AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In an experiment on the specific heat of a metal a \( 0.20 \mathrm{kg} \) block of the metal at
\( 150^{\circ} \mathrm{C} \) is dropped in a copper calorimeter (of water equivalent 0.025
kg) containing \( 150 \mathrm{cm}^{3} \) of water at
\( 27^{\circ} \mathrm{C} . \) The final temperature is \( 40^{\circ} \mathrm{C} \)
Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater or smaller than the actual value for
specific heat of the metal?
Subject: Chemistry
If the cell voltage is 1.23 V for the \( H_{2}-O_{2} \)
fuel cell and for the
half cell :
\( O_{2}+2 H_{2} O+4 e^{-} \rightleftharpoons 4^{\ominus} H \)
\( \boldsymbol{E}^{\ominus}=\mathbf{0 . 4 0} \boldsymbol{V}, \) then \( \boldsymbol{E}^{\ominus} \) for \( \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \mathbf{2} e^{-} \rightleftharpoons \boldsymbol{H}_{2}+\mathbf{2} \stackrel{\ominus}{O} \boldsymbol{H} \) will be:
\( \mathbf{A} \cdot 0.56 V \)
в. \( 0.73 V \)
c. \( 0.41 V \)
D. \( 0.83 V \)
Subject: Chemistry
\( A \operatorname{soap}\left(C_{17} H_{35} C O O N a\right) \) solution
becomes a colloidal sol at a
concentration of \( 1.2 \times 10^{3} M . \) On the
average, \( 2.4 \times 10^{13} \) colloidal particles
are present in \( 1 \mathrm{mm}^{3} \). What is the
average number of stearate ions (in
multiples of \( 10^{6} \) ) in one colloidal particle (micelle)?
A . 30
B. 40
\( c .50 \)
D. 60
Subject: Maths
\( \int \frac{e^{x}(x-1)}{x^{2}} d x= \)
A \( \cdot \frac{1}{x} e^{x}+c \)
B. \( x e^{-x}+c \)
c. \( \frac{1}{x^{2}} e^{x}+c \)
D. \( \left(x-\frac{1}{x}\right) e^{x}+c \)
Subject: Maths
Verify the property \( \boldsymbol{a} \times(\boldsymbol{b}+\boldsymbol{c})=(\boldsymbol{a} \times \)
\( b)+(a \times c) \) When \( a=\frac{1}{2}, b= \)
\( \frac{3}{7} \quad \& \quad c=\frac{5}{14} \)
Subject: Chemistry
For the properties mentioned, the correct trend for the different species
is :
A. inert pair effect - \( A l>G a>I n \)
B. first ionization enthalpy \( -B>A l>T l \)
C . strength as Lewis acid - \( B C l_{3}>A l C l_{3}>G a C l_{3} \)
D. oxidising property \( -A l^{+3}>I n^{+3}>T l^{+3} \)
Subject: Chemistry
Assertion
Hydrides of \( N, O \) and \( F \) have lower boiling points than the hydrides of their subsequent group members.
Reason

Boiling point depends upon the molecular mass only.
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
For each natural number \( k \), let \( C_{k} \)
denote the circle with radius \( k \)
centimeters and centre at the origin \( O \)
on the circle \( C_{k} \) a particle moves \( k \) centimetres in the counter-clockwise
direction. After completing its motion
on \( C_{k}, \) the particle moves to \( C_{k+1} \) in the radial direction (away from centre). The motion of the particle continues in this manner. The particle starts at \( (1,0) . \) If the particle crosses the positive direction of \( x \) -axis for the first time on
the circle \( C_{n}, \) then \( n= \)
A. 4
B. 5
c. 6
D.
Subject: Physics
Write the complete nuclear reactions:
(a) \( _{4}^{9} B e+_{2}^{4} H e \longrightarrow_{6}^{12} C+ \)
\( (b)_{1}^{3} H \longrightarrow_{2}^{3} H e+_{-} \)
\( (c) \frac{14}{7} N+_{2}^{4} H e \longrightarrow_{8}^{17} O+ \)
(d) \( _{92}^{235} U+_{0}^{1} n \longrightarrow_{38}^{92} S r+X e+3_{0}^{1} n \)
\( (\mathrm{e})_{3}^{7} L i+_{0}^{1} n \longrightarrow 2_{2}^{4} H e+ \)
\( (f)_{92}^{238} U+_{-\perp-}----\longrightarrow_{92}^{239} U \longrightarrow_{93}^{239} \)
\( N p+ \)
\( (g)_{7}^{14} N+_{0}^{1} n \longrightarrow_{-}-\ldots---+_{1}^{3} H \)
(h) \( _{3}^{7} L i+_{-} \) \( \longrightarrow_{4}^{8} B e+\gamma \)
radiations
(i) \( _{1}^{2} \boldsymbol{H}+_{\text {一一一一一一一 }}_{2}^{4} \boldsymbol{H} e+_{0}^{1} \boldsymbol{n} \)
\( (j)_{13}^{27} A l+_{0}^{1} n \longrightarrow_{11}^{24} N a+ \)
\( (\mathrm{k})_{13}^{27} A l+_{2}^{4} H e \longrightarrow_{-}------+_{1}^{1} H \)
(I) \( \frac{235}{92} \boldsymbol{U}+_{0}^{1} \boldsymbol{n} \longrightarrow \)
\( +_{52}^{137} \boldsymbol{T} \boldsymbol{e}+_{40}^{97} \boldsymbol{Z} \boldsymbol{r} \)
\( (\mathrm{m})_{34}^{86} \mathrm{Se} \longrightarrow_{-1}-\mathrm{-}_{-1} \mathrm{e} \)
Subject: Chemistry
When \( K_{2} C r_{2} O_{7} \) is treated with \( H_{2} O_{2} \)
then:
This question has multiple correct options
A. in strong acidic medium deep blue-violet complex \( C r O\left(O_{2}\right)_{2} \) is formed
B. in less acidic medium violet, coloured complex \( \left[\mathrm{CrO}\left(\mathrm{O}_{2}\right)(\mathrm{OH})\right]^{-} \) is formed
C . in alkaline medium \( \left[\mathrm{Cr}\left(\mathrm{O}_{2}\right)_{4}\right]^{3-} \) is formed
D. in ammonical solution \( \left(N H_{3}\right)_{3} C r O_{4} \) dark red-brown compound is formed.
Subject: Chemistry
What is the voltage of the voltaic cell \( Z n\left|Z n^{2+}\right|\left|C u^{2+}\right| C u \) at \( 298 K \) if
\( \left[Z n^{2+}\right]=0.2 M \) and \( \left[C u^{2+}\right]=4.0 M ? \)
\( \boldsymbol{C u}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{C u} \boldsymbol{E}^{\circ}=+\mathbf{0 . 3 4} \boldsymbol{V} \)
\( Z n^{2+}+2 e^{-} \rightarrow Z n E^{\circ}=-0.76 V \)
\( \left[\text { Note }: \boldsymbol{E}=\boldsymbol{E}^{\circ}-(\mathbf{0 . 0 5 9 1} / \boldsymbol{n})(\log \boldsymbol{Q})\right. \)
A. \( +1.10 V \)
в. \( -1.10 \mathrm{V} \)
c. \( +1.07 V \)
D. \( +1.14 V \)
E . \( -1.07 \mathrm{V} \)
Subject: Chemistry
An iron wire is immersed in a solution
containing \( Z n S O_{4} \) and \( N i S O_{4} . \) Predict giving reasons which of the following reactions is likely to proceed?
(i) Iron reduces \( Z n^{2+} \) ions
(ii) Iron
reduces \( N i^{2+} \) ions.
Given: \( \boldsymbol{E}_{\boldsymbol{Z} n^{2+} / \boldsymbol{Z} \boldsymbol{n}}= \)
-0.76 volt; \( E_{F e^{2+} / F e}^{\circ}=-0.44 \) volt and
\( \boldsymbol{E}_{N i^{2+} / N i}^{\circ}=-\mathbf{0 . 2 5} \) volt.
Subject: Physics
A stone thrown upwards with speed \( u \) attains maximum height \( h \). Another stone thrown upwards from the same
point with sapped \( 2 u \) attains maximum
height \( \boldsymbol{H} \). What is the relation between
\( h \) and \( H ? \)
A. \( 2 h=H \)
\( H \)
в. \( 3 h=H \)
\( c \cdot 4 h=H \)
D. \( 5 h=H \)
Subject: Chemistry
Which of the following salts has the
greatest molar solubility in pure water?
A \( \cdot C a C O_{3} ; K_{s p}=8.7 \times 10^{-9} \)
B. \( C u S ; K_{s p}=8.5 \times 10^{-45} \)
C \( \cdot A g_{2} C O_{3} ; K_{s p}=6.2 \times 10^{-12} \)
D. \( P b\left(I O_{3}\right)_{2} ; K_{s p}=2.6 \times 10^{-13} \)
Subject: Physics
If a car is to travel with a speed v along the frictionless, banked circular track of
radius \( r, \) the required angle of banking so that the car does skid is
A \( \cdot \theta=\tan ^{-1}\left(\frac{v^{2}}{r g}\right) \)
B . \( \theta=\tan ^{-1}\left(\frac{v}{r g}\right) \)
c. \( \theta=\tan ^{-1}\left(\frac{\pi^{2}}{v g}\right) \)
D \( \cdot \theta=\tan ^{-1}\left(\frac{v^{2}}{2-g}\right) \)
Subject: Chemistry
\( \boldsymbol{A}(\boldsymbol{g}) \rightarrow \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \)
\( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} t}=\boldsymbol{k}[\boldsymbol{A}] \)
At the start, the pressure is \( 100 \mathrm{mm} \) and after 10 min, the pressure is 120
mm. Hence, rate constant \( \left(\min ^{-1}\right) \) is:
A \( \cdot \frac{2.303}{10} \log \left(\frac{120}{100}\right) \)
В. \( \frac{2.303}{10} \log \left(\frac{100}{20}\right) \)
c. \( \frac{2.303}{10} \log \left(\frac{100}{80}\right) \)
D. \( \frac{2.303}{10} \log \left(\frac{100}{120}\right) \)
Subject: Maths
If \( A=\left|\begin{array}{ccc}3 & -1 & 0 \\ -1 & 2 & 3\end{array}\right| \) and \( B=\left|\begin{array}{ccc}-1 & 1 & 2 \\ 0 & 2 & -1\end{array}\right| \)
then find \( \left(A B^{T}\right)^{T} \)
A \( \cdot\left|\begin{array}{cc}2 & -5 \\ 1 & 6\end{array}\right| \)
в. \( \left|\begin{array}{cc}3 & -4 \\ 7 & -6\end{array}\right| \)
с. \( \left|\begin{array}{cc}-4 & 9 \\ -2 & 1\end{array}\right| \)
D \( \cdot\left|\begin{array}{cc}-3 & 8 \\ 4 & 2\end{array}\right| \)
Subject: Maths
Draw a \( \triangle A B C \) in which \( B C= \)
\( \mathbf{6} c \boldsymbol{m}, \boldsymbol{A} \boldsymbol{B}=\mathbf{4} \boldsymbol{c m} \) and \( \boldsymbol{A} \boldsymbol{C}=\mathbf{5} \boldsymbol{c m} \)
Draw a triangle similar to \( \triangle A B C \) with its sides equal to \( \left(\frac{3}{4}\right)^{t h} \) of the corresponding sides of \( \triangle \boldsymbol{A B C} \)
Subject: Chemistry
Consider the two gaseous equilibrium involving \( S O_{2} \) and the corresponding
equilibrium constant at \( \mathbf{2} 99 K S O_{2}(g)+^{1 / 2} O_{2}(g) \rightleftharpoons S O_{3}(g) ; K_{1} \)
\( \mathbf{4} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{4} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{2} \)
The value of the equilibrium constant are related by :
A \( \cdot K_{2}=\frac{1}{\left(K_{1}\right)^{4}} \)
B \( . K_{2}=K_{1}^{4} \)
\( \mathrm{C} \cdot_{\mathrm{K}_{2}}=\left(\frac{1}{K_{1}}\right)^{1 / 4} \)
D. \( K_{2}=\frac{1}{K_{1}} \)
Subject: Maths
\( \sqrt{x} e^{\sqrt{x}} d x \) is equal to:
A \( \cdot 2 \sqrt{x}-e^{\sqrt{x}}-4 \sqrt{x e^{\sqrt{x}}}+c \)
B \( \cdot(2 x-4 \sqrt{x}+4) e^{\sqrt{x}}+c \)
c. \( (2 x+4 \sqrt{x}+4) e^{\sqrt{x}}+c \)
D. \( (1-4 \sqrt{x}) e^{\sqrt{x}}+c \)
Subject: Maths
Two dice are thrown. The events
\( A, B, C, D, E \) and \( F \) are described as follows:
\( A= \) Getting an even number on the
first die.
\( B= \) Getting an odd number on the first
die.
\( C= \) Getting at most 5 as sum of the number on the two dice.
\( D= \) Getting the sum of the numbers on
the dice greater than 5 but less than 10 .
\( \boldsymbol{E}=\operatorname{Getting} \) at least 10 as the sum of the numbers on the dice.
\( \boldsymbol{F}= \) Getting an odd number on one of
the dice

Describe the following events: \( A \) and \( B, B \) or \( C, B \) and \( C, A \) and \( E, A \) or \( F, A \) and \( \boldsymbol{F} \)
Subject: Maths
Let \( Z \) be the set of all integers and \( Z_{0} \) be
the set of all non-zero integers. Let a
relation \( \boldsymbol{R} \) on \( \boldsymbol{Z} \times \boldsymbol{Z}_{\mathbf{0}} \) be defined as
follows:
\( (a, b) R(c, d) \Leftrightarrow a d=b c \) for all
\( (a, b),(c, d) \in Z \times Z_{0} \)
Prove that \( R \) is an equivalence relation
on \( Z \times Z_{0} \)
Subject: Physics
When a body is placed on a surface, the body exerts a force downwards on the
surface equal to its weight on the surface, but the body does not move because
A. The surface exerts an equal and opposite force on the body normal to the surface.
B. The surface exerts an equal and opposite force on the body parallel to the surface
c. The surface exerts no force on the body
D. The surface exerts an infinite force on the body parallel to the surface
Subject: Physics
Three point charges \( Q_{1}=25 \mu C, Q_{2}= \)
\( 50 \mu C \) and \( Q_{3}=100 \mu C, \) are kept at the
corners \( A, B \) and \( C \) respectively of an
equilateral triangle ABC having each side equal to \( 7.5 \mathrm{m} \). Calculate the total electrostatic potential energy of the
system
Subject: Maths
If the orthocentre, circumcentre of a
triangle are (-3,5,2),(6,2,5)
respectively then the centroid of the triangle is
\( \mathbf{A} \cdot(3,3,4) \)
В. \( \left(\frac{3}{2}, \frac{7}{2}, \frac{9}{2}\right) \)
c. (9,9,12)
D. \( \left(\frac{9}{2} \frac{-3}{2}, \frac{3}{2}\right) \)
Subject: Chemistry
Conversation of a] sulphur b] iron pyrites to sulphur dioxide in the first
step of the Contact process is
\( \boldsymbol{S}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{S} \boldsymbol{O}_{2} \)
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S}_{2}+\boldsymbol{x} \boldsymbol{F} \boldsymbol{e}^{3+}+\boldsymbol{8} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \mathbf{1 5} \boldsymbol{F} \boldsymbol{e}^{2+}+ \)
\( \boldsymbol{y} \boldsymbol{S} \boldsymbol{O}_{4}^{2-}+\mathbf{1 6} \boldsymbol{H}^{+} \)
find then value of \( x \) and \( y: \)
A . \( x=15, y=1 \)
в. \( x=14, y=2 \)
c. \( x=7, y=2 \)
D. \( x=14, y=1 \)
Subject: Biology
The gases which absorb most of IR (infrared) rays are
\( A \cdot \mathrm{s} \mathrm{O}_{2}, \mathrm{CO}_{2}, \) and \( \mathrm{NO}_{2} \)
B. \( \mathrm{SO}_{2}, \mathrm{CH}_{4}, \) and \( \mathrm{O}_{3} \)
\( \mathrm{c} \cdot \mathrm{co}_{2}, \mathrm{CH}_{4}, \) and \( \mathrm{cFCs} \)
D. \( \mathrm{NO}_{2}, \mathrm{CO}_{2}, \) and \( \mathrm{O}_{3} \)
Subject: Chemistry
\( \left[B a^{2+}\right] \) when \( C a S O_{4} \) starts just precipitation will be:
\( \mathbf{A} \cdot\left[B a^{2+}\right]=4.58 \times 10^{-7} M \)
B . \( \left[B a^{2+}\right]=5.58 \times 10^{-7} M \)
C \( \cdot\left[B a^{2+}\right]=4.85 \times 10^{-7} M \)
D. None of these
Subject: Physics
The internal resistance of cell of e.m.f.
\( 2 V \) is \( 0.1 . \) It is connected to a resistance
of \( 3.9 . \) The voltage across the cell is
\( \mathbf{A} \cdot 2.71 V \)
B . \( 1.95 V \)
c. \( 1.68 V \)
D. \( 0.52 V \)
Subject: Maths
If \( \mathrm{BC} \) and \( \mathrm{AD} \) are equal perpendiculars
to line segment \( A B, \) then \( \Delta O B C \cong \)
\( \Delta O A D \) by which of the following tests
of congruence? What can be said about
\( A B \) and \( C D ? \)
A. \( A S A \) test, CD bisects AB
B. \( S A S \) test, AB bisects \( c \) D
c. \( A S A \) test, AB bisects \( c \) D
D. \( S A S \) test, CD bisects AB
Subject: Physics
If dimensions of length are expressed
\( \operatorname{as} G^{x} C^{y} h^{z} \) where \( G, C \) and \( h \) are
universal gravitational constant, speed of light and Planck's constant respectively. Then This question has multiple correct options
\( \mathbf{A} \cdot x=y \)
B. \( x=z \)
c. \( y=-3 / 2 \)
D. \( z=1 / 2 \)
Subject: Maths
Two \( n \times n \) square matrices \( A \) and \( B \) are
said to be similar if there exists a non-
singular matrix \( \boldsymbol{P} \) such that
\( \boldsymbol{P}^{-1} \boldsymbol{A} \boldsymbol{P}=\boldsymbol{B} \)
If \( A \) and \( B \) are similar matrices such
that \( \operatorname{det}(A)=1, \) then
A. \( \operatorname{det}(B)=1 \)
B. \( \operatorname{det}(A)+\operatorname{det}(B)=0 \)
c. \( \operatorname{det}(B)=-1 \)
D. none of these
Subject: Physics
Assertion
Two balls of different masses are
thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed.
Reason
The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.
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 incorrect
Subject: Maths
Two numbers \( X \) and \( Y \) are chosen at
random (without replacement) from the \( \operatorname{set} 1,2, \dots, 5 N . \) The probability that
\( X^{n} \sim Y^{n} \) is divisible by 5 is
A \( \frac{N-1}{5 N-1} \)
в. \( \frac{4(4 N-1)}{5(5 N-1)} \)
c. \( \frac{17 N-5}{5(5 N-1)} \)
D. None of these
Subject: Physics
A Zener diode having break-down voltage \( 5.6 V \) is connected in reverse
bias with a battery of emf \( 10 \mathrm{V} \) and a
resistance of \( 100 \Omega \) in series. The
current flowing through the Zener is
\( \mathbf{A} \cdot 88 m A \)
в. \( 0.88 m A \)
c. \( 4.4 m A \)
D. \( 44 m A \)
Subject: Physics
The Young's double slit experiment is
done in a medium of refractive index
4/3. A light of 600 nm wavelength is falling on the slits have \( 0.45 \mathrm{mm} \)
separation. The lower slit \( S_{2} \) is covered
by a thin glass sheet of thickness 10.4
mm and refractive index 1.5. The
interference pattern is observed on a
screen placed at \( 1.5 \mathrm{m} \) from the slits as
shown in the fig.
(All wavelength in this problem are for
the given medium of refractive index
4/3. Ignore dispersion.) Find the location
of central maxima (bring fringe with
zero path difference ) on the y-axis.
Subject: Physics
The capacitance of a capacitor becomes \( \frac{7}{6} \) times its original value if a dielectric slab of thickness, \( t=\frac{2}{3} d \) is introduced in
between the plates. \( d \) is the separation
between the plates. The dielectric
constant of the dielectric slab is:
\( \mathbf{A} \cdot \frac{14}{11} \)
B. \( \frac{11}{14} \)
\( c \cdot \frac{7}{11} \)
D. \( \frac{11}{7} \)
Subject: Physics
Three rods of the same mass are placed as shown in the figure. What will be the coordinate of centre of mass of the
system?
A \( \cdot\left(\frac{2 a}{3}, \frac{2 a}{3}\right) \)
B・ \( \left(\frac{4 a}{3}, \frac{4 a}{3}\right) \)
\( \mathbf{c} \cdot\left(\frac{a}{3}, \frac{a}{3}\right) \)
D. \( \left(\frac{5 a}{6}, \frac{4 a}{9}\right) \)
Subject: Chemistry
Which of the following has a bond
formed by overlap of \( s p^{3}- \) hybrid
orbitals?
A. \( C H_{3}-C \equiv C-C H_{3} \)
в. \( C H_{3}-C H=C H-C H_{3} \)
C \( . C H_{2}=C H-C H=C H_{2} \)
D. \( H C \equiv C H \)
Subject: Chemistry
The correct sequence of thermal
stability of the following carbonates is:
A. \( B a C O_{3}<C a C O_{3}<S r C O_{3}<M g C O_{3} \)
в. \( M g C O_{3}<C a C O_{3}<S r C O_{3}<B a C O_{3} \)
c. \( B a C O_{3}<S r C O_{3}<C a C O_{3}<M g C O_{3} \)
D. \( M g C O_{3}<S r C O_{3}<C a C O_{3}<B a C O_{3} \)
Subject: Chemistry
The magnetic moment of \( \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{M} \boldsymbol{n} \boldsymbol{C l}_{4}\right] \)
corrected to the nearest integer is
\( \mathbf{A} \cdot 6 B M \)
в. \( 7 B M \)
\( \mathbf{c} \cdot 8 B M \)
D. \( 5 B M \)
Subject: Chemistry
A first order reaction takes 23.1 min.
for \( 50 \% \) completion. Calculate the time required for \( 75 \% \) completion of this
reaction.
\( [\text {Given }: \log 2=\mathbf{0 . 3 0 1}, \log \mathbf{3}=\mathbf{0 . 4 4 7 7 1} \)
Subject: Maths
Verify whether the following are zeros of the polynomial indicated against them:
\( \boldsymbol{g}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}^{2}+\mathbf{7} \boldsymbol{x}, \boldsymbol{x}=\mathbf{0},-\frac{\mathbf{7}}{\mathbf{5}} \)
A. True
B. False
Subject: Maths
General solution for \( |\sin x|=\cos x \) is
A \( \cdot 2 n \pi+\frac{\pi}{4}, n \in I \)
В \( \cdot 2 n \pi \pm \frac{\pi}{4}, n \in I \)
c. \( n \pi+\frac{\pi}{4}, n \in I \)
D. None of these
Subject: Chemistry
The white solid compound \( A \) decomposes quite rapidly on heating in the presence of a black substance \( X \) to form a solid compound \( \mathrm{B} \) and a gas \( \mathrm{C} \) When an aqueous solution of compound \( \mathrm{B} \) is reacted with silver nitrate solution,
then a white precipitate of silver chloride is obtained along with potassium nitrate solution. Gas C does not burn itself but helps to burn other things. What is compound B?
Subject: Physics
A metal rope of density \( 6000 \mathrm{kg} / \mathrm{m}^{3} \) has
breaking stress \( 9.8 \times 10^{8} N m^{-2} . \) This
rope is used to measure the depth of the sea. Then the depth of the sea that can be measured with out breaking is
A \( \cdot 10 \times 10^{3} \)
B . \( 20 \times 10^{3} \)
c. \( 30 \times 10^{3} \)
D. \( 40 \times 10^{3} \mathrm{m} \)
Subject: Chemistry
To the equilibrium system \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}), \) gaseous \( \boldsymbol{C l}_{2} \) is
added, increasing the volume at the same time in such a manner so that
\( P C l_{3} \) in the system remains unchanged temperature remains constant what
happens to the equilibrium?
A. Shifted backward
B. Remains unaffected
c. Shifted forward
D. Depends on the magnitude of \( P C l_{3} \)
Subject: Chemistry
Which of the following ions has a magnetic moment of 5.93 BM?
\( [A t . N o .: V=23, C r=24, M n=25, F e=26] \)
\( \mathbf{A} \cdot M n^{2}+ \)
B. \( F e^{2} \)
\( c \cdot C r^{2} \)
\( D \cdot V^{3} \)
Subject: Chemistry
How much \( N a F \) should be added to 100
mL of solution having \( 0.016 M \) in \( S r^{2}+ \)
ions to reduce its concentration to
\( 2.5 \times 10^{-3} M ?\left(K_{s p} S r F_{2}=8 \times 10^{-10}\right) \)
A. 0.098 g
ggg \( . . .998 \)
B. 0.168 g
c. 0.177 g
D. 0.118 g
Subject: Maths
Construct a scalene triangle \( \boldsymbol{A B C} \)
given base \( A B=3 c m, \) base angle \( = \)
\( 90^{\circ} \) and sum of the lengths \( B C+ \)
\( \boldsymbol{A C}=\mathbf{9} \boldsymbol{c m} \)
Subject: Maths
A high school had 1200 students
enrolled in 2003 and 1500 students in
\( 2006 . \) If the student population \( P ; \) grows as a linear function of time \( t, \) where \( t \) is
the number of years after 2003
(a) How many students will be enrolled
in the school in \( 2010 ? \)
(b) Find a linear function that relates
the student population to the time \( t \)
Subject: Physics
The potential at point \( B, C \) and \( D \) in the following circuit will be
A . \( 12 \vee, 10 \vee, 6 v \)
B. \( 11 \vee, 9 \vee, 6 v \)
c. \( 11 \vee, 9 \vee, \) o \( v \)
D. \( 12 \vee, 10 \vee, \) o \( v \)
Subject: Maths
The projection of a line segment joining
the points \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}, \boldsymbol{z}_{1},\right) \) and
\( Q\left(x_{1}, y_{1}, z_{1},\right) \) on another line whose
DC's are \( l, m, n \) is given by This question has multiple correct options
A \( \cdot l\left(x_{1}+x_{2}\right)+m\left(y_{2}+y_{2}\right)+n\left(z_{1}+z_{2}\right) \)
B. \( 2\left[\frac{\left(l x_{2}+m y_{2}+n z_{2}\right)}{2}-\frac{\left(l x_{1}+m y_{1}+n z_{1}\right)}{2}\right. \)
c. \( l\left(x_{2}-x_{1}\right)+m\left(y_{2}-y_{1}\right)+n\left(z_{2}-z_{1}\right) \)
D. \( \frac{x_{2}-x_{1}}{l}+\frac{y_{2}-y_{1}}{m}+\frac{z_{2}-z_{1}}{n} \)
Subject: Physics
The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The
dipole axis makes an angle of \( 11.3^{\circ} \) with the axis of the earth. At mumbai
declination is nearly zero. Then
A. the declination varies between \( 11.3^{\circ} \) W to \( 11.3^{\circ} \) E
B. the least declination is \( 0^{\circ} \)
c. the plane defined by dipole and the earth axis posses through greenwich
D. declination average over the earth must be always negative
Subject: Chemistry
An equilibrium mixture, \( N_{2}(g)+ \) \( O_{2}(g) \rightleftharpoons 2 N O(g) \) in a vessel of
capacity 100 litre contain
1 mol \( N_{2}, 2 \) mol \( O_{2} \) and 3 mol \( N O \)
Calculate the number of moles of \( O_{2} \) to
be added so that at new equilibrium the
conc. of \( N O \) is found to be 0.04 mol \( / \)lit
A . \( (101 / 18) \)
в. \( (101 / 9) \)
c. \( (202 / 9) \)
D. None of these
Subject: Physics
If the area of parallelogram, whose diagonals are represented by \( (3 \hat{i}+\hat{j}+\hat{k}) \) and \( (\hat{i}-\hat{j}-\hat{k}), \) is in the
form of \( x \sqrt{2} \) square unit, the value of \( x \)
is :
A . 4
B. 2
\( c \cdot 3 \)
D. 6
Subject: Chemistry
In the equilibrium, \( C a C O_{3}(s) \rightleftharpoons \)
\( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}), \) the number of
moles of \( C O_{2} \) is increased by
This question has multiple correct options
A. Increasing the volume of the vessel
B. Removing some \( C a C O_{3} \) from the mixture
c. Adding a few drops of NaOH to the reaction mixture.
D. Adding a few drops of HCI to the reaction mixture
Subject: Maths
A.P.
\( \mathbf{A} \cdot 2 a_{2}^{3}-3 a_{0} a_{1} a_{2}+a_{0}^{2} a_{3}=0 \ldots(1) \)
B \( \cdot 2 a_{2}^{3}-3 a_{0} a_{1} a_{2}+a_{0}^{2} a_{1}=0 \ldots(1) \)
C \( \cdot 2 a_{1}^{3}-3 a_{0} a_{1} a_{2}+a_{0}^{2} a_{3}=0 \ldots(1) \)
D. \( 2 a_{1}^{3}-3 a_{0} a_{1} a_{2}+a_{0}^{2} a_{1}=0 \ldots(1) \)
Subject: Maths
The line passes through the points \( (5,1, a) \&(3, b, 1) \) crosses the \( y z \) plane at the point \( \left(0, \frac{17}{2},-\frac{13}{2}\right), \) then
A \( . a=4, b=6 \)
B. \( a=6, b=4 \)
c. \( a=8, b=2 \)
D. \( a=2, b=8 \)
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