AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The outermost configuration of the least reactive element is:
A \( \cdot n s^{2} n p^{3} \)
B . \( n s^{2} n p^{4} \)
\( \mathbf{c} \cdot n s^{2} n p^{5} \)
D. \( n s^{2} n p^{6} \)
Subject: Maths
\( \int e^{x}\left(\frac{1+\sqrt{1-x^{2}} \sin ^{-1} x}{\sqrt{1-x^{2}}}\right) d x= \)
A \( \cdot \frac{e^{x}}{\sqrt{1-x^{2}}}+c \)
B . \( e^{x} \sin ^{-1} x+c \)
c. \( e^{x}\left(e^{\sin ^{-1} x}+\frac{1}{\sqrt{1-x^{2}}}\right)+c \)
D. \( e^{\sin ^{-1} x}+\frac{1}{\sqrt{1-x^{2}}}+c \)
Subject: Maths
\( p^{t h}, q^{t h} \) and \( r^{t h} \) terms of an A.P. are
\( a, b, c \) respectively, then show that
(i) \( \boldsymbol{a}(\boldsymbol{q}-\boldsymbol{r})+\boldsymbol{b}(\boldsymbol{r}-\boldsymbol{p})+\boldsymbol{c}(\boldsymbol{p}-\boldsymbol{q})=\mathbf{0} \)
(ii) \( (a-b) r+(b-c) p+(c-1) q=0 \)
Subject: Physics
Calculate the diameter of the brass
wire
A \( .2 .1 \times 10^{-4} \mathrm{m} \)
3. \( 4.2 \times 10^{-4} \mathrm{m} \)
c. \( 8.4 \times 10^{-4} \mathrm{m} \)
D. \( 16.8 \times 10^{-4} \mathrm{m} \)
Subject: Physics
A simple circuit consisting of three
resistors is shown above. \( \boldsymbol{R}_{1} \) has the
same resistance of \( \boldsymbol{R}_{2} \) and \( \boldsymbol{R}_{2} \) has twice
the resistance of \( \boldsymbol{R}_{3} \). If the switch
remains closed, determine the ratio of
heat dissipated of \( \boldsymbol{R}_{1} \) to \( \boldsymbol{R}_{2} \)
\( \mathbf{A} \cdot 1: 9 \)
B. 1: 3
c. 1:
D. 3:
E. 9: 1
Subject: Maths
If \( f(x)=x^{2}+x \) for all \( x \) and if \( f(a- \)
1) \( =-\frac{1}{4}, \) find the value of \( a \)
A. \( -\frac{1}{2} \)
B. \( -\frac{1}{4} \)
\( c \cdot \frac{1}{4} \)
D.
E.
Subject: Physics
The temperature coefficient of
resistance of a wire is 0.00125 per
degree celcius. At \( 300 K \) its resistance
is 1 ohm. The resistance of the wire will
be 2 ohm at following temperature :-
A . \( 1154 K \)
в. \( 400 K \)
\( c .600 K \)
D. \( 1400 K \)
Subject: Maths
On dividing the polynomial \( 3 x^{3}+ \) \( 4 x^{2}+5 x-13 \) by a polynomial \( g(x), \) the
quotient and the remainder were \( (3 x+ \)
10) and \( (16 x-43) \) respectively. Find
\( \boldsymbol{g}(\boldsymbol{x}) \)
Subject: Maths
A fair die is rolled once.
STATEMENT - 1: The probability of getting a composite number is \( 1 / 3 \)
STATEMENT - 2: There are three
possibilities for the obtained number
\( (i) \)
the number is a prime number (ii) the number is a composite number (iii) the
number is \( 1, \) and hence probability of
getting a prime number \( =1 / 3 \)
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement - 1
B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement -
c. Statement - 1 is True, Statement - 2 is False
D. Statement - 1 is False, Statement - 2 is True
Subject: Physics
The volume of an air bubble becomes
three times as it rises from the bottom
of a take to its surface.

Assuming atmospheric pressure to be \( 75 \mathrm{cm} \) of \( \mathrm{Hg} \) and the density of water to be \( \frac{1}{10} \) of the density of mercury, the
depth of the take is :
\( \mathbf{A} \cdot 5 m \)
в. 10 т
\( c .15 m \)
D. \( 20 m \)
Subject: Chemistry
Consider a hypothetical atom where
\( \boldsymbol{p}_{\boldsymbol{x}}, \boldsymbol{p}_{\boldsymbol{y}}, \boldsymbol{p}_{\boldsymbol{z}}, \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{y}}, \boldsymbol{d}_{\boldsymbol{x} z}, \boldsymbol{d}_{\boldsymbol{y} \boldsymbol{z}} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{d} \boldsymbol{x}^{2}-\boldsymbol{y}^{2} \)
orbital are present for principal quantum number \( n=3 \) Find the number of other orbitals whose
lobes are fully present in the nodal
plane of \( \boldsymbol{p}_{\boldsymbol{x}} \) orbital:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Maths
The pressure \( \boldsymbol{P} \) and the volume \( \boldsymbol{v} \) of \( \mathbf{a} \)
gas are connected by the relation \( p v^{1.4}= \) const. Find the percentage error in \( p \) corresponding to a decrease of \( \frac{1}{2} \% \)
in \( \boldsymbol{v} \)
Subject: Maths
Solve the simultaneous equations by
substitution method.
\( -\boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{0} ; \mathbf{1 0} \boldsymbol{x}+\mathbf{1 5} \boldsymbol{y}=\mathbf{1 0 5} \)
Subject: Chemistry
At equilibrium, if \( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1}, \) then:
\( \mathbf{A} \cdot \Delta G^{o}>1 \)
В. \( \Delta G^{o}<1 \)
c. \( \Delta G^{o}=0 \)
D. \( \Delta G^{o}=1 \)
Subject: Maths
If \( \vec{a}+2 \vec{b}, 2 \vec{a}+\vec{b} \) be the position vectors
of the points \( A \) and \( B \), then the position
vector of the point \( C \) which divides \( A B \)
internally in the ratio 2: 1 is
A \( \cdot \frac{5 \vec{a}-4 \vec{b}}{3} \)
в. \( \frac{5 \vec{a}+4 \vec{b}}{3} \)
c. \( \frac{5 \vec{a}-2 \vec{b}}{3} \)
D. \( \frac{5 \vec{a}+2 \vec{b}}{3} \)
Subject: Maths
Assertion
The points (1,1)\( \&(-1,-1) \) lie on the
same side of the line \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \)
Reason
The algebraic perpendicular distances from the given points to the line have
same sign
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: Chemistry
Which one of the following pairs do not impart colour to the flame?
A. \( B e C l_{2} \) and \( S r C l_{2} \)
в. \( B e C l_{2} \) and \( M g C l_{2} \)
c. \( C a C l_{2} \) and \( B a C l_{2} \)
D. \( B a C l_{2} \) and \( S r C l_{2} \)
Subject: Physics
A body of mass \( 5 k g \) is moving with
velocity \( 2 m s^{-1} . \) Calculate its linear
momentum
A \( .2 .5 \mathrm{kg} \mathrm{ms}^{-1} \)
B. \( 10 \mathrm{kg} \mathrm{ms}^{-1} \)
c. 5 kg \( m s^{-1} \)
D. \( 20 \mathrm{kg} \mathrm{ms}^{-1} \)
Subject: Physics
A uniform sphere of mass \( M \) and radius \( R \) is placed on a smooth horizontal ground. The angular acceleration of sphere if force \( \boldsymbol{F} \) is
applied on it at a distance \( 7 \frac{R}{5} \) from
ground level is
\( ^{\mathrm{A}} \cdot \frac{F}{2 M R} \)
в. \( \frac{F}{M R} \)
c. \( \frac{F R}{M} \)
D. \( \frac{2 F}{M R} \)
Subject: Chemistry
The correct increasing order of basic nature among Be, Mg, Ca and Sr is :
A. \( B e<C a<M g<S r \)
в. \( B e<M g<S r<C a \)
c. \( B e<M g<C a<S r \)
\( \mathrm{D} \cdot \mathrm{Ca}<\mathrm{Sr}<\mathrm{Be}<\mathrm{Mg} \)
Subject: Chemistry
\( \boldsymbol{A} \boldsymbol{g} \mid \boldsymbol{A} \boldsymbol{g}^{\oplus}(\boldsymbol{1} \boldsymbol{M})\left\|\boldsymbol{A} \boldsymbol{g}^{\oplus}\right\| \boldsymbol{A} \boldsymbol{g} \)
\( 0.5 \mathrm{F} \) electricity is first passed in this LHS (anode) and 1 F of electricity is passed in the RHS (cathode) making them independent electrolytic cells at 298 K. EMF of the cell after electrolysis
will:
A. increase
B. decrease
c. not change
D. none of the above
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\underset{C l}{\boldsymbol{C}} \boldsymbol{H}-\underset{\boldsymbol{B} \boldsymbol{r}}{\boldsymbol{C} \boldsymbol{H}}-\underset{\boldsymbol{O} \boldsymbol{H}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C H}_{3} \)
The IUPAC name of the compound is
A. 3 - Bromo - 4 - chloropentan - 2 - ol
B. 3 - Bromo - 2 - chloro- 4 hydroxypentane
c. 3 - Bromo - 2 - chloropentan - 4 - - о।
D. none of these
Subject: Maths
If the vectors \( \overline{\boldsymbol{a}}=\mathbf{3} \overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}-\mathbf{2} \overline{\boldsymbol{k}}, \overline{\boldsymbol{b}}= \)
\( -\overline{\boldsymbol{i}}+\mathbf{3} \overline{\boldsymbol{j}}+4 \overline{\boldsymbol{k}}, \overline{\boldsymbol{c}}=\mathbf{4} \overline{\boldsymbol{i}}-\mathbf{2} \overline{\boldsymbol{j}}-\mathbf{6} \overline{\boldsymbol{k}} \) form
the sides of the triangle then length of the median bisecting the vector \( c \) is
A. \( \sqrt{12} \) units
B. \( \sqrt{6} \) units
c. \( 2 \sqrt{6} \) units
D. \( 2 \sqrt{3} \) units
Subject: Maths
Mr. Albert's gross annual income is Rs. \( \mathbf{5}, \mathbf{0 0}, \mathbf{0 0 0} \) for \( \mathbf{F . Y .} \mathbf{2 0 1 2}-\mathbf{1 3 .} \) His annual
savings in this year are as follows:
(a) L.I.C. premium Rs. 70,000
(b) Contribution towards P.F. Rs. 12,000
(c) P.P.F. Rs. 30,000
(d) N.S.C. Rs. 10,000 Find his taxable income and income tax
for F.Y. \( 2012-13 \)
Subject: Chemistry
Bromine vapours are passed into a soln.
of ethyne in carbon tetrachloride gives:
A. \( C H B r_{2}-C H B r_{2} \)
в. \( C H_{2} B r-C H B r_{2} \)
c. \( C H_{2} B r-C H_{2} B r \)
D. \( C H_{3}-C H_{3} \)
Subject: Chemistry
Which is/are correct?
\( \mathbf{A} \cdot 2.303 \log K=-\Delta H^{o} / R T+\Delta S^{o} / R \)
B \( \cdot \Delta G^{o}=-2.303 \log K \)
\( \mathbf{c} \cdot-2.303 \log K=-\Delta H^{o} / R T^{2}+\Delta S^{o} / R \)
D. \( 2.303 \log K=(1 / R T)\left(\Delta H^{o}+\Delta S^{o}\right) \)
Subject: Maths
In a right angled \( \triangle \mathrm{ABC}, \mathrm{AC} \perp \) the
hypotenuse BC then \( A D^{2} \) is
\( \mathbf{A} \cdot A C \times C D \)
B. \( A C \times B A \)
c. \( D C \times B D \)
D. None of these
Subject: Physics
Two soap bubbles of radii \( x \) and \( y \)
coalesce to constitute a bubble of
radius \( z . \) Then \( z \) is equal to:
\( \mathbf{A} \cdot \sqrt{x^{2}+y^{2}} \)
B. \( \sqrt{x+y} \)
c. \( x+y \)
\( \frac{x+y}{2} \)
Subject: Chemistry
An equilibrium mixture in a vessel of
capacity 100 litre contain 1 mol \( N_{2}, 2 \) mol
\( O_{2} \) and 3 mol \( N O . \) 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 is:
A . \( 101 / 18 \)
в. \( 101 / 9 \)
c. \( 202 / 9 \)
D. none of these
Subject: Chemistry
Which of the following catalysts is not correctly matched with the reaction?
A. Vanadium (V) oxide in contact process for oxidation of \( S O_{2} \) to \( S O_{3} \)
B. Finely divided iron in Habers process in conversion of \( N_{2} \) and \( H_{2} \) to \( N H_{3} \)
C. \( P t C l_{2} \) catalyzes the oxidation of ethyne to ethanal in the Wacker process
D. Ni in presence of hydrogen for conversion of vegetable oil to ghee
Subject: Maths
Points \( (\mathbf{6}, \mathbf{8}),(\mathbf{3}, \mathbf{7}),(-\mathbf{2},-\mathbf{2}) \) and
(1,-1) are joined to form a quadrilateral. What will be the structure of the quadrilateral?
A. Rhombus
B. Parallelogram
c. square
D. Rectangle
Subject: Chemistry
A gas cylinder can hold \( 1 \mathrm{Kg} \) of hydrogen at mom temperature and pressure:
i) Find the number of moles of hydrogen present
ii) What weight of \( C O_{2} \) can the cylinder hold under similar conditions of
temperature and pressure? \( (\boldsymbol{H}= \) \( \mathbf{1}, \boldsymbol{C}=\mathbf{1 2}, \boldsymbol{O}=\mathbf{1 6}) \)
iii) If the number of molecules of
hydrogen in the cylinder is \( X \), calculate
the number of \( C O_{2} \) molecules in the
cylinder under the same conditions of
temperature and pressure
iv) State the law that helped you to arrive at the above result.
Subject: Biology
What will be the \( p O_{2} \) and \( p C O_{2} \) in the atmospheric air compared to those in the alveolar air?
(i) \( p O_{2} \) lesser, \( p C O_{2} \) higher
(ii) \( p O_{2} \) higher, \( p C O_{2} \) lesser
(iii) \( p O_{2} \) higher, \( p C O_{2} \) higher
(iv) \( p O_{2} \) lesser, \( p C O_{2} \) leser
Subject: Physics
Moment of inertia of a thin semi
circular disc \( (\operatorname{mass}=M \& \text { radius }=R) \)
about an axis through point 0 and perpendicular to plane of disc, is given
by :
\( ^{\mathrm{A}} \cdot \frac{1}{4} M R^{2} \)
B. \( \frac{1}{2} M R^{2} \)
c. \( \frac{1}{8} M R^{2} \)
D. \( M R^{2} \)
Subject: Chemistry
Monomers of Natural Rubber and
Neoprene are Respectively:
\( \begin{array}{c}\mathbf{A} \cdot C H_{3}-C=C H-C H_{3}, C H_{3}-C=C H-C H_{3} \\ _{C H_{3}}\end{array}=\begin{array}{c}C_{3}=C H H \\ C l\end{array} \)
\( \mathbf{B} \cdot C H_{2}=C-C H=C H_{2} C H_{2}=C-C H=C H_{2} \)
\( _{C H_{3}} \)
\( \mathbf{c} \cdot C H_{2}=C H-C H=C H_{2}, C H_{2}=C H-C l \)
\( \mathbf{D} \cdot C H_{2}=C-C H=C H_{2} C H_{2}=C-C H=C H_{2} \)
\( C l \)
Subject: Physics
A wire of length \( 1 \mathrm{m} \) fixed at one end has a sphere attached to it at the other end.
The sphere is projected horizontally with a velocity of \( \sqrt{9 g} \). When it describes a vertical circle, the ratio
of elongations of the wire when the sphere is at the top and bottom of the circle is:
A .2: 5
B. 5: 2
c. 3: 5
D. 5: 3
Subject: Chemistry
Determine at 298 for cell :
\( \boldsymbol{P t}\left|\boldsymbol{Q}, \boldsymbol{Q} \boldsymbol{H}_{2}, \boldsymbol{H}^{+}\right||\mathbf{1} \boldsymbol{M} \boldsymbol{K} \boldsymbol{C l}| \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2} \mid \boldsymbol{H} \)
the pH when \( \boldsymbol{E}_{\text {cell}}=\mathbf{0} \)
\( \operatorname{given} E_{R P(R H S)}^{\circ}=0.28, E_{R P(L H S)}^{\circ}= \)
0.699 (write the value to the nearest
integer)
Subject: Physics
If \( n_{1}, n_{2}, n_{3} \) be the frequency of the segments of a stretched string, then the frequency \( n \) of the string itself in terms
of \( n_{1}, n_{2} \) and \( n_{3} \) is
A. \( \frac{\left(n_{1} n_{2}+n_{2} n_{3}+n_{1} n_{3}\right)}{n_{1} n_{2} n_{3}} \)
B. \( \frac{\left(\mathrm{n}_{1} \mathrm{n}_{2}+\mathrm{n}_{3} \mathrm{n}_{1}\right)}{\mathrm{n}_{1} \mathrm{n}_{2} \mathrm{n}_{3}} \)
c. \( \frac{\mathrm{n}_{1} \mathrm{n}_{2} \mathrm{n}_{3}}{\left(\mathrm{n}_{1} \mathrm{n}_{2}+\mathrm{n}_{3} \mathrm{n}_{1}\right)} \)
D. \( \frac{\mathrm{n}_{1} \mathrm{n}_{2} \mathrm{n}_{3}}{\left(\mathrm{n}_{1} \mathrm{n}_{2}+\mathrm{n}_{2} \mathrm{n}_{3}+\mathrm{n}_{3} \mathrm{n}_{1}\right)} \)
Subject: Physics
There are two long co-axial solenoids of
same length \( l \). the inner and outer coils
have radii \( r_{1} \) and \( r_{2} \) and number of
turns per unit length \( n_{1} \) and \( n_{2} \)
respectively. The rate of mutual
inductance to the self-inductance of the
inner-coil is :
\( \mathbf{A} \cdot \frac{n_{2}}{n_{1}} \cdot \frac{r_{2}^{2}}{r_{1}^{2}} \)
B. \( \frac{n_{2}}{n_{1}} \cdot \frac{r_{1}}{r_{2}} \)
c. \( \frac{n_{1}}{n_{2}} \)
D. \( \frac{n_{2}}{n_{1}} \)
Subject: Physics
Calculate the force of gravitation between two objects of masses \( 80 \mathrm{kg} \) and \( 1200 \mathrm{kg} \) kept at a distance of \( 10 \mathrm{m} \) from each other.Given \( (G=\mathbf{6 . 6 7} \times \)
\( \left.10^{-11} N m^{2} / k g^{2}\right) \)
Subject: Maths
\( \left|\begin{array}{ccc}1 & \cos \alpha & \cos \beta \\ \cos \alpha & 1 & \cos \gamma \\ \cos \beta & \cos \gamma & 1\end{array}\right|= \)
\( \left|\begin{array}{ccc}\mathbf{0} & \cos \boldsymbol{\alpha} & \cos \boldsymbol{\beta} \\ \cos \boldsymbol{c} & \boldsymbol{0} & \cos \gamma \\ \cos \boldsymbol{\beta} & \cos \gamma & \boldsymbol{0}\end{array}\right| \) then
A \( \cdot \cos \alpha+\cos \beta+\cos \gamma=0 \)
B. \( \cos \alpha \cdot \cos \beta \cdot \cos \gamma=0 \)
C \( \cdot \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \)
D. \( \sum \cos \alpha \cos \beta=0 \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) is surjective then
A. no two elements of \( A \) have the same image in \( B \)
B. every element of \( A \) has an image in \( B \)
C. every element of \( B \) has at least one pre-image in \( A \)
D. \( A \) and \( B \) are finite non empty sets
Subject: Maths
A radar unit is used to measure speeds
of cars on a motorway. The speeds are normally distributed with a mean of 9
\( \mathrm{km} / \mathrm{hr} \) and a standard deviation of 10
km/hr. What is the probability that a car picked at random is travelling at
more than \( 100 \mathrm{km} / \mathrm{hr} ? \)
A .0 .1698
B. 0.1548
c. 0.1587
D. 0.1236
Subject: Maths
Statement-I: The equation \( \frac{x^{3}}{4}- \) \( \sin \pi x+3=2 \frac{1}{2} \) has at least one
solution in [2,2]
Because
Statement-II : If \( \boldsymbol{f}:[\boldsymbol{a}, \boldsymbol{b}] \rightarrow \boldsymbol{R} \) be a
function \& let \( c \) be a number such that
\( f(a)<c<f(b), \) then there is at least
one number \( n \in(a, b) \) such that
\( \boldsymbol{f}(\boldsymbol{n})=\boldsymbol{c} \)
A. Statement-l is true, Statement-ll is true ; Statement-I is correct explanation for Statement-
is NOT a correct explanation for statement-
c. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true
Subject: Chemistry
The products \( X \) and \( Z \) in the following
reaction sequence are
\[
\begin{array}{l}
\| f+\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2} \frac{\mathrm{AlCl}_{3} / \text { ether }}{\text { Heat }} \times \mathrm{x} \\
\qquad \frac{\mathrm{OH}}{\mathrm{O}_{2} / 130^{\circ} \mathrm{C}} \mathrm{Y} \frac{\mathrm{H}^{+} / \mathrm{H}_{2} \mathrm{O}}{\text { Heat }}
\end{array}
\]
A. Isopropylbenzene and acetone
B. Cumene peroxide and acetone
C. Isopropylbenzene and isoproply alcohol
D. Phenol and acetone
Subject: Physics
Assertion
Resonance is exhibited by a circuit only
if both L and \( C \) are present in the circuit
Reason
Only then the voltage across L and \( C \) cancel each other, both being out of
phase
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
Q Type your question-
(a) Colour the map as follows: BlueWater, Red-Fire station, Orange-Library,
Yellow-Schools, Green-park, PinkCollege, Purple-Hospital, BrownCemetery.
(b) Mark a green \( ^{\prime} X^{\prime} \) at the intersection
of Road \( ^{\prime} C^{\prime} \) and Nehru Road, Green \( ^{\prime} Y^{\prime} \)
at the intersection of Gandhi Road and
Road \( \boldsymbol{A} \)
(c) In red, draw a short street route from
Library to the bus depot.
(d) Which is further east, the city park
or the market?
(e) Which is further south, the primary
school or the Sr. Secondary School?
Subject: Chemistry
0.4037 g of an organic compound containing \( S \) was treated with conc.
\( H N O_{3} \) in a Carius tube. On
precipitation with \( B a C l_{2} 0.1936 \) g of \( B a S O_{4} \) was 0.35 g. Find the percentage of sulphur.
A . 6.58
B. 7.12
\( c .8 .33 \)
D. 1.67
Subject: Physics
A body of mass \( m \) rests on a horizontal
plane with a friction coefficient \( \mu \). At
\( t=0, \) a horizontal force is applied \( (F= \)
\( a t) \) where \( a \) is a constant vector. Find
the distance traversed in first \( t \) sec.
\( ^{\mathbf{A}} \cdot \frac{a}{6 m}\left(t-\frac{\mu m g}{a}\right)^{3} \)
в. \( \frac{a}{6 m} t^{3} \)
c. \( \frac{a}{6 m} t^{3}-\frac{\mu g t^{2}}{2} \)
D. \( \frac{a}{6 m} t^{3}-\frac{\mu g t^{2}}{3} \)
Subject: Maths
Show that the following system of linear equations is consistent and also find their solution:
\( \mathbf{5} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{7} \boldsymbol{z}=\mathbf{4} \)
\( \mathbf{3} \boldsymbol{x}+\mathbf{2 6} \boldsymbol{y}+\mathbf{2} \boldsymbol{z}=\mathbf{9} \)
\( \mathbf{7} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{1 0} \boldsymbol{z}=\mathbf{5} \)
Subject: Physics
Consider a new system of units in which \( c( \) speed of light in vacuum), h(Planck's constant) and G (gravitational constant) are taken as fundamental
units. Which of the following would correctly represent mass in this new
system?
\( ^{\mathrm{A}} \cdot \sqrt{\frac{h c}{G}} \)
B. \( \sqrt{\frac{G c}{h}} \)
c. \( \sqrt{\frac{h G}{c}} \)
D. \( \sqrt{h G c} \)
Subject: Physics
\( \mathbf{A} \)
\( 2 \Omega \) resistor is connected in series
with \( R \Omega \) resistor. This combination is
connected across a cell. When the
potential difference across \( 2 \Omega \) resistor is balanced on potentiometer wire, null
point is obtained at length of 300cm.
When the same procedure is repeated for \( R \Omega \) resistor, null point is obtained at
length \( 350 \mathrm{cm}, \) value of \( \mathrm{R} \) is:
A. 5
в. 3.33
c. 4.6
D. 2.83
Subject: Physics
The \( (x, y, z) \) co-ordinate of two points \( A \)
and B are given respectively as (0,3,-1) and \( (-2,6,4) . \) The
displacement vector from \( A \) to \( B \) may be given by :
A. \( -2 i+6 j+4 k \)
\( k \)
в. \( -2 i+3 j+3 k \)
c. \( -2 i+3 j+5 k \)
D. \( 2 i-3 j-5 k \)
Subject: Physics
A steel wire of length \( 4 \mathrm{m} \) and diameters \( 5 \mathrm{mm} \) is stretched by \( 5 \mathrm{kg} \) weight find the change in it's diameter if \( \boldsymbol{y}=\mathbf{0 . 4} \times \)
\( \mathbf{1 0}^{12} \boldsymbol{d} \boldsymbol{y} \boldsymbol{n} e / \boldsymbol{c m}^{2} \) and \( \boldsymbol{\sigma}=\mathbf{0 . 3} \)
Subject: Maths
If \( \lim _{x \rightarrow \infty} f(x) \) exists and is finite and nonzero and if \( \lim _{x \rightarrow \infty}\left\{f(x)+\frac{3 f(x)-1}{f^{2}(x)}\right\}=3, \) then the
value of \( \lim _{x \rightarrow \infty} f(x) \) is
A . 2
B.
\( c \cdot-1 \)
D. 3
Subject: Physics
In a double slit experiment, the separation between the slits is \( d=0.25 \) \( \mathrm{cm} \) and the distance of the screen \( \mathrm{D}= \)
\( 100 \mathrm{cm} \) from the slits, If the wavelength of light used is \( \lambda=6000 \mathrm{A} \) and \( \mathrm{I}_{0} \) is the
intensity of the central bright fringe, the intensity at a distance \( y=4 \times 10^{-5} \mathrm{m} \)
from the central maximum is
A . \( I_{0} \)
в. \( I_{0} / 2 \)
c. \( 3 I_{0} / 4 \)
D. \( I_{0} / 3 \)
Subject: Physics
Assertion
Two protons and two neutrons are each
separated by a distance of \( \mathbf{r}=\mathbf{1 0}^{-14} \mathbf{m} \)
which is the size of the nucleus. Hence
the force between two neutrons will be
greatest.
Reason
At distances of the order of \( 10^{-14} \mathrm{m} \)
neutrons and protons exert very strong attractive forces on each other and this
force does not depend on the charge.
A. Statement l is True and Statement 2 is True and is a correct explanation of Statement 1
B. Statement lis True and Statement 2 is True but not a correct explanation of Statement
c. statement lis True and Statement 2 is False
D. Statement lis False and Statement 2 is True
Subject: Maths
Find the product. Write the answer in standard form
\( i(6-2 i)(7-5 i) \)
A. \( 52+16 i \)
B. \( 10 i^{3}+44 i^{2}+42 i \)
c. \( -44-32 i \)
D. \( 44+32 i \)
Subject: Chemistry
Which of the following statements is the most accurate with regard to the significance of Avogadro's number, \( 6.02 \times 10^{23} ? \)
A. It is the conversion factor between grams and atomic mass units
B. It is a universal physical constant just as the speed of light
C. It is the number of particles that is required to fill a 1 liter container
D. It is the inverse diameter of an H atom.
E. It is the number of electrons in the universe
Subject: Maths
A cricket team has 15 members, of
whom only 5 can bowl. If the names of the 15 members are put into a hat and 11 drawn random, then the chance of obtaining an eleven containing at least
3 bowlers is
\( A \cdot \frac{7}{13} \)
B. \( \frac{11}{15} \)
c. \( \frac{12}{13} \)
D. None of these.
Subject: Maths
Find the amount of water displaced by a solid spherical ball of diameter \( 28 \mathrm{cm} \)
A \( \cdot_{11498} \frac{2}{3} c m^{3} \)
В \( \cdot_{11498} \frac{2}{7} c m^{3} \)
c. \( _{11498} \frac{1}{3} c m^{3} \)
D. \( _{11498} \frac{2}{5} \)cm\( ^{3} \)
Subject: Chemistry
Which of the above represents the formula for the most common
compound of \( X \) and \( Y ? \) Where \( X \) is \( C a \)
and \( Y \) is \( F \)
A. \( X_{2} Y \)
\( Y \)
в. \( X Y \)
c. \( X Y_{2} \)
D. \( X Y_{3} \)
E. \( X Y_{4} \)
Subject: Biology
Find the nucleotide sequence of the
MRNA which codes for the sequence of amino acids - 'Met - Leu - Val - Arg - Ala' and choose the correct option from
below:
A. AUG - GAU - GAA - UAU - UGU
B. AUG - GAU - GAA - CGU - GCC
c. AUG - CUA - GUG - UAU - UGU
D. AUG - CUA - GUG - CGU - GCC
Subject: Physics
A. liquid drop of radius 'R' breaks into
64 tiny droplets each of radius 'r'. If the surface tension of the liquid is 'T' then
gain in energy is:
\( \mathbf{A} \cdot 48 \pi R^{2} T \)
В. \( 12 \pi r^{2} T \)
\( \mathbf{c} \cdot 96 \pi r^{2} T \)
D. \( 192 \pi r^{2} T \)