AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( A \) and \( B \) be points with position vectors \( \bar{a} \) and \( \bar{b} \) with respect to origin \( O \)
If the point \( C \) on \( O A \) is such that \( \mathbf{2} \overline{\boldsymbol{A} \boldsymbol{C}}=\overline{\boldsymbol{C} \boldsymbol{O}}, \overline{\boldsymbol{C} \boldsymbol{D}} \) is parallel to \( \overline{\boldsymbol{O} \boldsymbol{B}} \) and
\( |\overline{C D}|=3|\overline{O B}| \) then \( A D \) is
A \( \cdot \bar{b}-\frac{a}{9} \)
в. \( 3 \bar{b}-\frac{a}{3} \)
C \( \cdot \bar{b}-\frac{a}{3} \)
D. \( \bar{b}+\frac{a}{3} \)
Subject: Maths
If \( x \sin ^{3} \theta+y \cos ^{3} \theta=\cos \theta \sin \theta \) and
\( \boldsymbol{x} \sin \boldsymbol{\theta}=\boldsymbol{y} \cos \boldsymbol{\theta} \operatorname{then} \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{1} \)
If the statement is True, enter 1 , else
enter 0
A.
Subject: Chemistry
Which of the following is correct?
A. \( S_{3} O_{9} \) contains no \( S-S \) linkage.
B. \( S_{3} O_{9} \) contains \( O-O \) linkage.
C. \( \left(H P O_{3}\right)_{3} \) contains \( P-P \) linkage
D. \( S_{2} O_{8}^{2-} \) contains \( S-S \) linkage
Subject: Chemistry
What would be the best method to bring about the following conversion? \( C H_{3} \)
\( C H_{3}-C_{1}^{\prime}-C H=C H_{2} \longrightarrow C H_{3}- \)
\( \boldsymbol{C H}_{3} \)
\( \dot{C}-C H C H_{3} \)
\( C H_{3} \quad O H \)
\( \mathbf{A} \cdot B H_{3}, T H F ; \) then \( H_{2} O_{2}, O H^{-} \)
B. \( H B r ; \) then \( N a O H / H_{2} O \)
c. conc. \( H_{2} S O_{4}, \) then \( H_{2} O \), heat
D. \( H g(O A c)_{2} / T H F-H_{2} O \), then \( N a B H_{4}, O H^{-} \)
Subject: Maths
For what values of \( m \in R, \) both roots of
the equation \( x^{2}-6 m x+9 m^{2}- \)
\( 2 m+2=0 \) exceed \( 3 ? \)
B. \( \left(\frac{11}{9}, \infty\right) \)
c. \( [1, \infty] \)
D. \( [0, \infty] \)
Subject: Maths
If the lines \( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{y}+\mathbf{1}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+ \)
\( \mathbf{1}=\mathbf{0} \& \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{c}=\mathbf{0} \) where \( \mathbf{a}, \mathbf{b} \& \mathbf{c} \)
are distinct real numbers different from
are concurrent, then the value of \( \frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}= \)
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)
Subject: Physics
A 5 watt source emits monochromatic
light of wavelength 5000 A when placed \( 0.5 \mathrm{m} \) away, it liberates photoelectric
from a photosensitive metallic surface. When the source is moved to a distance
of \( 1.0 \mathrm{m}, \) The numbers of photo electrons liberated will:
A. be reduced by a factor of 2
B. be reduced by a factor of 4
c. be reduced by a factor of 8
D. be reduced by a factor of 16
Subject: Physics
A voltmeter has a resistance of \( G \) ohms
and range \( V \) volts. The value of
resistance required in series to convert
it into voltmeter of range \( n V \) is
A \( . n G \)
в. \( G / n \)
c. \( G /(n-1) \)
D. \( (n-1) G \)
Subject: Physics
The adjoining diagram shows the view
through the eyepiece of a prism
spectrometer with its slit illuminated
by the source of light emitting three wavelengths corresponding to yellow
(Y), Green (G) and unknown colour (X).
The colour at \( X \) may be:
\( \mathbf{A} \cdot \operatorname{Red} \)
B. Orange
c. Pink
D. Blue
Subject: Physics
If the self inductance of 500 turns coil
is \( 125 \mathrm{mH} \), then the self inductance of
the similar coil of \( 800 \mathrm{mH} \)
A. \( 48.8 \mathrm{mH} \)
B. 200 mH
c. \( 290 \mathrm{mH} \)
D. 320 mH
Subject: Maths
Find the integrals of the functions.
i) \( \sin ^{3} x \cos ^{3} x \)
ii) \( \sin x \sin 2 x \sin 3 x \)
iii) \( \sin 4 x \sin 8 x \)
iv \( \frac{1-\cos x}{1+\cos x} \)
v) \( \frac{\cos x}{1+\cos x} \)
Subject: Maths
Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\begin{array}{l}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y} \\
x y<1 \\
\quad \pi+\tan ^{-1} \frac{x+y}{1-x y}, \quad x y>1
\end{array}
\]
Prove that
\[
\tan ^{-1} \frac{1-x}{1+x} \tan ^{-1} \frac{1-y}{1+y}=
\]
\[
\sin ^{-1} \frac{\boldsymbol{y}-\boldsymbol{x}}{\sqrt{1+\boldsymbol{x}^{2}} \sqrt{1+\boldsymbol{y}^{2}}}
\]
Subject: Physics
At what change in temperature will the resistance of a copper wire become three times its value at \( 0^{0} C ? \) [Temperature coefficient of resistance for copper \( \left.4 \times 10^{-3}\right]: \)
A \( .400^{\circ} \mathrm{C} \)
B. 450 \( ^{0} C \)
c. \( 500^{\circ} \mathrm{C} \)
D. \( 60^{\circ} \mathrm{C} \)
Subject: Physics
A flexible wire loop in the shape of a circle has a radius that grows linearly with time. There is a magnetic field perpendicular to the plane of the loop that has a magnitude inversely proportional to the distance from the
center of the loop, \( B(r) \propto \frac{1}{r} . \) How does
the emf vary with time?
A. \( E \propto r^{2} \)
в. \( E \propto t \)
\( c \cdot E \propto \sqrt{t} \)
D. \( E \) is constant
Subject: Maths
If 2,8 are the roots of \( x^{2}+a x+\beta=0 \)
and 3,3 are the roots of \( x^{2}+\alpha x+b= \)
0 then find the roots of \( x^{2}+a x+b=0 \)
A . -1,-9
в. 1,9
c. -2,-8
D. 2,8
Subject: Physics
A sample of a radioactive element has a mass of \( 10 g \) at an instant \( t=0 . \) The
approximate mass of this element in
the sample after two mean lives is
A. \( 1.35 g \)
в. \( 2.50 g \)
c. \( 3.70 g \)
D. \( 6.30 g \)
Subject: Maths
The distance between the parallel lines
\( 9 x^{2}-6 x y+y^{2}+18 x-6 y+8=0 \) is?
A \( \cdot \frac{1}{\sqrt{10}} \)
B. \( \frac{2}{\sqrt{10}} \)
c. \( \frac{4}{\sqrt{10}} \)
D. \( \sqrt{10} \)
Subject: Biology
Which of the following statement is/are
correct for photorespiration?
A. Glycerate diffuses out of peroxisome and enters chloroplast, here it is phosphorylated
B. Glyoxylate is used in the synthesis of glycine in peroxisome
C. In mitochondria when glycine is converted into serin at that time glycine first oxidized and later reduced
D. Coordinated of chloroplast, peroxisome and mitochondrion is essential in photorespiration
Subject: Maths
If the \( p^{t h}, q^{t h} \) and \( r^{t h} \) terms of an A.P. are
\( P, Q, R \) respectively, then \( P(q-r)+ \)
\( Q(r-p)+R(p-q) \) equals
A.
B.
c. par
D. p \( + \) ar
Subject: Chemistry
Consider the following statements and arrange in the order of true/false as
given in the codes.
\( \boldsymbol{S}_{1}: \) Cuprite, limorite and Zincite are
oxide ores.
\( S_{2}: \) Dolomite contains \( C a C O_{3} \) and
\( M g C O_{3} \)
\( S_{3}: \) Chalcocyte and azurite are ores of
copper.
\( \boldsymbol{S}_{4}: \) Feldspar and mica minerals contain
aluminium.
A. TT TT
B. FTFF
c. F F T T
D. TTFT
Subject: Maths
Consider the following statements:
Statement I
\( x>\sin x \) for all \( x>0 \)
Statement II:
\( f(x)=x-\sin x \) is an increasing
function for all \( x>0 \)
Which one of the following is correct in respect of the above statements?
A. Both Statements I and II are true and Statement II is the correct explanation of statement
B. Both Statements I and II are true and Statement II is the not correct explanation of Statement
c. statement lis true but Statement II is false
D. Statement I is true but Statement II is true
Subject: Chemistry
For the following reaction, identify the
gaseous product formed. \( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C O}_{3}+ \)
\( \boldsymbol{H} \boldsymbol{C l} \rightarrow \)
A \( . C O \)
в. \( C O_{2} \)
\( c \cdot O_{2} \)
D. \( H_{2} O \)
Subject: Maths
An urn contains five balls alike in every respect save colour. If three of these
balls are white and two are black and
we draw two balls at random from this
urn without replacing them. If A is the event that the first ball drawn is white and \( \mathrm{B} \) the event that the second ball
drawn is black, are \( A \) and \( B \)
independent? If \( A \) and \( B \) are independent then enter 1 , else enter 0 .
Subject: Chemistry
In photosynthesis in plants, \( \boldsymbol{H}_{2} \boldsymbol{O} \) and
\( C O_{2} \) react in presence of light and chlorophyll to give carbohydrate and oxygen.When the carbohydrate is burnt in air, the gases produced are:
A. \( C O_{2}+H_{2} \)
в. \( C O_{2}+C O \)
c. \( C O_{2}+H_{2} O \)
D. \( C O_{2}+O_{2} \)
Subject: Physics
If a capillary tube is tilted to \( 45^{\circ} \) and
\( 60^{\circ} \) from the vertical then the ratio
of length \( l_{1} \) and \( l_{2} \) of liquid columns in
it will be -
A. \( 1: \sqrt{2} \)
B. \( \sqrt{2}: 1 \)
c. 1: 2
D. 2:
Subject: Physics
Three charges \( +4 q,-q \) and \( +4 q \) are kept on
a straight line at position \( (0,0,0),(a, 0,0) \) and \( (2 a, 0,0) \) respectively. Considering that they are free to move along the \( x \) -
axis only
A. All the charges are in stable equilibrium
B. All the charges are in unstable equilibrium.
C. Only the middle charge is in stable equilibrium.
D. Only middle charge is in unstable equilibrium.
Subject: Chemistry
Identify the incorrect statement related
to \( P C l_{5} \) from the following:
A. Three equitorial \( P-C l \) bonds makes an angle of \( 120^{\circ} \) with each other
B. Two axial \( P-C l \) bonds make an angle of \( 180^{\circ} \) with each other
c. Axial \( P-C l \) bonds are longer than equatorial \( P-C l \) bonds
D. \( P C l_{5} \) molecules is non reactive
Subject: Chemistry
The volume of a colloidal particle, \( V_{c} \) as
compared to volume of solute particle
\( V_{s}, \) in a true solution could be
A \( \cdot \frac{V_{c}}{V_{s}}=10^{-3} \)
в. \( \frac{V_{c}}{V_{s}}=10^{3} \)
c. \( \frac{V_{c}}{V_{s}}=10 \)
D. \( \frac{V_{C}}{V_{s}}=10^{22} \)
Subject: Maths
\( \boldsymbol{x}, \mathbf{2} \boldsymbol{x}, \mathbf{4} \boldsymbol{x}, \dots \)
The first term in the sequence above is
\( x, \) and each term thereafter is equal to twice the previous term. Find the sum of the first five terms of this sequence.
A . \( 10 x \)
в. \( 15 x \)
c. \( 30 x \)
D. \( 31 x \)
E. \( 32 x \)
Subject: Physics
The horizontal ranges described by two
projectiles, projected at angles \( \left(45^{\circ}-\right. \)
\( \theta \) ) and \( \left(45^{\circ}+\theta\right) \) from the same point
and same velocity are in the ratio.
A . 2: 1
B. 1: 1
\( c \cdot 2: 3 \)
D. 1: 2
Subject: Chemistry
The given arranged sequence on the basis of their increasing atomic masses represents which law of classification of elements?
\( \boldsymbol{F}, \boldsymbol{N} \boldsymbol{a}, \boldsymbol{M} \boldsymbol{g}, \boldsymbol{A l}, \boldsymbol{S} \boldsymbol{i}, \boldsymbol{P}, \boldsymbol{S}, \boldsymbol{C l} \& \boldsymbol{K} \)
A. Modern table
B. Newton's law
c. Newland's law of octaves
D. Mendeleev's periodic table
Subject: Physics
If \( a, b, c \) are the percentage errors in the measurement of \( A, B \) and \( C, \) then the
percentage error in ABC would be
approximately
A \( . a b c \)
B . \( a+b+c \)
c. \( a b+b c+a c \)
D. \( \frac{a}{b}+\frac{b}{c}+\frac{c}{a} \)
Subject: Chemistry
If we plot a graph between \( \log _{10} k \) and \( \frac{1}{T} \) by Arrhenius equation, the slope is:
A \( .-E_{a} / R \)
в. \( +E_{a} / R \)
c. \( -\frac{E_{a}}{2.303 R} \)
D. \( +\frac{E_{a}}{2.303 R} \)
Subject: Physics
Fossil \( X \) is older than fossil \( Y \). Most
evident answer is:
A. Fossil Y has got some of the vestigial organs which are functional in \( x \).
B. Fossil Y has got homologous and analogous organs of fossil X.
C. Fossil \( X \) is found in deeper sedimentation than \( Y \)
D. Fossil \( Y \) was found in better state than that of \( x \).
Subject: Chemistry
Column - I Column - II
(Metals) (Ores)
A) Tin
1) Calamine
B) Zinc
2) Cassiterite
C) Titanium
3) Cerrusite
D) Lead
4) Rutile
A . A-1, B-2, C-3, D-4
B. A-2, B-1, C-4, D-3
c. \( A-4, A-3, C-2, D-1 \)
D. A-2, B-1, C-3, D-4
Subject: Physics
The pulley in arrangements in Fig. (a) and Fig. (b) are identical. The mass of
the rope is negligible. In Fig (a), the mass \( m \) is lifted up by attaching a mass \( 2 \mathrm{m} \) to the other end of the rope. In
(b), \( m \) is lifted up by pulling the other end of the rope with a constant
downwards force \( F=2 m g \). The acceleration of \( \mathrm{m} \) is the same in both
cases.
\( (\mathbf{a}) \)
(b)
A. True
B. False
Subject: Maths
Let \( A_{n} \) be the constant number such
that \( c>1 . \) If the least area of the figure
given by the line passing through the point (1,c) with gradient 'm' and the parabola \( \boldsymbol{y}=\boldsymbol{x}^{2} \) is 36 sq.units find the
value of \( \left(c^{2}+m^{2}\right) \)
A \( \cdot 104 \)
B. 105
\( c \cdot 10 \)
D. 100
Subject: Chemistry
Cerium \( (z=58) \) is an important member of the lanthanides. Which of
the following statements about cerium is incorrect?
A. The common oxidation states of cerium are +3 and +4
B. The +3 oxidation state of cerium is more stable than the +4 oxidation state
c. The +4 oxidation state of cerium is not known in solutions
D. Cerium (IV) acts as an oxidising agent.
Subject: Maths
Solve:
\( \lim _{n \rightarrow \infty}\left\{\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{2 n}\right\}= \)
\( A \cdot \log 2 \)
B . \( \log 3 \)
\( c \)
D. \( \frac{\pi}{2} \)
Subject: Chemistry
Given \( 2 N O_{(g)}+O_{2(g)} \rightarrow 2 N O_{2(g)} ; \) rate
\( =\mathbf{k}[\boldsymbol{N} \boldsymbol{O}]^{2}\left[\boldsymbol{O}_{2}\right]^{1} . \) By how many times does
the rate of the reaction change when the volume of the reaction vessel is reduced
to \( 1 / 3 \) rd of its original volume? Will there be any change in the order of the reaction?
Subject: Physics
Through a non-uniform pipe, a nonviscous liquid is flowing from section \( \mathbf{A} \) to B as shown in figure.Which of following is correct?
A. since liquid is flowing from A to B, therefore, pressure at A is greater than at
B. Velocity at B is greater than that at
C. Total energy per unit volume of the liquid is greater at than that at
D. Axis of pipe can be horizonta
Subject: Physics
figure. The system is released from rest
and the block of mass 1 kg is found to
have a speed \( 0.3 m / s \) after it has
descended through a distance of 1 m.
The coefficient of kinetic friction
between the block and the table is (All
pulleys are massless and smooth and
strings are inextensible and light
acceleration due to gravity \( =10 m / s^{2} . \) ):
A . 0.12
B. 0.5
\( c .0 . \)
D. 0.15
Subject: Chemistry
Complete the following equation:
\( \boldsymbol{C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
A. \( H C l+H C l O \)
в. \( H C l+O_{2} \)
c. \( H C l O+O_{2} \)
D. None of the above
Subject: Chemistry
Given J-tube has \( 2.4 ~ m L \) of air at a
pressure of 1 atm. On adding mercury,
volume of air is reduced to \( 1.9 m L \) as
shown. Difference in the level of mercury
in two columns is?
\( A .700 m m \)
В. \( 200 \mathrm{mm} \)
\( c .900 m m \)
D. \( 760 \mathrm{mm} \)
Subject: Physics
\( A \) and \( B \) are two concentric spherical
shells, If \( A \) is given a charge \( +q \) while \( B \) is earthed as show in the figure, then :
A. Charge on the outer surface of shell B is zero
B. The charge on B is equal and opposite to that of \( A \)
C. The field inside \( A \) and outside \( B \) is zero
D. All of the above
Subject: Chemistry
Match the list of noble gas compounds
in column I with their shapes in column
II and mark the appropriate choice.
Column I Column II
(A) \( X e F_{4} \)
(i) Distorted octahedral
(B) \( X e F_{6} \)
(ii) Tetrahedral
(С) \( X e O_{3} \)
(iii) Square planar
(D) \( X e O_{4} \)
(iv) Trigonal pyramidal
\( \mathbf{A} \cdot(A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i i),(D) \rightarrow(i) \)
B. \( (A) \rightarrow(i),(B) \rightarrow(\text { ii }),(C) \rightarrow(\text { iii), }(D) \rightarrow(i v) \)
C \( \cdot(A) \rightarrow(\text { ii }),(B) \rightarrow(\text { iii }),(C) \rightarrow(i v),(D) \rightarrow(i) \)
\( \mathbf{D} \cdot(A) \rightarrow(\text { iii }),(B) \rightarrow(i),(C) \rightarrow(\text { iv }),(D) \rightarrow(\text { ii }) \)
Subject: Chemistry
Which of the following statements
is/are correct about the following
reactions?

This question has multiple correct options
\( A \). path I is feasible.
B. path II is feasible.
C. PhCl cannot be trinitrated because Cl and two \( N O_{2} \) atoms deactivate the ring towards further SE reaction.
D. 2,4 -Dinitrophenol can be nitrated beacuse the two deactivating \( N O_{2} \) groups prevent ring oxidation
Subject: Physics
An ideal gas at a pressure of 1
atmosphere and temperature of \( 27^{\circ} \mathrm{C} \) is compressed adiabatically until its pressure becomes 8 times the initial
pressure, then the final temperature is
\( (\gamma=3 / 2) \)
\( \mathbf{A} \cdot 627^{0} C \)
В. \( 527^{\circ} \mathrm{C} \)
c. \( 427^{\circ} \mathrm{C} \)
D. \( 327^{\circ} \mathrm{C} \)
Subject: Chemistry
Which of the reactants act as oxidant or
reductant if any:
\( 2 C u S O_{4}+S O_{2}+2 K B r+2 H_{2} O \rightarrow \)
\( 2 C u B r+2 H_{2} S O_{4}+K_{2} S O_{4} \)
A \( . C u S O_{4} \)
в. \( S O_{2} \)
c. Both of these
D. None of these
Subject: Chemistry
Write IUPAC name of the given
compound:
\[
\mathbf{C H}_{3}-\underset{\mathbf{C} \mathbf{H}_{3}}{\mathbf{I}} \mathbf{U}-\mathbf{C}_{\mathbf{O H}}-\frac{\mathbf{C} \mathbf{H}_{3}}{\mathbf{C} \mathbf{H}_{3}}-\mathbf{C H}_{3}
\]
Subject: Maths
Find the value of \( k \) so that the function \( f \)
is continuous at the indicated point. \( f(x)=\begin{array}{cc}k x^{2} & , x \leq 2 \\ 3 & , x>2\end{array} \) at \( x=2 \)
A \( \cdot k=\frac{1}{4} \)
B. \( _{k=\frac{1}{2}} \)
c. \( _{k=\frac{3}{4}} \)
D. \( k=1 \)
Subject: Maths
if \( z=\frac{1+3 i}{1+i} \) then
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{Re}(z)=2 \operatorname{Im}(z) \)
B. \( \operatorname{Re}(z)+2 \operatorname{Im}(z)=0 \)
\( \mathbf{c} .|z|=\sqrt{5} \)
D. \( a m p z=\tan ^{-1} 2 \)
Subject: Maths
\( \sqrt{3} \) percent of \( 2 \sqrt{12} \) is equal to
A . 12
в. \( 6 \sqrt{12} \)
c. \( \frac{3}{25} \)
D. \( \frac{6}{25} \)
E \( \cdot \frac{3 \sqrt{12}}{25} \)
Subject: Chemistry
If the solubility of the salt
\( \boldsymbol{L} \boldsymbol{i}_{3} \boldsymbol{N} \boldsymbol{a}_{3}\left(\boldsymbol{A l} \boldsymbol{F}_{6}\right)_{2} \) is \( \boldsymbol{x}, \) then its solubility
product would be:
A \( \cdot 26 x^{8} \)
B . \( 2916 x^{8} \)
\( \mathbf{c} \cdot 256 x^{6} \)
D. none of these
Subject: Chemistry
Which pair of substances will have the most similar geometry?
\( A \cdot S O_{3}, S O_{3}^{2-} \)
в. \( S O_{3}, S O_{4}^{2-} \)
\( \mathrm{c} \cdot \mathrm{SO}_{3}, \mathrm{CO}_{3}^{2} \)
D. \( S O_{4}^{2-}, C O_{3}^{2} \)
Subject: Chemistry
Assertion
In physical adsorption, enthalpy of adsorption is very low.
Reason
In physical adsorption, attraction between gas molecules and solid surface is due to weak van der Waals
forces
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
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{2} \\ \mathbf{3} & \mathbf{0} & -\mathbf{2} \\ \mathbf{1} & \mathbf{0} & \mathbf{3}\end{array}\right] \) verify that
\( \boldsymbol{A}(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=|\boldsymbol{A}| \boldsymbol{I} \)
Subject: Physics
The diagram shows the change of phase of a substance on a temperature-time
graph. What is the boiling point of the substance?
\( \mathbf{A} \cdot t_{1}^{\circ} C \)
B . \( t_{2}^{\circ} C \)
c. \( t_{3} \circ C \)
D. \( t_{4}^{\circ} C \)
Subject: Chemistry
Which of the reactants act as oxidant or
reductant if any:
\( \boldsymbol{C a}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{C a} \boldsymbol{C l}_{2} \)
A \( \cdot C l_{2} \)
в. \( C a \)
c. Both of these
D. None of these
Subject: Physics
A radioactive sample decays by two different processes. Half-life of first
process is \( t_{1}, \) and for second process is
\( t_{2} . \) Then, the effective half-life is
A \( \cdot t_{1}-t_{2} \)
в. \( t_{1}+t_{2} \)
c. \( \frac{t_{1}, t_{2}}{t_{1}+t_{2}} \)
D. \( \frac{t_{1}^{2}+\frac{2}{2}}{t_{1}-t_{2}} \)
Subject: Maths
The value of \( \boldsymbol{S}=\sqrt{\mathbf{1}+\frac{\mathbf{1}}{\mathbf{1}^{2}}+\frac{\mathbf{1}}{\mathbf{2}^{2}}}+ \)
\( \sqrt{1++\frac{1}{2^{2}}+\frac{1}{3^{2}}}+\ldots+ \)
\( \sqrt{1++\frac{1}{(2014)^{2}}+\frac{1}{(2015)^{2}}} \)
A . 2015
в. \( _{2015}-\frac{1}{2015} \)
c. \( _{2016}-\frac{1}{2016} \)
D. \( _{2014}-\frac{1}{2014} \)
Subject: Physics
Drops of liquid of density \( d \) are floating
half immersed in a liquid of density \( \rho . \) If
the surface tension of liquid is \( \boldsymbol{T} \) then the radius of the drop will be \( (\boldsymbol{d}= \) density of liquid drop).
A \( \cdot \sqrt{\frac{3 T}{g(2 d-\rho)}} \)
в. \( \sqrt{\frac{6 T}{g(2 d-\rho)}} \)
c. \( \sqrt{\frac{2 T}{g(2 d-\rho)}} \)
D. \( \sqrt{\frac{3 T}{g(4 d-3 \rho)}} \)
Subject: Maths
Differentiate with respect to \( \times \frac{(1+x)}{e^{x}} \)
A \( .-x e^{-x} \)
B . \( x e^{-x} \)
\( \mathrm{c} \cdot-x e^{-2 x} \)
D. \( x^{2} e^{-x} \)
Subject: Maths
\( \left[\begin{array}{cc}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{2} \\ \mathbf{5} & \boldsymbol{b}\end{array}\right]=\left[\begin{array}{ll}\mathbf{6} & \mathbf{5} \\ \mathbf{2} & \mathbf{2}\end{array}\right], \) then find \( \boldsymbol{a} \)
Subject: Chemistry
In neutral or faintly alkaline medium, thiosulphate is quantitatively oxidized
by \( K M n O_{4} \) to:
\( \mathbf{A} \cdot S O_{3}^{2-} \)
B. \( S O_{4}^{2-} \)
\( c \cdot s O_{2} \)
D. \( S O_{5}^{2-} \)
Subject: Physics
A person needs a lens of power -4.5 D for correction of her vision. What is the
focal length of the corrective lens?
A. \( f=-0.25 \mathrm{m} \)
B. \( f=+0.22 \mathrm{m} \)
c. \( f=1.22 \mathrm{m} \)
D. \( f=-0.22 \mathrm{m} \)
Subject: Physics
A thin brass sheet at \( 10^{\circ} C \) and a thin
steel sheet at \( 20^{\circ} C \) have the same
surface area. The common temperature at which both would have the same area
is: (Coefficients of linear expansion for brass and steel are \( 19 \times 10^{-6} /^{\circ} \mathrm{C} \) and
\( 11 \times 10^{-6} /^{\circ} C \quad \) respectively
A. \( -3.75^{\circ} \mathrm{C} \)
B . \( -2.75^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 2.75^{\circ} \mathrm{C} \)
D. \( 3.75^{\circ} \mathrm{C} \)
Subject: Maths
Let \( A \) be a square matrix. Which of the
following is/are not skew-symmetric matrix/ces?
A . \( A-A^{T} \)
B. \( A^{T}-A \)
c. \( A A^{T}-A^{T} A \)
D. \( A+A^{T} \), when A is skew-symmetric
Subject: Maths
A triangle is specified by the coordinates of its vertices \( A(3,2,-3), B \)
\( (5,1,-1), \) and \( C(1,-2,1) \). Calculate the coordinates of the vector a which is of the same direction as the vector \( \overrightarrow{A B} \)
and has the same length as the vector \( \boldsymbol{A C} \)
Subject: Biology
According to Bharat IV, the emission of carbon monoxide should be
\( A \cdot 0.18 \mathrm{gm} / \mathrm{km} \)
B. \( 0.1 \mathrm{gm} / \mathrm{km} \)
c. \( 0.5 \mathrm{gm} / \mathrm{km} \)
D. \( 1 \mathrm{gm} / \mathrm{km} \)
Subject: Chemistry
The decreasing order of power of boron
halides to act as Lewis acids is :
A. \( B F_{3}>B C l_{3}>B B r_{3} \)
B. \( B B r_{3}>B C l_{3}>B F_{3} \)
c. \( B C l_{3}>B F_{3}>B B r_{3} \)
D. \( B C I_{3}>B B r_{3}>B F_{3} \)
Subject: Physics
A closely wound solenoid \( 80 \mathrm{cm} \) long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8
\( \mathrm{cm} . \) If the current carried is \( 8.0 \mathrm{A} \)
estimate the magnitude of B inside the solenoid near its centre :
A \( .1 .5 \times 10^{-2} T \), opposite to the axis of solenoid
B . \( 2 \times 10^{-2} T \), along the axis of solenoid
C . \( 3.5 \times 10^{-2} T \), along the axis of solenoid
D. \( 1.5 \times 10^{-2} T \) along the axis of solenoid
Subject: Chemistry
I. Nitrogen \( \left(N_{2}\right) \) reacts with oxygen \( \left(O_{2}\right. \)
, the compound \( N O_{2} \) can be formed as
a product.
II. Nitrogen atoms donate four
electrons to form \( N^{4+} \) ions and oxygen
atoms gain two electrons to form \( O^{2-} \)
ions when nitrogen and oxygen form an ionic bond.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement \( I I \) is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false