AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Match the following
Set- Set - II
A) \( F_{2} \)
1) pale yellow colour gas
B) \( C l_{2} \)
2) violet colour solid
C) \( B r_{2} \)
3) orange liquid
D) \( \boldsymbol{I}_{2} \)
4) greenish colour gas
Correct the matching is
A . A-1, B-3, C-2, D-4
B. A-1, B-4, C-3, D-2
c. \( A-2, B-3, C-4, D-1 \)
D. A-3, B-2, C-1, D-4
Subject: Maths
If \( P(A)=\frac{3}{5} \) and \( P(B)=\frac{1}{5}, \) find
\( \mathbf{1 0 0} \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \) if \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are
independent events.
Subject: Maths
If a function satisfies \( (\boldsymbol{x}-\boldsymbol{y}) \boldsymbol{f}(\boldsymbol{x}+ \)
\( \boldsymbol{y})-(\boldsymbol{x}+\boldsymbol{y}) \boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})=\boldsymbol{2}\left(\boldsymbol{x}^{2} \boldsymbol{y}-\right. \)
\( \left.\boldsymbol{y}^{3}\right), \forall \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and \( \boldsymbol{f}(1)=2, \) then
This question has multiple correct options
A. \( f(x) \) must be polynomial function
В. \( f(3)=12 \)
c. \( f(0)=0 \)
D. \( f(x) \) may not be differentiable
Subject: Physics
If \( \boldsymbol{v}_{1} \sin \boldsymbol{\theta}_{1}=\boldsymbol{v}_{2} \sin \theta_{2}, \) then choose the
incorrect statement
A. The time of flight of both the particles will be same
B. The maximum height attained by the particles will be same
C. The trajectory of one with respect to another will be a horizontal straight line
D. None of these
Subject: Physics
A weight of \( 120 k N \) is placed on top of a metal column. The length of the column is compressed by 0.25 mm. The column obeys Hooke's law when compressed. How much energy is stored in the compressed column?
\( \mathbf{A} \cdot 15 J \)
в. \( 30 J \)
\( c .15 k J \)
D. 30kJ
Subject: Chemistry
\( H_{2} \) is more reactive than \( D_{2} \) because:
A. \( H_{2} \) is lighter than \( D_{2} \).
B. \( H_{2} \) has low bond dissociation energy than \( D_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \) is non radioactive while \( D_{2} \) is radioactive
D. \( D_{2} \) has two neutrons.
Subject: Chemistry
In a reaction, 4 mol of electrons are
transferred to one mol of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) when it acts as an oxidant. The possible reduction product is :
A. 0.5 mol \( N_{2} \)
B. 0.5 mol \( N_{2} \),
c. 1 mol \( N O_{2} \)
D. 1 mol \( N H_{3} \)
Subject: Maths
Differentiate the following function with
respect to \( x \)
\( \left(2 x^{2}-3\right) \sin x \)
A \( \cdot 4 x \sin x+\left(2 x^{2}+3\right) \cos x \)
B. \( 4 x \sin x+\left(2 x^{2}-3\right) \sin x \)
c. \( 4 x \sin x+\left(2 x^{2}-3\right) \cos x \)
D. \( 4 x \cos x+\left(2 x^{2}-3\right) \cos x \)
Subject: Maths
Solve the differential equation:
\( \sec ^{2} y \frac{d y}{d x}+\tan y=x^{3} \)
A \( \cdot \tan y=x^{3}+3 x^{2}+6 x-6+c e^{-x} \)
B . \( \tan y=x^{3}-3 x^{2}-6 x-6+c e^{-x} \)
C. \( \tan y=x^{3}-3 x^{2}+6 x-6+c e^{-x} \)
D. None of these.
Subject: Chemistry
\( \boldsymbol{C u O}(\boldsymbol{s})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
In this reaction, is reduced.
A. copper oxide
B. copper
c. hydrogen
D. water
Subject: Physics
Three fluids 1,2 and 3 have Bulk Moduli
of \( k 1, k 2 \) and \( k 3 \) respectively. If \( k 1>k 2> \)
k3, which liquid will have the highest compressibility
A . liquid 1
B. liquid 2
c. liquid 3
D. theyll have equal compressibilities
Subject: Physics
In the region of only gravitational fields of mass ' \( M^{\prime} \) a particle is shifted from \( \boldsymbol{A} \)
to \( B \) via three different paths of length
\( 5 m, 10 m \) and \( 25 m . \) The work done in
different paths is \( W_{1}, W_{2}, W_{3} \) respectively then:
A. \( W_{1}=W_{2}=W_{3} \)
В. \( W_{1}>W_{2}>W_{3} \)
C \( . W_{1}=W_{2}>W_{3} \)
D. \( W_{1}<W_{2}<W_{3} \)
Subject: Physics
A meter bridge is set-up as shown, to
determine an unknown resistance. \( \boldsymbol{X} \)
using a standard 10 ohm resistor. The
galvanometer shows null point when
tapping key is a \( 52 \mathrm{cm} \) mark. The end-
corrections are \( 1 \mathrm{cm} \) and \( 2 \mathrm{cm} \)
respectively for the ends \( A \) and \( B \). The
determined value of \( X \) is:
\( \mathbf{A} \cdot 10.2 \mathrm{ohm} \)
B. 10.6 ohm
c. 10.8 ohm
D. 11.1 ohm
Subject: Chemistry
The high boiling point of ethanol \( 78.2^{\circ} \)
compared to dimethyl ether \( -23.6^{\circ} \)
though they have the same molecular
formula \( \left[\boldsymbol{C}_{2} \boldsymbol{H}_{6} \boldsymbol{O}\right], \) is due to:
A. Hydrogen bonding
B. lonic bonding
c. co-ordinate covalent bonding
D. Resonance
Subject: Physics
Two blocks of mass \( 3 \mathrm{kg} \) and \( 4 \mathrm{kg} \) hang
from the ends of a massless rod marked
in seven equal parts.
Find out at which of the points
indicated should a string of mass
suspended so that whole system
remain in equilibrium?
\( \mathbf{A} \cdot \mathbf{A} \)
B.
\( c \cdot c \)
\( D \cdot D \)
\( E . \)
Subject: Physics
An object is placed at a distance of \( \boldsymbol{f} / \mathbf{2} \)
from a convex lens. The image will be
A. At one of the foci, virtual and double its size
B. At \( 3 f / 2 \), real and inverted and erect
c. At \( 2 f \), virtual and inverted
D. At \( f \), real and inverted
Subject: Maths
\( f \frac{1}{x\left(x^{2}+a^{2}\right)}=\frac{A}{x}+\frac{B x+C}{x^{2}+a^{2}}, \) then
\( \tan ^{-1}\left(\frac{A}{B}\right)= \)
A \( \cdot \frac{3 \pi}{4} \)
в.
\( c \cdot-\frac{\pi}{4} \)
D.
Subject: Chemistry
The IUPAC name of \( K_{2}\left[N i(C N)_{4}\right] \) and
\( K_{2}\left[N i(C l)_{4}\right] \) are:
A. potassium tetracyanonickelate(II), potassiumtetrachloronickelate(II)
B. tetracyanopotassiumnickelate(II),tetrorachlropotassic
C. tetracyanonickel(II), tetrachlornickel(II)
D. potassium tetracyanonickel(II), potassiumtetrachloronickel(II)
Subject: Physics
A parallel plate condenser with oil between the plates (dielectric constant of oil \( K=2 \) ) has a capacitance \( C . \) If the oil is removed, then capacitance of the capacitor becomes:
A \( \cdot \sqrt{2} C \)
в. \( 2 C \)
c. \( \frac{C}{\sqrt{2}} \)
D. \( \frac{c}{2} \)
Subject: Biology
Select the characters which are not
applicable to the anatomy of dicot roots:
(a) Conjunctive tissue present (b) Presence of protein compound in casparian strips
(c) Polyarch xylem bundles (d) Presence of pericycle
\( A \cdot(a) \) and \( (b) \)
B. (b) and (d)
\( c \cdot(c) \) and \( (d) \)
\( D \cdot(a) \) and \( (d) \)
E. (b) and (c)
Subject: Physics
A galvanometer of resistance, \( G \) is
shunted by a resistance \( S \) ohm. To keep
the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is
A \( \cdot \frac{S^{2}}{(S+G)} \)
B. \( \frac{S G}{(S+G)} \)
c. \( \frac{G^{2}}{(S+G)} \)
D. \( \frac{G}{(S+G)} \)
Subject: Biology
Match the following.
A. Gave the concept of
1. John Ray \( \quad \) Systematics
B. First described species as a
2. C. Linnaeus \( \quad \) unit of classification
3. Augustin Pyrame de
C. Coined the term, taxonomy candolle
D. Introduced binomial
4. Julian Huxley \( \quad \) nomenclature
A. \( 1-B, 2-C, 3-D, 4-A \)
B. \( 1-A, 2-C, 3-D, 4-B \)
\( c \cdot 1-c, 2-B, 3-D, 4-A \)
D. \( 1-B, 2-D, 3-C, 4-A \)
Subject: Maths
ABCD a parallelogram. \( \boldsymbol{E} \) is a point on \( A D \) and \( C E \) is produced to meet \( B A \) at
\( F . \) If \( A E=4 c m, A F=8 \mathrm{cm} \) and
\( A B=12 \mathrm{cm} . \) Find the perimeter (in \( \mathrm{cm} \)
of parallelogram \( \boldsymbol{A B C D} \)
Subject: Chemistry
What is ratio of time periods \( \left(T_{1} / T_{2}\right) \) in
second orbit of hydrogen atom to third orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion?
\( A \cdot \frac{8}{27} \)
в. \( \frac{32}{27} \)
c. \( \frac{27}{32} \)
D. \( \frac{27}{8} \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a differentiable
function, such that \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{2} \boldsymbol{y})= \)
\( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{2} \boldsymbol{y})+\boldsymbol{4} \boldsymbol{x} \boldsymbol{y} \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \)
then
A \( \cdot f^{\prime}(1)=f^{\prime}(0)+1 \)
B . \( f^{\prime}(1)=f^{\prime}(0)-1 \)
C \( \cdot f^{\prime}(0)=f^{\prime}(1)+2 \)
D. \( f^{\prime}(1)=f^{\prime}(0)+2 \)
Subject: Maths
\( \frac{\boldsymbol{x}^{2}-\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}^{3}-\mathbf{8}}=\frac{\boldsymbol{A}}{\boldsymbol{x}-\mathbf{2}}+\frac{\boldsymbol{B} \boldsymbol{x}+\boldsymbol{C}}{\boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}+\mathbf{4}} \Rightarrow \)
\( \boldsymbol{A}+\boldsymbol{B}= \)
\( A \cdot 0 \)
B.
\( c .-1 \)
\( D \)
Subject: Maths
Assume that the chances of a patient
having a heart attack is \( 40 \% \). Assuming that a mediation and yoga course
reduces the risk of heart attack by \( 30 \% \) and prescription of certain drug reduces its chance by \( 25 \% \). At a time a patient can choose any one of the two options with equal possibilities. It is given that after going through one of the two options, the patient selected at random suffers a heart attack. Find the
probability that the patient followed a course of mediation and yoga. Interpret the result and state which of the above
stated methods is more beneficial for
the patient.
Subject: Chemistry
\( H_{2} C O_{3} \) ionises as
\( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{C O}_{3}^{-} ; \boldsymbol{K}_{1}=\mathbf{4 . 3} \times \)
\( \mathbf{1 0}^{-\mathbf{7}} \)
\( \boldsymbol{H} \boldsymbol{C O}_{3}^{-} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{C} \boldsymbol{O}_{3}^{2-} ; \boldsymbol{K}_{2}=\mathbf{5} . \boldsymbol{6} \times \)
\( \mathbf{1 0}^{-11} \)
Calculate the degree of hydrolysis and pH value of \( 0.12 M N a_{2} C O_{3} \) solution.
Subject: Physics
An \( L E D \) is constructed from a pn
junction based on a certain semiconducting material whose energy gap is \( 1.9 e V . \) Then the wavelength of the emitted light is
A \( .2 .9 \times 10^{-9} \mathrm{m} \)
в. \( 1.6 \times 10^{-8} \mathrm{m} \)
c. \( 6.5 \times 10^{-7} m \)
D. \( 9.1 \times 10^{-5} m \)
Subject: Physics
The density of a cube is measured by measuring its mass ad length of its side. If the maximum errors in the
measurement of its mass and length are \( 3 \% \) and \( 2 \% \) respectively, the maximum error in the measurement of
density would be:
A . \( 12 \% \)
B. \( 14 \% \)
c. \( 7 \% \)
D. \( 9 \% \)
Subject: Chemistry
\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{\mathbf{6}}\right] \) is 60\% ionized.
What will be its van't Hoff factor?
A . 1.4
B. 2.4
c. 3.4
D. 4.4
Subject: Maths
If \( A \) is \( 3 \times 4 \) matrix and \( B \) is matrix such
that \( A^{\prime} B \) and \( B A^{\prime} \) are both defined, then \( B \)
is of the type.
\( A \cdot 3 \times 4 \)
B. \( 3 \times 3 \)
\( \mathbf{c} \cdot 4 \times 4 \)
D. \( 4 \times 3 \)
Subject: Maths
Which of the following is/are correct?
This question has multiple correct options
A. Area of a circle with radius \( 6 \mathrm{cm} \), if angle of sector is \( 60^{\circ}, \) is \( \frac{132}{14} \mathrm{cm}^{2} \)
B. If a chord of circle of radius \( 14 \mathrm{cm} \) makes an angle of
\( 60^{\circ} \) at the centre of the circle, then area of major sector is \( 512.87 \mathrm{cm}^{2} \)
C. The ratio between the circumference and area of a
circle of radius \( 5 \mathrm{cm} \) is 2: 5
D. Area of a circle whose radius is \( 6 \mathrm{cm} \), when the length
of a arc is \( 22 \mathrm{cm}, \) is \( 66 \mathrm{cm}^{2} \)
Subject: Chemistry
Which of the following reactions will yield 2,2-dibromopropane?
A. \( C H_{3}-C H=C H_{2}+H B r \)
в. \( C H_{3}-C \equiv C H+2 H B r \)
c. \( C H_{3}-C H=C H B r+H B r \)
D. \( C H \equiv C H+2 H B r \)
Subject: Chemistry
At \( 227^{0} C, 60 \% \) of 2 moles of \( P C l_{5} \) gets dissociated in a two-litre. the value of
\( \boldsymbol{K}_{\boldsymbol{p}} \) will be
\( A \cdot 450 R \)
B. 400 R
\( c . \) 50
D. 100 R
Subject: Maths
ff \( \boldsymbol{y}=\boldsymbol{x}^{n} \log \boldsymbol{x}+\boldsymbol{x}(\log \boldsymbol{x})^{n}, \) find \( \boldsymbol{d} \boldsymbol{y} / \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot x^{n-1}(1+n \log x)+(\log x)^{n-1}[n+\log x \)
B. \( x^{n}(1+\text { nlog } x)+(\log x)^{n}[n+\log x] \)
C. \( x^{n-1}(1+(n-1) \log x)+(\log x)^{n-1}[n-1+\log x] \)
D. none of these
Subject: Physics
Calculate focal length of a spherical mirror from the following observations.
Object distance, \( \boldsymbol{u}=(\mathbf{5 0 . 1} \pm \mathbf{0 . 5}) \mathrm{cm} \)
and image distance, \( \boldsymbol{v}=(\mathbf{2 0 . 1} \pm \mathbf{0 . 2}) \)
\( \mathrm{cm} \)
\( \mathbf{A} \cdot f=(14.3 \pm 0.2) \mathrm{mm} \)
B . \( f=(14.3 \pm 0.2) \mathrm{cm} \)
C \( \cdot f=(14.3 \pm 0.4) \mathrm{cm} \)
D. None of these
Subject: Physics
A bullet of mass \( 50 g \) travelling at \( 500 m / s \) penetrates \( 100 \mathrm{cm} \) into a
wooden block. Find the average force exerted on the block.
B . \( 62.5 \times 10^{4} N \)
c. \( 6.25 \times 10^{4} N \)
D. \( 2.65 \times 10^{4} N \)
Subject: Physics
A thin film with index of refraction 1.50
coats a glass lens with index of
refraction \( 1.80 . \) What is the minimum
thickness of the film that will strongly
reflect light with wavelength 600 nm?
A . \( 150 \mathrm{nm} \)
B. \( 200 n m \)
c. 300 nm
D. \( 450 n m \)
Subject: Physics
A galvanometer (coil resistance \( 99 \Omega) \)
is converted into a ammeter using a
shunt of \( 1 \Omega \) and connected as shown in
the figure ( \( i \) ). The ammeter reads \( 3 A \)
The same galvanometer is converted
into a voltmeter by connecting a
resistance of \( 101 \Omega \) in series. This
voltmeter is connected as shown in
figure ( \( i i \) ). Its reading is found to be \( 4 / 5 \)
of the full scale reading. Find the internal resistance \( r \) of the cell (in
ohms)
Subject: Physics
In this circuit, when certain current
flows, the heat produced in \( 5 \Omega \) is \( 4.05 J \)
in a time \( t . \) The heat produced in \( 2 \Omega \) coil
in the same time interval is
A . 5.76
в. 1.44
\( c .2 .88 \)
D. 2.02
Subject: Biology
Examine the figures of diploblastic (i) and triploblastic (ii) organisation in animals given below and identify the
labelled parts A to D.
A. A - Mesoglea, B - Ectoderm, C - Endoderm,
D- Mesoderm
B. A- Endoderm, B - Mesoderm,
C - Mesoglea, Ectoderm
c. A - Mesoderm, B - Mesoglea, C - Ectoderm, Endoderm
D. A - Ectoderm, B - Endoderm
C - Mesoglea, Mesoderm
Subject: Chemistry
Compound A contains 20\% C, 46.66\% N and
\( 6.66 \% \) H. It gave \( N H_{3} \) on heating with
NaOH.
A can be :
A. \( C H_{3} C O N H_{2} \)
в. \( N H_{2} C O N H_{2} \)
c. \( C_{6} H_{5} \) СОМН\( _{2} \)
D. \( C H_{3} N H C O N H_{2} \)
Subject: Chemistry
(a) Account for the following:
(i) \( N H_{3} \) acts as a Lewis base.
(ii) \( P C l_{3} \) fumes in moist air
(iii) Fluorine shows only - 1 oxidation
state.
(b) (i) Suggest any two fluorides of Xenon.
(ii) Write a method to prepare any
one of the above mentioned Xenon
fluorides.
Subject: Chemistry
Assertion
Chlorobenzene on treatment with
\( \boldsymbol{C l}_{2} / \boldsymbol{A l} \boldsymbol{C l}_{3} \) gives mainly \( \mathbf{p} \)
dichlorobenzene.
Reason
Chlorine activate the ring towards an electrophile at ortho and para positions.
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
Calculate the electronegativity time) of fluorine on Pauling scale form the following data:
\( \boldsymbol{E}_{\boldsymbol{H}-\boldsymbol{H}}=\mathbf{1 0 4 . 2 k c a l} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{E}_{\boldsymbol{F}-\boldsymbol{F}}=\boldsymbol{3 6 . 6 k c a l} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{E}_{\boldsymbol{H}-\boldsymbol{F}}=\mathbf{1 3 4 . 6 k c a l} \boldsymbol{m o l}^{-1} \)
Given \( =\boldsymbol{X}_{\boldsymbol{H}}=\mathbf{2 . 1} \)
Subject: Maths
Solve the following pair of equations by cross multiplication rule.
\( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{a}+\boldsymbol{b}, \boldsymbol{a} \boldsymbol{x}-\boldsymbol{b} \boldsymbol{y}=\boldsymbol{a}^{2}-\boldsymbol{b}^{2} \)
A . \( x=1, y=a b \)
в. \( x=a+b, y=b \)
c. \( x=a, y=b \)
D. \( x=b, y=1 \)
Subject: Physics
A disc and a ring of same mass are rolling and if their kinetic energies are equal, then the ratio of their velocities
will be:
A. \( \sqrt{4}: \sqrt{3} \)
B. \( \sqrt{3}: \sqrt{4} \)
c. \( \sqrt{3}: \sqrt{2} \)
D. \( \sqrt{2}: \sqrt{3} \)
Subject: Chemistry
What is the percent \( \boldsymbol{X} \) by mass for
compound \( X Y_{2} \) if compound \( X Y \) is 74
\( \% X \) by mass?
A . \( 25 \% \) \%
B . \( 40 \% \)
c. \( 60 \% \)
D. 75\%
Subject: Physics
An object is thrown from the height of \( 125 \mathrm{cm} \) take \( \mathrm{g}=10 \mathrm{m} / \mathrm{s} \). Find the ratio of distance covered by object in the 1 st and last 1 sec
A . 1: 9
B. 4:
\( c \cdot 4: 4 \)
D. 2:
Subject: Maths
\( \int_{\mathbf{A}}^{\boldsymbol{A}} \cdot \frac{\mathbf{1}}{\boldsymbol{x}^{2}} \sqrt{\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}} \boldsymbol{d} \boldsymbol{x}= \)
B. \( \cos ^{-1} \frac{1}{|x|}-\frac{\sqrt{x^{2}-1}}{x}+c \)
C \( \cdot \sin ^{-2} \frac{1}{|x|}-\frac{\sqrt{x^{2}-1}}{x}+c \)
D. \( \sin ^{-1} \frac{1}{|x|}+\frac{\sqrt{x^{2}-1}}{x}+c \)
Subject: Physics
The engine of a car produces an acceleration of \( 6 m / s^{2} \) in the car. If this
car pulls a block of the same mass, then the acceleration would be:
\( \mathbf{A} \cdot 6 m / s^{2} \)
B . \( 12 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 3 m / s^{2} \)
D. \( 1.5 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Maths
If \( \omega \neq 1 \) is cube root of unity, and \( A= \) \( \left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \mathbf{1} \\ \boldsymbol{\omega}^{2} & \mathbf{1} & \boldsymbol{\omega}\end{array}\right] \) is
This question has multiple correct options
A. symmetric
B. skew symmetric
c. singular
D. orthogonal
Subject: Physics
Nuclei of a radio-active element \( A \) are
being product at a constant rate \( \alpha \). The
element has a decay constant \( \lambda \). At time
\( t=0 \) there are \( N_{0} \) nuclei of the element
present
(a) Calculate the number of nuclei \( A \) as
a function of time \( t \)
(b) If \( \alpha=2 N_{0} \lambda \), calculate the number
of nuclei of \( A \) after one half-life of \( A \)
and also the limiting value of \( N \) as \( t \rightarrow \)
\( \infty \)
Subject: Chemistry
For a \( 1^{s t} \) order reaction (gaseous)
(costant \( \vee, T) \)
\( \boldsymbol{a} \boldsymbol{A} \rightarrow(\boldsymbol{b}-\mathbf{1}) \boldsymbol{B}+\mathbf{1} \boldsymbol{C}(\text { with } \mathbf{b}>\mathbf{a}) \) the
pressure of the system rose by
\( 50\left(\frac{b}{a}-1\right) \% \) in a time of 10 min. The half
life of the reaction is therefore:
\( A \cdot 10 \) min
B. 20 min
\( c . \) 30 min
D. 40 min
Subject: Biology
For synthesis of one gram of hexose, the
land plant consumes
A. Only \( 1 / 3 \) rd of the \( C O_{2} \) of air
B. Only \( 1 / 4 \) th of the \( C O_{2} \) of air
C. only \( 2 / 3 \) rd of the \( C O_{2} \) of air
D. None of the above
Subject: Biology
Identify the correct order of phases for
the cell cycle?
I. \( G_{2} \) phase- growth and preparation for mitosis
II. Mitosis
III. \( G_{1} \) phase-cell growth
IV.S phase - DNA copied
V. Cytokinesis
в. ॥॥, ।, IV, v, II
c. ॥, ॥॥, ।, IV, v
D. IV, III, 1, , I, v
E. \( \mathrm{V}, \) ॥I, IV, ।, ।
Subject: Chemistry
The following electrochemical cell has been set-up:
\( \boldsymbol{P t}(1) \mid \boldsymbol{F} e^{3+}, \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a}= \)
\( \mathbf{1})\left|\boldsymbol{C} \boldsymbol{e}^{\boldsymbol{4}+}, \boldsymbol{C} \boldsymbol{e}^{\boldsymbol{3}+}(\boldsymbol{a}=\mathbf{1})\right| \boldsymbol{P} \boldsymbol{t}(\boldsymbol{2}) \)
\( E^{0}\left(F e^{2+}, F e^{2+}\right)=0.77 \mathrm{V} \)
and \( \boldsymbol{E}^{0}\left(\boldsymbol{C} \boldsymbol{e}^{\boldsymbol{4}+}, \boldsymbol{C} \boldsymbol{e}^{\boldsymbol{3}+}\right)=1.61 \mathrm{V} \)
If an ammeter is connected between the
two platinum electrodes, predict the
direction of flow of current, will the
current increases or decreases with
time?
Subject: Physics
f the lattice constant of this
semiconductor is decreased, then
\( \mathbf{A} \cdot \) all \( E_{c}, E_{g}, E_{v} \) increases
B. \( E_{c} \) and \( E_{v} \) increases, but \( E_{g} \) decreases
\( \mathrm{C} \cdot E_{c} \) and \( E_{v} \) decreases, but \( E_{g} \) increases.
D. all \( E_{c}, E_{g}, E_{v} \) decreases.
Subject: Physics
When a force is applied on a wire of uniform cross-sectional area \( 3 \times \)
\( 10^{-6} m^{2} \) and length \( 4 m, \) the increase in
length is 1 \( m m . \) Energy stored in it will
be \( \left(Y=2 \times 10^{11} N / m^{2}\right) \)
A . \( 6250 J \)
в. 0.177 Л
c. \( 0.075 J \)
D. \( 0.150 J \)
Subject: Biology
Choose the correct option for the flow of
energy in an ecosystem
A. Sun- - - >> Producer- - - - -> Herbivore- - - -> Carnivore
B. Producer - - - -> Herbivore- - - -> Carnivore- - - -> Sun
c. Herbivore- - - -> Carnivore- - - -> Sun- - - -> Producer
D. Carnivore- - - -> Sun- - - -> Producer- - - -> Herbivore
Subject: Physics
A ray of light enters a medium of
refractive index \( \mu_{m} . \) It is observed that
the angle of refraction is half the angle of incidence. Then, the angle of incidence will be :
\( \mathbf{A} \cdot \cos ^{-1} \mu \)
B \( \cdot 2 \cos ^{-1} \frac{\mu}{2} \)
\( c \cdot 2 \cos ^{-1} \mu \)
D. \( \cos ^{-1} \frac{\mu}{3} \)
Subject: Physics
There is a regular bus service between towns \( A \) and \( B \), with a bus leaving towns A and B every \( T \) minutes. A cyclist
moving with a speed of \( 20 \mathrm{kmh}^{-1} \) in the direction \( A \) to \( B \) notices that a bus goes
past him every 18 mins in his direction
and every 6 mins in the opposite direction. What is the period \( \boldsymbol{T} \)
of bus service?
A. 9 minutes
B. 12 minutes
c. 15 minutes
D. 18 minutes
Subject: Chemistry
Which of the following expression is
correct?
\( \mathbf{A} \cdot \frac{d[H I]}{d t}=\frac{k_{3} k_{1}}{k_{2}}\left[H_{2}\right]\left[I_{2}\right] \)
B. \( \frac{d[H]}{d t}=\frac{k_{1} k_{3}}{k_{2}} 2\left[H_{2}\right]\left[I_{2}\right] \)
\( \frac{d[H I]}{d t}=k_{2}\left[H_{2}\right]\left[I_{2}\right]^{2} \)
D. None of the above
Subject: Physics
The diameter of neck and bottom of a
bottle are \( 2 \mathrm{cm} \) and \( 10 \mathrm{cm} \) respectively. The bottle is completely filled with oil. If the cork in the neck is pressed in with a force of \( 1.2 k g f, \) the amount of force
applied on the bottom is
B. \( F=15 ~ k g f \)
c. \( F=1.2 k g f \)
D. \( F=60 \mathrm{kg} f \)
Subject: Biology
Match the items in Column I with
Column II and choose the correct
alternative.
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { A. Tubercular storage roots } & \text { 1. Tinospora } \\ \text { B. Pneumatophores } & \text { 2. Heritiera } \\ \text { C. Haustoria } & \text { 3. Asparagus } \\ \text { D. Prop-roots } & \text { 4. Viscum } \\ \text { E Assimilatory roots } & \text { 5. Screwpine }\end{array} \)
A . A- 2, B- 3, C- 4, D- 5, E- -
B. A- \( 3, \) B-4, C- 5, D-1, E-2
c. \( A-3, \) В- \( 1, \) С- \( 2, \) D- \( 5, \) Е- 4
D. A- 5, B- 4, C- 3, D- 2, E- -
E. \( A-3, B-2, C-4, D-5 \)
Subject: Maths
A point on XOZ-plane divides the join of (5,-3,-2) and (1,2,-2) at
\( ^{\mathrm{A}} \cdot\left(\frac{13}{5}, 0,-2\right) \)
в. \( \left(\frac{13}{5}, 0,2\right) \)
c. (5,0,2)
D. (5,0,-2)
Subject: Maths
The function \( f(x)=\int_{-1}^{x} t\left(e^{t}-1\right)(t- \)
1) \( (t-2)^{3}(t-3)^{5} d t \) has a local
\( \operatorname{maximum} \operatorname{at} x= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3
Subject: Chemistry
Which of the following pairs is obtained on heating ammonium dichromate?
A. \( N_{2} \) and \( H_{2} O \)
B. \( N_{2} O \) and \( H_{2} O \)
c. \( N O_{2} \) and \( H_{2} O \)
D. \( N O \) and \( N O_{2} \)