AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Each of Kirchoff's two laws presumes
that some quantity is conserved.

Which row states Kirchhoff's first law
and names the quantity that is
conserved?

This question has multiple correct options
A. Statement: the algebraic sum of currents into a junction is zero ; quantity : charge
B. statement: the algebraic sum of currents into a junction is zero ; quantity : energy
c. statement : the e.m.f in a loop is equal to the algebraic sum of the product of current and resistance round the loop ; quantity : charge
D. statement: the e.m.f in a loop is equal to the algebraic sum of the product of current and resistance round the loop ; quantity : energy
Subject: Maths
\( \boldsymbol{A}-[\boldsymbol{B} \cup \boldsymbol{C} \cup \boldsymbol{D}]=(\boldsymbol{A}-\boldsymbol{B}) \cap \ldots \ldots \cap \)
A \( . A-C \) and \( A-D \)
B. \( C-A \) and \( A-D \)
c. \( C-A \) and \( D-A \)
D. \( A-C \) and \( D-A \)
Subject: Chemistry
Which of the following statements are true regarding Werner's theory are true?
(1) Ligands are connected to the metal ions by covalent bonds
(2) Secondary valencies have directional properties
(3) Secondary valencies are non- ionizable
A. 1,2 and 3 are correct
B. 2 and 3 are correct
c. 1 and 3 are correct
D. 1 and 2 are correct
Subject: Physics
The focal lengths of the objective and the eyepiece of a compound microscope are \( 2.0 \mathrm{cm} \) and \( 3.0 \mathrm{cm}, \) respectively. The distance between the objective and the eyepiece is \( 15.0 \mathrm{cm} . \) The final image formed by the eyepiece is at infinity. The two lenses are thin. The distance, in \( c m \)
of the object and the image produced by the objective, measure from the objective lens, are respectively
A . 2.4 and 12.0
B. 2.4 and 15.0
c. 2.0 and 12.0
D. 2.0 and 3.0
Subject: Physics
The area of cross section, length, and density of a piece of metal of atomic
weight 60 are \( 10^{-6} m^{2}, 1 \mathrm{m}, \) and \( 5 \times 10^{3} \)
\( \mathrm{kgm}^{-3}, \) respectively. If every atom
contributes one free electron, find the
drift velocity (in \( \mathrm{mms}^{-1} \) ) of electrons in
the metal when a current of 16 A passes
through it. Avogadro's number is \( N_{A}= \)
\( 6 \times 10^{23} / \) mol and charge on an electron
is \( e=1.6 \times 10^{-19} C \)
Subject: Physics
The initial speed with which water flows out from the orifice in \( \mathrm{ms}^{-1} \) is \( \mathrm{g} \)
\( \left.=10 \mathrm{ms}^{-2}\right) \)
A . 10
B. 5
\( c \cdot 5 \cdot \sqrt{2} \)
D. \( 10 . \sqrt{2} \)
Subject: Chemistry
A 0.4 molal aqueous solution of \( \boldsymbol{M}_{\boldsymbol{x}} \boldsymbol{A} \)
has freezing point \( 3.72^{\circ} \mathrm{C} \). The \( K_{f} \) of
\( H_{2} O \) is \( 1.86 K m o l a l i t y^{-1} . \) The value of \( x \) is :
Subject: Maths
A cylindrical vessel with internal diameter \( 10 \mathrm{cm} \) and height \( 10.5 \mathrm{cm} \) is full of water. A solid cone of base diameter \( 7 \mathrm{cm} \) and height \( 6 \mathrm{cm} \) is completely immersed in water. Find the volume of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take \( \left.\pi=\frac{22}{7}\right) \)
\( \mathbf{A} \cdot(\mathbf{i}) 77 \mathrm{cm}^{3} \) and (ii) \( 748 \mathrm{cm}^{3} \)
B. (i) 70 \( c m^{3} \) and (ii) \( 740 \mathrm{cm}^{3} \)
c. \( \left(\text { i) } 85 ~ c m^{3} \text { and (ii) } 786 ~ c m^{3}\right. \)
D. (i) 88 \( c m^{3} \) and (ii) \( 797 \mathrm{cm}^{3} \)
Subject: Chemistry
What are the objectives of petroleum conservation research association:
A. To create awareness among masses about the importance, benefits and methods of conserving petroleum products \& clean environment by enhancing information and capacity building.
B. To provide training and technical advisory services, designed to achieve economy \& efficiency in use of petroleum products for cleaner environment.
c. To function as a Think Tank to the Govt. of India for proposing policies and strategies on petroleum conservation and environment protection aimed at reducing excessive dependence on oil
D. all of these.
Subject: Maths
For \( \boldsymbol{r}=\mathbf{0}, \mathbf{1}, \mathbf{2},, \dots \mathbf{1 0} \) let \( \boldsymbol{A}_{r}, \boldsymbol{B}_{r} \) and \( \boldsymbol{C}_{\boldsymbol{r}} \)
denote respectively the coefficient of \( \boldsymbol{x}^{r} \) in the expansions of \( (1+x)^{10},(1+x)^{20} \) and \( (1+x)^{30} . \) Then
\( \sum_{r=1}^{10} A_{r}\left(B_{10} B_{r}-C_{10} A_{r}\right) \) is equal to
A. \( B_{10}-C_{10} \)
B . \( A_{10}\left(B_{10}^{2}-C_{10} A_{10}\right) \)
c.
D. \( C_{10}-B_{10} \)
Subject: Physics
Find the change in the potential energy of the proton in the displacement.
A. \( -6.4 \times 10^{-15} J \)
В. \( 6.4 \times 10^{-15} \mathrm{J} \)
c. \( -6.4 \times 10^{-19} J \)
D. \( 6.4 \times 10^{-19} \mathrm{J} \)
Subject: Physics
If the dipole of moment \( 2.57 \times \)
\( 10^{-17} \mathrm{C} . \mathrm{m} \) is placed into an electric
field of magnitude \( 3.0 \times 10^{4} N / C \) such
that the fields lines are aligned at \( 30^{\circ} \) with the line joining the dipole, what torque will act on the dipole?
A. \( 7.7 \times 10^{-13} \mathrm{Nm} \)
B . \( 3.855 \times 10^{-13} \mathrm{Nm} \)
\( \mathbf{c} \cdot 3.855 \times 10^{-15} \mathrm{Nm} \)
D. \( 7.7 \times 10^{-15} \mathrm{Nm} \)
Subject: Physics
toppr
Q Type your question
removed. They are termed as elastic.
Those of which not regaining are called
plastic. There may be delay in the regaining in some materials. They are said to have got elastic aftereffect, since they have gone beyond the elastic limit. Repeated application and removal of force break at any point time and so are avoided.
The stress strain graph for two materials \( A \) and \( B \) is shown in the
following figure:
The strength of the material \( A \) and \( B \) is
\( \boldsymbol{S}_{A} \) and \( \boldsymbol{S}_{B}, \) respectively, while the longevity of plastic behaviour is \( L_{A} \) and
\( \boldsymbol{L}_{\boldsymbol{B}} \cdot \) Then
A. \( S_{A}>S_{B}, L_{A}<L_{B} \)
B. \( S_{A}=S_{B}, L_{A}=L_{B} \)
c. \( S_{A}>S_{B}, L_{A}>L_{B} \)
D. \( S_{A}<S_{B}, L_{A}<L_{B} \)
Subject: Physics
Find the current flows through a copper wire of length \( 0.2 \mathrm{m}, \) area of crosssection \( 1 m m^{2}, \) when connected to a
battery of \( 4 \mathrm{V} \). Given that electron
mobility is \( 4.5 \times 10^{-6} m^{2} s^{-1} \) and
charge on an electron is \( 1.6 \times 10^{-19} C \)
The number density of electron in copper wire is \( 8.5 \times 10^{2} 8 m^{3} \)
Subject: Chemistry
The rusting of iron takes place as follows \( 2 H^{+}+2 e+\frac{1}{2} O_{2} \rightarrow H_{2} O(l) ; E^{o}= \)
\( +1.23 V \)
\( F e^{2+}+2 e \rightarrow F e(s) ; E^{o}=-0.44 V \)
\( \Delta G^{o} \) for the net process is:
В. \( -161 k J \) mol \( ^{-1} \)
C. -152 kJ \( m o l^{-1} \)
D. \( -76 k J \) mol\( ^{-1} \)
Subject: Physics
The image of the needle placed \( 45 \mathrm{cm} \) from a lens is formed on a screen placed \( 90 \mathrm{cm} \) on the other side of the lens. The
displacement of the image, if the needle is moved by \( 5.0 \mathrm{cm} \) away from the lens is
A. \( 10 \mathrm{cm} \), toward the lens
B. \( 15 \mathrm{cm} \), away from the lens
c. \( 15 \mathrm{cm} \), towards the lens
D. \( 10 \mathrm{cm}, \) away from the lens
Subject: Maths
Parabolas \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{a}\left(\boldsymbol{x}-\boldsymbol{c}_{1}\right) \) and \( \boldsymbol{x}^{2}= \)
\( 4 a\left(y-c_{2}\right), \) where \( c_{1} \) and \( c_{2} \) are variable
are such that they touch each other. Locus of their point of contact is
A \( . x y=2 a^{2} \)
В . \( x y=4 a^{2} \)
c. \( x y=a^{2} \)
D. none of these
Subject: Chemistry
Which of the following is incorrect
about \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} ? \)
A \( . \) It can be prepared from \( K_{2} C r O_{4} \)
B. It is used in redox titrations
c. It is stable in both acid \& base
D. It is orange in colour
Subject: Maths
If the surface area of a sphere is \( 324 \pi c m^{2} \) then its volume is
\( \mathbf{A} \cdot 950 \pi \mathrm{cm}^{3} \)
В. \( 972 \pi \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 975 \pi \mathrm{cm}^{3} \)
D. \( 980 \pi \mathrm{cm}^{3} \)
Subject: Physics
A particle is moving in a circle of radius \( 4 \mathrm{cm} \) with constant speed of \( 1 \mathrm{cm} / \mathrm{s} \)
Find
(a) time period of the particle
(b) average speed, average velocity and average acceleration in a time interval from \( t=0 \) to \( t=T / 4 \). here \( T \) is the time
period of the particle. Give only their magnitudes
Subject: Physics
The rubber cord of a catapult has cross-
section area \( 2 m m^{2} \) and a total
unstretched length \( 15 \mathrm{cm} \). It is stretched
to \( 18 c m \) and then released to project a
particle of mass \( 3 g \). Calculate the
velocity of projection if \( Y \) for rubber is
\( 8 \times 10^{8} N / m^{2} \)
A \( .56 .5 m s^{-1} \)
B. \( 10 m s^{-1} \)
\( \mathrm{c} \cdot 20 \mathrm{ms}^{-1} \)
D. \( 40 m s^{-1} \)
Subject: Chemistry
According to the collision theory, most molecular collisions do not lead to a
reaction. Which of the following is(are) necessary for collisions to successfully
lead to the reaction?
This question has multiple correct options
A. The total kinetic energy of the collision must be greater than some minimum value
B. A catalyst must be present at the collision.
c. The colliding particles must be properly oriented in space when they collide.
D. None of the above
Subject: Biology
Choose the correct answer among the alternatives given :
What is true for lactational
amenorrhea?
(i) It means absence of menstruation.
(ii) Ovulation does not occur during the lactational period.
(iii) Chances of contraception are almost nil upto six months following parturition.
(iv) Side effects are almost nil
(v) Contraceptive efficiency reduces after the period of intense lactation.
(vi) It is a natural method of
contraception.
(vii) It increases phagocytosis of
sperms.
A . (ii), (iii), (iv), (v) and (vi)
B. (i), (ii), (iii) and (iv)
\( c . \) (ii), (iii), (iv), (v) and (vii)
\( D \cdot(i),(\text { ii) }, \) (iii), (iv), (v) and (vi)
Subject: Maths
If \( \boldsymbol{x}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{\omega}+\boldsymbol{c} \boldsymbol{\omega}^{2}, \boldsymbol{y}=\boldsymbol{a} \boldsymbol{\omega}+\boldsymbol{b} \boldsymbol{\omega}^{2}+\boldsymbol{c} \)
and \( z=a \omega^{2}+b+c \omega \) then find the
value of \( \frac{x^{2}}{y z}+\frac{y^{2}}{z x}+\frac{z^{2}}{x y} \)
Subject: Physics
A man of mass \( 30 \mathrm{kg} \) uses a rope to
climb which bears only 450 N.The
maximum acceleration with which he
can climb safely,.......
A \( \cdot 10 m / s e c^{2} \)
B \( \cdot 15 \mathrm{m} / \mathrm{sec}^{2} \)
\( \mathrm{c} \cdot 20 \mathrm{m} / \mathrm{sec}^{2} \)
D. \( 25 \mathrm{m} / \mathrm{sec}^{2} \)
Subject: Maths
Assertion The value of \( \left(\begin{array}{c}51 \\ 3\end{array}\right)+\left(\begin{array}{c}50 \\ 3\end{array}\right)+\left(\begin{array}{c}49 \\ 3\end{array}\right)+ \)
\( \left(\begin{array}{c}48 \\ 3\end{array}\right)+\left(\begin{array}{c}47 \\ 3\end{array}\right)+\left(\begin{array}{c}47 \\ 4\end{array}\right) \) is equal to
\( \left(\begin{array}{c}52 \\ 4\end{array}\right) \)
Reason
\( ^{n-1} C_{r}+^{n} C_{r+1}=^{n+1} C_{r+1} \)
A. Both (A) \& (R) are individually true \&
(R) is the correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A).
C. (A) is true but (R) is false,
D. (A) is false but (R) is true.
Subject: Chemistry
Beryllium gives a compound \( \boldsymbol{X} \) with the
following percentage composition: \( \boldsymbol{B} \boldsymbol{e}- \)
\( 6.1 \%, N-37.8 \%, C l-48 \%, H-8.1 \% \)
Molecular weight of \( \boldsymbol{X} \) is 148 g \( \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1} \)
and that of \( B e \) is \( 9 g \) mol\( ^{-1} \). The
molecular formula of the compound is:
A. \( B e N_{4} C l_{l} H_{12} \)
в. \( B e N_{2} C l H_{6} \)
c. \( B e N_{4} C l_{2} H_{6} \)
D. \( B e N_{4} C l H_{8} \)
Subject: Maths
A function \( y=f(x) \) satisfying the
differential equation \( \frac{d y}{d x} \cdot \sin x- \)
\( y \cos x+\frac{\sin ^{2} x}{x^{2}}=0 \) such that \( y \rightarrow 0 \) as
\( x \rightarrow \infty \) then the correct statement
which is correct is
\( \mathbf{A} \cdot \lim _{x \rightarrow 0} i t f(x)=1 \)
B. \( \int_{0}^{\pi / 2} f(x) d x \) is less than \( \frac{\pi}{2} \)
c. \( \int_{0}^{\pi / 2} f(x) d x \) is greater than unit
D \cdot \( f(x) \) is an odd function
Subject: Maths
show that: The modulus and argument
of the complex number \( z_{1}=z^{2}-z, \) if
\( z=\cos \phi+i \sin \phi . \) is
\( \mathbf{2}|\sin \phi / \mathbf{2}|,\left(\frac{\mathbf{3} \boldsymbol{\pi}+\mathbf{3} \boldsymbol{\phi}}{\mathbf{2}}\right) \)
Subject: Physics
A square \( A B C D \) of side 1 mm is kept
at distance \( 15 \mathrm{cm} \) in front of the
concave mirror as shown in fig. The
focal length of the mirror is \( 10 \mathrm{cm} \). The
length of the perimeter of its image will
be :
\( A \cdot 8 m m \)
B. \( 2 m m \)
\( \mathrm{c} .12 \mathrm{mm} \)
D. \( 6 m m \)
Subject: Biology
Consider following features
(a) Organ system level of organisation
(b) Bilateral symmetry
(c) True coelomates with segmentation
of body
Select the correct option of animal groups which possess all the above characteristic's.
A. Annelida, Arthropoda and Chordata
B. Annelida, Arthropoda and Mollusca
c. Arthropoda, Mollusca and chordata
D. Annelida, Mollusca and Chordata
Subject: Physics
On large scale, tritium is produced by which of the following nuclear
reactions?
A \( \cdot_{3}^{6} L i+_{0}^{1} n \rightarrow_{2}^{4} H e+_{1}^{3} T \)
B \( \cdot_{1}^{2} D+_{1}^{2} D \rightarrow_{1}^{3} T+_{1}^{1} H \)
C \( \cdot \frac{14}{7} N+_{0}^{1} n \rightarrow_{6}^{12} C+_{1}^{3} T \)
D \( \cdot \frac{14}{7} N+_{1}^{1} H \rightarrow_{1}^{3} T+ \) Other fragments
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}3 x-8 & \text { if } x \leq 5 \\ 2 k & \text { if } x>5\end{array}\right. \)
continuous, find \( k \)
\( A \cdot \frac{2}{7} \)
B. 3 \( \overline{7} \)
\( c \cdot \frac{4}{7} \)
D.
Subject: Chemistry
In which of the following equilibrium
equation, \( \boldsymbol{K}_{\boldsymbol{p}}>\boldsymbol{K}_{\boldsymbol{c}} \)
A \( \cdot 2 S O_{3}(g) \rightleftharpoons 2 S O_{2}(g)+O_{2}(g) \)
B \( \cdot P C l_{3}(g)+C l_{2} \rightleftharpoons P C l_{5}(g) \)
C \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
D. \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
Subject: Maths
For the function \( f(x)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+ \)
\( +\frac{x^{2}}{2}+x+1, f^{\prime}(1)= \)
\( \mathbf{A} \cdot x^{100} \)
в. 100
\( c .10 \)
D. None of these
Subject: Maths
For how many real values of \( ^{\prime} m^{\prime} \) the points \( \boldsymbol{A}(\boldsymbol{m}+\mathbf{1}, \mathbf{1}), \boldsymbol{B}(\boldsymbol{2 m}+\mathbf{1}, \boldsymbol{3}) \) and
\( C(2 m+2,2 m) \) are collinear.
Subject: Maths
Let \( f \) be any continuously differentiable function on \( [a, b] \) and twice
differentiable on \( (a, b) \) such that
\( \boldsymbol{f}(\boldsymbol{a})=\boldsymbol{f}^{\prime}(\boldsymbol{a})=\mathbf{0} \) and \( \boldsymbol{f}(\boldsymbol{b})=\mathbf{0} . \) Then
This question has multiple correct options
A \( \cdot f^{\prime \prime}(a)=0 \)
B. \( f^{\prime}(x)=0 \) for some \( x \in(a, b) \)
C \( . f^{\prime \prime}(x) \neq 0 \) for some \( x \in(a, b) \)
D. \( f^{\prime \prime \prime}(x)=0 \) for some \( x \in(a, b) \)
Subject: Physics
A dipole of dipole moment 'p' is placed in non-uniform electric field along \( x \) axis. Electric field is increasing at the
rate of \( 1 ~ V m^{-1} . \) The force on dipole is:
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 2 p \)
c. \( p / 2 \)
D.
Subject: Maths
Coordinates of the centre of the circle
which bisects the circumferences of the
circles \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{1}: \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{x}- \)
\( \mathbf{3}=\mathbf{0} \) and \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\mathbf{2} \boldsymbol{y}-\mathbf{3}=\mathbf{0} \) is
A \( \cdot(-3,-3) \)
B. (3,3)
c. (2,2)
D. (-2,-2)
Subject: Biology
Assertion
G-phase is also called anaphase, as during this phase the cell stores ATP for
cell division.
Reason
Cell produces structural and functional proteins. Cell's metabolic rate is high and is controlled by the enzymes.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Physics
The length of a potentiometer wire is \( 1200 \mathrm{cm} \) and it carries a current of
\( 60 m A . \) For cell of emf \( 5 V \) and internal
resistance of \( 20 \Omega \), the null point on it is
found to be at \( 1000 \mathrm{cm} . \) The resistance
of whole wire is:
A . \( 60 \Omega \)
в. \( 100 \Omega \)
\( c .80 \Omega \)
D. \( 120 \Omega \)
Subject: Chemistry
I. Ethanol
II. Acetic acid
III. Phenol
IV. Acetonitrile
The acidity of compounds I-IV in water follows the order:
A. \( I V<I<I I I<I I \)
в. \( I<I I<I I I<I V \)
c. \( I V<I<I I<I I I \)
D. \( I V<I I I<I<I I \)
Subject: Maths
If \( \left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=\ldots \ldots . .=\left|z_{n}\right|=1 \)
then \( \left|z_{1}+z_{2}+z_{3}+\ldots \ldots .+z_{n}\right|= \)
A \( \cdot\left|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}+\ldots . .+\frac{1}{z_{n}}\right| \)
в. \( \left|\frac{1}{z_{1}}-\frac{1}{z_{2}}-\frac{1}{z_{3}}-\ldots . .+\frac{1}{z_{n}}\right| \)
с \( \cdot\left|\frac{1}{z_{1}^{2}}+\frac{1}{z_{2}^{2}}+\frac{1}{z_{3}^{2}}+\ldots . .+\frac{1}{z_{n}^{2}}\right| \)
D \( \cdot\left|\frac{1}{z_{1}^{2}}-\frac{1}{z_{2}^{2}}-\frac{1}{z_{3}^{2}}-\ldots . .+\frac{1}{z_{n}^{2}}\right| \)
Subject: Chemistry
For a sparingly soluble salt \( \boldsymbol{A}_{\boldsymbol{p}} \boldsymbol{B}_{\boldsymbol{q}} \)
the relationship between its solubility
product \( \boldsymbol{K}_{s p} \) and its solubility \( (s) \) is:
\( \mathbf{A} \cdot K_{s p}=s^{p+q} \cdot p^{p} \cdot q^{q} \)
B . \( K_{s p}=s^{p+q} . p^{q} . q^{p} \)
\( \mathbf{c} \cdot K_{s p}=s^{p q} \cdot p^{p} \cdot q^{q} \)
D・ \( K_{s p}=s^{p q} .(p q)^{p+q} \)
Subject: Physics
A \( 100 e V \) electron collides with a
stationary helium ion \( \left(H e^{+}\right) \) in its ground state and excites to a higher
level. After the collision, \( \boldsymbol{H} e^{+} \) ion emits
two photons in succession with wavelengths \( 1085 A \) and 304 A. Find the
principal quantum number of the excited state. Also, calculate the energy
of the electron after the collision. Given
\( \boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4} \mathbf{J}} \boldsymbol{s} \)
Subject: Physics
Assertion
In case of oscillatory motion the average speed for any time interval is always greater than or equal to its average velocity
Reason
Distance travelled by a particle cannot be less than its displacement.
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
A particle executes SHM between \( \boldsymbol{x}= \)
\( -A \) to \( x=+A . \) The time taken for it to
go from 0 to \( \frac{A}{2} \) is \( T_{1} \) and to go from \( \frac{A}{2} \) to \( A \) is \( T_{2} \) then \( \frac{T_{1}}{T_{2}} \) is?
\( A \cdot 2 \)
B. \( \frac{1}{2} \)
\( c \cdot 4 \)
D.
Subject: Chemistry
Which of the following group contains coloured ions?
1. \( \boldsymbol{C} \boldsymbol{u}^{+} \)
2. \( \boldsymbol{T} \boldsymbol{i}^{4+} \)
3. \( C o^{2+} \)
4. \( \boldsymbol{F} \boldsymbol{e}^{2+} \)
A .1,4
в. 3,4
c. 2,3
D. 1,2
Subject: Physics
If a mass of \( 20 g \) having charge \( 3.0 m C \) moving with velocity 20 ms\( ^{-1} \) enters a
region of electric field of \( 80 N C^{-1} \) in
the same direction as the velocity of
mass, then the velocity of mass after \( 3 s \)
in the region will be
A \( \cdot 40 \mathrm{ms}^{-1} \)
B. \( 44 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 56 \mathrm{ms}^{-1} \)
D. \( 80 m s^{-1} \)
Subject: Maths
If \( A=\{2,3\} \) and \( B=\{1,2\}, \) find \( A \times \)
\( \boldsymbol{B} \)
A \( \cdot\{(2,1),(2,2),(3,1),(3,2)\} \)
в. \{(2,1),(2,1),(3,1),(3,2)\}
\( \mathbf{c} \cdot\{(2,1),(2,2),(2,1),(3,2)\} \)
D. \( \{2,1),(2,2),(3,1),(2,2)\} \)
Subject: Physics
In a free space a rifle (fixed) of mass \( M \)
shoots a bullet of mass \( m \) at a
stationary block of mass \( M \) distance \( D \) away from it. When the bullet has
moved through a distance \( d \) towards the
block the centre of mass of the bullet-
block system is at a distance of:
A \( \cdot \frac{(D-d) m}{M+m} \) from the block
B. \( \frac{m d+M D}{M+m} \) from the rifle
c. \( \frac{2 d m+D M}{M+m} \) from the rifle
D. \( (D-d) \frac{M}{M+m} \) from the bullet
Subject: Maths
If \( \boldsymbol{x}+\boldsymbol{y}=\tan ^{-1} \boldsymbol{y} \) and \( \boldsymbol{y}^{\prime \prime}=\boldsymbol{f}(\boldsymbol{y}) \boldsymbol{y}^{\prime} \) then
\( \boldsymbol{f}(\boldsymbol{y})= \)
A \( \cdot \frac{1}{y\left(1+y^{2}\right)} \)
В. \( \frac{3}{y\left(1+y^{2}\right)} \)
c. \( \frac{2}{y\left(1+y^{2}\right)} \)
D. \( \frac{-2}{y\left(1+y^{2}\right)} \)
Subject: Physics
A car covers first \( 2 k m \) of the total
distance of \( 4 k m \) with a speed of
\( 30 k m / h \) and the remaining distance of \( 2 k m \) with a speed of \( 20 k m / h \). The
average speed of the car is:
\( \mathbf{A} \cdot 24 k m / h \)
в. \( 25 k m / h \)
\( c .50 k m / h \)
D. \( 26 k m / h \)
Subject: Physics
The maximum value of \( \mathbf{V}_{0} \) for which the
disk will roll without slipping is
\( ^{4} \cdot \mu g \sqrt{\frac{M}{k}} \)
\( ^{3} \cdot \mu \mathrm{g} \sqrt{\frac{\mathrm{M}}{2 \mathrm{k}}} \)
\( ^{c} \cdot \operatorname{ag} \sqrt{\frac{3 M}{k}} \)
\( \mu_{g} \sqrt{\frac{5 \mathrm{M}}{2 \mathrm{k}}} \)
Subject: Maths
The length of the side is \( 3.9 \mathrm{ft} \). Find the
surface area of a cube .
A \( \cdot 41.82 f t^{2} \)
B. \( 94.16 f t^{2} \)
c. \( 91.26 f t^{2} \)
D. \( 40.41 f t^{2} \)
Subject: Chemistry
A first-order reaction is \( 50 \% \) completed
in 20 minutes at \( 27^{0} \) C and in 5 min at
\( 47^{0} \mathrm{C} . \) The energy of activation of the reaction is :
A. \( 43.85 k J / \) mol
в. \( 55.33 k J / \) mol
c. \( 11.97 k J / \) mol
D. \( 6.65 k J / \) mol
Subject: Physics
Two metal spheres (radii \( r_{1}, r_{2} \) with
\( \left.r_{1}<r_{2}\right) \) are very far apart but are
connected by a thin wire. If their combined charge is \( Q \), then what
is their common potential?
A \( \cdot k Q /\left(r_{1}+r_{2}\right) \)
B . \( k Q /\left(r_{1}-r_{2}\right) \)
\( \mathbf{c} \cdot-k Q /\left(r_{1}+r_{2}\right) \)
D. \( -k Q / r_{1} r_{2} \)
Subject: Chemistry
How would you account for the following:
(i) Many of the transition elements are known to form interstitial compounds.
(ii) The metallic radii of the third (5d)
series of transition metals are virtually the same as those of the corresponding group members of the seconds \( (4 d) \) series.
(iii) Lanthanoids form primarily +3 ions, while the actinoids usually have higher oxidation states in their compounds, +4 or even +6 being typical
Subject: Chemistry
Total kinetic energy of sample of a gas which contains \( 1 \times 10^{22} \) molecules is
\( 24 \times 10^{2} J \) at \( 127^{\circ} C . \) Another sample of
\( \operatorname{gas} \operatorname{at} 27^{\circ} C \) has a total kinetic energy
of \( 48 \times 10^{2} J . \) The number of molecules
in the second sample are:
A. \( 2.67 \times 10^{22} \)
B. \( 1 \times 10^{2} \)
C \( .1 \times 10^{24} \)
D. \( 5.5 \times 10^{21} \)
Subject: Maths
\( \left|\begin{array}{cc}\boldsymbol{x} & \mathbf{2} \\ \mathbf{1 8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{cc}\mathbf{6} & \mathbf{2} \\ \mathbf{3} \boldsymbol{x} & \mathbf{6}\end{array}\right|, \) then \( \boldsymbol{x} \) is equal to
\( A \cdot 6 \)
B. ±6
\( c .-6 \)
\( D \)