AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The equation of a plane progressive wave is \( \boldsymbol{y}=\mathbf{0 . 0 2} \sin 8 \boldsymbol{\pi}\left[\boldsymbol{t}-\frac{\boldsymbol{x}}{\mathbf{2 0}}\right] . \) When it
is reflected at a rarer medium, its
amplitude becomes \( 75 \% \) of its previous value. The equation of the reflected wave is
A \( \cdot y=0.02 \sin 8 \pi\left[t-\frac{x}{20}\right. \)
B・ \( y=0.02 \sin 8 \pi\left[t+\frac{x}{20}\right. \)
c. \( y=0.15 \sin 8 \pi\left[t+\frac{x}{20}\right. \)
D. \( y=0.15 \sin 8 \pi\left[t-\frac{x}{20}\right] \)
Subject: Chemistry
Give the IUPAC name of the following compounds:
\[
\begin{array}{r}
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \\
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{3}
\end{array}
\]
Subject: Maths
If \( x^{2}+a x+b \) is an integer for every
integer \( \boldsymbol{x} \) then
A. \( a \) is always an integer but b need not be an integer
B. \( b \) is always an integer but a need not be an integer
\( \mathrm{c} \cdot a+b \) is always an integer
D. none of these
Subject: Chemistry
The energies of activation for forward
and reverse reactions for \( \left(\boldsymbol{A}_{2}+\boldsymbol{B}_{2} \rightleftharpoons\right. \)
\( 2 A B \) are \( 180 k J \) mol \( ^{-1} \) and \( 200 k J \) mol
-1 respectively. The presence of a
catalyst lowers the activation energy of both (forward and reverse) reactions by
\( 100 k J \) mol \( ^{-1} . \) The enthalpy change of
the reaction \( \left(A_{2}+B_{2} \rightarrow 2 A B\right) \) in the
presence of catalyst will be (in kJ mol-1
A. 300
B. 120
c. 280
D. 20
Subject: Physics
A particle executes linear simple harmonic motion with an amplitude of \( 3 \mathrm{cm} . \) When the particle is at \( 2 \mathrm{cm} \) from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
\( ^{\mathrm{A}} \cdot \frac{\sqrt{5}}{\pi} \)
в. \( \frac{\sqrt{5}}{2 \pi} \)
c. \( \frac{4 \pi}{\sqrt{5} \pi} \)
D. \( \frac{2 \pi}{\sqrt{3}} \)
Subject: Physics
Two vectors whose magnitudes are in ratio 1: 2 gives resultant of magnitude
30. If angle between these two vectors is
\( 120^{\circ}, \) then the magnitude of two vectors will be
A. \( 10 \sqrt{3}, 20 \sqrt{3} \)
3
B . \( 5 \sqrt{3}, 10 \sqrt{3} \)
D. \( 2 \sqrt{3}, 4 \sqrt{3} \)
Subject: Maths
The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:
Year
\( \begin{array}{lll}1960- & 1970- & 1980-\end{array} \)
is and 61
Route length (in \( \quad \) 56 \( \quad \) 60 thousand kilometres)
Represent the above data with the help of a bar graph.
Subject: Physics
An astronaut, orbiting in a spaceship round the earth, has a centripetal
acceleration of \( 6.67 m / s^{2} . \) Find the
height of the spaceship above the surface of the earth.
\( \left(G=6.67 \times 10^{11} N m^{2} / k g^{2}, \) radius of \right.
the earth \( =6400 \mathrm{km} \)
Subject: Physics
Two identical balls \( A \) and \( B \) are
released from the position shown in Fig.
1.205. They collide elastically with each other on the horizontal portion. The ratio
of heights attained by \( A \) and \( B \) after collision is (neglect friction)
\( A \cdot 1: 4 \)
в. 2: 1
\( c .4: 13 \)
D. 2: 5
Subject: Physics
From the top of a tower, a particle is thrown vertically downwards with a velocity of \( 10 \mathrm{m} / \mathrm{s} \). The ratio of the
distances, covered by it in the \( 3^{r d} \) and
\( 2^{n d} \) seconds of the motion is (Take \( g= \)
\( \left.\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A . 5: 7
B. 7: 5
\( c \cdot 3: 6 \)
D. 6: 3
Subject: Maths
Assertion
STATEMENT -1: If \( x, y, z \) are the sides of
a triangle such that \( x+y+z=1 \), then \( \left[\frac{2 x-1+2 y-1+2 z-1}{3}\right] \geq((2 x- \)
1) \( (2 y-1)(2 z-1))^{1 / 3} \)
Reason
STATEMENT-2: For positive numbers their A.M., G.M. and H.M. satisfy the relation \( \boldsymbol{A} . \boldsymbol{M} .>\boldsymbol{G} . \boldsymbol{M} .>\boldsymbol{H} . \boldsymbol{M} \)
A. Statement-1 is True, Statement-2 is True; Statement
-2 is a correct explanation for Statement- -
B. Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-
c. Statement- - is True, Statement- -2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Maths
\( \ln a \Delta A B C, \) if \( \cos A \cos B \cos C= \)
\( \frac{\sqrt{3}-1}{8} \) and \( \sin A . \sin B . \sin C= \)
\( \frac{\mathbf{3}+\sqrt{\mathbf{3}}}{\mathbf{8}} \)
then- \( 0 n \) the basis of above information, answer the following questions:The
value of \( \tan A+\tan B+\tan C \) is:
A \( \frac{3+\sqrt{3}}{\sqrt{3}-1} \)
B. \( \frac{\sqrt{3}+4}{\sqrt{3}-1} \)
c. \( \frac{6-\sqrt{3}}{\sqrt{3}-1} \)
D. \( \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-1} \)
Subject: Chemistry
Which among the following molecules
have \( s p^{3} d \) hybridisation with one lone pair of electrons on the central atom?
(i) \( \boldsymbol{S} \boldsymbol{F}_{4}\left(\text { ii) }\left[\boldsymbol{P C I}_{4}\right]^{+}\left(\text {iii) } \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{2} \boldsymbol{F}_{2}(\text { iv })\right.\right. \)
ClOF \( _{3} \)
A . (i), (ii) and (iii) only
B. (i), (iii) and (iv) only
c. (i) and (ii) only
D. (iii) and (iv) only
Subject: Maths
If \( \alpha \) and \( \beta \) are the roots of the equation
\( 375 x^{2}-25 x-2=0, \) then the value of
\( \lim _{n \rightarrow \infty}\left(\sum_{r=1}^{n} \alpha^{r}+\sum_{r=1}^{n} \beta^{r}\right) \) the value of is?
A \( \cdot \frac{29}{248} \)
в. \( \frac{17}{348} \)
c. \( \frac{29}{358} \)
D. \( \frac{11}{34} \)
Subject: Chemistry
Which of the following will produce a buffer solution when mixed in equal
volumes?
A. 0.1 mol \( d m^{-3} N H_{4} O H \) and 0.1 mol \( d m^{-3} H C l \)
B. 0.05 mol \( d m^{-3} N H_{4} O H \) and 0.1 mol \( d m^{-3} \) HCl
c. 0.1 mol \( d m^{-3} N H_{4} O H \) and 0.05 mol \( d m^{-3} H C l \)
D. 0.1 mol \( d m^{-3} C H_{3} C O O N a \) and 0.1 mol \( d m^{-3} \) NaOH
Subject: Maths
The area (in sq. units) of the region
described by \( \boldsymbol{A}= \)
\( \left\{(x, y) \mid y \geq x^{2}-5 x+4, x+y \geq 1, y \leq\right. \)
is:
A \( \cdot \frac{17}{6} \)
в. \( \frac{13}{6} \)
c. \( \frac{19}{6} \)
D. \( \frac{7}{2} \)
Subject: Chemistry
Make the correct pairs for the following
given \( \mathrm{X} \) and \( \mathrm{Y} . \mathrm{X} \) contains substance
and Y has method of manufacture:
\[
x
\]
1. Extraction of Sulphur \( \quad \) p. Contact process
2. Production of Nitric acid
q. Frasch method
3. Production of Sulphuric \( \quad \) r. Haber's process acid
4. Production of Ammonia \( \quad \) s. Ostwald's gas \( \quad \) process
A \( \cdot(1-s),(2-r),(3-q),(4-p) \)
B. \( (1-r),(2-q),(3-s),(4-p) \)
C \( .(1-q),(2-s),(3-p),(4-r) \)
D. \( (1-s),(2-q),(3-r),(4-p) \)
Subject: Maths
With out expanding show that \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{b}^{2} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c}^{2}\end{array}\right|=(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-\boldsymbol{a}) \)
Subject: Chemistry
The equilibrium constant for the
reaction
\( \boldsymbol{P}+\boldsymbol{Q} \rightleftharpoons \boldsymbol{R}+\boldsymbol{S} ; \boldsymbol{K}_{c}=\mathbf{0 . 2} \)
hence, the equilibrium constant for the following reaction will be:
\( \boldsymbol{R}+\boldsymbol{S} \rightleftharpoons \boldsymbol{P}+\boldsymbol{Q} \)
Subject: Maths
If \( x \) and \( y \) are sides of two squares such
that \( y=x-x^{2} \). Find the rate of change
of area of second square (side \( y \) ) with respect to area of the first square (side
\( x) \) when \( x=1 \mathrm{cm} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3
Subject: Physics
Two liquids at temperatures \( 60^{\circ} \mathrm{C} \) and
\( 20^{\circ} \mathrm{C} \) respectively have masses in the ratio 3: 4 and their specific heats in the
ratio \( 4: 5 . \) If the two liquids are mixed, the resultant temperature is
\( \mathbf{A} \cdot 70^{\circ} C \)
B. \( 50^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} C \)
D. \( 35^{\circ} \mathrm{C} \)
Subject: Physics
Velocity of sound in air is about :
A. \( 330 \mathrm{m} / \mathrm{s} \)
B. \( 460 \mathrm{m} / \mathrm{s} \)
c. \( 380 m / s \)
D. \( 400 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
The pH of a \( 10 \mathrm{ml} \) aqueous solution of
HCl is \( 4 . \) The amount of water to be
added to this solution in order to
change its pH from 4 to 5 is
A . 30 \( m 1 \)
B. 60 \( m \)
c. \( 90 \mathrm{ml} \)
D. 120 m
Subject: Physics
f the magnetic field in the following figure is increased then
\begin{tabular}{l|lllllll}
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\hline\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & \\
\hline
\end{tabular}
\( x x \)
\[
x \times x \times x
\]
A. plate A of the condenser will get positively charged
B. plate B of the condenser will get positively chargec
c. the condenser will not be charged
D. both the plates will be charged alternately
Subject: Chemistry
Represent the cell in which the following
reaction takes place \( M g(s)+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{0 . 0 0 0 1} \boldsymbol{M}) \rightarrow \)
\( M g^{2+}(0.130 M)+2 A g(s) \)
Calculate its \( E_{(c e l l)} \) if \( E_{(c e l l)}^{o}=3.17 V \)
Subject: Physics
An inclined plane makes an angle \( 30^{\circ} \)
with horizontal. A groove OA=5cm cut on the plane makes an angle \( 30^{0} \) with \( 0 x \)
A short smooth cylinder is free ti slide down the groove under the influence of gravity. the time taken by the cylinder to
reach from \( A \) to 0 is \( \left(g=10 m / s^{2}\right) \)
\( \mathbf{A} \cdot 4 s \)
в. \( 10 s \)
c. \( 2 s \)
D. \( 5 s \)
Subject: Physics
A light particle moving horizontally with a speed of \( 12 m / s \) strikes a very heavy
block moving in the same direction at
\( \mathbf{1 0} \boldsymbol{m} / \boldsymbol{s} . \) The collision is one-
dimensional and elastic. If the speed of
the block does not change after the collision, the particle will
A. Move at \( 2 \mathrm{m} / \mathrm{s} \) in its original direction
B. Move at \( 8 \mathrm{m} / \mathrm{s} \) in its original direction
c. Move at \( 8 \mathrm{m} / \mathrm{s} \) opposite to its original direction
D. Move at \( 12 \mathrm{m} / \mathrm{s} \) opposite to its original direction
Subject: Chemistry
If 90 g of water is electrolyzed completely with \( 50 \% \) current efficiency.
1) 10 Faraday of electricity will be consumed
2) 20 faraday of electricity will be consumed
3) \( 168 \mathrm{L}(\mathrm{STP}) \) of gases will be produced
4) \( 84 \mathrm{L}(\mathrm{STP}) \) of gases will be produced. Select the correct options.
A .2,3
В. 1,2,3
c. 1,3,4
D. 1,2,3,4
Subject: Physics
A body travels \( 200 \mathrm{cm} \) in the first two
seconds and \( 220 \mathrm{cm} \) in the next 4
seconds with same acceleration. The velocity of the body at the end of the 7 th second is:
\( A \cdot 5 \mathrm{cm} / \mathrm{s} \)
B. \( 10 \mathrm{cm} / \mathrm{s} \)
\( c \cdot 15 \mathrm{cm} / \mathrm{s} \)
D. 20 cm/s
Subject: Biology
Present atmospheric \( \boldsymbol{C O}_{2} \)
concentration is not limiting factor for
\( C_{4} \) plants as \( C_{4} \) plants
A. Posses PEPcase as primary carboxylase enzyme
B. Primary carboxylation reaction product is a four carbon acid
C. No oxygenation of RUBP due to kranz anatomy
D. Primary carboxylation reaction occurs in mesophyll cells
Subject: Physics
The absolute temperature T of a gas is
plotted against its pressure \( \mathrm{P} \) for two
different constant volumes \( V_{1} \) and \( V_{2} \)
where \( V_{1}>V_{2} . \) T is plotted along \( x \) -axis
and \( \mathrm{P} \) along \( \mathrm{y} \) -axis.
A. Slope for curve corresponding to volume \( V_{1} \) is greater
than that corresponding to volume \( V_{2} \)
B. Slope for curve corresponding to volume \( V_{2} \) is greater than that corresponding to volume \( V_{1} \)
C. Slope for both curves are equal
D. Slope for both curves are unequal such that they intersect at \( T=0 \)
Subject: Physics
The equation of wave is given by \( Y= \)
\( A \sin \omega\left(\frac{x}{v}-k\right) \) where \( \omega \) is the angular
velocity and v is the linear velocity. The dimensions of k is:
A . \( [L T] \)
в. \( [T] \)
\( \mathbf{c} \cdot\left[T^{-1}\right] \)
\( \mathbf{D} \cdot\left[T^{-2}\right] \)
Subject: Maths
The sum to infinity of \( \frac{1}{7}+\frac{2}{7^{2}}+\frac{1}{7^{3}}+ \)
\( \frac{2}{7^{4}}+\dots \) is
A \( \cdot \frac{1}{5} \)
в. \( \frac{7}{24} \)
c. \( \frac{5}{48} \)
D. \( \frac{3}{16} \)
Subject: Maths
\( \ln a \triangle w i t h \) sides \( a, b \) and \( c, a \)
semicircle touching the sides \( A C \) and
\( C B \) is inscribed whose diameter lies on
\( A B . \) Then, the radius of the semicircle
is :
A \( \cdot \frac{a}{2} \)
в. \( \frac{\Delta}{s} \)
c. \( \frac{\Delta}{a+b} \)
D. \( \frac{2 \Delta}{a+b} \)
Subject: Maths
If \( \boldsymbol{S}_{\boldsymbol{n}}=\frac{\boldsymbol{3}}{\boldsymbol{4}}+\frac{\boldsymbol{5}}{\boldsymbol{3} \boldsymbol{6}}+\frac{\boldsymbol{7}}{\boldsymbol{1 4 4}}+\frac{\boldsymbol{9}}{\boldsymbol{4 0 0}}+\ldots \) to \( \boldsymbol{n} \)
terms, then find \( \frac{1}{1-S_{40}} \)
Subject: Physics
A astronomical telescope has objective
and eyepiece of focal lengths \( 40 \mathrm{cm} \) and
\( 4 \mathrm{cm} \) respectively. To view an object
\( 200 \mathrm{cm} \) away from the objective, the lenses must be separated by a distance:
A . \( 54.0 \mathrm{cm} \)
в. \( 37.3 \mathrm{cm} \)
c. \( 46.0 \mathrm{cm} \)
D. \( 50.0 \mathrm{cm} \)
Subject: Physics
A body is released from the top of an
inclined plane of inclination \( \theta . \) It
reaches the bottom with velocity \( v \). If the
length remain same and the angle of inclination is doubled, what will be the velocity of the body on reaching the ground
\( A \cdot v \)
B. \( 2 v \)
C. \( [2 \cos \theta]^{1 / 2} v \)
D. \( [2 \sin \theta]^{1 / 2} v \)
Subject: Physics
From a \( 200 m \) high tower, one ball is
thrown upwards with speed of \( 10 m / s \) and another is thrown vertically downwards at the same speed simultaneously. The time difference of their reaching the ground will be
nearest to
A . \( 12 s \)
B. \( 6 s \)
c. \( 2 s \)
D. \( 1 s \)
Subject: Physics
The angle of incidence for an equilateral prism of refractive index so that the ray is parallel to the base inside the prism is
A \( .30^{\circ} \)
B . \( 20^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 45^{\circ} \)
\( E \cdot 75^{\circ} \)
Subject: Physics
If two particles of masses \( 3 k g \) and \( 6 k g \)
which are at rest are separated by a distance of 15 m. The two particles are
moving towards each other under a
mutual force of attraction. Then the
ratio of distances travelled by the particles before collision is
A .2: 1
B. 1: 2
c. 1: 3
D. 3: 1
Subject: Physics
A \( 5-\mathrm{Kg} \) block is projected upwards with
an initial speed of \( 10 m s^{-1} \) from the
bottom of a plane inclined at \( 30^{0} \) with
horizontal. The coefficient of kinetic
friction between the block and the plane
is 0.2.
a. How far does move up the plane?
b. How long does it move up plane?
c. After what time from its projection does the block again come back to the bottom? With what speed does it arrive?
Subject: Physics
which of the following is/are not
proportional to the inverse square of the
distance \( \times ? \)
This question has multiple correct options
A. The potential at a distance \( x \) from an isolated point charge
B. the electric field at a distance \( x \) from an isolated point charge
C. The force per unit length between two thin, straight, infinitely long current carrying conductors, parallel to each other, separated by a distance \( x \)
D. The gravitational attraction between two small bodies kept at a distance x apart
Subject: Maths
\( \operatorname{Let} \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{F}(\boldsymbol{x})=\frac{\boldsymbol{e}^{\boldsymbol{s} \boldsymbol{m} \boldsymbol{x}}}{\boldsymbol{x}}, \boldsymbol{x}>\mathbf{0} \)
\( \int_{1}^{4} \frac{\mathbf{3}}{\boldsymbol{x}} \boldsymbol{e}^{s \boldsymbol{m} \boldsymbol{x}^{3}} \boldsymbol{d} \boldsymbol{x}=\boldsymbol{F}(\boldsymbol{k})-\boldsymbol{F}(1), \) then one
of the possible values of \( k \) is
A . 16
B. 62
c. 64
D. 15
Subject: Maths
As \( \theta \) increases from \( \frac{\pi}{4} \) to \( \frac{5 \pi}{4}, \) the value
of \( 4 \cos \frac{1}{2} \theta \)
A. increases, then decreases
B. decreases, and then increases
C. decreases throughout
D. increases throughout
E. decreases, increases, and then decreases again
Subject: Maths
Two events \( A \) and \( B \) will be
independent, if
\( \mathbf{A} . A \) and \( B \) are mutually exclusive
B \( \cdot P\left(A^{\prime} B^{\prime}\right)=[1-P(A)][1-P(B)] \)
\( \mathbf{c} \cdot P(A)=P(B) \)
D \( \cdot P(A)+P(B)=1 \)
Subject: Chemistry
From the given electrolytes, indicate which one will bring about the coagulation of a gold sol quickest and in the least of molar concentration?
A \( . \) NaCl
B . \( M g S O_{4} \)
\( ^{\mathrm{c}} \cdot_{A l_{2}}\left(S O_{4}\right)_{3} \)
D. \( K_{4}\left[F e(C N)_{6}\right] \)
Subject: Physics
Fill in the blanks.
A horizontal pipeline carries water in streamline flow. At a point along the pipe, where the cross-sectional area is \( 10 \mathrm{cm}^{2}, \) the water velocity is \( 1 \mathrm{ms}^{-1} \)
and the pressure is 2000 Pa. The
pressure of water at another point
where the cross-sectional area is \( 5 \mathrm{cm}^{2} \)
is
\( \left.10^{3} k g m^{-3}\right) \)
Subject: Physics
In a potentiometer arrangement, a cell of emf \( 1.25 \mathrm{V} \) gives a balance point at 35 cm length of the wire. If the cell is replaced by another cell, the balance point shifts to \( 63 \mathrm{cm} \), then emf of the second cell is
A . \( 4.25 \mathrm{v} \)
B. 2.25
c. 3.25 \( v \)
D. \( 1.25 \mathrm{v} \)
Subject: Physics
The truth tables of logic gates \( A, B, C, D \)
are given here. Identify them correctly.
\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|} { Input } & \multicolumn{1}{c|} { Output } \\
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{Y} \) \\
\hline 0 & 0 & 0 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 1 \\
\hline
\end{tabular} \begin{tabular}{|l|c|c|}
\hline \multicolumn{2}{|c|} { Input } & Output \\
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{Y} \) \\
\hline 0 & 0 & 0 \\
0 & 1 & 0 \\
1 & 0 & 0 \\
1 & 1 & 1 \\
\hline
\end{tabular}
\begin{tabular}{|l|l|l|}
\hline \multicolumn{2}{|c|} { Input } & \multicolumn{1}{|c|} { Output } \\
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{Y} \) \\
\hline 0 & 0 & 1 \\
0 & 1 & 0 \\
1 & 0 & 0 \\
1 & 1 & 0 \\
\hline
\end{tabular} \begin{tabular}{|l|c|c|}
\hline \multicolumn{2}{|c|} { Input } & \multicolumn{1}{|c|} { Output } \\
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{Y} \) \\
\hline 0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0 \\
\hline
\end{tabular}
A . A: OR
B: AND, C: NOR,
D: NAND
B. A: OR,
\( B: \) NOR, \( C: A N D \)
D: NAND
C. \( A: A N D \)
B: OR, C: NAND,
D: NOR
D. A: OR
B: NOR, C: NAND,
D: AND
Subject: Maths
A square and an equilateral triangle have the same perimeter. If the diagonal of the square is \( 12 \sqrt{2} \mathrm{cm} \), then the area
of the triangle is:
A \( \cdot 24 \sqrt{3} \mathrm{cm}^{2} \)
B \( \cdot 24 \sqrt{2} \mathrm{cm}^{2} \)
c. \( 64 \sqrt{3} \mathrm{cm}^{2} \)
D. \( 32 \sqrt{3} \mathrm{cm}^{2} \)
Subject: Maths
If \( \bar{a} \) and \( \bar{b} \) are non-collinear unit vectors
and \( |\bar{a}+\bar{b}|=\sqrt{3} \) then \( (2 \bar{a}+5 \bar{b}) \)
\( (3 \bar{a}-\bar{b})=? \)
A \( \cdot \frac{15}{4} \)
в. \( \frac{15}{2} \)
c. 15
D. 16
Subject: Physics
connected to a resistance \( R \) and two
ideal inductors \( L_{1} \) and \( L_{2} \) through a
switch \( S \) as shown. There is no mutual
inductance between the two inductors.
The switch \( S \) is initially open. At \( t=0 \)
the switch is closed and current beings
to flow. Which of the following options is/are correct?
A. After a long time, the current through \( L_{1} \) will be \( \frac{V L_{2}}{R L_{1}+L_{2}} \)
B. After a long time, the current through \( L_{2} \) will be \( \frac{V L_{2}}{R L_{1}+L_{2}} \)
c. The ratio of the currents through \( L_{1} \) and \( L_{2} \) is fixed at all times \( (t>0) \)
Det the current through the resistance \( R \) is \( \frac{V}{R} \)
Subject: Chemistry
At \( 527^{0} \mathrm{C} \), the reaction
\( N H_{3}(g) \rightleftharpoons \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g) \) has \( K_{c}= \)
4
What is the \( K_{c} \) for the reaction?
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
\( A \cdot \frac{1}{4} \)
B. 16
\( c \cdot 4 \)
D. \( \frac{1}{16} \)
Subject: Maths
If \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi} \) and \( \mathbf{A}, \mathbf{B}, \mathbf{C} \) are all
greater then 0 and angle \( C \) is obtuse then
\( \mathbf{A} \cdot \tan A \tan B \geq 1 \)
B. \( \tan A \tan B<1 \)
\( \mathbf{c} \cdot \tan A \tan B=1 \)
D. None of these
Subject: Chemistry
Give plausible explanation for each of the following:
(i) Cyclohexanone forms cyanohydrin in good yield but 2,2,6 trimethylcyclohexanone does not.
(ii) There are two \( N H_{2} \) groups in semicarbazide. However, only one is
involved in the formation of
semicarbazones.
(iii) During the preparation of esters from a carboxylic acid and an alcohol in the presence of an acid catalyst, the water or the ester should be removed as
soon as it is formed.
Subject: Maths
If \( \frac{5 x-7 y+10}{1}=\frac{3 x+2 y+1}{8}= \)
\( \frac{11 x+4 y-10}{9}, \) then what is the \( x+y \)
equal to?
A . 1
B. 2
\( c \cdot 3 \)
D. -
Subject: Physics
A steel rope has length \( L \), area of cross-
section \( A \), Young's modulus \( Y \) and density as \( d \). It is pulled on a horizontal
frictionless floor with a constant horizontal force \( F=\frac{d A L g}{2} \) applied at one
end. Find the strain at the midpoint.
\( \mathbf{A} \cdot \frac{d g L}{2 Y} \)
B. \( \frac{d g L}{4 Y} \)
\( \mathbf{c} \cdot \frac{d g L}{6 Y} \)
D. \( \frac{d g L}{8 Y} \)
Subject: Maths
\( \int\left(\frac{\cos ^{3} x+\cos ^{5} x}{\sin ^{2} x+\sin ^{4} x}\right) d x= \)
A \( \cdot \sin x-\frac{2}{\sin x}-6 \tan ^{-1}(\sin x)+c \)
в.
c. \( \sin x+\frac{2}{\sin x}-6 \tan ^{-1}(\sin x)+c \)
D. \( \sin x+\frac{2}{\sin x}+6 \tan ^{-1}(\sin x)+c \)
sin \( x+6 \tan ^{-1}(\sin x)+c \)
Subject: Physics
The de-Broglie wavelength \( \lambda_{n} \) of the electron in the nth orbit of hydrogen
atom is
A. Inversely proportional to \( n \)
B. Proportional to \( n^{2} \)
c. Proportional to \( n \)
D. Inversely Proportional to \( n^{2} \)
E. Inversely proportional to radius of the orbit in the nth state
Subject: Chemistry
When \( 262 g \) of xenon (atomic mass \( = \)
131) reacted completely with 152 g of
fluorine (atomic mass \( =\mathbf{1 9} \) ), a mixture
of \( X e F_{2} \) and \( X e F_{6} \) was produced. The
molar ratio \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}: \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \) is :
A . 1: 2
B. 1: 4
c. 1: 1
D. 1: 3
Subject: Chemistry
If a half cell \( \boldsymbol{X} \mid \boldsymbol{X}^{2+}(\mathbf{0 . 1} \boldsymbol{M}) \)
is connected to another half cell
\( \boldsymbol{Y} \mid \boldsymbol{Y}^{2+}(\mathbf{1} . \mathbf{0} \boldsymbol{M}) \) by means of \( \mathbf{a} \)
salt bridge and an external circuit at
\( 25^{\circ} C, \) the cell voltage would be:
\( \mathbf{A} \cdot 0.06 V \)
B. \( 0.12 V \)
c. \( 0.62 V \)
D. \( 0.72 V \)
Subject: Maths
\( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a}-\boldsymbol{c} & \boldsymbol{a}-\boldsymbol{b} \\ \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b}-\boldsymbol{a} \\ \boldsymbol{c}-\boldsymbol{b} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right|= \)
A. \( 4 a b c \)
B. \( 6 a b c \)
\( c .8 a b c \)
D. \( 2 a b c \)