AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \boldsymbol{x}=\sin (\boldsymbol{\alpha}-\boldsymbol{\beta}) \cdot \sin (\gamma-\boldsymbol{\delta}) ; \boldsymbol{y}= \)
\( \sin (\beta-\gamma) \cdot \sin (\alpha-\delta) \) and \( z= \)
\( \sin (\gamma-\alpha) \cdot \sin (\beta-\delta,) \) then
A. \( x+y+z=0 \)
в. \( x+y-z=0 \)
c. \( y+z-x=0 \)
D. None of these
Subject: Maths
A person drawn a card from a pack of 52 cards, replaces it \( \& \) shuffles the pack. He continues doing this till the draws a spade. The probability that he will fail exactly the first two times is
A \( \cdot \frac{1}{64} \)
в. \( \frac{9}{64} \)
c. \( \frac{36}{64} \)
D. \( \frac{60}{64} \)
Subject: Maths
\( \operatorname{Let} \int_{0}^{a} f(x) d x=\lambda \) and
\( \int_{0}^{a} \boldsymbol{f}(\boldsymbol{2} \boldsymbol{a}-\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}=\boldsymbol{\mu} \)
Then \( \int_{0}^{2 a} f(x) d x \) is equal to?
\( A \cdot \lambda+\mu \)
B. \( \lambda-\mu \)
\( c \cdot 2 \lambda-\mu \)
D. \( \lambda-2 \mu \)
Subject: Physics
A card sheet divided into squares each
of size \( 1 \mathrm{mm}^{2} \) is being viewed at a distance of \( 9 \mathrm{cm} \) through a magnifying glass (a converging lens of focal length \( 9 \mathrm{cm} \) ) held close to the eye.(a) What is the magnification produced by the lens? How much is the area of each
square in the virtual image?(b) What is the angular magnification (magnifying power) of the lens?(c) Is the magnification in
(a) equal to the magnifying power in (b)? Explain
Subject: Physics
A disc of mass \( 2 k g \) and diameter \( 2 m \) is
performing rotational motion. Find the work done, if the disc is rotating from \( 300 r p m \) to \( 600 r p m \)
A . \( 1479 J \)
в. \( 147.9 J \)
c. \( 14.79 J \)
D. \( 1.479 J \)
Subject: Maths
A straight line \( L \) on the \( x y \) -plane
bisects the angle between \( O X \) and \( O Y \)
What are the direction cosines of \( L ? \)
A \( \cdot(1 / \sqrt{2}, 1 / \sqrt{2}, 0) \)
в. \( (1 / 2, \sqrt{3} / 2,0) \)
c. (0,0,1)
D. \( (2 / 3,2 / 3,1 / 3) \)
Subject: Maths
Find \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \) when \( \boldsymbol{P}(\boldsymbol{A})= \)
\( \frac{\mathbf{5}}{\mathbf{1 1}}, \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{6}}{\mathbf{1 1}} \) and \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\frac{\mathbf{7}}{\mathbf{1 1}} \)
Subject: Chemistry
When 100 g of ethylene polymerises entirely to polyethene, the weight of polyethene formed as per the equation:
\( \boldsymbol{n}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{4}\right) \rightarrow-\left(\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}\right)_{n}- \) is:
A \( \cdot \frac{n}{2} g \)
B. 1009
c. \( \frac{100}{n} \mathrm{g} \)
D. \( 100 n \) g
Subject: Physics
An early model for an atom considered
it to have a positively charged point
nucleus of charge \( Z e \), surrounded by a
uniform density of negative charge upto a radius \( R \). The atom as a whole is
neutral. The electric field at a distance \( r \)
from the nucleus is \( (r<R) \)
A \( \cdot \frac{Z e}{4 \pi \epsilon_{0}}\left[\frac{1}{r^{2}}-\frac{r}{R^{3}}\right] \)
В \( \cdot \frac{Z e}{4 \pi \epsilon_{0}}\left[\frac{1}{r^{2}}-\frac{r}{R^{2}}\right] \)
c. \( \frac{Z e}{4 \pi \epsilon_{0}}\left[\frac{1}{R^{3}}-\frac{r}{r^{2}}\right] \)
D. \( \frac{Z e}{4 \pi \epsilon_{0}}\left[\frac{1}{R^{3}}+\frac{r}{r^{2}}\right] \)
Subject: Physics
Q Type your question
charge carried by the cylinder is NOT uniform; the charge density varies with radius according to the equation \( =\frac{A}{r} \)
Which of the following expressions
gives the electric field strength at point
\( P, \) a point that lies inside the cylinder
and is a distance \( r \) from the center of
the cylinder?
\( ^{A} \cdot \frac{A R^{2}}{\epsilon_{n^{2}}^{2}} \)
в. \( \frac{A r}{\epsilon_{0} R} \)
c. \( \frac{A r^{2}}{\epsilon_{6} R^{2}} \)
D. \( \frac{A R}{\epsilon_{0} r} \)
\( E \cdot \underline{A} \)
Subject: Physics
Assertion: PV/T=constant for 1 gram of
gas. This constant varies from gas to gas.
Reason: 1 gram of different gases at \( \mathrm{NTP} \) Occupy different volumes.
A. Both assertion (A) and reason (R) are correct and R gives the correct explanation
B. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation
C. A is true but R is false
D. A is false but R is true
Subject: Chemistry
What is the order of reactivity of hydrogen atoms attached to the carbon atom in an alkane for free radical
substitution?
\( \mathbf{A} \cdot 3^{\circ}>1^{\circ}>2^{\circ} \)
В . \( 2^{\circ}>1^{\circ}>3^{\circ} \)
c. \( 3^{\circ}>2^{\circ}>1^{\text {о }} \)
D. \( 1^{\circ}>2^{\circ}>3^{\circ} \)
Subject: Maths
Mean of 100 observations is 50 and
standard deviation is \( 10 . \) If 5 is added to
each observations, then what will be the
new mean and new standard deviation
respectively?
\( \mathbf{A} \cdot 50,10 \)
B. 50,15
\( \mathbf{c} .55,10 \)
D. 55,15
Subject: Physics
A large insulated sphere of radius \( r \)
charged with \( Q \) units of electricity is placed in contact with a small insulated uncharged sphere of radius \( r^{\prime} \) and is
then separated. The charge on the smaller sphere will now be:
A \( \cdot \frac{Q\left(r^{\prime}+r\right)}{r^{\prime}} \)
в. \( \frac{Q\left(r^{\prime}+r\right)}{r} \)
c. \( \frac{Q r}{\left(r^{\prime}+r\right)} \)
D. \( \frac{Q_{r}^{\prime}}{\left(r^{\prime}+r\right)} \)
Subject: Physics
The molar specific heat of the process
\( \boldsymbol{V} \propto \boldsymbol{T}^{4} \) for \( \boldsymbol{C} \boldsymbol{H}_{4} \) gas at room
temperature is:
\( A \cdot 4 R \)
B. 7R
\( c . \) зв
D. 8R
Subject: Physics
Two persons having mass \( 50 \mathrm{kg} \) each,
are standing 1 m apart from each other
Calculate the force of gravitation and also calculate the force of gravity on each. (Take \( G=6.67 \times 10^{-11} N m^{2} k g^{-2} \)
mass of earth \( M=6 \times 19^{24} k g \)
Radius of earth \( \boldsymbol{R}=\mathbf{6 . 4} \times \mathbf{1 0}^{\mathbf{6}} \boldsymbol{m} \) )?
Subject: Maths
The equation of altitude through \( B \) to
side \( A C \) is
A. \( r=k+t(7 i-10+2 k) \)
в. \( r=k+t(-9 i+6 j-2 k) \)
c. \( r=k+t(7 i-10 j-2 k) \)
D. \( r=k+t(7 i+10 j+2 k) \)
Subject: Maths
If \( a_{1}, a_{2}, a_{3}, \dots, a_{n} \) are in A.P. and \( a_{i}>0 \) for all i, then show that \( \frac{1}{a_{1} a_{2}}+\frac{1}{a_{2} a_{3}}+ \)
\( \ldots+\frac{1}{a_{n-1} a_{n}}=\frac{n-1}{a_{1} a_{n}} \)
Subject: Maths
If the function \( f \) is defined by \( f(x)= \) \( 3 x+4, \) then \( 2 f(x)+4= \)
\( \mathbf{A} \cdot 5 x+4 \)
B. \( 5 x+8 \)
c. \( 6 x+4 \)
D. \( 6 x+8 \)
E \( .6 x+12 \)
Subject: Physics
A body of mass \( 40 \mathrm{kg} \) resting on rough horizontal surface is subjected to a
force \( P \) which is just enough to start the
motion of the body. If \( \mu_{s}=5, \mu_{k}= \)
\( \mathbf{0 . 4}, \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}, \) and the force \( P \) is
continuously applied on the body, then the acceleration of the body is?
A. zero
B . \( 1 m / s^{2} \)
\( \mathrm{c} \cdot 2 m / s^{2} \)
D. \( 2.4 m / s^{2} \)
Subject: Physics
A dog weighing \( 5 \mathrm{kg} \) is standing on a flat boat so that it is 10 metres from the shore. It walks \( 4 \mathrm{m} \) on the boat towards
the shore and then halts. The boat
weighs \( 20 \mathrm{kg} \) and one can assume that there is no friction between it and water
The dog from the shore at the end of this
time is:
A. \( 3.4 \mathrm{m} \)
B. \( 6.8 m \)
c. \( 12.6 \mathrm{m} \)
D. \( 10 \mathrm{m} \)
Subject: Physics
Assertion
Gauss law holds good only to those
closed surfaces which is enclosing non-
zero electric charge.
Reason
The electric flux through a closed surface is unaltered due to the
presence of outside charge.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( \boldsymbol{A}(\boldsymbol{y}, \mathbf{2}), \boldsymbol{B}(\mathbf{1}, \boldsymbol{y}) \) and \( \boldsymbol{A} \boldsymbol{B}=\mathbf{5}, \) then the
possible values are
A .6,2
B. 5,-2
c. -2,-6
D. 2,0
Subject: Maths
\( y=\sin \left(2 \sin ^{-1} x\right), \frac{d y}{d x}= \)
A \( \cdot \sqrt{\left(\frac{1-y^{2}}{1-x^{2}}\right)} \)
в. \( \sqrt[2]{\left(\frac{1+y^{2}}{1-x^{2}}\right)} \)
\( ^{\mathrm{c}} \cdot \sqrt{\left(\frac{1-y^{2}}{1+x^{2}}\right)} \)
D. \( \sqrt{\left(\frac{1+y^{2}}{1+x^{2}}\right)} \)
Subject: Physics
An artillery machine consistently shoots its shells with the same muzzle
speed, so that the maximum range of each shell is \( R \). To hit a target which is
\( \boldsymbol{R} \)
at a distance \( \frac{i c}{2} \) from the gun and at the same level, the elevation angle of the gun should be
A \( \cdot 15^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 60^{\circ} \)
Subject: Maths
Which of the following sets are finite
sets.
(i) The sets of months in a year.
\( (i i)\{1,2,3, \dots\} \)
\( (i i i)\{1,2,3, \dots, 99,100\} \)
\( (i v) \) The set of positive integers greater
than 100 .
A. ( \( i \) ) and \( (i i i) \)
B. (i) only
c. \( (i i),(i i i) \) and \( (i v) \)
D. (ii) and (iv)
Subject: Physics
Which statement best explains why a
rubber rod becomes negatively charged
when rubbed with fur?
A. The rubber that the rod is made of is a better insulator than fur.
B. The fur is a better insulator than the rubber.
C. Molecules in the rubber rod have a stronger attraction for electrons than the molecules in the fur.
D. Molecules in the fur have a stronger attraction for electrons than the molecules in the rubber rod.
Subject: Maths
A die is thrown. \( A \) is the event that
prime number comes up, \( B \) is the event
that the number divisible by three comes up, \( C \) is the event that the
perfect square number comes up. Then, \( A, B \) and \( C \) are :
A. Mutually exclusive
B. Mutually exhaustuve
c. Same
D. None of these
Subject: Physics
A smooth steel ball strikes a fixed
smooth steel plate at an angle \( \theta \) with the vertical. If 'e' is the coefficient of
restitution, the angle at which the rebounce will take place with the vertical is
A \( \cdot \alpha=\tan ^{-1}\left(\frac{\tan \theta}{e}\right) \)
B. \( \alpha=\tan ^{-1}\left(\frac{\cot \theta}{e}\right) \)
c. \( _{\alpha=\tan ^{-1}\left(\frac{\sin \theta}{e}\right)} \)
D・ \( \alpha=\tan ^{-1}\left(\frac{e}{\tan \theta}\right) \)
Subject: Maths
Assertion
\( (A): P(n)=n^{2}+n+41 \) is a prime
\( \forall \boldsymbol{n} \in \boldsymbol{N} \)
Reason
(R): If a number is prime then it
contains only two factors; 1 and number itself.
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A).
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
c. (A)is true but (R) is false.
D. (A)is false but (R) is true
Subject: Physics
A uniform rod of length \( L \) has a mass
per unit length \( \lambda \) and area of cross
section \( A \). If the Young's modulus of the
rod is \( Y . \) The elongation in the rod due to its own weight is
A \( \cdot \frac{2 \lambda g L^{2}}{A Y} \)
B. \( \frac{\lambda g L^{2}}{2 A Y} \)
c. \( \frac{\lambda g L^{2}}{4 A Y} \)
D. \( \frac{\lambda g L^{2}}{6 A Y} \)
Subject: Chemistry
Identify the pair in which the two species are isostructural.
A. \( S i F_{4} \) and \( S F_{4} \)
B. \( I O_{3}^{-} \) and \( X e O_{3} \)
c. \( B H_{4}^{-} \) and \( N H_{4}^{+} \)
D. \( P F_{6}^{-} \) and \( S F_{6} \)
Subject: Maths
The number of ways of arranging \( \boldsymbol{m} \)
positive and \( n(<m+1) \) negative
signs in a row so that no two negative signs are together is
A \( .^{m+1} P_{n} \)
B. \( n+1 P_{m} \)
\( \mathrm{c} \cdot^{m+1} C_{n} \)
D. \( n+1 C_{m} \)
Subject: Physics
The density of a metal at normal
pressure is \( \rho . \) It's density when it is
subjected to an excess pressure p is \( \rho \) '.
If \( \mathrm{B} \) is the bulk modulus of the metal,
the ratio \( \rho^{\prime} / \rho \) is :
A. \( \frac{1}{1-p / B} \)
в. \( 1+\frac{P}{B} \)
c. \( \frac{1}{1-B / p} \)
D. \( 1+B / p \)
Subject: Maths
If \( \left(A+B^{T}\right)^{T} \) is a matrix of order \( 4 \times 3 \)
then the order of matrix B is
\( A \cdot 3 \times 4 \)
B. \( 4 \times 3 \)
\( c \cdot 3 \times 3 \)
D. \( 4 \times 4 \)
Subject: Biology
Choose the correct answer among the alternatives given:
Consider the following statements each
with one or two blanks.
(A) Lippes loop is a (i). IUD while multiload 375 is a \( (\mathrm{ij}) \) IUD.
(B) Surgical methods of contraception are also called as (iii), methods.
(C) High MMR and IMR play a significant role in \( ( \) iv ) human
population. Which one of the following options,
gives the correct fill ups for the
respective blank numbers from
(i) to
(iv) in the above statements?
A. (i) copper releasing,
(ii) non-medicated (iv) decreasing
B. (iii) barrier, (iv) increasing
c. (i) non-medicated,
(ii) copper releasing, (iv) decreasing
D. (i) copper releasing, (ii) non-medicated, (iii) sterilisation
Subject: Maths
If \( A A^{T}=I \) and \( \operatorname{det}(A)=1, \) then
A. Every element of \( A \) is equal to it's co-factor
B. Every element of A and it's co-factor are additive inverse of each other
C. Every element of A and it's co-factor are multiplicative inverse of each other
D. None of these
Subject: Physics
A particle is moved from (0,0) to \( (a, a) \) under a free force \( \overrightarrow{\boldsymbol{F}}=(3 \hat{\boldsymbol{i}}+4 \hat{\boldsymbol{j}}) \) from
two paths, I is OP and path 2 is OQP. Let
\( W_{1} \) and \( W_{2} \) be the work done by this force in these two paths. Then:
A. \( W_{1}=W_{2} \)
в. \( W_{1}, W_{2} \)
c. \( W_{2}-2 W_{1} \)
D. \( W_{2}-4 W_{1} \)
Subject: Chemistry
Which of the following statement
regarding free radical halogenation of
alkane is not true?
A. Hydrogen abstraction by halogen radical in the propagation step is exothermic in both chlorination and bromination
B. Hydrogen abstraction by halogen radical in the propagation step is exothermic in cholorination but endothermic in bromination
C. A single halogen radical may bring about halogenation to thousands of alkane molecule
D. Continuous source of energy is required to continue the halogenation reaction
Subject: Chemistry
Faraday can be defined as:
A. the magnitude of the charge of 1 mole of electrons
B. the magnitude of the electric dipole
C. a fundamental constant of nature equal to \( 6.63 \times \) \( 10^{-34} J s / \)photon
D. a constant that accounts for the existence of ions in
solution
E. the assignment of charges to individual atoms
Subject: Maths
If \( \boldsymbol{S}=^{404} \boldsymbol{C}_{4}-^{4} \boldsymbol{C}_{1} \cdot^{303} \boldsymbol{C}_{4}+^{4} \)
\( C_{2} \cdot^{202} C_{5}-^{4} C_{3} \cdot^{101} C_{4}=(101)^{k} \) then \( k \)
equal to
A . 1
B . 2
\( c \cdot 4 \)
D. 6
Subject: Maths
\( \mathbf{f} \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \in \boldsymbol{R} \& \boldsymbol{\Delta}= \)
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \\ \mathbf{2} \boldsymbol{x} & \mathbf{5} \boldsymbol{x}+\mathbf{2} \boldsymbol{y} & \mathbf{7} \boldsymbol{x}+\mathbf{5} \boldsymbol{y}+\mathbf{2} z \\ \mathbf{3} \boldsymbol{x} & \mathbf{7} \boldsymbol{x}+\mathbf{3} \boldsymbol{y} & \mathbf{9} \boldsymbol{x}+\mathbf{7} \boldsymbol{y}+\mathbf{3} \boldsymbol{z}\end{array}\right|=-\mathbf{1} \mathbf{6} \)
then value of \( x \) is
A . -2
B. -3
\( c \cdot 2 \)
\( D \)
Subject: Maths
\( \int \frac{\cos x-\sin x}{7-9 \sin 2 x} d x \)
A. \( \frac{1}{24} \ln \frac{(4+3 \sin x+3 \cos x)}{(4-3 \sin x-3 \cos x)}+c \)
B. \( \frac{1}{24} \ln \frac{(4-3 \cos x-3 \sin x)}{(4-3 \cos x+3 \sin x)}+c \)
c. \( \frac{1}{12} \ln \frac{(4+3 \sin x-3 \cos x)}{(4-3 \sin x+3 \cos x)}+c \)
D. \( \frac{1}{12} \ln \frac{(4+3 \cos x+3 \sin x)}{(4-3 \sin x-3 \cos x)}+c \)
Subject: Physics
The lens of a simple magnifier has a focal length of \( 2.5 \mathrm{cm} . \) Calculate the angular magnification produced when
(a) the image is at least distance of distinct vision, and
(b) infinity.
A \( \cdot 11,10 \)
B. 11,13
\( c \cdot 10,13 \)
D. 11,12
Subject: Maths
\( \frac{d}{d x}\left\{\cos ^{-1} x+\sin ^{-1} \sqrt{1-x^{2}}\right\}= \)
A .
B.
c. \( \frac{2}{\sqrt{1-x^{2}}} \)
D. \( \frac{-2}{\sqrt{1-x^{2}}} \)
Subject: Maths
The direction cosines to two lines at
right angles are (1,2,3) and \( \left(-2, \frac{1}{2}, \frac{1}{3}\right), \) then
the direction cosine perpendicular to both given lines are:
A \( \cdot \sqrt{\frac{25}{219}} \cdot \sqrt{\frac{19}{2198}} \cdot \sqrt{\frac{729}{21988}} \)
B. \( \sqrt{\frac{24}{2198} \cdot \sqrt{\frac{38}{2198}}} \sqrt{\frac{730}{21988}} \)
c. \( \frac{1}{3},-2, \frac{-7}{2} \)
D. None of the above
Subject: Physics
A block of mass \( 10 k g \) is released on a
fixed wedge inside a cart which is
moved with constant velocity \( 10 \mathrm{ms}^{-1} \)
towards right. There is no relative
motion between block and cart. Then
work done by normal reaction on block
in two seconds from ground frame will
be \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A . \( 1320 J \)
В. \( 960 J \)
c. \( 1200 J \)
D. \( 240 J \)
Subject: Maths
There are three bags \( B_{1}, B_{2} \) and \( B_{3} . \) The
bag \( \boldsymbol{B}_{1} \) contains \( \mathbf{5} \) red and \( \mathbf{5} \) green balls.
\( B_{2} \) contains 3 red and 5 green balls and
\( B_{3} \) contains 5 red and 3 green balls.
Bags \( B_{1}, B_{2} \) and \( B_{3} \) have probabilities \( \mathbf{3} / \mathbf{1 0}, \mathbf{3} / \mathbf{1 0} \) and \( \mathbf{4} / \mathbf{1 0} \) respectively of
being chosen. A bag is selected at random and a ball is chosen at
random from the bag. Then which of the following options is/are correct? This question has multiple correct options
A. Probability that the chosen ball is green, given that the selected bag is \( B_{3} \), equal \( \frac{3}{8} \)
B. Probability that the selected bag is \( B_{3} \), given that the chosen ball is green, equals \( \frac{5}{13} \)
C ' probability that the chosen ball is green equals \( \frac{39}{80} \)
D. Probability that the selected bag is \( B_{3} \), given that the chosen ball is green, equals \( \frac{3}{10} \)
Subject: Chemistry
For the gas-phase decomposition,
\( \boldsymbol{P C I}_{5}(\boldsymbol{g}) \triangle \rightleftharpoons \boldsymbol{P C I}_{3}(\boldsymbol{g})+\boldsymbol{C I}_{2}(\boldsymbol{g}) \)
A. \( \triangle H<0, \Delta S<0 \)
B. \( \triangle H>0, \Delta S>0 \)
c. \( \triangle H>0, \Delta S<0 \)
D. \( \triangle H<0, \Delta S>0 \)
Subject: Physics
Q Type your question
i. If electrical resistivity of metal \( \boldsymbol{X} \) is
lower than that of metal \( Y \), it means
metal \( X \) is better conductor
of electricity than metal \( Y \)
ii. If a wire of resistance \( 8 \Omega \) is doubled
on itself, the resistance of the new wire
will be \( 2 \Omega \)
iii. The coils of electric toasters and
irons are made of an alloy rather than a pure metal because resistivity of the alloy is higher than that of its constituent metals.
iv. If a conductor of length \( 65 \mathrm{cm} \) has a
resistance of \( 4 \Omega, \) the same conductor of
length \( 260 \mathrm{cm} \) will have the resistance
of \( 16 \Omega \)
v. The maximum amount of current that
can pass through a conductor is \( 440 A \)
A. i, iii and v
B. i, ii, iii and iv
c. iii, iv and \( v \)
D. iii and iv only
Subject: Maths
The value of \( \lim _{x \rightarrow 0} \frac{(\tan (\{x\}-1)) \sin \{x\}}{\{x\}(\{x\}-1)} \)
is given by :
where \( \{x\} \) denotes the fractional part
function
\( A \cdot 1 \)
B. \( \tan 1 \)
\( c \cdot \sin 1 \)
D. Does not exist
Subject: Chemistry
Assertion
cell constant is the EMF of a cell.
Reason
Cell constant is determined by using
saturated KCl solution.
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
Two thin lenses of focal lengths \( 20 \mathrm{cm} \)
and \( 25 c m \) are placed in contact. The effective power of the combination is
A \( \cdot \frac{1}{9} D \)
B. \( 45 D \)
\( c . \$ \$ 6 D \$ \)
D. \( 9 D \)
Subject: Physics
Water is flowing continuously from a
\( \operatorname{tap} \) an ineternal diameter \( 8 \times 10^{-3} m \)
The water as it leaves the tap is \( 0.4 m s^{-1} . \) The diameter water stream at
a distance \( 2 \times 10^{-1} m \) be tap is close to
A \( \cdot 3.6 \times 10^{-3} \mathrm{m} \)
В. \( 5.0 \times 10^{-3} \mathrm{m} \)
c. \( 7.5 \times 10^{-3} m \)
D. \( 9.6 \times 10^{-3} m \)
Subject: Chemistry
How many more co-ordination isomers
are possible of the compoun \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] ? \)
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D. 8
Subject: Maths
Find the inverse of \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{3} & \mathbf{3} \\ \mathbf{1} & \mathbf{4} & \mathbf{3} \\ \mathbf{1} & \mathbf{3} & \mathbf{4}\end{array}\right] \)
column transformation.
Subject: Physics
A steel tape is calibrated at \( 20^{\circ} \mathrm{C} \). It is used to measure a length of an object on a hot summer day when the
temperature is \( 40^{\circ} \mathrm{C} \). If measured length is \( 5 \mathrm{m} \), the actual
length is \( \left(a=1 \times 10^{-5} /^{\circ} \mathrm{C}\right) \)
A. \( 5.001 \mathrm{m} \)
B. 5.01 \( m \)
\( c .5 .1 \mathrm{m} \)
D. 4.99 \( m \)
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{I} \) is an:
A. iodine derivative of alkanes
B. derivative of iodo alkanes
c. both \( A \) and \( B \)
D. None of these
Subject: Physics
A body of mass \( 3 \mathrm{kg} \) is under a force, which causes a displacement in it given by \( S=\frac{t^{3}}{3}(\text { in } \mathrm{m}) . \) Find the work
done by the force in first 2 seconds
A . 24
B. 3.83
c. 5.2 J
D . 2.6
Subject: Physics
A progressive wave is represented as \( \boldsymbol{y}=\mathbf{0 . 2} \cos \boldsymbol{\pi}\left(\mathbf{0 . 0 4 t}+\mathbf{0 . 2 x}-\frac{\boldsymbol{\pi}}{\mathbf{6}}\right) \) where
distance is expressed in cm and time in second. What will be the minimum
distance between two particles having
the phase difference of \( \frac{\pi}{2} ? \)
A. \( 4 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
c. \( 25 \mathrm{cm} \)
D. 12.5 cm
Subject: Maths
If \( \left.A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \text { (where } b \neq c\right) \) and satisfies the equation \( A^{2}+k I=0, \) then
\( \mathbf{A} \cdot a+d=0 \)
B . \( k=-|A| \)
c. \( k=|A| \)
D. None of the above
Subject: Maths
Type your question
List-I
\[
\begin{array}{l}\text { List-II } \\ \text { I) } \cos x=-\frac{1}{2} & \text { a) } \mathrm{x}=\frac{7 \pi}{3}\end{array}
\]
\( \begin{array}{ll}\text { II) } \sin x=\frac{\sqrt{3}}{2} & \text { b) } x=\frac{7 \pi}{6} \\ \text { ( } \| \text { ) } \tan x=\sqrt{3} & \text { c) } x=\frac{8 \pi}{3}\end{array} \)
\( A \cdot b, d, c, a \)
\( B \cdot c, a, b, e \)
\( \mathbf{C} \cdot b, c, e, a \)
\( \mathbf{D} \cdot b, e, e, a \)
Subject: Maths
Let \( \boldsymbol{O} \) be the origin and \( \boldsymbol{A} \) be the point \( (64,0) . \) If \( P \) and \( Q \) divide \( O A \) in the ratio
\( \mathbf{1}: \mathbf{2}: \mathbf{3}, \) then the point \( \boldsymbol{P} \) is
\( ^{\mathbf{A}} \cdot\left(\frac{32}{3}, 0\right) \)
в. (32,0)
\( ^{\mathbf{c}} \cdot\left(\frac{64}{3}, 0\right) \)
D. (16,0)
E \( \cdot\left(\frac{16}{3}, 0\right) \)
Subject: Physics
When a steady current of \( 1 A \) flows
through a copper wire, the number of electrons crossing any cross-section area of the wire in one second is
A \( \cdot 6.25 \times 10^{16} \)
B . \( 6.25 \times 10^{18} \)
\( \mathbf{c} \cdot 625 \times 10^{18} \)
D. \( 6.25 \times 10^{20} \)