
(i) \( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C} \boldsymbol{H} \boldsymbol{N} \boldsymbol{H}_{2} \)
\( \boldsymbol{C H}_{3}\left(\boldsymbol{C H}_{2}\right)_{2} \boldsymbol{N} \boldsymbol{H}_{2} \)
\( \left(\text { iii) } C H_{3} N H C H\left(C H_{3}\right)_{2}\right. \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C} \boldsymbol{N} \boldsymbol{H}_{2} \)
\( (v) C_{6} H_{5} N H C H_{3} \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2}\right)_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}_{3} \)
\( (v i i) m-B r C_{6} H_{4} N H_{2} \)
Subject: Maths
Solve: \( \left[\begin{array}{ccc}\mathbf{5} & \mathbf{1 0} & \mathbf{8} \\ \mathbf{3} & \mathbf{2} & \mathbf{6} \\ \mathbf{8} & \boldsymbol{x}+\mathbf{9} & \mathbf{9}\end{array}\right]=\mathbf{1 0 0} \)
Subject: Maths
The area of the region bounded by the
parabola \( \boldsymbol{y}=\boldsymbol{x}^{2}-\mathbf{4} \boldsymbol{x}+\mathbf{5} \) and the
straight line \( \boldsymbol{y}=\boldsymbol{x}+\mathbf{1} \) is
A \( \cdot \frac{1}{2} \)
B. 2
\( c \cdot 3 \)
D. \( \frac{9}{2} \)
Subject: Maths
If \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\mathbf{0} \) and \( |\boldsymbol{a}|=\mathbf{3} ;|\boldsymbol{b}|= \)
\( \mathbf{5} ;|\boldsymbol{c}|=\mathbf{7}, \) find the angle between a
vector and
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. none of these
Subject: Physics
An intense stream of water of cross
section area A strikes a wall at an angle \( \theta \) with the normal to the wall and
returns back elastically. If the density of
water is \( \rho \) and its velocity is \( v \), then the force exerted on the wall will be :
A \( \cdot 2 A v^{2} \)
В. \( 2 A v^{2} \rho \)
c. \( 2 A v^{2} \rho \cos \theta \)
D \( \cdot 2 A v^{2} \rho \sin \theta \)
Subject: Physics
The capacitors \( C_{1}, C_{3}, C_{4}, C_{5} \) shave a
capacitance \( 4 \mu F \) each and \( C_{2} \)
has capacitance \( 10 \mu F \). The effective
capacitance between \( \mathrm{P} \) and \( \mathrm{Q} \) will be :
\( \mathbf{A} \cdot 8 \mu F \)
в. \( 6 \mu F \)
\( c .4 \mu F \)
D. \( 2 \mu F \)
Subject: Physics
Several spherical drops of a liquid of radius r coalesce to form single drop of radius \( R . \) If \( T \) is surface tension and \( V \) is
volume under consideration, then the release of energy is:
A \( \cdot \) a \( V T\left(\frac{1}{r}+\frac{1}{R}\right) \)
В \( \cdot \) s \( \operatorname{VT}\left(\frac{1}{r}-\frac{1}{R}\right) \)
c. \( v T\left(\frac{1}{r}-\frac{1}{R}\right) \)
D. \( V T\left(\frac{1}{r^{2}}-\frac{1}{R^{2}}\right) \)
Subject: Physics
The sun's angular diameter is
measured to be \( 1920^{\prime \prime} . \) The distance of
the sun from the earth is \( 1.496 \times \)
\( 10^{11} \) m. What is the diameter of the sun?
A \( \cdot 1 \times 10^{9} m \)
В. \( 1.39 \times 10^{9} m \)
c. \( 13.9 \times 10^{9} \mathrm{m} \)
D. \( 139 \times 10^{9} m \)
Subject: Physics
A rod of length \( 10 \mathrm{cm} \) lies along the principal axis of concave mirror of focal
length \( 10 c m \) in such a way that its end
closer to the pole is \( 20 \mathrm{cm} \) away from the mirror. The length of the image is-
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 2.5 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Maths
The incentre of the triangle formed by the points \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \boldsymbol{4} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \) and
\( 4 \hat{i}+5 \hat{j}+\hat{k} \) is
A \( \cdot \frac{\hat{i}+\hat{j}+\hat{k}}{3} \)
B. \( \hat{i}+2 \hat{j}+3 \hat{k} \)
c. \( 3 \hat{i}+2 \hat{j}+\hat{k} \)
D. \( \hat{i}+\hat{j}+\hat{k} \)
Subject: Physics
A common emitter amplifier circuit,
built using an npn transistor, is shown
in the figure. Its dc current gain is
\( 250, R_{C}=1 k \Omega \) and \( V_{C E} \) to reach
saturation?
A. \( 100 \mu A \)
B. \( 7 \mu A \)
\( c .40 \mu A \)
D. \( 10 \mu A \)
Subject: Maths
If in \( \triangle A B C \) and \( \triangle D E F, \frac{A B}{D E}=\frac{B C}{F D} \)
then they will be similar if
A. \( \angle B=\angle E \)
в. \( \angle A=\angle D \)
c. \( \angle B=\angle D \)
\( \mathbf{D} \cdot \angle A=\angle F \)
Subject: Physics
A body of mass \( 1 k g \) tied to one end of string is revolved in a horizontal circle of
radius \( 0.1 m \) with a speed of
3evolution/ sec, assuming the effect of gravity is negligible, then linear velocity, acceleration and tension in the string be :
A \( \cdot 1.88 m / s, 35.5 m / s^{2}, 35.5 N \)
B . 2.88m/s,45.5m/s \( ^{2} \), 45.5 \( N \)
c. \( 3.88 m / s, 55.5 m / s^{2}, 55.5 N \)
D. None
Subject: Physics
A particle is moving along a circular path of radius \( 5 m \) with a uniform
speed \( 5 m s^{-1} . \) What will be the average
acceleration when the particle completes half revolution?
A. Zero
B. \( 10 \mathrm{ms}^{-2} \)
\( \mathbf{c} \cdot 10 \pi \mathrm{ms}^{-2} \)
D. \( \frac{10}{\pi} m s^{-2} \)
Subject: Maths
The infinite sum \( 1+ \) \( \frac{4}{7}+\frac{9}{7^{2}}+\frac{16}{7^{3}}+\frac{25}{7^{4}}+\dots \dots \) equals
A \( \cdot \frac{27}{14} \)
в. \( \frac{21}{13} \)
c. \( \frac{49}{27} \)
D. \( \frac{256}{147} \)
Subject: Maths
From Delhi station, if we buy 2 ticket for
station \( A \) and 3 tickets for station \( B \), the
total cost is Rs.77. But if we buy 3 tickets for station \( A \) and 5 tickets for
station \( \mathrm{B} \), the total cost is Rs. 124. What
are the fares from Delhi to station \( A \) and
to station B ?
A. \( A=R s .12 ; B=R s .17 \)
в. \( A=R s .13 ; B=R s .17 \)
c. \( A=R s .18 ; B=R s .17 \)
D. \( A=R s .19 ; B=R s .17 \)
Subject: Physics
A charged particle \( X \) moves directly towards another charged particle Y. For the 'X plus Y' system, the total
momentum is p and the total energy is
\( E \)
This question has multiple correct options
A. p and \( E \) are conserved if both \( x \) and \( Y \) are free to move
B. (A) is true only if \( x \) and \( Y \) has similar charges.
c. If \( Y \) is fixed, \( E \) is conserved but not \( p \)
D. If \( Y \) is fixed, neither E nor \( p \) is conserved
Subject: Maths
A horse is tied to a peg at one corner of
a square shaped grass field of side \( 15 m \)
by means of a \( 5 m \) long rope. Find
(i) the area of that part of the field in
which the horse can graze.
(ii) The increase in the grazing area if
the rope were \( 10 m \) long instead of \( 5 m \)
(Use \( \boldsymbol{\pi}=\mathbf{3 . 1 4}) \)
Subject: Chemistry
Arrange the following acids in increasing order of their acid strength:
I. \( \boldsymbol{H} \boldsymbol{C l O}_{\mathbf{4}} \)
II. \( \quad H_{2} S O_{4} \)
III \( . \)
A. \( I I I<I I<I \)
B. \( I<I I<I I I \)
c. \( I I<I I I<I \)
D. III \( <I<I I \)
Subject: Maths
Two events \( A \) and \( B \) will be independent
if
\( \mathbf{A} \cdot P\left(A^{\prime} \cap B^{\prime}\right)=(1-P(A))(1-P(B)) \)
B \( \cdot P(A)+P(B)=1 \)
\( \mathbf{c} \cdot P(A)=P(B) \)
D. \( A \) and \( B \) are mutually exclusive
Subject: Chemistry
In a first-order reaction \( \boldsymbol{A} \rightarrow \boldsymbol{B} \), if k is
rate constant and initial concentration
of the reactant \( A \) is 0.5 M then the half-
life is:
A \( \cdot \frac{\ln 2}{k} \)
в. \( \frac{0.693}{0.5 k} \)
c. \( \frac{\log 2}{k} \)
D. \( \frac{\log 2}{k \sqrt{0.5}} \)
Subject: Physics
You are given a resistance wire of length \( 100 \mathrm{cm} \) and a battery of negligible internal resistance. In which of the
following cases is the largest amount of heat generated?
A. When the wire is divided in two parts and both the parts are connected to the battery in parallel
B. When the wire is connected to the battery directly
c. when the wire is divided in to four parts and all the fou parts are connected in parallel to the battery
D. When only half of the wire is connected to the battery
Subject: Chemistry
A solution containing
0.1 mole of naphthalene and 0.9 mole of benzene is cooled out until some benzene freezes
out. The solution is then decanted off
from the solid and warmed up to \( 353 \mathrm{K} \) where its vapour pressure was found to
be 670 torr. The freezing point and boiling point of benzene are \( 278.5 \mathrm{K} \) and
\( 353 \mathrm{K} \) respectively and its enthalpy of fusion is \( 10.67 \mathrm{kJ} \) mol \( ^{-1} \). Calculate the
depression in freezing point for original solution to the nearest integer. Assume ideal behaviour
Subject: Physics
The resistance \( \boldsymbol{R}=\frac{\boldsymbol{V}}{\boldsymbol{I}} \) where \( \boldsymbol{V}= \)
\( (100 \pm 5) V \) and \( I=(10 \pm 0.2) A . \) The
percentage error in \( \mathrm{R} \) is?
A \( .5 .2 \% \)
в. \( 4.8 \% \)
c. \( 7 \% \)
D. \( 3 \% \)
Subject: Chemistry
In a chemical reaction, when 14 g of sodium carbonate reacted with 10 g of acetic acid (ethanoic acid), then it was
observed that, 16.67 g of sodium acetate solution in water and 7.33 g of carbon dioxide were produced. Which law does this depicts?
A. Law of definite proportions
B. Law of conservation of mass
c. Law of constant proportions
D. Avogadro's law
Subject: Physics
A hydraulic lift at a service station can
lift cars with a mass of 3500 kg. The
area of cross section of the piston
carrying the load is \( 500 \mathrm{cm}^{2} \). What
pressure does the smaller piston
experience? \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \)
Subject: Physics
An inductor is connected to a battery
through \( e_{1} \) switch induced emf is a
when the switch is pressed and \( e_{2} \) when
the switch is opened. Then:
A \( \cdot e_{1}=e_{2} \)
в. \( e_{1}>e_{2} \)
c. \( e_{1}<e_{2} \)
D. \( e_{1}>\mid<e_{2} \)
Subject: Chemistry
(1) : For natural polymers, PDI value is always equal to unity
(2) : The ratio of \( \bar{M}_{w} \) and \( \bar{M}_{n} \) of
a polymer is called PDI.
A. Both 1 and 2 are correct and 2 is the correct explanation of the 1
B. Both 1 and 2 are correct but 2 is not the correct explanation of the 1
c. 1 is correct but 2 is in correct
D. 1 is incorrect but 2 is correct
Subject: Maths
The tenth term in the expansion of
\( \left(2 x^{2}+\frac{1}{x}\right)^{12} \)
A \( \cdot \frac{1760}{x^{3}} \)
в. \( -\frac{1760}{x^{3}} \)
c. \( \frac{1760}{x^{2}} \)
D. none of the above
Subject: Physics
The energy \( E \) of an oscillating body in simple harmonic motion depends on its
mass \( m \), frequency \( n \) and amplitude \( a \)
Using the method of dimensional analysis find the relation between
\( \boldsymbol{E}, \boldsymbol{m}, \boldsymbol{n} \) and \( \boldsymbol{a} \)
A \( \cdot E=k m n^{2} a^{2}(k=a \text { dimensionless constant }) \)
B . \( E=k m^{2} n^{2} a^{3}(k=a \text { dimensionless constant }) \)
C . \( E=k m^{1} n^{1} a^{2}(k=a \text { dimensionless constant }) \)
D. \( E=k m^{2} n^{1} a^{2}(k=a \text { dimensionless constant }) \)
Subject: Maths
If \( f(x)=\sin x \) and \( g(x)=\cos x \) then
\( D *(f \circ g) \) is equal to
\( \mathbf{A} \cdot-\sin 2(\cos x) \sin x \)
B. - sin (cos \( x \) ) \( \sin x \)
c. \( -\sin ^{2}(\cos x) \sin x \)
D. \( -\sin (\cos x) \sin ^{2} x \)
Subject: Physics
During the melting of a slab of ice at
\( 273 \mathrm{K} \) at atmospheric pressure.
This question has multiple correct options
A. Positive work is done by the ice-water system on the atmosphere
B. Positive work is done on the ice-water system by the atmosphere
C. The internal energy of ice-water system increases
D. The internal energy of the ice-water system decreases
Subject: Maths
n \( \triangle A B C \) and \( \triangle P Q R, \) if \( A B= \) \( 2.5 c m, A C=3.5 c m, B C= \)
\( 4.0 c m, P Q=5 c m, P R=7 c m \) and
\( Q R=8 c m, \) then find whether \( \triangle A B C \)
and \( \triangle P Q R \) are similar or not
Subject: Maths
If \( \boldsymbol{E} \) and \( \boldsymbol{F} \) are events such that \( \boldsymbol{P}(\boldsymbol{E})= \) \( \frac{1}{4}, P(F)=\frac{1}{2} \) and \( P(E a n d F)=\frac{1}{8} \) find
(i) \( P(E \text { or } F) \)
(ii) \( P(\text { not } E \text { and } \operatorname{not} F) \)
Subject: Chemistry
The permanganate ion is an excellent oxidizing agent in aqueous solutions.
When the half reaction, \( M n O_{4}^{-}+ \)
\( \boldsymbol{H}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \) is
balanced, the correct coefficients for the species involved are:
A. 1,4,4,1,2
B. 1,4,2,1,2
c. 1,4,3,1,2
D. 1,4,1,1,2
Subject: Maths
A circle of radius \( 10 \mathrm{cm} \) has its centre at the vertex \( C \) of an equilateral triangle ABC and passes through the other two vertices. The side AC extended through C intersects the circle at D. The number
of degrees of angle ADB is:
A \( \cdot 15^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)
E \( .120^{\circ} \)
Subject: Maths
solve: \( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{2} & -\mathbf{1} \\ \boldsymbol{3} & -\boldsymbol{1} & \boldsymbol{4} \\ \boldsymbol{x} & \boldsymbol{2} & -\boldsymbol{5}\end{array}\right|=\mathbf{0} \)
Subject: Physics
A particle is oscillating simple harmonically with angular frequency \( \omega \)
and amplitude \( A . \) It is at a point \( (A) \) at certain instant (shown in figure). At this instant it is moving towards mean positive (B). It takes time \( t \) to reach
position (B). If time period of
oscillations is \( T, \) the average speed
between \( A \) and \( B \) is :
A \( \cdot \frac{A \sin \omega t}{t} \)
B. \( \frac{A \cos \omega t}{t} \)
c. \( \frac{A \sin \omega t}{T} \)
D. \( \frac{A \cos \omega t}{T} \)
Subject: Chemistry
(A) If water is heated to \( 350 \mathrm{K} \), then pOH
will increase to 8
(R) \( K_{w} \) increases with increase in
temperature.
\( A \). Both (R) and (A) are true and reason is the. correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
C. Assertion (A) is true but reason (R) is false
D. Assertion (A) and reason (R) both are false
E. Assertion (A) is false but reason (R) is true
Subject: Chemistry
In which of the following cases, the former change would require lesser energy than the latter?
This question has multiple correct options
A \( \cdot B e^{+}(g) \rightarrow B e^{2+}(g)+e^{-} ; \operatorname{Be}(g) \rightarrow B e^{+}(g)+e^{-} \)
B . \( N a(g) \rightarrow N a^{+}(g)+e^{-} ; C l^{-}(g) \rightarrow C l(g)+e^{-} \)
C. \( A g(g) \rightarrow A g^{+}(g)+e^{-} ; A u(g) \rightarrow A u^{+}(g)+e^{-} \)
D. \( O^{-}(g) \rightarrow O(g)+e^{-} ; S^{-}(g) \rightarrow S(g)+e^{-} \)
Subject: Physics
A satellite is launched into a circular
orbit of radius \( R \) around the earth. \( A \)
second satellite is launched into an
orbit of radius \( 1.01 R \). The time period of the second satellite is larger than that of the first one by approximately
A . \( 0.5 \% \)
в. \( 1.5 \% \)
\( c \cdot 1 \% \)
D. \( 3 \% \)
Subject: Chemistry
The mechanism of the reaction
\( \mathbf{2} N \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2} \) is:
\( N O+N O \underset{k_{-1}}{\Gamma} N_{2} O_{2}(\text { fast }) ; N_{2} O_{2}+ \)
\( O_{2} \stackrel{k_{2}}{\longrightarrow} 2 N O_{2}(s l o w) \)
The rate constant of the reaction is:
\( \mathbf{A} \cdot k_{2} \)
B. \( k_{2} k_{1}\left(k_{-1}\right) \)
\( \mathbf{c} . k_{2} k_{1} \)
D \( \quad k_{2}\left(\frac{k_{1}}{k_{-1}}\right) \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\boldsymbol{x}-\boldsymbol{3}, \quad \boldsymbol{x}<\mathbf{0} \\ \boldsymbol{x}^{2}-\mathbf{3} \boldsymbol{x}+\mathbf{2}, \quad \boldsymbol{x} \geq \mathbf{0}\end{array} \) and \right.
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(|\boldsymbol{x}|)+|\boldsymbol{f}(\boldsymbol{x})|, \) then \( \boldsymbol{g}(\boldsymbol{x}) \) is
This question has multiple correct options
A . continuous is \( R-\{0\} \)
B. Continuous in \( R \)
C . Differentiable in \( R-\{0,1,2\} \)
D. Differentiable in \( R-\{1,2\} \)
Subject: Chemistry
\( \boldsymbol{P}_{4}+\mathbf{3} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\Delta}{\longrightarrow} \boldsymbol{P} \boldsymbol{H}_{3}+ \)
\( \mathbf{3} N a H_{2} P O_{2} \)
The given reaction is a disproportionation reaction.
If true enter 1 , else enter 0
Subject: Maths
\( A B C \) is a right isosceles triangle right
angled at \( B . \) Then \( \sin ^{2} A+\cos ^{2} C= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D.
Subject: Maths
Let \( z_{1} \) and \( z_{2} \) be roots of the equation
\( z^{2}+p z+q=0, \) where the coefficients
\( p \) and \( q \) may be complex numbers. Let \( A \)
and \( B \) represents \( z_{1} \) and \( z_{2} \) in the
complex plane. If \( \angle A O B=\alpha \neq 0 \) and
\( \boldsymbol{O} \boldsymbol{A}=\boldsymbol{O} \boldsymbol{B}, \) where \( \boldsymbol{O} \) is the origin, then
\( p^{2}=k \cos ^{2} \frac{\alpha}{2}, \) where \( k= \)
\( \mathbf{A} \cdot \boldsymbol{q} \)
B. \( 2 q \)
c. \( 4 q \)
D. None of these