AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which pair of products would result from the acid cleavage of phenyl propyl ether with excess concentrated \( \boldsymbol{H} \boldsymbol{B r} \) ?
A. Phenol and 1-propanol
B. Bromobenzene and 1-propanol
c. Bromobenzene and 1-bromopropane
D. Phenol and 1-bromopropane
Subject: Maths
The value of \( x \) that satisfies the relation
\( \boldsymbol{x}=\mathbf{1}-\boldsymbol{x}+\boldsymbol{x}^{2}-\boldsymbol{x}^{\mathbf{3}}+\boldsymbol{x}^{4}-\boldsymbol{x}^{\mathbf{5}}+. \infty \) if
\( |\boldsymbol{x}|<\mathbf{1} \)
A \( \cdot \frac{-1 \pm \sqrt{5}}{2} \)
B. \( \frac{-1 \pm 3 i}{2} \)
\( c \)
D. none
Subject: Physics
The resistance \( R \) of a conductor varies
with the temperature as shown in the
figure. If it is written as \( \boldsymbol{R}_{1}=\boldsymbol{R}_{0}(\mathbf{1}+ \)
\( \left.\boldsymbol{\alpha} \boldsymbol{t}+\boldsymbol{\beta} \boldsymbol{t}^{2}\right) \)
A \( \cdot \alpha \) and \( \beta \) are both negative
B. \( \alpha \) is positive and \( \beta \) is negative
c. \( \alpha \) and \( \beta \) are both positive
D. \( \alpha \) is negative and \( \beta \) positive
Subject: Maths
If \( \cot ^{-1}\left(\frac{1}{a}\right)+\cot ^{-1}\left(\frac{1}{b}\right)+ \)
\( \cot ^{-1}\left(\frac{1}{c}\right)=\frac{\pi}{2}, \) then
\( \mathbf{A} \cdot a+b+c=a b c \)
B. \( a b+b c+c a=1 \)
c. \( a b+b c+c a=a b c \)
D. none of these
Subject: Maths
If \( A \) and \( B \) be two events associated
with a random experiment such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{A} \)
\( B)=0.6, \) then value of \( P\left(\frac{\bar{A}}{B}\right)+ \)
\( P\left(\frac{A}{\bar{B}}\right) \) is
\( A \)
в. \( \frac{3}{4} \)
\( c \cdot \frac{2}{5} \)
D. \( \frac{13}{12} \)
E. \( \frac{11}{12} \)
Subject: Maths
\( \mathbf{f} \boldsymbol{y}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{\left(\mathbf{1}+\boldsymbol{x}^{2}\right)^{3 / 2}} \) and \( \boldsymbol{y}=\mathbf{0} \) when
\( \boldsymbol{x}=\mathbf{0}, \) then value of \( \mathbf{y} \) when \( \boldsymbol{x}=\mathbf{1}, \) is
Subject: Maths
If \( x=A \cos 4 t+B \sin 4 t, \) then \( \frac{d^{2} x}{d t^{2}}= \)
\( A \)
B . \( -16 x \)
\( c .15 x \)
D. \( 16 x \)
E . \( -15 x \)
Subject: Physics
A very long straight solenoid carries a
current \( I . \) The cross-sectional area of
the solenoid is equal to \( S \), the number
of turns per unit length is equal to \( n \) The flux of the vector \( \vec{B} \) through the
end plane of the solenoid is \( \frac{\Phi_{0}}{x} . \) Find \( x \)
Subject: Physics
10 g ice at \%\%0^{lcirc } c \( \mathrm{~ i s c o n v e r t e d i n t o s t e a m a t l o o n \{ l c i r c \} ~} \)
.Findtotalheatrequired \( \left(\mathrm{L}_{-} \mathrm{f}=80\right. \)
cal/G, \( S_{-} w=1 \) cal/g \( \wedge\{\mid c \text { irc }\} C, L_{v}= \)
\( \mathbf{5 4 0} c a l / g) \)
Subject: Chemistry
Nalorphene \( \left(C_{19} H_{21} N O_{3}\right) \) similar to
morphine, is used to combat
withdrawal symptoms in narcotic uses. Dose of nalorphene generally given is 1.5mg. The mass of \( 1.5 \times 10^{-3} \mathrm{m} \)
aqueous solution required for the above dose is?
A . \( 5.2 \mathrm{g} \)
c. \( 4.6 \mathrm{g} \)
D. \( 1.9 g \)
Subject: Chemistry
Choose the correct options(s) from the
following.
This question has multiple correct options
A. Teflon is prepared by heating tetrafluoroethene in presence of a persulphate catalyst at high pressure
B. Natural rubber is polyisoprene containing trans alkene units
C. Nylon-6 has amide linkages
D. Cellulose has only \( \alpha-D-g l u \) cose units that are joined by glycosidic linkages.
Subject: Chemistry
Electrons with a kinetic energy of
\( 6.023 \times 10^{4} J / \) mol are evolved from the
surface of a metal when it is exposed to
radiation of a wavelength of 600 nm. The minimum amount of energy
required to remove an electron from the metal atom is:
A \( .2 .3125 \times 10^{-19} \mathrm{J} \)
B . \( 3 \times 10^{-19} J \)
\( c \cdot 6.02 \times 10^{-19} J \)
\( J \)
D. \( 6.62 \times 10^{-34} J \)
Subject: Chemistry
Which one of the following is an example of coordination isomerism?
A \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} B r\right] S O_{4} \) and \( \left[C o\left(N H_{3}\right)_{5} S O_{4}\right] B r \)
B . \( \left[\operatorname{Co}\left(N H_{3}\right)_{5} N O_{2}\right] C l_{2} \) and \( \left[C o\left(N H_{3}\right)_{5} O N O\right] C l_{2} \)
C \( \cdot\left[C r\left(H_{2} O\right)_{6}\right] C l_{3} \) and \( \left[C r\left(H_{2} O\right)_{5} C l\right] C l_{2} \cdot H_{2} O \)
D. \( \left[C r\left(N H_{3}\right)_{6}\right]\left[C o(C N)_{6}\right] \) and \( \left[C o\left(N H_{3}\right)_{6}\right]\left[C r(C N)_{6}\right] \)
Subject: Physics
To measure the specific heat of copper, an experiment is performed in the lab. \( A \) piece of copper is heated in an oven then dropped into a beaker of water. To
calculate the specific heat of copper, the experimenter must know or
measure the value of all of the
quantities below EXCEPT the
A. Original temperatures of the copper and the water
B. Mass of the water
C. Final (equilibrium) temperature of the copper and the water
D. Time taken to achieve equilibrium after the copper is dropped into the water
E. Specific heat of the water
Subject: Chemistry
The correct order of increasing bond
order is :
\( \mathbf{A} \cdot C O<C O_{2}<C O_{3}^{2-}(\mathrm{CO} \text { bond }) \)
B. \( C N^{-}<N C N^{2-}<R-C(N H)-N H_{2}(C-N \text { Bond}) \)
c. \( C l O<C l O_{2}<C l O_{3}<C l O_{4} \) (Cl-O bond)
D. \( S O_{2}<S O_{4}^{2-}<S O_{3}^{2-}(\text { SO bond }) \)
Subject: Chemistry
Select incorrect statement(s):
A. Surface active agent like soaps and synthetic detergents are micelles.
B. Soaps are emulsifying agents.
C \( . C_{17} H_{35} \) (hydrocarbon part) and \( \mathrm{COO} \) (carboxylate part) of stearate ion \( \left(C_{17} H_{35} C O O^{-}\right) \) are both hydrophobic
D. The hydrophobic part accumulates inside of the micelle when soap is mixed in water.
Subject: Physics
A charged particle of mass \( 5 \times 10^{-6} k g \)
is held stationary in space by placing it
in an electric field of strength \( 10^{6} N C^{-1} \) directed vertically downwards. The charge on the particle is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)
A. \( -20 \times 10^{-5} \mu C \)
B. \( -5 \times 10^{-5} \mu C \)
c. \( 5 \times 10^{-5} \mu C \)
D. \( 20 \times 10^{-5} \mu C \)
Subject: Physics
A closed container of volume \( V \) contains
an ideal gas at pressure \( P \) and Kelvin
Temperature T. The temperature of the gas is changed to 4 T due to passing heat to the container. Choose correct
pairs of pressure and volume after
change of the temperature.
A . P and \( V \)
B \( \cdot \operatorname{Pand}_{2}^{1} V \)
c. 4 Pand \( 4 V \)
D. \( 4 P \) and \( V \)
E \( \cdot \frac{1}{4} P \) and \( V \)
Subject: Physics
For the displacement-time graph shown
in the figure above, find the velocity at
point \( \mathbf{A} \)
A. \( 4 \mathrm{m} \mathrm{s}^{-1} \)
B. 3 \( \mathrm{m} \) s \( ^{-1} \)
\( c \cdot 5 m s^{-} \)
D. \( 6 \mathrm{m} \) s \( ^{-1} \)
Subject: Chemistry
In the following sequence of reactions, identify the end product (D). \( N a_{2} C O_{3} \stackrel{S O_{2}}{\rightarrow}(A) \stackrel{N a_{2} C O_{3}}{\longrightarrow}(B) \)
Elemental \( S, \Delta \)
\( (\boldsymbol{C}) \stackrel{\boldsymbol{I}_{2}}{\rightarrow}(\boldsymbol{D}) \)
A \( \cdot N a_{2} S O_{4} \)
в. \( N a_{2} S_{4} O_{6} \)
c. \( N a_{2} S \)
D. \( N a_{2} S_{2} O_{3} \)
Subject: Physics
A conductor of length \( x \) and diameter \( x \)
has a resistance \( x \). The resistivity of the
material is:
A \( \cdot \pi x^{3} / 4 \)
B . \( \pi x^{2} \)
c. \( \pi x^{2} / 4 \)
D. \( \pi x / 2 \)
Subject: Physics
A circular loop of radius \( 0.3 \mathrm{cm} \) lies parallel to a much bigger circular loop of radius \( 20 \mathrm{cm} . \) The centre of the small
loop is on the axis of the bigger loop. The distance between their centres is \( 15 \mathrm{cm} \)
If a current of 2.0 A flows trough the smaller loop, then the flux linked with bigger loop is
A. \( 9.1 \times 10^{-11} \) weber
B. \( 6 \times 10^{-11} \) weber
c. \( 3.3 \times 10^{-11} \) weber
D. \( 6.6 \times 10^{-9} \) weber
Subject: Physics
A planet in a distant solar system is 10 times more massive than the earth and
its radius is 10 times smaller. Given
that the escape velocity from the earth is \( 11 \mathrm{kms}^{-1} \), the escape velocity from
the surface of the planet would be
A. \( 1.1 \mathrm{km} / \mathrm{s} \)
в. \( 11 \mathrm{km} / \mathrm{s} \)
c. \( 110 \mathrm{km} / \mathrm{s} \)
D. \( 0.11 \mathrm{km} / \mathrm{s} \)
Subject: Maths
In how many ways can four people, each
throwing a dice once, make a sum of \( 6 ? \)
\( \mathbf{A} \cdot^{9} C_{2} \)
в. \( ^{10} C_{3} \)
\( \mathbf{c} \cdot^{8} C_{3} \)
D. \( ^{9} C_{3} \)
Subject: Maths
If \( a=\frac{\sin x \times \cos 3 x}{\sin 3 x \times \cos x} \) then which of the
following is wrong?
A \( \cdot a<\frac{1}{3} \)
\( \mathbf{B} \cdot a>3 \)
c. \( \frac{1}{3}<a<3 \)
D. None of these
Subject: Physics
The shunt required to send \( 10 \% \) of the main current through a moving coil galvanometer of resistance \( 99 \Omega \) is
\( \mathbf{A} \cdot 99 \Omega \)
в. \( 9.9 \Omega \)
c. \( 9 \Omega \)
D. \( 10 \Omega \)
E . \( 11 \Omega \)
Subject: Maths
Suppose \( E F G H \) is a trapezium in
which \( \boldsymbol{E F} \) is parallel to \( \boldsymbol{H} \boldsymbol{G} \). Through \( \boldsymbol{X} \) the mid-point of \( E H, X Y \) is drawn
parallel to \( E F \) meeting \( F G \) at \( Y \). Prove that \( X Y \) bisects \( F G \)
Subject: Physics
\( A \) and \( B \) are two wires. The radius of \( A \)
is twice that of \( B \). They are stretched by
the same load. Then the stress on \( B \) is
A. equal to that on \( A \)
B. four times that on \( A \)
c. two times that on \( A \)
D. half that on \( A \)
Subject: Chemistry
Assertion \( (\mathrm{A}): C_{2} H_{5} C l \) gives ethyl benzene with benzene in presence of
anhydrous aluminium chloride.
Reason (R) : Anhydrous aluminium
chloride acts as Lewis acid and
generates ethyl carbonium ion
electrophile.
A. Both A and R are true and R is the correct explanation to A
B. Both A and R are true and R is not the correct explanation to A
c. A is true but R is false
D. A is false but R is true
Subject: Maths
Let \( \left(1+x^{2}\right)^{2} \cdot(1+x)^{n}=\sum_{K=0}^{n+4} a_{K} \cdot x^{K} \)
\( f\left(a_{1}, a_{2} \text { and } a_{3} \text { are in A.P, find } n\right. \)
Subject: Physics
One end of a cylindrical glass rod \( (\mu= \)
1.5) is in the shape of a concave refracting surface of radius \( 10 \mathrm{cm} . \) An
air bubble is situated in the glass rod at a point on its axis such that it appears to be at distance \( 10 \mathrm{cm} \) from the
surface and inside the glass when seen from the other medium. The actual
location of air bubble is
A. \( 15 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 30 \mathrm{cm} \)
D. 25 cm
Subject: Chemistry
The vapour pressure of pure water at
\( 25^{\circ} \mathrm{C} \) is 23.76 torr. The vapour pressure of a solution containing 5.40 g of a nonvolatile substance in 90.0 g water is 23.32 torr. The molecular weight of the solute is:
A. \( 97.24 \mathrm{g} / \mathrm{mol} \)
B. 24.29 g/mol
c. \( 50.44 \mathrm{g} / \mathrm{mol} \)
D. \( 57.24 \mathrm{g} / \mathrm{mol} \)
Subject: Physics
A man is slipping on a fritionless inclined plane \( \& \) a bag falls down from the same height. Then the final speed of both is related as:-
A. \( V_{B}>V_{m} \)
B. \( V_{B}<V_{m} \)
c. \( V_{B}=V_{m} \)
D. \( V_{B} \) and \( V_{m} \) can't related
Subject: Chemistry
Among the following compounds, which
on heating do not produce \( N_{2} ? \)
A \( \cdot\left(N H_{4}\right)_{2} C r_{2} O_{7} \)
B. \( N H_{4} C l+N a N O_{2} \)
c. \( N H_{4} C l+C a O \)
D. \( B a\left(N_{3}\right)_{2} \)
Subject: Maths
Suppose \( J=\int \frac{\sin ^{2} x+\sin x}{1+\sin x+\cos x} d x \) and
\( K=\int \frac{\cos ^{2} x+\cos x}{1+\sin x+\cos x} d x . \) If \( C \) is an
arbitrary constant of integration then which of the following is correct?
A \( \cdot J=\frac{1}{2}(x-\sin x+\cos x)+C \)
B. \( J=K-(\sin x+\cos x)+C \)
\( \mathbf{c} . J=x+K+C \)
D. \( K=\frac{1}{2}(x-\sin x+\cos x)+C \)
Subject: Maths
Given three vectors \( \vec{a}=6 \hat{i}-3 \hat{j}, \vec{b}= \) \( 2 \hat{i}-6 \hat{j} \) and \( \vec{c}=-2 \hat{i}+21 \hat{j} \) such that
\( \overrightarrow{\boldsymbol{\alpha}}=\overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}}, \) then the resolution of
the vector \( \vec{\alpha} \) into components with respect to \( \vec{a} \) and \( \vec{b} \) is given by
A \( .3 \vec{a}-2 \vec{b} \)
в. \( 3 \vec{b}-2 \vec{a} \)
c. \( 2 \vec{a}-3 \vec{b} \)
D. \( \vec{a}-2 \vec{b} \)
Subject: Biology
Of the following statements about
enzymes, which ones are true?
(i) enzymes lack in nucleophilic groups
(ii) enzymes are highly specific both in binding chiral substrates and in
catalyzing their reactions
(iii) enzymes catalyze chemical reactions by lowering the activation energy
(iv) pepsin in proteolytic enzyme
\( A \cdot(i) \)
B. (i) and (iv)
c. (i) and (iii)
D. (ii), (iii) and (iv)
Subject: Maths
Evaluate \( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ -\mathbf{1} & \mathbf{1} & -\mathbf{1} \\ \mathbf{1} & \mathbf{- 1} & \mathbf{1}\end{array}\right| \)
Subject: Maths
If \( \frac{x-3}{3+i}+\frac{y-3}{3-i}=i \) where \( x, y \in R \)
then
A. \( x=2 \) \& \( y=-8 \)
B. \( x=-2 \) \& \( y=8 \)
c. \( x=-2 \& y=-6 \)
D. \( x=2 \) \& \( y=8 \)
Subject: Physics
Two balls of equal masses are projected upward simultaneously, one from the ground with speed of \( 50 \mathrm{m} / \mathrm{s} \) and other from a \( 40 \mathrm{m} \) high tower with initial speed of \( 30 \mathrm{m} / \mathrm{s} \). Find the maximum height attained by their center of mass.
Subject: Maths
If \( \left(a_{1}+i b_{1}\right)\left(a_{2}+i b_{2}\right) \dots\left(a_{n}+i b_{n}\right)= \)
\( A+i B \) then \( \left(a_{1}^{2}+b_{1}^{2}\right)\left(a_{2}^{2}+b_{2}^{2}\right) \dots\left(a_{n}^{2}+\right. \)
\( \left.b_{n}^{2}\right)= \)
A. \( A^{2}-B^{2} \)
B. \( A^{2}+B^{2} \)
c. \( A-B \)
D. \( A+B \)
Subject: Maths
For all real numbers \( b \) and \( c \) such that
the product of \( c \) and 3 is \( b \), the
expression which represents the sum of \( c \) and 3 in terms of \( b \) is
B. \( 3 b+3 \)
\( c \cdot 3(b+3) \)
D. \( \frac{b+3}{3} \)
E \( \cdot \frac{b}{3}+3 \)
Subject: Chemistry
The degree of dissociation of an electrolyte is \( \alpha \) and its van't Hoff factor
is \( i \). The number of ions obtained by complete dissociation of 1 molecule of the electrolyte is:
A. \( \frac{i+\alpha-1}{\alpha} \)
B. \( i-\alpha-1 \)
c. \( \frac{i-1}{\alpha} \)
D. \( \frac{i+\alpha+1}{1-\alpha} \)
Subject: Maths
Consider three vectors \( \vec{P}=\hat{i}+\widehat{j}+ \) \( \widehat{k} ; \overrightarrow{\boldsymbol{q}}=2 \widehat{\hat{\boldsymbol{i}}}+4 \widehat{\boldsymbol{j}}-\widehat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{4} \widehat{\boldsymbol{j}}+ \)
3 \( \widehat{k} \). If \( \vec{p}, \vec{q} \) and \( \vec{r} \) denotes the position vector of three non-collinear points, then the equation of the plane containing these points is
A. \( 2 x-3 y+1=0 \)
B. \( x-3 y+2 z=0 \)
c. \( 3 x-y+z-3=0 \)
D. \( 3 x-y-2=0 \)
Subject: Physics
Two electrons are entering
perpendicularly to the magnetic field. The velocity of one of the electrons is
three times greater than the velocity of
the other electron. Calculate the ratio of
the circular radii of the path followed by
the two electrons?
A. The faster electron has a radius two times larger than the slower electron
B. The faster electron has a radius three times larger than the slower electron
C. The faster electron has a radius eight times larger than the slower electron
D. The faster electron has a radius sixteen times larger than the slower electron
E. The faster electron has a radius sixty-four times larger than the slower electron
Subject: Maths
The d.rs of the lines \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y}+\boldsymbol{b}, \boldsymbol{z}= \)
\( \boldsymbol{c} \boldsymbol{y}+\boldsymbol{d} \) are:
A. \( 1, a, c \)
B. \( a, 1, c \)
c. \( b, 1, c \)
D. \( c, a, 1 \)
Subject: Chemistry
Which of the following is isoprene?
A \( \cdot C H_{2}=C H-C H=C H_{2} \)
в. \( C H_{2}=C\left(C H_{3}\right)-C H=C H_{2} \)
c. \( C H_{2}=C(C l)-C H=C H_{2} \)
D. \( C H_{2}=C\left(C H_{3}\right)-C\left(C H_{3}\right)=C H_{2} \)
Subject: Maths
The relative humidity (in \%) of a certain
city for a September month of 30 days was as follows:
\( \begin{array}{lllll}98.1 & 98.6 & 99.2 & 90.3 & 86.5 \\ 89.2 & 92.3 & 97.1 & 93.5 & 92.7 \\ 96.0 & 92.1 & 84.9 & 90.0 & 95.7\end{array} \)
What is the range of the data?
Subject: Physics
The pressure of a liquid is plotted on the Y-axis at a depth h in a liquid of density \( \rho \) and the value of h on the X-axis, the
graph is a straight line. The slope of the straight line is : \( (\mathrm{g}= \) acceleration due to gravity
\( \mathbf{A} \cdot \rho g \)
B. \( 1 / \rho g \)
\( \mathbf{c} \cdot \rho / g \)
D. \( g / \rho \)
Subject: Maths
ff \( y=\log _{\sin x}(\tan x), \) then \( \left(\frac{d y}{d x}\right)_{\pi / 4} \) is
equal to
A \( \cdot \frac{4}{\log 2} \)
B. \( -4 \log 2 \)
c. \( \frac{-4}{\log 2} \)
D. None of these
Subject: Chemistry
In the compound \( \boldsymbol{C H}_{2}=\boldsymbol{C H}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C} \equiv \boldsymbol{C H}, \) the \( \boldsymbol{C}_{2}-\boldsymbol{C}_{3} \)
bond is of the type.
A \( \cdot s p-s p^{2} \)
B \( \cdot s p^{3}-s p^{3} \)
\( \mathbf{c} \cdot s p-s p^{3} \)
D. \( s p^{2}-s p^{3} \)
Subject: Maths
The numbers of \( 3 \times 3 \) matrices A whose
entries are either 0 or 1 and for which the system \( \boldsymbol{A}\left[\begin{array}{l}\boldsymbol{x} \\ \boldsymbol{y} \\ \boldsymbol{z}\end{array}\right]=\left[\begin{array}{l}\mathbf{1} \\ \mathbf{0} \\ \mathbf{0}\end{array}\right] \) has exactly
two distinct solutions is?
A .
B . \( 2^{9}-1 \)
\( c .168 \)
D.
Subject: Physics
\( \ln \) a \( A C \) circuit the current is given by \( \boldsymbol{i}=\mathbf{5} \sin \left(\mathbf{1 0 0 t}-\frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \) and \( \boldsymbol{V}= \)
\( 200 \sin (100 t) V \) then power
consumption is
\( \mathbf{A} \cdot 20 W \)
в. \( 1000 \mathrm{W} \)
c. \( 500 W \)
D. \( 0 W \)
Subject: Biology
Point out the correct floral formula of
cruciferae
\( \mathbf{A} \cdot K_{2+2} C_{4 x} A_{2+4} G_{(2)} \)
B . \( K_{5} C_{6} A_{3} G_{(2)} \)
C. \( K_{2+2} C_{4} A_{2+4} G_{(2)} \)
D. \( K_{4} C_{4} A_{2} G_{(2)} \)
Subject: Maths
A tree increases annually by one-fourth of its height. By how much will it increase after 2 years, if it stands today \( 64 \mathrm{cm} \) high?
A. \( 76 \mathrm{cm} \)
B. 80 cm
\( c .100 \mathrm{cm} \)
D. \( 105 \mathrm{cm} \)
Subject: Maths
If \( \sin y=x \sin (a+y), \) then show that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\sin ^{2}(\boldsymbol{a}+\boldsymbol{y})}{\sin \boldsymbol{a}} \)
Subject: Maths
\( \mathbf{A}=\left[\begin{array}{ccc}-\boldsymbol{q} \boldsymbol{r} & \boldsymbol{p}(\boldsymbol{q}+\boldsymbol{r}) & \boldsymbol{p} \boldsymbol{r}+\boldsymbol{p} \boldsymbol{q} \\ \boldsymbol{p} \boldsymbol{q}+\boldsymbol{q} \boldsymbol{r} & -\boldsymbol{p} \boldsymbol{r} & \boldsymbol{p} \boldsymbol{q}+\boldsymbol{q} \boldsymbol{r} \\ \boldsymbol{q} \boldsymbol{r}+\boldsymbol{p} \boldsymbol{r} & \boldsymbol{q} \boldsymbol{r}+\boldsymbol{p} \boldsymbol{r} & \boldsymbol{-} \boldsymbol{p} \boldsymbol{q}\end{array}\right] \)
then \( |\boldsymbol{A}| \) equals:
\( ^{A} \cdot\left(\sum p q\right)^{2} \)
\( ^{\mathrm{B}}\left(\sum p^{2} q^{2}\right)^{2} \)
\( c \cdot\left[\sum(q r)^{3}\right. \)
\( ^{\mathrm{D}} \cdot\left(\sum p q\right)^{\frac{3}{2}} \)
Subject: Physics
Two non-conducting solid spheres of radii R and 2R, having uniform volume
charge densities \( \rho_{1} \) and \( \rho_{2} \) respectively, touch each other. The net electric field
at a distance \( 2 \mathrm{R} \) from the centre of the
smaller sphere, along the line joining the centre of the spheres is zero. The
ratio \( \rho_{1} / \rho_{2} \) can be:
This question has multiple correct options
\( A \cdot-4 \)
B. \( -\frac{32}{25} \)
c. \( \frac{32}{25} \)
D. 4
Subject: Physics
A slit of width a is illuminated by white light. The first minimum for red light \( (\lambda=6500 A) \) will fall at \( \theta=30 \) when
a will be:
A \( \cdot 3200 \)
В. \( 6.5 \times 10^{-4} \mathrm{mm} \)
c. 1.3 micron
D. \( 2.6 \times 10^{-4} \mathrm{cm} \)
Subject: Physics
Slit 1 of Young's double-slit experiment is wider than slit \( 2, \) so that the light
from slits are given as \( A_{1}=A_{0} \sin \omega t \) and \( A_{2}=A_{0} \sin \left(\omega t+\frac{\pi}{3}\right) . \) The
resultant amplitude and intensity, at a point where the path difference between them is zero, are \( A \) and \( I \) respectively.
Then
This question has multiple correct options
A \( \cdot A=\sqrt{3} A_{0} \)
B \( \cdot A=4 A_{0} \)
\( \mathbf{c} \cdot I \propto 16 A_{0}^{2} \)
D. \( I \propto 3 A_{0}^{2} \)
Subject: Chemistry
The pressure of a monoatomic gas increases linearly from \( 4 \times \) \( 10^{5} N m^{-2} t o 8 \times 10^{-5} N m^{-2} \) when its
volume increases from \( 0.2 m^{3} \) to \( 0.5 m^{3} \)
calculate (a) work done by the gas, (b) increase in internal energy (c) mass of heat supplied and (d) molar heat
capacity of the gas.
Subject: Physics
A particular rocket is propelled such that its velocity increases as a function of time according to \( v(t)=A t^{\frac{1}{2}}, \) where
\( A \) is a constant.
Which of the following represents the correct acceleration function?
A \( \cdot a(t)=\frac{2}{3} A t^{3 / 2} \)
B \( \cdot a(t)=2 A t^{3 / 2} \)
c. \( a(t)=\frac{1}{2} A t^{-1 / 2} \)
D. \( a(t)=\frac{-1}{2} A t^{-1 / 2} \)
E. None of the above
Subject: Maths
Parveen wanted to make a temporary shelter for her car, by making box-like structure with tarpoulin that covers all
the four sides and the top of the car (With the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height \( 2.5 m \), with base
dimensions \( 4 m \times 3 m ? \)
Subject: Chemistry
The formula of prussian blue is:
\( \mathbf{A} \cdot N a_{4}\left[F e(C N)_{6}\right] \)
В. \( \operatorname{Fe}(C N)_{2} \)
c. \( \operatorname{Fe}(C N S)_{3} \)
D. \( F e_{4}\left[F e(C N)_{6}\right]_{3} \)
Subject: Physics
A particle of mass \( 0.1 k g \) executes \( S H M \)
under a force \( \boldsymbol{F}=(-10 x) N . \) Speed of
particle at mean position is \( 6 m / s \). Then amplitude of oscillations is
A. \( 0.6 m \)
B. \( 0.2 m \)
\( c \cdot 0.4 m \)
D. \( 0.1 m \)
Subject: Chemistry
The rate of a reaction increases four
fold when the concentration of reactant
is increased 16 times. If the rate of
reaction is \( 4 \times 10^{-6} \) mol \( L^{-1} s^{-1} \) when
the concentration of the reactant is
\( 4 \times 10^{-4} \) mol \( L^{-1} . \) The rate constant of
the reaction will be:
B. \( 1 \times 10^{-2} \mathrm{s}^{-1} \)
C . \( 2 \times 10^{-4} \mathrm{mol}^{-1 / 2} \mathrm{L}^{1 / 2} \mathrm{s}^{-1} \)
D. 25 mol-1 L min \( ^{-1} \)
Subject: Chemistry
An element has an atomic number 20 .
How many electrons will be present in \( \boldsymbol{K}, \boldsymbol{L}, \boldsymbol{M} \) and \( \boldsymbol{N} \) shells of its atom?
A .2,8,6,4
в. 2,8,7,3
c. 3,7,7,3
D. 2,8,8,
Subject: Biology
A possible explanation for a smoker cough that develops when the tracheal epithelium changes from pseudostratified columnar to stratified
squamous is that
A. This change is accompanied by tumours that irritate the upper respiratory tractt
B. Stratified squamous epithelium secretes more mucin than pseudostratified columnar.
C. The stratified squamous epithelium has no cilia to remove accumulating mucus
D. The two events are unrelated