AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
(a) Complete the following chemical
equations:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4}+\boldsymbol{S} \boldsymbol{b} \boldsymbol{F}_{5} \rightarrow \)
(ii) \( C l_{2}+F_{2}(\text {excess}) \rightarrow \)
(b) Explain each of the following:
(i) Nitrogen is much less reactive than
phosphorus.
(ii) The stability of +5 oxidation state
decreases down group 15.
(iii) The bond angles \( (O-N-O) \) are
not of the same value in \( N O_{2}^{-} \) and \( N O_{2}^{+} \)
Subject: Biology
Which is true of glycolysis
A. In aerobic organisms, it is the only process in respiration
B. In this process glucose undergoes complete oxidation to form pyruvic acid
C. Enzyme hexokinase catalyses phosphorylation of glucose to glucose 6 -phosphate
D. ATP is utilised in conversion of PEP to pyruvic acid
E. \( \mathrm{NADH}+H^{+} \) is formed when
1, 3-biphosphoglyceric acid is converted to 3-phosphoglyceric acid
Subject: Physics
A small metal ball of diameter 4 mm
and density \( 10.5 g / c m^{3} \) in dropped in glycerine of density \( 1.5 g / c m^{3} . \) The ball attains a terminal velocity of \( 8 \mathrm{cm} / \mathrm{sec} \)
The coefficient of viscosity of glycerine
is
A. 4.9 poise
B. 9.8 poise
c. 98 poise
D. 980 poise
Subject: Physics
A particle moves along the side \( A B, B C \)
CD of a square of side 25 m with a
velocity of 15 m/s. Its average velocity
is
A \( .15 \mathrm{m} / \mathrm{s} \)
в. \( 10 \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} .7 .5 \mathrm{m} / \mathrm{s} \)
D. \( 5 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Assertion
Perfectly ideal solution is not possible with respect to binary solution of two liquids.
Reason
No two substances can have exactly the same nature of intermolecular forces
and also of the same magnitude.
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
If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{x} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{y}\end{array}\right] \) for \( \boldsymbol{x} \neq \)
\( \mathbf{0}, \boldsymbol{y} \neq \mathbf{0}, \) then \( \boldsymbol{D} \) is:
A. divisible by neither \( x \) nor \( y \)
B. divisible by both \( x \) nor \( y \)
c. divisible by \( x \) but not \( y \)
D. divisible by \( y \) but not \( x \)
Subject: Maths
Minimum and maximum \( z=5 x+2 y \)
subject to the following constraints:
\( x-2 y \leq 2 \)
\( 3 x+2 y \leq 12 \)
\( -3 x+2 y \leq 3 \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Maths
\( \sum_{r=1}^{n} \tan ^{-1}\left(\frac{2^{r-1}}{1+2^{2 r-1}}\right) \) is equal to:
\( \mathbf{A} \cdot \tan ^{-1}\left(2^{n}\right) \)
B \cdot \( \tan ^{-1}\left(2^{n}\right)-\frac{\pi}{4} \)
c. \( \tan ^{-1}\left(2^{n+1}\right) \)
\( \mathbf{D} \cdot \tan ^{-1}\left(2^{n+1}\right)-\frac{\pi}{4} \)
Subject: Biology
In the following table the ecological
units are mentioned in the first column
vertically and their attributes are
mentioned horizontally Which of the following options is correct for
ecological units with their respective attributed indicated by \( A \) to \( P \)
Attributes Age of Age of Ecological \( \quad \) Age
Individual \( B \) Organism
Population \( E \)
I
Community
\( V \)
\( M \) Ecosystem
A . I-C II-B III-K IV-P
B. I-A II-G III-LIV-N
c. I-C II-A III-K IV-L
D. I-A II-B III-C IV-D
Subject: Chemistry
For the reaction given below,
\( \mathbf{2} \mathbf{O}_{\mathbf{3}}(\mathbf{g}) \rightarrow \mathbf{3} \mathbf{O}_{\mathbf{2}}(\mathbf{g}) \)
\( \operatorname{Step} \mid: \mathbf{O}_{3}(\mathbf{g}) \rightarrow \mathbf{O}_{2}(\mathbf{g})+\mathbf{O}(\mathbf{g}) \)
Step \( 2: \mathrm{O}_{3}(\mathrm{g})+\mathrm{O} \rightarrow^{\text {slow }} 2 \mathrm{O}_{2}(\mathrm{g}) \)
Statement I: The molecularity of the first step is 1 and of the second step is 2
Statement-II: \( O(g) \) is an intermediate
and rate of reaction is \( \mathbf{K}\left[\mathbf{O}_{3}\right]^{2}\left[\mathbf{O}_{2}\right]^{-1} \) and
order of reaction is 1
A. Both statements are true Statement - - ll is correct explanation of Statement- -
B. Both statements are true but Statement- -II is not correct explanation of Statement- -
c. Statement - - lis true but Statement - II is false
D. Statement-lis false but Statement- 11 is true
Subject: Maths
In a trapezium, the vector \( \overline{B C}=\lambda \overline{A D} \)
and \( \bar{P}=\overline{A C}+\overline{B D}=\mu \overline{A D}, \) then
A. \( \mu=\lambda+1 \)
в. \( \lambda=\mu+1 \)
c. \( \lambda+\mu=1 \)
D. \( \mu=2+\lambda \)
Subject: Maths
Find the median of the following data.
\( \begin{array}{lllll}\text { class } & 0- & 20- & 40- & 60 \\ \text { interval } & 20 & 40 & 60 & 800\end{array} \)
12 Frequency \( \quad 8 \quad 10 \)
A . 45
B. 40
c. 55
D. 50
Subject: Maths
Hasan buys two kinds of cloth material for school uniforms, shirt material that
\( \operatorname{costs} \) hom Rs 50 per metre and trouser
material that costs him Rs 90 per
metre.for every 3 meters of shirt
material he buys 2 meters of the trouser
material. he sells the material at \( 12 \% \)
and \( 10 \% \) profit respectively. his total sale is Rs 36,600 . how much trouser material did he buy?
Subject: Chemistry
For a reaction \( \boldsymbol{A}_{(g)} \rightarrow \boldsymbol{B}_{(g)}+\boldsymbol{C}_{(g)}, \) the
rate constant for the reaction is \( 3 x \)
\( 10^{-3} M^{-} \) min \( ^{-1} . \) At what concentration
of \( A \) will at the rate of reaction be \( 2 x \)
\( 10^{-3} \mathrm{M} \mathrm{min} \)
A. 1 м
в. 0.52 М
c. 0.82 М
D. \( \frac{2}{3} \) N
Subject: Physics
At what temperature the reading on Celsius scale is half of that on
Fahrenheit scale?
A \( \cdot 160^{\circ} \mathrm{C} \)
B . \( 170^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 180^{\circ} C \)
D. \( 190^{\circ} \mathrm{C} \)
Subject: Physics
Pick up the correct statements:
This question has multiple correct options
A. The changing (with time) magnetic field need not be in existence at the location of induced electric field.
B. A uniform magnetic field increasing at constant rate, induces an electric field which is constant and non
conservative
C. Non zero force exerted by uniform and constant magnetic field on a moving charged particle does no work but always changes momentum of the particle.
D. All the above statements are wrong.
Subject: Physics
An electric dipole of moment 'p' is placed in an electric field of intensity 'E'. The dipole acquires a position such that the axis of the dipole makes an angle \( \theta \) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \( =90^{0}, \) the torque and the
potential energy of the dipole will respectively be
A. \( p E \sin \theta, p E \cos \theta \)
B. \( p E \sin \theta,-2 p E \cos \theta \)
c. \( p E \sin \theta, 2 p E \cos \theta \)
D. \( p E \cos \theta,-p E \cos \theta \)
Subject: Chemistry
Assertion
Hydrolysis of ester is an example of
auto-catalytic reaction.
Reason
A catalyst speeds up the process
without participating in the
mechanism.
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: Chemistry
Assertion
Bakelite is first completely synthesized thermoplastic.
Reason
Thermosetting plastics are harder.
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: Physics
Assertion
In a motion picture, the consecutive frames are almost the same and
quickly switched.
Reason
In the retina of human eyes these
continuous images get fused into one another
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
If \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{4}, \mathbf{5}\}, \boldsymbol{B}=\{\mathbf{7}, \mathbf{8}, \mathbf{9}\} \) then
\( \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B}) \) is equal to
\( A \cdot 6 \)
B. 9
\( c .3 \)
\( D \)
Subject: Physics
The \( 3^{r d} \) crest of a transverse wave from
its centre of disturbance is \( 32.4 \mathrm{cm} \)
away. The \( 6^{t h} \) crest of this wave is
\( 75.6 c m \) from its centre of disturbance.
a) Find the wave length of the wave.
b) If time period of a wave is \( 0.2 s, \) what
will be the velocity of the wave?
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{e}^{\sin ^{2} \boldsymbol{x}+\sin ^{4} \boldsymbol{x}+\sin ^{6} \boldsymbol{x}+\ldots \infty}, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot e^{\tan ^{2} x} \)
B. \( e^{\tan ^{2} x} \sec ^{2} x \)
C \( \cdot 2 e^{\tan ^{2} x} \tan x \cdot \sec ^{2} x \)
D. 1
Subject: Chemistry
What is the best term to describe the
rearrangement that causes the conversion of 3 -bromo- 2,2
dimethylbutane to 2,3 -dimethyl-2butanol?
A. 1,2 -methyl shift
B. 1, 3- hydride shift
c. 1,3 -methyl shift
D. 1,2 - hydride shift
Subject: Physics
A sphere is rotating between two tough
inclined walls as shown in figure.

Coefficient of friction between each wall
and the sphere is \( 1 / 3 . \) If \( f_{1} \) and \( f_{2} \) be the
friction forces at \( P \) and \( Q . \) Then \( \frac{f_{1}}{f_{2}} \) is:
A \( \cdot \frac{4}{\sqrt{3}}+1 \)
B. \( \frac{1}{\sqrt{3}}+2 \)
c. \( \frac{4}{2}+\sqrt{3} \)
D. \( 1+2 \sqrt{3} \)
Subject: Chemistry
Choose the correct answer form the
alternatives given. Match the column I with column II and
mark the appropriate choice.
Column I Column I
(A) Quick
lime
(i) Setting fractured bones
(B) Plaster of
Paris
(ii) A constituent of gum chewing
Manufacture Slaked
lime O
\( (c) \)
(iii) bleaching powder
(D) limestone
(iv) Manufacture of dyestuffs
A \( \cdot(A) \rightarrow(i),(B) \rightarrow(i v),(C) \rightarrow(i i),(D) \rightarrow(i i i) \)
B. \( (A) \rightarrow(i v),(B) \rightarrow(i),(C) \rightarrow(i i i),(D) \rightarrow(i i) \)
c. \( (A) \rightarrow(i i),(B) \rightarrow(i i i),(C) \rightarrow(i),(D) \rightarrow(i v) \)
\( D \)
\( (i i i),(B) \rightarrow(i i),(C) \rightarrow(i v),(D) \rightarrow(i) \)
Subject: Maths
If the equation \( k x^{2}+4 x+1=0 \) has
real and distinct roots, then:
\( \mathbf{A} \cdot k<4 \)
B. \( k>4 \)
\( \mathbf{c} \cdot k \leqslant 4 \)
D. \( k \geqslant 4 \)
Subject: Maths
Let \( \mathbb{Z} \) be the set of integers and \( \boldsymbol{f}: \mathbb{Z} \rightarrow \)
\( \mathbb{Z} \) be defined as \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}, \boldsymbol{x} \in \mathbb{Z} \)
then function is
A. bijection
B. injection
c. surjection
D. none of these
Subject: Chemistry
For a cell, the cell reaction is \( M g(s)+ \) \( C u^{2+}(a q) \rightarrow M g^{2+}(a q)+C u(s) . \) If the
S.R.P. values of \( M g \) and \( C u \) are \( -2.37 V \)
and \( +0.34 V \) respectively, the EMF of the
cell is:
A \( .+2.03 V \)
B . \( -2.03 \mathrm{V} \)
\( \mathrm{c} \ldots+2.71 \mathrm{V} \)
D. \( -2.71 V \)
Subject: Maths
Suppose that two cards are drawn at random from a deck of cards. Let \( X \) be
the number of aces obtained. Then the
value of \( \boldsymbol{E}(\boldsymbol{X}) \) is
A \( \cdot \frac{37}{221} \)
в. \( \frac{5}{13} \)
c. \( \frac{1}{13} \)
D. \( \frac{2}{13} \)
Subject: Physics
The velocity of an object varies with time as \( V=A t^{2}+B t+C . \) Taking the
unit of time as \( s \) and velocity as \( m s^{-1} \) the units of \( A, B, C \) respectively are :
\( \mathbf{A} \cdot m s^{-3}, m s^{-2}, m s^{-1} \)
B . \( m s^{-2}, m s^{-1}, m s^{-3} \)
c. \( m s^{-1}, m s^{-2}, m s^{-3} \)
D. \( m s^{-1}, m s^{-1}, m s^{-1} \)
Subject: Chemistry
Br \( F_{3} \) is a liquid which considerably undergoes self ionization to form cationic and anionic species.
\( 2 B r F_{3} \rightleftharpoons\left[B r F_{2}\right]^{+}+\left[B r F_{4}\right]^{-} \)
Based on \( V S E P R \) theory, how many
\( 90^{\circ} F-B r-F \) bond angles are
there in anionic species?
\( A \cdot 4 \)
B. 5
\( c \cdot 3 \)
D.
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}^{2}- \)
\( 3 x+5, \) then find the value of
\( \frac{\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{h})-\boldsymbol{f}(\boldsymbol{x})}{\boldsymbol{h}} \) at \( \boldsymbol{h} \neq \mathbf{0} \)
A. \( 4 x+2 h \)
B. \( 4 x+2 h-3 \)
c. \( 4 x-2 h+3 \)
D. \( 4 x-2 h-3 \)
Subject: Physics
If energy required to remove one of the two electron from He atom is \( 29.5 e V \)
then what is the value of energy
required to convert a helium atom into
\( \boldsymbol{\alpha}- \) particle?
A . \( 54.4 e V \)
B. \( 83.9 e V \)
c. \( 29.5 e V \)
D. 24.9eV
Subject: Physics
In Thomsons method, a beam of
electrons accelerated through a p.d. of \( 285 V, \) passes undeflected through
perpendicular electric and magnetic
fields of intensities \( 10^{5} V / m \) and
\( 10^{-2} W b / m^{2} \) respectively. Then the value of e/m of electron is:
A \( \cdot 1.75 \times 10^{11} C / k g \)
В. \( 1.66 \times 10^{11} C / k g \)
c. \( 1.84 \times 10^{11} C / k g \)
D. \( 1.89 \times 10^{11} C / k g \)
Subject: Physics
Two radioactive sources \( A \) and \( B \)
initially contain equal number of radioactive. Source \( \boldsymbol{A} \) has a half-life of
1 hour and source \( B \) has a half-life of
2hours. the ratio of the rate of
disintegration of \( \boldsymbol{A} \) to that of \( \boldsymbol{B} \) is:
A .1: 2
B . 2: 1
c. 1: 1
D. 1: 4
Subject: Chemistry
\( N a \rightarrow N a^{+}+e^{-} \)
\( \boldsymbol{C l}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C l}^{-} \)
a) Is sodium a metal or a non-metal?
b) Write the name of \( C l^{-} \) ion.
Subject: Chemistry
Assertion
The mobility of sodium ion is lower than
that of potassium ion.
Reason
The ionic mobilities depend on the
effective radius of the ion.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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
Ethylene chloro hydrin is the product of following reaction:
A. \( C H_{2}=C H_{2}+H O C l \)
в. \( C H_{2}=C H_{2}+H_{2} \)
\( \mathbf{c} \cdot C H_{2}=C H_{2}+C l_{2} \)
D. \( C H_{2}=C H_{2}+H O B r \)
Subject: Chemistry
A molecule of \( \boldsymbol{H} \boldsymbol{X} \) can form stronger
hydrogen bond than another molecule
\( \boldsymbol{H}_{2} \boldsymbol{Y} . \) But \( \boldsymbol{H} \boldsymbol{X} \) boils at a lower
temperature than \( \boldsymbol{H}_{2} \boldsymbol{Y} \). Identify \( \boldsymbol{H} \boldsymbol{X} \)
and \( H_{2} Y \) and give a reason for the
peculiar behavior.
Subject: Physics
Assertion
(A) : In a metrebridge ; Copper wire is connected in the left gap and
silicon is connected in the right gap. When the temperature of both wires increase, balancing point shifts to right. Reason
(R) :Temperature coeficient of copper is (-)Ve and that of silicon is \( (+) \)
Ve.
A. Both A \& R are true and R is the correct explanation of \( A \)
B. Both A \& R are true and R is not a correct explanation of
c. A is true but R is false
D. A is false but R is true
Subject: Physics
Assertion
The bob of a simple pendulum is a ball full of water. If a fine hole is made in the
bottom of the ball, the time period first increases and then decreases.
Reason
As water flows out of the bob the weight of bob decreases.
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
Which of the following is the range of temperature recorded by a laboratory thermometer?
A \( \cdot 0^{\circ} C \) to \( 100^{\circ} \mathrm{C} \)
B . \( -10^{\circ} \mathrm{C} \) to \( 110^{\circ} \mathrm{C} \)
c. \( 30^{\circ} C \) to \( 120^{\circ} C \)
D. \( 45^{\circ} \mathrm{C} \) to \( 145^{\circ} \mathrm{C} \)
Subject: Maths
\( \int \frac{3 x^{2}}{\sqrt{\left(9-16 x^{6}\right)}} d x \)
A. \( \frac{1}{4} \sin ^{-1} \frac{4}{3} x^{3} \)
B \( \cdot \frac{1}{2} \sin ^{-1} \frac{4}{3} x^{3} \)
c. \( \frac{1}{4} \sin ^{-1} \frac{2}{3} x^{3} \)
D. \( \frac{1}{4} \sin ^{-1} \frac{4}{3} x^{6 .} \)
Subject: Physics
A half meter rod is pivoted at the centre
with two weights of \( 20 g f \) and \( 12 g f \)
suspended at a perpendicular distance of \( 6 \mathrm{cm} \) and \( 10 \mathrm{cm} \) from the pivot respectively
as shown below.
¡) Which of the two force acting on the
rigid rod causes clockwise moment?
ii) is the rod in equilibrium?
Subject: Chemistry
The calculated spin-only magnetic moments (BM) of the anionic and
cationic species of \( \left[\boldsymbol{F} e\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]_{2} \) and
\( \left[\boldsymbol{F e}(\boldsymbol{C} \boldsymbol{N})_{\mathbf{6}}\right], \) respectively, are:
A .4 .9 and 0
B. 2.84 and 5.92
c. 0 and 4.9
D. 0 and 5.92
Subject: Chemistry
The correct statement is/are:
A) Vitamins in high concentrations catalyse biological reactions
B) Daily dose of vitamins for an individual depend on his or her age, site and rate of metabolism
C) Youngsters need higher quantities of vitamins than elders
D) The need of vitamins for younger,
growing children and pregnant women is lower
A. \( A \) and \( B \)
B. \( A, B \) and \( C \)
c. \( A \) and \( D \)
D. \( C \) and \( D \)
Subject: Physics
The dimensional formula for Young's
modulus is :
\( \mathbf{A} \cdot\left[M L^{-1} T^{-2}\right] \)
B \( \cdot\left[M^{0} L T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-2}\right] \)
D. \( \left[M L^{2} T^{-2}\right] \)
Subject: Maths
Let \( a, b, c \) be real numbers with \( a^{2}+ \)
\( b^{2}+c^{2}=1 \)
show that the equation \( \mid \begin{array}{ccc}\boldsymbol{a} \boldsymbol{x}-\boldsymbol{b} \boldsymbol{y}-\boldsymbol{c} & \boldsymbol{b} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y} & \boldsymbol{c} \boldsymbol{x}+ \\ \boldsymbol{b} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y} & \boldsymbol{-} \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}-\boldsymbol{c} & \boldsymbol{c} \boldsymbol{y}+ \\ \boldsymbol{c} \boldsymbol{x}+\boldsymbol{a} & \boldsymbol{c} \boldsymbol{y}+\boldsymbol{b} & \boldsymbol{-} \boldsymbol{a} \boldsymbol{x}-\boldsymbol{b}\end{array} \)
represents a straight line.
Subject: Chemistry
The common name, "cream of tartar"
refers to:
\( \mathbf{A} \cdot K H C_{4} H_{4} O_{6} \)
\( \mathbf{B} \cdot K(S b O) C_{4} H_{4} O_{6} \)
\( \mathbf{c} \cdot K N a C_{4} H_{4} O_{6} \)
D. \( M g_{2}(O H)_{2}\left(C_{4} H_{4} O_{6}\right) H_{2} O \)
Subject: Chemistry
What is the structural formula of
fumaric acid?
\( A \)
\[
\text { HOOC }-\mathbf{C}-\mathbf{C H}_{3}
\]
B.
\[
\mathbf{H}_{3} \mathbf{C}-\mathbf{C}-\mathbf{C O O H}
\]
\( c \)
D.
HOOC \( -\mathbf{C}-\mathbf{H} \)
Subject: Maths
If \( f(x) \) is continuous function such that
\( \int_{0}^{x} f(t) d t \rightarrow \infty \) as \( x \rightarrow \infty, \) show that
every line \( y=m x \) intersect the curve
\( \boldsymbol{y}^{2}+\int_{0}^{x} \boldsymbol{f}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t}=\boldsymbol{a} \) where \( \boldsymbol{a} \in \boldsymbol{R}^{+} \)
Subject: Physics
(1):In uniform circular motion,
tangential acceleration is zero.
(2) : In uniform circular motion, velocity is constant.
A. Both 1 and 2 are true and 2 is correct explanation of
B. Both 1 and 2 are true and 2 is not correct explanation of 1
c. 1 is true and 2 is false
D. 1 is false and 2 is true
Subject: Chemistry
If enthalpies of formation for \( \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g}) \)
\( C O_{2}(g) \) and \( H_{2} O(l) \) at \( 25^{\circ} \mathrm{C} \) and 1 atm pressure be 52,-394 and -286
\( k J \) mol\( ^{-1} \) respectively, then the
enthalpy of combustion of \( C_{2} H_{4}(g) \) will be:
A. \( -141.2 \mathrm{kJ} \mathrm{mol}^{-1} \)
B. - 1412 k J mol \( ^{-1} \) ?
c. \( +141.2 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. +1412 k \( \mathrm{mol}^{-1} \)
Subject: Maths
If \( \boldsymbol{A}=\tan ^{-1}\left(\frac{1}{7}\right) \) and \( \boldsymbol{B}=\boldsymbol{t a n}^{-1}\left(\frac{1}{3}\right) \)
then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \cos 2 A=\frac{24}{25} \)
В. \( \cos 2 B=\frac{4}{5} \)
c. \( \cos 2 A=\sin 4 B \)
D. \( \tan 2 B=\frac{3}{4} \)
Subject: Physics
Determine the electric field everywhere
outside the sphere at a distance \( r(>> \)
\( \boldsymbol{a}) \) from the centre
A \( \cdot E=\frac{Q}{4 \pi \epsilon_{0} r^{2}} \)
B. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} r} \)
c. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} a^{2}} \)
D. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} a} \)
Subject: Maths
Jill is putting a tile floor in her kitchen She needs 52 tiles to cover the whole
floor. There are 24 tiles in a box. A box
\( \operatorname{costs} R s .23 .95 . \) Individual tiles cost \( R s \)
2.95. Sales tax is \( 5 \% \). How much will 52
tiles cost approximately, including sales tax?
A . \( R s .50 \)
B. Rs. 57
c. \( R s .60 \)
D. \( R s .63 \)
Subject: Chemistry
The reaction of slaked lime with \( C l_{2} \) gas
gives:
\( \mathbf{A} \cdot \) only \( C a(O C l)_{2} \)
B. only \( C a C l_{2} \)
C . a mixture of \( C a(O C l)_{2}, C a(O H)_{2}, C a C l_{2}, H_{2} O \)
D. quick lime
Subject: Chemistry
Which of the following is a biodegradable polymer?
A.
\[
f H N-\left(C H_{2}\right)_{6} N H C O-\left(C H_{2}\right)_{4}-C_{7}^{\prime}
\]
B. \( \quad_{t H N-\left(C H_{2}\right)_{5}-C \dagger_{n}}^{o} \)
\( c \)
\( \left.\left[\begin{array}{l}\mathbf{0} \\ \mathbf{c}\end{array}\right]\left[\begin{array}{l}- \\ \end{array}\right]-\mathbf{C O O}-\left(\mathbf{C H}_{2}\right)_{2}-\mathbf{O}\right] \)
D. \( +H N-\left(C H_{2}\right)_{5} C O N H-C H_{2}-\stackrel{\|}{C}+_{n} \)
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{H}^{+}+\boldsymbol{O} \boldsymbol{H}^{-} \)
The above reaction is dissociation or
ionization?
A. Dissociation
B. Ionization
c. Both dissociation and ionization together
D. None of these
Subject: Physics
A beam of light converges towards a point \( 0, \) behind a convex mirror of focal length \( 20 \mathrm{cm} . \) Find the magnification
and nature of the image when point 0 is \( 30 \mathrm{cm} \) behind the mirror.
A. 2 (virtual, inverted)
B. 3 (real, inverted)
c. 3, (virtual, enlarged)
D. +1 (real, enlarged)
Subject: Chemistry
8
box and covered it with a black paper
from all sides. They fixed a source of light (a torch) at one end of the box by making a hole in it and made another
hole on the other side to view the light.
They placed a milk sample contained in a beaker/tumbler in the box as shown
in the Fig.2.4. They were amazed to see
that milk taken in the tumbler was
¡IIluminated. They tried the same
activity by taking a salt solution but
found that light simply passed through
it?
Explain why the milk sample was illuminated. Name the phenomenon
involved.
Subject: Maths
\( \cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x \)
then \( \sin x \) is equal to
\( A \cdot \tan ^{2} \frac{\alpha}{2} \)
B \( \cdot \cot ^{2} \frac{\alpha}{2} \)
c. \( \tan \alpha \)
D. \( \cot \frac{\alpha}{2} \)
Subject: Chemistry
Which is a set of acid salts and can
react with base?
A. \( N a H_{2} P O_{2}, N a_{2} H P O_{3}, N a H_{2} P O_{4} \)
B. \( N a_{2} H P O_{3}, N a H_{2} P O_{3}, N a H P O_{4} \)
c. \( \operatorname{NaHCO}_{3}, \operatorname{NaH}_{2} \mathrm{PO}_{3}, \mathrm{Na}_{2} \mathrm{HPO}_{4} \)
D. All of the above