AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A radioactive nucleus emits an \( \alpha \)
particle and a neutron simultaneously with speed but in opposite direction in order to form a stable nuclei. If the
speed of emitted particles is \( v \) and \( A \) is
the mass number of radioactive
nucleus, then speed of stable nucleus is:
A. \( \frac{3 v}{A-5} \)
B. \( \frac{2 v}{A-5} \)
c. \( \frac{4 v}{A-5} \)
D. \( \frac{2 v}{A+5} \)
Subject: Maths
\( \operatorname{Let}\left|\frac{z_{1}-2 z_{2}}{2-z_{1} \bar{z}_{2}}\right|=1 \) and \( \left|z_{2}\right| \neq 1, \) where
\( z_{1} \) and \( z_{2} \) are complex numbers. Find
the value of \( \left|z_{1}\right| \)
Subject: Physics
In the figure \( A B=B C, A C=C D \) and
\( \angle A C D=90^{\circ} . \) If the radius of the circle
is "r" units then find the length of the
chord BC.
A \( \cdot r \sqrt{\sqrt{2-1}} \)
B \( \cdot r \sqrt{\sqrt{3-1}} \)
c. \( r \sqrt{2-\sqrt{2}} \)
D. \( r \sqrt{2-\sqrt{3}} \)
Subject: Physics
Assertion: The upper surface of the wings of an aeroplane is made convex
Reason: The air current at the top will
have greater velocity and thus pressure at the bottom will be greater than at the
top
A. Both assertion and reason are true and reason is correct explanation of assertion
B. Both assertion and reason are true but reason is not the correct explanation of assertion.
c. Assertion is true but reason is false.
D. Both assertion and reason are false
Subject: Physics
The coordinates of a particle moving in x-y plane at any instant of time t are \( x=4 t^{2} ; y=3 t^{2} . \) The speed of the
particle at that instant is :
A . 10
B. 5t
\( c \cdot 3 t \)
D. \( 2 t \)
E . \( \sqrt{13} t \)
Subject: Biology
Read the following four statements
carefully.
(i) Ventral respiratory group of neurons of medulla oblongata can cause both inspiration and expiration.
(ii) The part of the respiratory system starting with the external nostrils up to the terminal bronchioles constitutes
the respiratory or exchange part of the respiratory system.
(iii) During swallowing epiglottis can be covered by a thin elastic cartilaginous flap called glottis to prevent the entry of food into the larynx.
(iv) Binding of oxygen with haemoglobin is primarily related to
partial pressure of \( \boldsymbol{O}_{2} \) Which of the above two statements are
correct?
A. (ii) and (iii)
B. (iii) and (iv)
c. (i)and(ii)
D. (i) and (iv)
Subject: Maths
\( p: H e \) is hard working.
\( \boldsymbol{q}: \) He is intelligent.
Then \( \sim \boldsymbol{q} \Rightarrow \sim \boldsymbol{p}, \) represents
A. If he is hard working, then he is not intelligent.
B. If he is not hard working, then he is intelligent
c. If he is not intelligent, then he is not had working
D. If he is not intelligent, then he is hard working
Subject: Physics
Naturally occurring argon (Ar) consists of three isotopes the atoms of which occur in the abundances as given in the table The atomic weight of argon is:
Isotopes Abundance
\( ^{36} A r \) 0.34\%
\( ^{38} A r \) 0.07\%
\( \begin{array}{ll}40 & \text { 99.59\% }\end{array} \)
A. 38.45 u
в. 37.20
c. 39.98 и
D. 40.98 u
Subject: Maths
If \( \mathbf{f}:[\mathbf{0}, \infty) \rightarrow[\mathbf{0}, \infty), \) and \( \mathbf{f}(\mathbf{x})=\frac{\mathbf{x}}{\mathbf{1}+\mathbf{x}} \)
then \( \boldsymbol{f} \) is
A. one - one and onto
B. one - one but not onto
c. onto but not one - one
D. neither one - one nor onto
Subject: Maths
The area of a rectangular garden, ABCD,
is \( 100 m^{2} . \) Inside the garden there is a
rectangular lawn, EFGH, whose sides
are parallel to those of the garden. Find the area of the lawn, EFGH(in sq
metres).
A \( \cdot 110-5 x-\frac{200}{x} \)
B. \( 110+5 x-\frac{200}{x} \)
c. \( _{110}+5 x+\frac{200}{x} \)
D. \( 110-5 x+\frac{200}{x} \)
Subject: Chemistry
Give reasons.
\( \boldsymbol{E}^{o} \) value for \( \boldsymbol{M} \boldsymbol{n}^{3+} / \boldsymbol{M} \boldsymbol{n}^{2+} \) couple is
much more positive than that for \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} / \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{2}+} \)
Subject: Chemistry
Compare vitamin (Part I) with its
deficiency disease (Part II)
Part I Part II
A. Vitamin - \( B_{12} \)
1.Sterility
B. Vitamin- \( B_{6} \) 2. Haemorrhagic condition
\( \begin{array}{ll}\text { C. Vitamin }-E & \text { 3. Pernicious anaemia }\end{array} \)
Vitamin - \( K \quad \) 4. Skin disease
\( D \)
A \( \cdot \) A- \( -1 ; \) B-2; \( c-3 ; D-4 \)
c. \( A-3 ; B-4 ; C-1 ; D-2 \)
D. A-3; B-4; C-2; D-1
Subject: Physics
A block rest on a horizontal table which
is executing SHM in the horizontal with
an amplitude \( a \) if the coefficient of friction is \( \mu, \) then the block just start to slip when the frequency of oscillation is
A \( \cdot \frac{1}{2 \pi} \sqrt{\frac{\mu g}{a}} \)
В \( \cdot 2 \pi \sqrt{\frac{a}{\mu g}} \)
\( ^{\mathrm{C}} \cdot \frac{1}{2 \pi} \sqrt{\frac{a}{\mu g}} \)
D. \( \sqrt{\frac{a}{\mu g}} \)
Subject: Biology
The correct sequence of plants in a hydrosere is
\( \mathbf{A} \cdot O a k \rightarrow \)Lantana\( \rightarrow V o l v o x \rightarrow H y d r i l l a \rightarrow P i s t i a \rightarrow \)
Scirpus
B. \( O a k \rightarrow \)Lantana\( \rightarrow \)Scirpus\( \rightarrow \)Pistia\( \rightarrow \)Hydrilla\( \rightarrow \)
Volvox
C . \( V \) olvox \( \rightarrow \) Hydrilla \( \rightarrow \) Pistia \( \rightarrow \) Scirpus \( \rightarrow \)
Lantana\( \rightarrow \)Oak
D. Pistia \( \rightarrow \) Volva \( \rightarrow \) Scirpus \( \rightarrow \) Hydrilla\( \rightarrow \) Oak \( \rightarrow \)
Lantana
Subject: Physics
The de-Broglie wavelength associated with a proton changes by \( 0.25 \% \) if its
momentum is changed by \( P_{o} \). The initial momentum of proton is
A \( \cdot 100 P_{o} \)
в. \( 400 P_{o} \)
\( c \cdot P_{o} / 400 \)
D. \( P_{o} \)
Subject: Physics
Match items in column A with one or
more items in column
\( \begin{array}{ll}\text { Column } A & \text { Column } B \\ \text { (i) Inner planet } & \text { (a) Saturn } \\ \text { (ii) Outer planet } & \text { (i) }\end{array} \) er planet (k Outer p er plane I (b) Pole star (iii) Constellation
(iv) Satellite of the earth
(d) Moon
(e) Earth
(f) Orion
(g) Mars
\( A \)
\( (i)-g, e(i i)-a(i i i)-c, f(i v)-d \)
B \( \cdot(i)-g, e(i i)-c, f(i i i)-a(i v)-d \)
C \( .(i)-a(i i)-b(i i i)-c, f(i v)-d \)
D. None of these
Subject: Physics
Which of the following is true for universal law of gravitation?
(1) It acts on all the objects irrespective of their nature, shape and size
(2) \( \boldsymbol{F} \propto \boldsymbol{M} \times \boldsymbol{m} \)
(3) It acts along the line joining the centers of the two objects.
(4) \( \boldsymbol{F} \propto \frac{1}{d^{2}} \)
A . a and c
B. b and d
\( c \cdot a, b \) and \( d \)
D. All of the above
Subject: Chemistry
Silver ore dissolves in dilute solution of
NaCN in the presence of air to form:
A \( . A g C N \)
В \( \cdot\left[A g(C N)_{2}\right]^{-} \)
c. \( A g S C N \)
\( \mathbf{D} \cdot\left[A g(C N)_{4}\right] \)
Subject: Physics
Assertion
The compressive strength of a typical brittle material is significantly higher than its tensile strength.
Reason
In compression force between the
molecules increases.
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
If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as fundamental units, the dimensions
of gravitational constant (G) are:
A \( \cdot c^{0} g p^{-3} \)
B \( \cdot c^{2} g^{3} p^{-2} \)
C. \( c^{0} g^{2} p^{-1} \)
D \cdot \( c^{2} g^{2} p^{-2} \)
Subject: Chemistry
How much energy is given off when \( 22 g \)
of \( C_{3} H_{8} \) burns?
The heat of combustion for \( C_{3} H_{8} \) is
\( \mathbf{2}, \mathbf{2 2 0} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l} \)
A \( .2242 k J \)
в. \( 1110 k J \)
c. \( 2220 k J \)
D. \( 1500 k J \)
Subject: Maths
The probability that a man hits a target is \( \frac{3}{4} . \) If tried 5 time, the probability that he will hit the target at least three
times,is
A \( \cdot \frac{918}{10184} \)
B. \( \frac{884}{10244} \)
c. \( \frac{924}{1024} \)
\( D \cdot \frac{848}{1024} \)
Subject: Chemistry
Consider the van der Waals constants, \( a \)
and \( b, \) for the following gases.
Gas What is and \( A r \) \( N e \)
\( \boldsymbol{K} \boldsymbol{r} \)
\( \mathrm{a} / \mathrm{catm} \)
\( d m^{6} m o l^{-2} \)
5.1
0.2
1.3
\( \begin{array}{lll}\text { 3.2 } & \text { 1.7 } & \text { 1.0 }\end{array} \) \( \mathrm{b} / \mathrm{c} \)
\( 10^{-2} \mathrm{dm}^{3} \mathrm{mol}^{-1} \)
Which gas is expected to have the highest critical temperature?
\( \mathbf{A} \cdot K r \)
B. \( N e \)
c. \( A r \)
D. \( X e \)
Subject: Maths
\( f\left|\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \mathbf{1} & \boldsymbol{6}\end{array}\right|=\left|\begin{array}{ll}\mathbf{1} & \mathbf{8} \\ \mathbf{1} & \mathbf{6}\end{array}\right| \) then \( \mathbf{x}+2 \mathbf{y}= \)
\( A \cdot 9 \)
B. 17
c. 10
\( D \)
Subject: Physics
A lens is placed between the source of light and a wall. It forms images of area
\( A_{1} \) and \( A_{2} \) on the wall for its two different positions. The area of the source of light is :
в. \( \frac{A_{1}+A_{2}}{2} \)
\( ^{\mathrm{c}}\left(\frac{\sqrt{A_{1}}+\sqrt{A_{2}}}{2}\right)^{2} \)
D. None of these
Subject: Chemistry
Which of the following transitions will involve maximum amount of energy?
A \( . M \rightarrow M^{+}+e^{-} \)
B. \( M^{-} \rightarrow M^{+}+2 e^{-} \)
\( \mathbf{c} \cdot M^{2+} \rightarrow M^{3+}+e^{-} \)
D. \( M^{+} \rightarrow M^{2+}+e^{-} \)
Subject: Physics
Which of the following statements is
incorrect?
A. When a material is under tensile stress, the restoring forces are caused by interatomic attraction while under compressional stress, the restoring force is due to interatomic repulsion
B. The stretching of a coil is determined by its shear modulus
C. Rubber is more elastic than steel
D. Shearing stress plays an important role in the buckling of shafts
Subject: Maths
If statement \( \boldsymbol{p} \rightarrow(\boldsymbol{q} \vee \boldsymbol{r}) \) is true then
the truth values of statements \( p, q, r \)
respectively
\( \mathbf{A} \cdot \mathbf{T}, \mathbf{F}, \mathbf{T} \)
в. F, Т, F
\( \mathrm{c} \cdot \mathrm{F}, \mathrm{F}, \mathrm{F} \)
D. all of these
Subject: Chemistry
According to the reaction: \( P b(s)+ \)
\( S(s) \rightarrow P b S(s), \) when 20.7 grams of
lead are reacted with 6.4 grams of
Sulfur:
A. there will be an excess of 20.7 grams 04 lead
B. the sulfur will be in excess by 3.2 grams
C. the lead and sulfur will react completely without any excess reactants
D. the sulfur will be the limiting factor in the reaction
E. there will be an excess of 10.35 grams of lead
Subject: Maths
The sides of a triangle are \( 3 x+ \)
\( 4 y, 4 x+3 y \) and \( 5 x+5 y \) units, where
\( \boldsymbol{x}, \boldsymbol{y}>0 . \) The triangle is
A. right angled
B. equilateral
c. obtuse angled
D. none of these
Subject: Chemistry
\( P C l_{5} \) dissociates into \( P C l_{3} \) and \( C l_{2} . \) If
the total pressure of the system in equilibrium is \( P \) at a density \( \rho \) and
temperature \( T, \) show that the degree of dissociation \( \boldsymbol{\alpha}=\frac{\boldsymbol{P} \boldsymbol{M}}{\boldsymbol{\rho} \boldsymbol{R} \boldsymbol{T}}-1, \) where \( \boldsymbol{M} \) is
the relative molar mass of \( \boldsymbol{P} \boldsymbol{C l}_{5} \). If the
vapour density of the gas mixture at
equilibrium has the value of 62 when
the temperature is \( 230^{\circ} \mathrm{C} \), what is the
value of \( \boldsymbol{P} / \rho ? \)
Subject: Chemistry
Assertion
STATEMENT 1 (Assertion)- Absolute
value of H cannot be determined
Reason
STATEMENT 2 (Reason)- \( \Delta \boldsymbol{H}_{(g)}= \)
\( \boldsymbol{\Delta} \boldsymbol{E}_{(\boldsymbol{g})}+\boldsymbol{\Delta} \boldsymbol{n}_{(g)} \boldsymbol{R} \boldsymbol{T} \)
A. Statement 1 is True, statement 2 is True; statement 2 is a correct explanation for statement 1
B. Statement 1 is True, statement 2 is True; statement 2 is not a correct explanation for statement 1
c. Statement 1 is True, statement 2 is False.
D. Statement 1 is False, statement 2 is True
Subject: Physics
The electric field for \( r<R_{1} \) is given by \( \boldsymbol{E}=\frac{\boldsymbol{X} \boldsymbol{Q}}{\boldsymbol{\pi} \varepsilon_{0} \boldsymbol{r}^{2}}\left[\frac{r^{3}-\boldsymbol{R}_{1}^{3}}{\boldsymbol{R}_{2}^{3}-\boldsymbol{R}_{1}^{3}}\right] . \) Find \( \boldsymbol{X} \)
Subject: Physics
A current carrying loop is placed in a
uniform magnetic field in four different
orientations as shown in figure. Arrange them in the decreasing order of
potential energy
\( \widehat{Q} \)
2
3
A. 4,2,3,1
В. 1,4,2,3
\( \mathbf{c} \cdot 4,3,2,1 \)
D. 1,2,3,4
Subject: Chemistry
Balance the following redox reactions in basc medium:
\[
M n O_{4}^{-}+I^{-} \longrightarrow M n O_{2}+I O_{3}^{-}
\]
A \( \cdot 2 M n O_{4}^{-}+I^{-}+H_{2} O \longrightarrow 2 M n O_{2}+I O_{3}^{-}+2 O H^{-} \)
B. \( 3 M n O_{4}^{-}+I^{-}+H_{2} O \longrightarrow 4 M n O_{2}+I O_{3}^{-}+2 O H^{-} \)
\( \mathrm{c} \cdot 3 \mathrm{Mn} \mathrm{O}_{4}^{-}+I^{-}+\mathrm{H}_{2} \mathrm{O} \longrightarrow 5 \mathrm{MnO}_{2}+\mathrm{IO}_{3}^{-}+2 \mathrm{OH}^{-} \)
D. None of these
Subject: Maths
When \( x \geq 2, \) then function \( f(x)= \)
\( \mathbf{2}|\boldsymbol{x}-\mathbf{2}|-|\boldsymbol{x}+\mathbf{1}|+\boldsymbol{x} \) is reduced to
A. \( f(x)=-2 x+3 \)
в. \( f(x)=2 x-5 \)
\( \mathbf{c} \cdot f(x)=5 \)
D. \( f(x)=-1 \)
E. \( f(x)=2 x+4 \)
Subject: Maths
Obtain all the zeroes of \( 3 x^{4}+6 x^{3}- \) \( 2 x^{2}-10 x-5, \) if of its zeroes are \( \sqrt{\frac{5}{3}} \) \( \mathfrak{Q}-\sqrt{\frac{\mathbf{5}}{\mathbf{3}}} \)
Subject: Physics
The figure shows two identical paralle plate capacitors connected to a battery
with the switch \( S \) closed. The switch is
now opened and the free space between
the plates of the capacitors is filled with
a dielectric of dielectric constant (or
relative permittivity) 3.Find the ratio of
the total electrostatic energy stored in both capacitors before and after the
introduction of the dielectric.
\( A \cdot \frac{2}{3} \)
B . 5 \( \overline{3} \)
\( c \cdot 3 \)
\( \overline{5} \)
\( D \cdot 3 \)
\( \overline{2} \)
Subject: Chemistry
If the thio-cyanide ion is added to potash-ferric alum then red colour appears. This colour is due to the
formation of:
A. \( K S C N \)
в. \( F e(S C N)_{3} \)
\( \mathbf{c} \cdot \operatorname{Fe}(S C N)_{2} \)
D. \( F e(S C N) \)
Subject: Maths
If the coefficients of \( a^{m} \) and \( a^{n} \) in the
expansion of \( (1+a)^{m+n} \) are \( \alpha \) and \( \beta \) then which one of the following is correct?
A \( \cdot \alpha=2 \beta \)
в. \( \alpha=\beta \)
c. \( 2 \alpha=\beta \)
Subject: Physics
The Bohr radius of the fifth electron of
phosphorus (atomic number = 15) acting as dopant in silicon (relative dielectric constant \( =12 \) ) is
A \( \cdot 10.6 ~ A^{\circ} \)
B. 0.53 \( A^{0} \)
c. \( 21.2 A^{\circ} \)
D. None of these
Subject: Maths
Write \( \frac{120 m^{2} n^{-3}}{60 m^{5} n^{-2}} \) in simplest form
using only positive exponents. Assume that \( m \neq 0 \) and \( n \neq 0 \)
A \( \cdot \frac{2 n}{m^{3}} \)
в. \( \frac{2}{m^{3} n} \)
c. \( \frac{2 m^{3}}{n} \)
D. \( \frac{1}{2 m^{3} n} \)
Subject: Physics
A particle of mass \( \boldsymbol{m}=12 \boldsymbol{k} \boldsymbol{g} \) falling
freely from rest under gravity and air resistance force \( (\boldsymbol{F}) \). The velocity of the particle when reaches ground is \( 6 m / s \)
Then total external work done on the
particle is
\( \mathbf{A} \cdot 216 J \)
в. \( (120-F) J \)
\( \mathbf{c} .6 F J \)
D. Data insufficient
Subject: Chemistry
\( E_{O_{3} \mid O_{2}}^{0} \) (acidic medium) \( =2.07 \mathrm{V} \)
\( E_{O_{3} \mid O_{2}}^{0} \) (basic medium) \( =1.24 \mathrm{V} \)
\( E_{H_{2}}^{0} o_{2} \mid H_{2} O \) (acidic medium) \( =1.78 \mathrm{V} \)
\( E_{O_{2} \mid H_{2}}^{0} O_{2}(\text { acidic medium })=0.695 \mathrm{V} \)
\( E_{O_{2} \mid H_{2}}^{0},_{\Omega_{2}} \) (basic medium) \( =0.076 \mathrm{V} \)
\( E_{H O_{2}^{-} \mid O H^{-}}^{0}(\text { basic medium })=0.878 \mathrm{V} \)
Using the above data, find which of the following is incorrect?
A. Ozone is a better oxidising agent than \( H_{2} O_{2} \) in both acidic and basic medium.
B. \( H_{2} O_{2} \) is better oxidising agent in acidic medium than in basic medium.
C. \( H_{2} O_{2} \) is better reducing agent in basic medium than in acidic medium.
D. In basic medium \( H_{2} O_{2} \) reduces all \( O_{3} \) to \( O_{2} \) completely.
Subject: Physics
A solution is to be kept between \( 68^{\circ} \) F
and \( 77^{\circ} \) F. What is the range in temperature in degree Celsius
(C) if the
Celcius / Fahrenheit (F) conversion
formula is given by \( \mathbf{F}=\frac{9}{5} \mathbf{C}+\mathbf{3 2} ? \)
Subject: Maths
\( \boldsymbol{I} \boldsymbol{f} \sin 5 \boldsymbol{\theta}=\boldsymbol{a} \sin ^{5} \boldsymbol{\theta}+\boldsymbol{b} \sin ^{3} \boldsymbol{\theta}+ \)
\( \operatorname{csin} \theta \) then
\( (A) a-2 c=5 \)
(B) \( a-2 c=6 \)
(C) \( b+3 c=5 \)
(D) \( b+3 c=-5 \)
The general solution of \( \tan 3 \theta \tan \theta= \)
1 is given \( (n \in \boldsymbol{I}) \)
\( \mathbf{A} \cdot a=20, b=-10, c=5 \)
B . \( a=1, b=-20, c=5 \)
\( \mathbf{c} . a=16, b=-2, c=5 \)
D. \( a=16, b=-20, c=5 \)
Subject: Physics
The linear velocity of a rotating body is given by \( \overrightarrow{\boldsymbol{v}}=\overrightarrow{\boldsymbol{\omega}} \times \overrightarrow{\boldsymbol{r}}, \) where \( \overrightarrow{\boldsymbol{\omega}} \) is the
angular velocity and \( \vec{r} \) is the radius vector. The angular velocity of a body is \( \vec{\omega}=\hat{i}-2 \hat{j}+2 \hat{k} \) and the radius vector
\( \vec{r}=4 \hat{j}-3 \hat{k}, \) then \( |\vec{v}| \) is:
B. \( \sqrt{31} \) units
c. \( \sqrt{37} \) units
D. \( \sqrt{41} \) units
Subject: Chemistry
Two oxides of lead were separately reduced to metallic lead by heating in a current of, hydrogen and the following data obtained:
i) Mass of yellow oxide taken \( =3.45 g \)
Loss in mass during reduction \( =\mathbf{0 . 2 4 g} \)
ii) Mass of brown oxide taken \( =1.227 g \)
Loss in mass during reduction \( =\mathbf{0 . 1 6} \boldsymbol{g} \)
Show that the above data illustrate the
Law of Multiple Proportions.
Subject: Chemistry
For the equilibrium \( N_{2}+3 H_{2} \rightleftharpoons \)
\( \mathbf{2} N \boldsymbol{H}_{3}, \boldsymbol{K}_{6} \) at \( 1000 \mathrm{K} \) is \( \mathbf{2 . 3 7} \times \mathbf{1 0}^{-3} \)
Equilibrium \( \left[N_{2}\right]=2 . M\left[H_{2}\right]=3 M \) the
concentration of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is:
A . 0.00358 M
в. 0.0358 М
c. 0.358 М
D. 3.58 м
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{c}x \\ \frac{a e^{|x|}+3 . e^{\frac{-1}{x}}}{1} \\ (a+2) e^{\frac{1}{|x|}-e^{\frac{-1}{x}}}\end{array}\right) \begin{array}{l}x \neq 0 \\ 0\end{array} \)
differentiable at \( \boldsymbol{x}=\mathbf{0} \) then \( [\boldsymbol{a}]=_{--}(\mathbb{D} \)
denotes greatest integers function
4
B. -1
\( c \cdot 2 \)
\( 0 .-3 \)
Subject: Physics
A force of \( 100 N \) is applied on an area of
\( 4 m^{2} . \) the pressure being applied on the
area is
\( \mathbf{A} \cdot 50 P a \)
B. \( 25 P a \)
c. \( 12.5 P a \)
D. \( 400 P a \)
Subject: Chemistry
Assertion
Ethane is a gas while ethyl alcohol is a liquid.
Reason
Ethyl alcohol has greater molecular
mass than ethane.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
The perimeter of a triangle is \( 9 m^{2}- \)
\( 2 n+8 \) and its two sides are \( 4 m^{2}+3 n \)
and \( 7 m^{2}+5 n-12 . \) Find the third side
of the triangle.
A \( \cdot m^{2}-10 n-10 \)
B. \( -2 m^{2}-10 n+20 \)
c. \( -2 m^{2}-14 n+20 \)
D. \( m^{2}-10 n+10 \)
Subject: Physics
A stone dropped from the top of a tower travels \( 4.9 \mathrm{m} \) in the last second, then the
velocity of the stone on reaching the
ground is
A \( \cdot 19.6 m^{-1} \)
в. \( 9.8 m s^{-1} \)
\( \mathrm{c} \cdot 4.9 \mathrm{ms}^{-1} \)
D. \( 29.4 m s^{-1} \)
Subject: Chemistry
In addition to Bombyx mori, there are several other organisms, which produce commercial silk. Match the name of the
species with the correct commercial name of their produce by selecting appropriate answers from the given codes.
\( \begin{array}{llll} & \text { List I } & & \text { List II } \\ \text { A } & \text { Antheraea pernyi } & 1 & \text { Eri silk } \\ \text { B } & \text { Attacus atlas } & 2 & \text { Oak tasar } \\ \text { C } & \text { Ailanthus } & 3 & \text { Fagara silk } \\ \text { D } & \text { Pinna squamosa } & 4 & \text { Mussel silk }\end{array} \)
A . A- 2, B- 3, C-1, D- 4
B. A- 4, B- 3, C- 2, D-1
c. \( A-1, B-2, C-4, D-3 \)
D. A- 3, B- 2, C-1, D-4
Subject: Maths
f \( \boldsymbol{y}=\mathbf{1}+\boldsymbol{x} \cdot \boldsymbol{e}^{\boldsymbol{y}}, \) show that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{e}^{\boldsymbol{y}}}{\boldsymbol{2}-\boldsymbol{y}} \)
Subject: Physics
A wave of amplitude \( 10 \mathrm{cm} \) and frequency 1000 Hz is travelling with a velocity of \( 300 \mathrm{m} / \mathrm{s} \). Calculate the phase difference of a particle at a distance of \( 3 \mathrm{m} \) from the origin after \( 1.001 \mathrm{s} \)
Subject: Chemistry
Which of the reactant act as oxidant?
\( \boldsymbol{P C l}_{3}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{P C l}_{5} \)
A \( \cdot C l_{2} \)
в. \( P C l_{3} \)
c. Both of these
D. None of these
Subject: Maths
Two line segments \( A B \) and \( A C \) include an angle of \( 60^{0} \) where \( A B=5 \mathrm{cm} \) and \( A C \)
\( =7 \mathrm{cm} . \) Locate points \( \mathrm{P} \) and \( \mathrm{Q} \) on \( \mathrm{AB} \)
and \( A C, \) respectively such that \( A P=\frac{3}{4} \)
\( A B \) and \( A Q=\frac{1}{4} A C . \) Join \( P \) and \( Q \) and
measure the length PQ.
A. \( 3.25 \mathrm{cm} \)
B. \( 4.25 \mathrm{cm} \)
\( c .5 .25 \mathrm{cm} \)
D. \( 6.25 \mathrm{cm} \)
Subject: Physics
A body of mass \( 15 \mathrm{kg} \) is raised from certain depth. If the work done in
raising it by \( 10 \mathrm{m} \) is \( 1620 \mathrm{J} \), its velocity at this position is
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. \( 4 m s^{-1} \)
\( \mathrm{c} \cdot 1 \mathrm{ms}^{-1} \)
D. \( 8 m s^{-1} \)
Subject: Physics
Find the magnitude and direction of the force vector applied to the loop if the
vector \( \vec{p}_{m} \) is parallel to the straight conductor.
A \( \cdot \vec{F}=20 \)
В . \( \vec{F}=10 \)
c. \( \vec{F}=0 \)
D. \( \vec{F}=50 \)
Subject: Maths
Assertion
If \( a>0 \) and \( b^{2}-4 a c<0 . \) then the
value of the integral \( \int \frac{d x}{a x^{2}+b x+c} \) will be of the type \( \mu \tan ^{-1}\left(\frac{x+A}{B}\right)+ \)
\( C ; \) where \( A, B, C, \mu \) are constant.
Reason
\( f\left(a>0, b^{2}-4 a c<0, \text { then } a x^{2}+b x+\right. \)
\( c \) can be written as sum of two squares.
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
The angular frequency of motion whose equation is \( 4 \frac{d^{2} y}{d t^{2}}+9 y=0 \) is \( (y= \)
displacement and \( t= \) time
A \( \cdot \frac{9}{4} \)
в. \( \frac{4}{9} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{2}{3} \)
Subject: Maths
Suppose that \( n \) is a natural number and
\( \boldsymbol{I}, \boldsymbol{F} \) are respectively the integral part
and fractional part of \( (7+4 \sqrt{3})^{n} . \) Then
show that
i) \( I \) is an odd integer
ii) \( (\boldsymbol{I}+\boldsymbol{F})(\mathbf{1}-\boldsymbol{F})=\mathbf{1} \)