AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
are connected together by a light spring
of stiffness \( k . \) The system is lying on a
smooth horizontal surface with the
block \( A \) in contact with a fixed vertical
wall as shown in the figure. The block \( \boldsymbol{B} \)
is pressed towards the wall by a
distance \( x_{0} \) and then released. There is
no friction anywhere. If spring takes
time \( \Delta t \) to acquire its natural length
then average force on the block \( A \) by the
wall is :
A. Zero
B. \( \frac{\sqrt{2 m k}}{\Delta t} x_{0} \)
c. \( \frac{\sqrt{m k}}{\Delta t} x_{0} \)
D. \( \frac{\sqrt{3 m k}}{\Delta t} x_{0} \)
Subject: Physics
A thin circular ring of mass \( \mathrm{M} \) and radius R is rotating about its axis with a constant angular velocity \( \omega . \) Two objects, each of mass \( \mathrm{m}, \) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity:
A. \( \frac{M \omega}{(M+m)} \)
в. \( \frac{\omega(M-2 m)}{(M+2 m)} \)
c. \( \frac{M \omega}{M+2 m} \)
D. \( \frac{\omega(M+2 m)}{M} \)
Subject: Chemistry
The depressions in freezing point for \( 1 \mathrm{m} \) urea, \( 1 \mathrm{m} \) glucose and \( 1 \mathrm{m} \) NaCl are in
the ratio:
A .1: 2: 3
B. 3:2:2
c. 1: 1: 2
D. None of these
Subject: Physics
The plot represents the flow of current
through a wire at three different times.
The ratio of charges flowing through the wire at different times is (second
figure
\( \mathbf{A} \cdot 2: 1: 2 \)
B. 1: 3: 3
\( \mathbf{c} \cdot 1: 1: 1 \)
\( \mathbf{D} \cdot 2: 3: 4 \)
Subject: Biology
Assertion
Darwin's finches show a variety of beaks suited for eating large seeds, flying insects and cactus seeds.
Reason
Ancestral seed-eating stock of Darwin's finches radiated out from South
American mainland to different
geographical areas of the Galapagos Islands, where they found competitor for new habitats.
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
Calculate the age of a vegetarian beverage whose tritium content is only \( 15 \% \) of the level in living plants. Given \( \boldsymbol{t}_{\frac{1}{2}} \) for \( _{1} \boldsymbol{H}^{3}=\mathbf{1 2 . 3} \) years. \( (\log \mathbf{2}= \)
\( 0.3, \log 3=0.48) \)
Subject: Chemistry
Which of the following sequences would yield m-nitro chlorobenzene \( (Z) \) from benzene?
A. Benzene \( \frac{C l_{2} / F e C l_{3}}{\longrightarrow}(X) \frac{H N O_{3}}{H_{2} S O_{4}}(Z) \)
B. Benzene \( \frac{H_{2} S O_{4} / H N O_{3}}{\longrightarrow}(Z) \)
c. Benzene \( \frac{H_{2} S O_{4} / H N O_{3}}{\rightarrow}(X) \frac{C_{l 2} / F e C l_{3}}{\longrightarrow}(Z) \)
D. All of these
Subject: Physics
The vertical displacement traveled by
the proton as it exits the region between
the plates is (mass of proton is \( 1.67 \times \)
\( \left.10^{-27} k g .\right) \)
A \( \cdot 1.6 \times 10^{-8} \mathrm{m} \)
B . \( 3.25 \times 10^{-8} \mathrm{m} \)
\( c \cdot 5.25 \times 10^{-6} m \)
D. \( 2.73 \times 10^{-6} \mathrm{m} \)
Subject: Maths
The value of ' \( a \) ' so that the curves \( y= \) \( 3 e^{x} \) and \( y=\frac{a}{3} e^{-x} \) are perpendicular to
each other:
A \( \cdot \frac{1}{3} \)
B. - 1
\( c .3 \)
D.
Subject: Physics
A conducting rod \( P Q \) of length \( L= \)
1.0 \( m \) is moving with a uniform speed
\( \boldsymbol{v}=20 \boldsymbol{m} / \boldsymbol{s} \) in a uniform magnetic field
\( B=4.0 T \) directed into the paper \( A \)
capacitor of capacity \( \boldsymbol{C}=\mathbf{1 0} \boldsymbol{\mu} \boldsymbol{F} \) is
connected as shown in figure. Then
\( \mathbf{A} \cdot q_{A}=+800 \mu C \) and \( q_{B}=-800 \mu C \)
B \( \cdot q_{A}=-800 \mu C \) and \( q_{B}=+800 \mu C \)
\( \mathbf{c} \cdot q_{A}=0=q_{B} \)
D. charged stored in the capacitor increases exponentially with time
Subject: Chemistry
Which of the following are correctly matched?
(a) \( D_{2} O- \) Hard water
(b) \( H_{2} O- \) Heavy water
\( (c) D- \) Heavy hydrogen
\( (d) B a O_{2} \cdot 8 H_{2} O- \) True peroxide
\( \mathbf{A} \cdot a, b, c, d \) are correct
B. \( c, d \) are correct
c. \( a, b, c \) are correct
D. \( a, c, d \) are correct
Subject: Physics
Two coils \( P \) and \( Q \) are lying parallels and very close to each other. Coil P is
connected to an AC source whereas Q is
connected to a sensitive galvanometer. On pressing key \( \mathrm{K} \)
A. small variations are observed in the galvanometer for applied 50 Hz voltage
B. deflections in the galvanometer can be observed for applied voltage of 1 Hz to 2 Hz.
c. no deflection in the galvanometer will be observed
D. constant deflection will be observed in the galvanometer for 50 Hz supply voltage
Subject: Chemistry
Which of the following is/are true when milk changes into curd?
(i) Its state is changed from liquid to semi liquid.
(ii) It changes colour.
(iii) It changes taste.
(iv) The change cannot be reversed. Choose the correct statement.
\( \mathbf{A} \cdot i, i i \)
B. \( i i, \) ii i
c. \( i, i i i, \) iv
D. \( i, i v \)
Subject: Chemistry
Roasting is carried out to:
1) convert sulphide to oxide and
sulphate.
2) remove the water of hydration.
3) melt the ore
4) remove arsenic and sulphur impurities.
Choose the correct options.
A. \( 1.2, \) and 3 are correct
B. 1 and 4 are correct
c. \( 1,2, \) and 4 are correct
D. \( 2,3, \) and 4 are correct
Subject: Chemistry
Answer the questions based on the
following flow-sheet.
Following are some statements about
species \( C \)
Select correct statement(s).
This question has multiple correct options
\( \mathbf{A} \cdot \mathrm{C} \) is \( N H_{4} C l \)
B. \( \mathrm{C} \) is \( \mathrm{NaHCO}_{3} \)
C \( \cdot \mathrm{C} \) is recycled into \( \mathrm{Ca}(\mathrm{OH})_{2} \) chamber to from \( \mathrm{NH}_{3} \)
\( D \cdot \mathrm{C} \) is \( N a_{2} C O_{3} \)
Subject: Maths
\( \frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}+\dots n \)
terms \( = \)
A. \( \frac{n\left(2 n^{2}+9 n+13\right)}{24} \)
B. \( \frac{n\left(2 n^{3}+9 n+13\right)}{8} \)
c. \( \frac{n\left(n^{2}+9 n+13\right)}{24} \)
D. \( \frac{n\left(n^{2}+9 n+13\right)}{8} \)
Subject: Maths
Let \( a=m i n\left[x^{2}+2 x\right], x \in R \) and \( b= \)
\( \lim _{x \rightarrow 0} \frac{\sin x \cdot \cos x}{e^{x}+e^{-x}} . \) Then value of \( a+b \) is
A . -1
B . 2
\( c .1 \)
D.
Subject: Maths
Find \( x \)
\[
\frac{\mathbf{5} \boldsymbol{x}-\mathbf{4}}{\mathbf{6}}=\mathbf{4} \boldsymbol{x}+\mathbf{1}-\frac{\mathbf{3} \boldsymbol{x}+\mathbf{1 0}}{\mathbf{2}}
\]
Subject: Maths
If
\( * \) is defined on the set \( R \) of all real
numbers by \( *: \boldsymbol{a} * \boldsymbol{b}=\sqrt{\boldsymbol{a}^{2}+\boldsymbol{b}^{2}}, \) find
the identify element, if it exists in \( \boldsymbol{R} \)
with respect to \( * \)
Subject: Maths
Evaluate
\( \frac{\sin ^{2} 63^{\circ}+\sin ^{2} 27^{\circ}}{\cos ^{2} 17^{\circ}+\cos ^{2} 73^{\circ}} \)
2) \( \sin 25^{\circ} \cos 65^{\circ}+\cos 25^{\circ} \sin 65^{\circ} \)
Subject: Biology
Assertion
As long as the mother breast-feeds the
child fully, chances of conception are almost nil.
Reason
Lactational amenorrhea method is
based on the fact that ovulation does
not occur during the period of intense lactation.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
For what value of \( k \) the function \( f(x)= \) \( \left\{\begin{array}{l}\frac{\sin 5 x}{3 x}, i f, x \neq 0 \\ k, \text { if } x=0\end{array} \) is continuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)
Subject: Chemistry
Three elements \( A, B, C \) belong to
\( \boldsymbol{I I} \boldsymbol{A}, \boldsymbol{I} \boldsymbol{V} \boldsymbol{A}, \boldsymbol{V} \boldsymbol{I} \boldsymbol{A} \) group respectively of
the periodic table. Identify the elements that form covalent bonds and that form electrovalent bond respectively?
\( \mathbf{A} \cdot A \) and \( B \)
B. \( B \) and \( C \)
c. \( C \) and \( B \)
D. None of the above
Subject: Maths
\( \boldsymbol{I f} \mathbf{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{3} \\ \mathbf{2} & \mathbf{1}\end{array}\right], \) then the determinant
\( \mathbf{A}^{2}-2 \mathbf{A}: \)
A . 5
B . 25
\( c .-5 \)
D. -25
Subject: Maths
Write \( \left[\sqrt{2}\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right]^{2} \) in the
form \( a+b i \)
A \( .2+i \sqrt{3} \)
B . \( \frac{3}{2}+\frac{1}{2} i \)
\( \mathrm{c} \cdot 1-i \sqrt{3} \)
D. \( \frac{3}{2}-\frac{1}{2} i \)
\( E \cdot 1+i \sqrt{3} \)
Subject: Maths
Assertion
A bag contains \( n+1 \) coins. It is known
that one of these coins has a head on
both sides while the other coins are fair.
One coins is selected at random and
tossed. If head turns up, the probability that the selected coin was fair, is \( \frac{n}{n+2} \)
Reason

If an event \( A \) occurs with two mutually
exclusive and exhaustive events \( \boldsymbol{E}_{1} \) and
\( E_{2}, \) then \( \boldsymbol{P}\left(\frac{\boldsymbol{E}_{\boldsymbol{i}}}{\boldsymbol{A}}\right)= \)
\( \frac{\boldsymbol{P}\left(\boldsymbol{E}_{\boldsymbol{i}}\right) \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{E}_{i}}\right)}{\boldsymbol{P}\left(\boldsymbol{E}_{1}\right) \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{E}_{1}}\right)+\boldsymbol{P}\left(\boldsymbol{E}_{2}\right) \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{E}_{2}}\right)}, \boldsymbol{i}= \)
\( \mathbf{1}, \mathbf{2} \)
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: Physics
If in a transformer the number of turns
of primary coil and secondary coil are 5 and 4 respectively and \( 240 \mathrm{V} \) is applied to primary coil, then the ratio of current
in primary and secondary coil is
A .4: 5
B. 5: 4
\( c \cdot 5: 10 \)
D. 8: 12
Subject: Physics
A. wavelength of microwave is greater than that of ultraviolet rays.
B. The wave length of infrared rays is lesser than that of ultraviolet rays.
C. wavelength of microwave is lesser than that of ultraviolet rays
D. Gamma rays has shortest wavelength in the electromagnetic spectrum. Choose the correct option from the
given options.
\( A \). A and \( B \) are true
B. B and C are true
c. \( c \) and \( D \) are true
D. A and D are true
Subject: Physics
A 0.5 kg ball is thrown up with an initial speed \( 14 \mathrm{m} / \mathrm{s} \) and reaches a maximum
height of \( 8.0 \mathrm{m} . \) How much energy is dissipated by air drag acting on the ball during the ascent?
A. 19.6 Joule
B. 4.9 Joule
c. 10 Joule
D. 9.8 Joule
Subject: Chemistry
The \( (I E)_{1} \) and the \( (I E)_{2} \) in \( \mathrm{kJ} \mathrm{mol}^{-1} \) of
a few elements designated by Roman
numerals are shown below
\( \begin{array}{lll}\text { Element } & (I E)_{1} & (I E)_{2} \\ A & 2372 & 5251 \\ B & 520 & 7300 \\ C & 900 & 1760 \\ D & 1680 & 3380\end{array} \) Based on above information, Which
represents a noble gas?
\( \mathbf{A} \cdot A \)
B. \( B \)
\( c \cdot C \)
D. \( D \)
Subject: Physics
A boy is swinging on a swing such that his lowest and highest position are at heights of \( 2 m \) and \( 4.5 m \) respectively. His velocity at the lowest position is
A \( .2 .5 m s^{-} \)
B. \( 7 m s^{-1} \)
\( \mathrm{c} \cdot 14 \mathrm{ms}^{-1} \)
D. \( 20 m s^{-1} \)
Subject: Maths
The parallel sides of a trapezium are \( 15 c m \) and \( 9 c m . \) The distance between
them is \( 5 c m \). A rectangle has same area as the trapezium. If its length is \( 10 \mathrm{cm} \) what is its breadth?
A \( .6 \mathrm{cm} \)
в. 3 ст
\( c .5 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Physics
The balancing length for a cell is \( 560 \mathrm{cm} \)
in a potentiometer experiment. When an external resistance of \( 10 \Omega \) is connected
in parallel to the cell, the balancing length changes by \( 41 c m \). The internal resistance of the cell in ohms is
A . 1.6
B. 1.
\( c \cdot 12 \)
D. 0.8
Subject: Maths
If \( \boldsymbol{P}(\boldsymbol{n})=\mathbf{1}+\mathbf{2}+\mathbf{3}+\cdots+\boldsymbol{n} \) is a
perfect square, \( N \) is less than 100 , then
possible values of \( n \) is/are
A. only 1
B. 1 and 8
c. only 8
D. 1,8,49
Subject: Chemistry
In the replacement reaction:
The reaction will be most favourable if
M happens to be:
\[
\frac{\lambda}{\nearrow} \mathrm{CI}+\mathrm{MF} \rightarrow \frac{\searrow}{/} \mathrm{CF}+\mathrm{MI}
\]
\( A \cdot K \)
B. Rb
\( c \cdot L \)
D. Na a
Subject: Maths
Assertion: The value of \( \frac{\tan ^{-1} \frac{4}{3}}{\tan ^{-1} \frac{1}{2}} \) is equal
to
2
Reason: \( \forall \boldsymbol{x} \in[\mathbf{0}, \mathbf{1}], \tan ^{-1}\left(\frac{\mathbf{2} \boldsymbol{x}}{\mathbf{1 - x}^{2}}\right)= \)
\( 2 \tan ^{-1} x \)
A. Both A and R are true and R is the correct explanation of
B. Both A and R are true but R is not the correct explanation of A
c. \( R \) is true but \( A \) is false
D. A is true but R is false
Subject: Chemistry
The oxidising ability of the given anions
follows the order:
A \( \cdot \operatorname{Ti} 0_{4}^{4-}<V O_{4}^{3-}<C r O_{4}^{2-}<M n O_{4} \)
B. \( V O_{4}^{3-}<C r O_{4}^{2-}<M n O_{4}^{-}<T i O_{4}^{4} \)
c. \( C r O_{4}^{2-}<M n O_{4}^{-}<V O_{4}^{3-}<T i O_{4}^{4} \)
D. \( V O_{4}^{3-}<T i O_{4}^{4-}<C r O_{4}^{2-}<M n O_{4} \)
Subject: Chemistry
Draw the diagram showing micelle formation by the following detergent.
\( \boldsymbol{C H}_{3}\left(\boldsymbol{C H}_{2}\right)_{10} \boldsymbol{C H}_{2} \boldsymbol{O} \boldsymbol{S} \overline{\boldsymbol{O}}_{3} \boldsymbol{N} \boldsymbol{a} \)
Subject: Chemistry
What is the oxidation number of Pt in
\( \boldsymbol{K}\left[\boldsymbol{P t} \boldsymbol{N} \boldsymbol{H}_{3} \boldsymbol{C l}_{5}\right] ? \)
\( A \cdot O \)
B. +1
\( c \cdot+2 \)
\( D \cdot+4 \)
Subject: Chemistry
Consider the reaction,
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{S} \boldsymbol{C} \boldsymbol{N}^{-}(\boldsymbol{a} \boldsymbol{q}) \rightleftharpoons \)
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{C} \boldsymbol{N}^{2-}(\boldsymbol{a} \boldsymbol{q}) \)
How will the equilibrium position shift
if \( A g N O_{3}(a q) \) is added? \( (A g S C N \) is insoluble)
Subject: Chemistry
In the electrolysis of alumina using cryolite, the reaction that takes place at cathode is:
\( \mathbf{A} \cdot 4 H_{2} O+4 e^{-} \rightarrow 2 H_{2}+4 O H^{-} \)
B \( \cdot 4 A l^{3+}+12 e^{-} \rightarrow 4 A l \)
c. \( 6 F_{2}+2 A l_{2} O_{3} \rightarrow 4 A l F_{3}+3 O_{2} \)
D. \( 12 F^{-} \rightarrow 6 F_{2}+12 e^{-} \)
Subject: Maths
The fire terms of an arithmetic
sequence are given:- -7, -4, -1, 2, 5 .........
Find their common difference and next
term of the sequence.
A. common difference \( =3 ; a_{6}=8 \)
B. Common difference \( =2 ; a_{4}=7 \)
C. common difference \( =1 ; a_{6}=5 \)
D. common difference \( =0 ; a_{6}=0 \)
Subject: Physics
Four identical capillary tubes \( a, b, c \) and \( d \) are dipped in four beakers containing water with tube 'a' vertically, tube 'b' at
\( 30^{\circ}, \) tube \( ^{\circ} c^{\prime} \) at \( 45^{\circ} \) and tube ' \( d^{\prime} \) at \( 60^{\circ} \) inclination with the vertical. Arrange the lengths of water column in the tubes in descending order
A \( . d, c, b, a \)
в. \( d, a, b, c \)
c. \( a, c, d, b \)
D. \( a, b, c, d \)
Subject: Physics
A coil mean area \( 500 \mathrm{cm}^{2} \) and having
1000 turns is held perpendicular to a uniform field of 0.4 gauss. The coil is turned through \( 180^{0} \) in \( \frac{1}{10} \) second. The average induced emf is
\( \mathbf{A} \cdot 0.02 V \)
B. \( 0.04 V \)
c. \( 1.4 V \)
D. \( 0.08 V \)
Subject: Maths
If a sphere and a cube have the same volume then the ratio of the surface of
the sphere to that of the cube is
A \( \cdot \sqrt{6}: \sqrt{\pi} \)
B. \( \sqrt[3]{3 \pi}: \sqrt[3]{3} \)
C \( \cdot \sqrt[3]{\pi}: \sqrt[3]{6} \)
D. none of these
Subject: Chemistry
What mass of sodium chloride would be decomposed by \( 9.8 \mathrm{g} \) of sulphuric acid if \( 12 \mathrm{g} \) of sodium bisulphate and \( 2.75 \mathrm{g} \) of hydrogen chloride were produced in a
reaction?
\( A \cdot 14.75 \mathrm{g} \)
в. 3.8 g
c. \( 4.95 \mathrm{g} \)
D. 2.2 g
Subject: Chemistry
Which of the following is a volatile covalent liquid at \( 25^{\circ} \mathrm{C} \) and 1 atm?
A . \( N_{2} \)
в. \( K I \)
c. \( C C l_{4} \)
D. \( A g N O_{3} \)
ह. \( C a C O_{3} \)
Subject: Maths
From means value theorem \( \boldsymbol{f}(\boldsymbol{b})- \)
\( \boldsymbol{f}(\boldsymbol{a})=(\boldsymbol{b}-\boldsymbol{a}) \boldsymbol{f}^{\prime}\left(\boldsymbol{x}_{1}\right) ; \mathbf{0}<\boldsymbol{a}<\boldsymbol{x}_{1}<\boldsymbol{b} \) if
\( f(x)=\frac{1}{x}, \) then \( x_{1}= \)
A \( \cdot \sqrt{a b} \)
в. \( \frac{a+b}{2} \)
c. \( \frac{2 a b}{a+b} \)
D. \( \frac{b-a}{b+a} \)
Subject: Maths
The equation of line perpendicular to \( x-2 y+1=0 \) and passing through
(1,2) is.
A. \( 3 x-8 y+6=0 \)
B. \( 2 x+y=4 \)
c. \( 3 x-5 y+1=0 \)
D. \( 5 x+3 y=0 \)
Subject: Chemistry
When 0.2 mole of ethane is burnt completely in a bomb calorimeter, the temperature of calorimeter system increased by \( 2 K \). What should be the
increase in temperature of the same calorimeter system, when 0.4 mole of
\( C H_{4} \) is burnt?
Given: \( \Delta_{C} U_{C_{2} H_{6}(g)}=-400 K c a l / m o l \)
and \( \Delta_{c} U_{C H_{4}(g)}=-200 K c a l / m o l \)
A . \( 2 K \)
в. 4 К
\( c \cdot 1 k \)
D. 3 K
Subject: Physics
A glider is oscillating in SHM on an air track with an amplitude A. You slow it so that its amplitude becomes half.
Find the total mechanical energy in terms of previous value.
A \( \cdot 1 / 2 \)
в. \( 1 / 3 \)
c. \( 1 / \sqrt{5} \)
D. \( 1 / 4 \)
Subject: Physics
Carbon, silicon and germanium have
four valence electrons each. At room
temperature the appropriate statement
is
A. The number of free electrons for conduction is significant only in Si and Ge but small in \( \mathrm{C} \)
B. The number of free conduction electrons is significant in C but small si and Ge.
C. The number of free conduction electrons is negligibly small in all the three.
D. The number of free conduction electrons is significant in all the three.
Subject: Physics
The distance of two planets (Neptune and Saturn) from the sun are \( 10^{13} m \)
and \( 10^{12} m \) respectively. Find the ratio of
the time periods of the planets.
A . 100: 1
B. \( 1: \sqrt{10} \)
\( c \cdot \sqrt{10}: 1 \)
D. \( 10 \sqrt{10}: 1 \)
Subject: Maths
Represent the following mixed infinite decimal periodic fractions as common fractions:
\( 2(a+ \)
\( b)^{-1}(a b)^{1 / 2}\left(1+\frac{1}{4}(\sqrt{\frac{a}{b}}-\sqrt{\frac{b}{a}})^{2}\right)^{1 / 2} \)
Subject: Physics
A physical quantity \( \rho \) is related to four variables \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) and \( \boldsymbol{\eta} \) as \( \boldsymbol{\rho}=\frac{\boldsymbol{\alpha}^{3} \boldsymbol{\beta}^{2}}{\sqrt{\boldsymbol{\gamma} \boldsymbol{\eta}}} \) The
percentage errors of measurements in \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) and \( \boldsymbol{\eta} \) are \( 1 \%, 3 \%, 4 \% \) and \( 2 \% \)
respectively. Find the percentage error
in \( \rho \)
A . 6.5\%
B. 12\%
c. 21\%
D. 26\%
Subject: Physics
A series-parallel combination of battery consisting of a large number \( N=300 \)
of identical cells, each with an internal
resistance \( r=0.3 \Omega, \) is loaded with an
external resistance \( \boldsymbol{R}=\mathbf{1 0} \boldsymbol{\Omega} \). then, the
number \( n \) of parallel group consisting of an equal number of cells connected in
series at which the external resistance
generates highest thermal power is
A. 3
B. 4
\( c .5 \)
D. none of the above
Subject: Physics
The length of an elastic string is \( a \) metre when the longitudinal tension is \( 4 \mathrm{N} \) and \( b \) metre when the longitudinal
tension is 5 N. The length of the string in metre when longitudinal tension is \( 9 N \) is :
\( \mathbf{A} \cdot a-b \)
B. \( 5 b-4 a \)
c. \( 2 b-\frac{1}{4} a \)
D. \( 4 a-3 b \)
Subject: Maths
Circles with centres \( A, B \) and \( C \) touch
each other externally. If \( \boldsymbol{A B}= \)
\( \mathbf{3} c \boldsymbol{m}, \boldsymbol{B} \boldsymbol{C}=\mathbf{3} \boldsymbol{c m}, \boldsymbol{C} \boldsymbol{A}=\mathbf{4} \boldsymbol{c m}, \) then
find the radii of each circle
Subject: Maths
If \( A C \) passes through the centre of the
circle, then the area of the shaded
region in the given figure is
A \( \cdot \frac{a^{2}}{2}(3-\pi) \)
B \( \cdot a^{2}\left(\frac{\pi}{2}-1\right) \)
\( \mathbf{c} \cdot 2 a^{2}(\pi-1) \)
\( ^{\mathrm{D}} \cdot \frac{a^{2}}{2}\left(\frac{\pi}{2}-1\right) \)
Subject: Chemistry
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O N} \boldsymbol{H}_{2} \frac{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\Delta} \boldsymbol{A}+\boldsymbol{N} \boldsymbol{H}_{3} \)
In this reaction, \( \boldsymbol{A} \) is
\( \mathbf{A} \cdot C_{6} H_{6} \)
в. \( C_{6} H_{5} \)СООН
\( \mathbf{c} \cdot C_{6} H_{5} N H_{2} \)
D. \( C_{6} H_{5} C N \)
Subject: Chemistry
Find out the volume of gasses evolved by
passing 0.965 A current for 1 hr through
an aqueous solution of \( C H_{3} C O O N a \) at
\( 25^{0} C \) and 1 atm:
A . \( 0.036 L \)
B. 1.76 L
c. \( 0.072 \mathrm{L} \)
D. 1.12 L
Subject: Chemistry
The mole fraction of water in \( 20 \% \) (wt. \( / \)
wt.) aqueous solution of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is:
A \( \cdot \frac{77}{68} \)
в. \( \frac{68}{77} \)
c. \( \frac{20}{80} \)
D. \( \frac{80}{20} \)
Subject: Maths
If \( \tan A=-\frac{1}{2} \) and \( \tan B=-\frac{1}{3} . \) (where
\( A, B>0), \) then \( A+B \) can be
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{3 \pi}{4} \)
c. \( \frac{5 \pi}{4} \)
D. \( \frac{7 \pi}{4} \)
Subject: Physics
In a meter bridge with a standard resistance of \( 5 \Omega \) in the left gap, the ratio of balancing lengths on the meter bridge wire is \( 2: 3 . \) The unknown
resistance is
A . \( 3.3 \Omega \)
B. \( 7.5 \Omega \)
c. \( 10 \Omega \)
D. 15\Omega
Subject: Chemistry
What would be the reactant and reagent
used to obtain 2,4 dimethylpentan-3-ol?
A. Propanal and propyl magnesium bromide.
B. 3 - Methylbutanal and 2 - methyl magnesium iodide.
C. \( 2, \) 2-Dimethylpropanone and methyl magnesium iodide
D. 2 - Methylpropanal and isopropyl magnesium iodide
Subject: Physics
A block of mass \( 12 \mathrm{Kg} \) is attached to a
string wrapped around a wheel of
radius \( 10 \mathrm{cm} . \) The acceleration of the
block moving down an inclined plane is
measured as \( 2 m / s^{2} . \) The tension in the string is :
A . \( 24.5 N \)
B. \( 68.7 N \)
c. \( 23.4 N \)
D. \( 46.8 N \)
Subject: Physics
A light ray is travelling between two media as given below. The angle of incidence on the boundary in all the
cases is \( 30^{\circ} . \) Identify the sequence of increasing order of angles of refraction.
a) Air to water
b) Water to glass
c) Glass to water
\( A \cdot a, b, c \)
B. b, c, a
\( c \cdot c, a, b \)
D. a, c, b
Subject: Chemistry
When \( 1 k g \) of ice at \( 0^{\circ} C \) melts to water
at \( 0^{\circ} \mathrm{C}, \) the resulting change in its entropy, taking the latent heat of ice to
be \( 80 c a l / C^{o} ? \)
A. 273 cal / \( K \)
B . \( 8 \times 10^{4} c a l / K \)
c. 80 cal \( K \)
D. \( 293 c a l / K \)
Subject: Chemistry
The above reaction is a type of intramolecular disproportionation reaction.
If true enter 1 , else enter 0 .
\[
\underbrace{\mathrm{CHO}}_{\mathrm{CHO}} \stackrel{\mathrm{OH}^{-}}{\longrightarrow} \underbrace{\mathrm{COO}^{-}}_{\mathrm{CH}_{2} \mathrm{OH}}
\]
\( A \)