AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( A \) tower of \( x \) meters high has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant
\( y \) meters from the foot of the tower then
the length of the flagstaff in meters is
A \( \frac{y\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}} \)
B. \( \frac{x\left(y^{2}+x^{2}\right)}{y^{2}-x^{2}} \)
c. \( \frac{x\left(x^{2}+y^{2}\right)}{x^{2}-y^{2}} \)
D. \( \frac{x\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}} \)
Subject: Biology
Choose the correct statements from the
options below with regard to sexual
reproduction
(i) Sexual reproduction does not always require two individuals.
(ii) Sexual reproduction generally involves gametic fusion.
(iii) Meiosis never occurs during sexual reproduction.
(iv) External fertilization is a rule
during sexual reproduction.
\( A \cdot \) (i) and (iv)
B. (i) and (ii)
c. (ii) and (iii)
D. (ii) and (iv)
Subject: Maths
\( 20 \% \) of a mans salary is paid as rent, 60 \( \% \) are his living expenses and \( 10 \% \) is paid in LIC. If he spends the remaining
Rs. 3,000 on education of the children, his salary is
A. \( R s .9,000 \)
B. \( R s .90,000 \)
c. \( R s .35 .000 \)
D. Rs.30, 000
Subject: Physics
A particle makes a to and from motion
between two points \( A \) and \( B . \) On its onward path (from A to B), it moves with
a constant velocity \( \boldsymbol{v}=\mathbf{5} \mathrm{m} / \mathrm{s}, \) while in
its return path, it moves with a constant
acceleration of \( a=v t . \) The particle
comes to rest at the extremes. Can this
motion be termed as SHM
A. SHM from A to B
B. SHM from B to A
C. SHM is not performed in any direction by the particle
D. SHM is performed in both the directions
Subject: Physics
The expression for the determination of Poisson's ratio for rubber is
A \( \cdot \sigma=\frac{1}{2}\left[1-\frac{d V}{A d L}\right] \)
в. \( \sigma=\frac{1}{2}\left[1+\frac{d V}{A d L}\right] \)
c. \( _{\sigma}=\frac{1}{2} \frac{d V}{A d L} \)
D. \( \sigma=\frac{d V}{A d L} \)
Subject: Physics
fall the masses in the figure have a
mass of \( 2 k g \) and \( m_{2} \) has speed \( 2 m / s \)
and \( m_{3} \) has a speed of \( 4 m / s, \) what is
the \( x \) -component of the momentum of
the centre of mass of system?
A. 2 kg \( m / s \)
B. 4 kg \( m / s \)
c. \( 6 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. \( 10 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
Subject: Physics
A parallel plate capacitor with plates separated by air acquires \( 1 \mu \mathrm{C} \) of charge
when connected to a battery of \( 500 \mathrm{V} \). The
plates still connected to the battery are then immersed in benzene \( (k=2.25) \)
Then a charge flows from the battery is :
A. \( 1.25 \mu \) С
B. \( 2.28 \mu \) С
c. \( 1 / 4 \mu \) с
D. \( 4.56 \mu \) С
Subject: Physics
A capillary tube of radius \( r \) is immersed in water and water rises in it to a height
h. Mass of water in the capillary tube is
m. If the radius of the tube is doubled,
mass of water that will rise in the
capillary tube will now be
A .
B. \( 2 m \)
\( c \cdot \frac{m}{2} \)
D. \( 4 m \)
Subject: Physics
A wire loop that encloses an area of \( 20 \mathrm{cm}^{2} \) has a resistance of \( 10 \Omega \). The
loop is placed in a magnetic field of \( 2.4 T \) with its plane perpendicular to the field. The loop is suddenly removed from
the field. How much charge flows past a given point in the wire?
\( \mathbf{A} \cdot 12 \times 10^{-4} C \)
B. \( 10^{-1} C \)
c. \( 4.8 \times 10^{-4} C \)
D. \( 2.4 \times 10^{-3} C \)
Subject: Maths
Find the unknown value \( \boldsymbol{x}: \frac{\mathbf{5}}{\mathbf{1 3}}+\boldsymbol{x}= \)
\( \frac{5}{13} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( \frac{5}{13} \)
D. \( \frac{2}{13} \)
Subject: Maths
\( f S_{n} \) denotes the sum of \( n \) terms of an
AP whose common differences is \( d \)
show that \( \boldsymbol{d}=\boldsymbol{S}_{\boldsymbol{n}}-\boldsymbol{2} \boldsymbol{S}_{\boldsymbol{n}-1}+\boldsymbol{S}_{\boldsymbol{n}-\boldsymbol{2}} \)
Subject: Physics
Point charges \( q_{1} \) and \( q_{2} \) lie on the \( x- \)
axis at points \( \boldsymbol{x}=-\boldsymbol{a} \) and \( \boldsymbol{x}=+\boldsymbol{a} \)
respectively. Given the net electrostatic force on point charge \( +\boldsymbol{Q} \) placed at \( \boldsymbol{x}= \)
\( +a / 2 \) to be zero and \( q_{1}=n q_{2} . \) Find \( n \)
Subject: Chemistry
\( \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{S}+\mathbf{2} \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{O} \rightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{u}+\boldsymbol{S} \boldsymbol{O}_{2} \)
In which process of metallurgy of copper, above equation is involved -
A. roasting
B. self reduction
c. refining
D. purification
Subject: Physics
A rod lies across frictionless rails in
uniform magnetic field \( \vec{B} \) as shown in Fig. The rod moves to the right with
speed \( V . \) In order to make the induced
emf in the circuit to be zero, the
magnitude of the magnetic field should.
\begin{tabular}{|l|l|}
\hline & \\
\hline(8) & 8 \\
\hline & \( \bigotimes \) \\
\hline \\
\hline
\end{tabular}
Subject: Physics
n a thin spherical fish bowl of radius
\( 10 \mathrm{cm} \) filled with water of refractive
ndex \( \frac{4}{3}, \) there is a fish at a distance of
\( 4 \mathrm{cm} \) there is a small fish at a distance
of \( 4 \mathrm{cm} \) form the center \( C \) as shown. The
mage of the fish appears, when seen
from the point \( D \) would be
\( A \cdot 5.2 \mathrm{cm} \)
в. 4.8 ст
\( c .2 .6 \mathrm{cm} \)
\( 0.7 .4 \mathrm{cm} \)
Subject: Maths
The marks scored by students in Mathematics in a certain examination
are given below:
\( \begin{array}{lll}\text { Marks Scored } & \text { Number of Students } \\ 0-20 & 3 \\ 20-40 & 8 \\ 40-60 & 15 \\ 60-80 & 17 \\ 80-100 & 7\end{array} \) Draw histogram for the above data.
Subject: Chemistry
\( \begin{array}{cc}\boldsymbol{C H}_{\mathbf{3}}-\underset{\mathbf{O}}{\mathbf{C}} \boldsymbol{H}- & \boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \\ & \boldsymbol{O} \boldsymbol{H}\end{array} \)
IUPAC name of the given compound is :
A. Butane-2,3-diol
B. 1-Methy|-propane-1,2-diol
c. Both (A) and (B)
D. None of these
Subject: Maths
There are two urns. There are \( m \) white \( \& \)
\( \boldsymbol{n} \) black balls in the first urn and \( \boldsymbol{p} \) white
\& \( q \) black balls in the second urn. One
ball is taken from the first urn \& placed
into the second. Now, the probability of drawing a white ball from the second
urn is
A \( \cdot \frac{p m+(p+1) n}{(m+n)(p+q+1)} \)
B. \( \frac{(p+1) m+p n}{(m+n)(p+q+1)} \)
c. \( \frac{q m+(q+1) n}{(m+n)(p+q+1)} \)
D. \( \frac{(q+1) m+q n}{(m+n)(p+q+1)} \)
Subject: Physics
A diverging lens of focal length \( 10 \mathrm{cm} \) is placed \( 10 \mathrm{cm} \) in front of a plane mirror
as shown in the figure. Light from a very far away source falls on the lens. The final image is at a distance?
A. \( 20 \mathrm{cm} \) behind the mirror
B. \( 7.5 \mathrm{cm} \) in front of the mirror
c. \( 7.5 \mathrm{cm} \) behind the mirror
D. \( 2.5 \mathrm{cm} \) in front of the mirro
Subject: Maths
If \( y=\left(\cos ^{-1} x\right)^{2}, \) prove that \( (1- \)
\( \left.x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-2=0 . \) Hence find \( y_{2} \)
when \( \boldsymbol{x}=\mathbf{0} \)
Subject: Chemistry
\( 2 S O_{2}(g)+O_{2}(g) \leftrightharpoons 2 S O_{3}(g) \)
Given that the equilirbium constant for
the reaction above has a value of 278 at
a particular temperature, what is the value of equilibrium constant for the following reaction at same temperature?
\( \boldsymbol{S O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
A \( \cdot 1.3 \times 10^{-5} \)
B . \( 1.8 \times 10^{-3} \)
c. \( 3.6 \times 10^{-3} \)
D. \( 6 \times 10^{-2} \)
Subject: Chemistry
Which of the following represent redox reactions?
\( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+2^{\ominus} \boldsymbol{O} \boldsymbol{H} \longrightarrow 2 \boldsymbol{C r} \boldsymbol{O}_{4}^{2-}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
II. \( Z n+C u S O_{4} \longrightarrow Z n S O_{4}+C u \)
III. \( 2 M n O_{4}^{\ominus}+3 M n^{2+}+4 \stackrel{\theta}{O} H \longrightarrow \)
\( \mathbf{5} M n O_{2}+2 H_{2} O \)
IV. \( 2 C u^{\oplus} \longrightarrow C u+C u^{2+} \)
A . ।, । ।
в. ।, ॥
c. ॥ा, ।ा
D. ॥, ॥I, IV
Subject: Chemistry
Which of the following statement is true
statement?
A. Aldehydes and ketones have lower boiling points than alcohols and carboxylic acids of comparable molecular masses.
B. Aldehydes and ketones have higher boiling points than alcohols and carboxylic acids of comparable molecular masses.
C. Aldehydes and ketones have lower boiling points than alcohols but higher boiling points than carboxylic acids of comparable molecular masses.
D. Aldehydes and ketones have higher boiling points than alcohols but lower boiling points than carboxylic acids of comparable molecular masses.
Subject: Maths
f \( \triangle A B C \sim \triangle A D E \) and ar \( (\triangle A D E)= \)
\( 9 \operatorname{ar}(\triangle A B C) \) then \( \frac{B C}{D E} \) is equal to
\( A \)
B. 1
\( c \cdot \frac{3}{4} \)
D. None of these
Subject: Maths
Assertion
Let \( f: R \rightarrow R \) be defined as \( f(x)= \)
\( a x^{2}+b x+c, \) where \( a, b, c \varepsilon R \) and \( a \neq \)
0
If \( f(x)=0 \) is having non-real roots, then \( \int \frac{d x}{f(x)}=\lambda \tan ^{-1}(g(x))+k \)
where \( \lambda, k \) are constants and \( g(x) \) is
linear function of \( x \)
Reason
\( \tan \left(\tan ^{-1} g(x)\right)=g(x) \forall x \in R \)
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: Maths
A bag contains \( 100 A \times 4 \) sheets. The
weight of an \( A \times 4 . \) Sheet is \( 0.01 m g \) and weight of empty bag is \( 6.00 g m \)
Find weight of bag alone with all \( \boldsymbol{A} \times \mathbf{4} \)
sheets.
Subject: Maths
Equation of straight line \( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c}= \)
\( 0, \) where \( 3 a+4 b+c=0, \) which is at
maximum distance from \( (1,-2), \) is
A. \( 3 x+y-17=0 \)
B. \( 4 x+3 y-24=0 \)
c. \( 3 x+4 y-25=0 \)
D. \( x+3 y-15=0 \)
Subject: Chemistry
Lead nitrate on strong heating gives:
A. PbO, \( \mathrm{NO}_{2}, \mathrm{O}_{2} \)
в. \( \mathrm{PbO}_{2}, \mathrm{PbO}, \mathrm{NO}_{2} \)
\( \mathrm{c} \cdot \mathrm{PbO}, \mathrm{NO}, \mathrm{O}_{2} \)
D. \( \mathrm{PbO}, \mathrm{NO}, \mathrm{NO}_{2} \)
Subject: Chemistry
Resistance of \( 0.2 M \) solution of an
electrolyte is \( 50 \Omega \). The specific
conductance of the solution is \( 1.4 S \)
\( m^{-1} . \) The resistance of \( 0.5 M \) solution
of the same electrolyte is \( 280 \Omega \). The molar conductivity of \( 0.5 ~ M \) solution of
the electrolyte in \( S m^{2} m o l^{-1} \) is:
A \( .5 \times 10^{3} \)
В . \( 5 \times 10^{2} \)
c. \( 5 \times 10^{-4} \)
D. \( 5 \times 10^{-3} \)
Subject: Physics
A microscope consists of an objective with a focal length \( 2 \mathrm{mm} \) and an eye piece with a focal length \( 40 \mathrm{mm} \). The distance between the foci (which are between the lenses) of objective and eyepiece is \( 18 \mathrm{cm} . \) The total
magnification of the microscope is (Consider normal adjustment and take \( \mathrm{D}=25 \mathrm{cm} \)
A . 562.5
B. 625
c. 265
D. 62.5
Subject: Maths
If \( l_{1}, m_{1}, n_{1} \) and \( l_{2}, m_{2}, n_{2} \) are DCs of the two lines inclined to each other at an
angle \( \theta \), then the DCs of the internal bisector of the angle between these lines are
A \( \cdot \frac{l_{1}+l_{2}}{2 \sin \frac{\theta}{2}}, \frac{m_{1}+m_{2}}{2 \sin \frac{\theta}{2}}, \frac{n_{1}+n_{2}}{2 \sin \frac{\theta}{2}} \)
в. \( \frac{l_{1}+l_{2}}{2 \cos \frac{\theta}{2}}, \frac{m_{1}+m_{2}}{2 \cos \frac{\theta}{2}}, \frac{n_{1}+n_{2}}{2 \cos \frac{\theta}{2}} \)
c. \( \frac{l_{1}-l_{2}}{2 \sin \frac{\theta}{2}}, \frac{m_{1}-m_{2}}{2 \sin \frac{\theta}{2}}, \frac{n_{1}-n_{2}}{2 \sin \frac{\theta}{2}} \)
D. \( \frac{l_{1}-l_{2}}{2 \cos \frac{\theta}{2}}, \frac{m_{1}-m_{2}}{2 \cos \frac{\theta}{2}}, \frac{n_{1}-n_{2}}{2 \cos \frac{\theta}{2}} \)
Subject: Chemistry
During electrolysis of \( 1 \mathrm{L}, 1 \mathrm{M} \) AgNO \( _{3} \) using silver electrodes, 9.65 A current is used for one hour. Assuming the volume to remain unchanged, the molarity of
\( A g N O_{3} \) at the end of the electrolytic
process is :
A. 1 м
B. 0.36 м
c. 0.64 М
D. None of these
Subject: Maths
Show that \( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c}\end{array}\right|= \)
\( \boldsymbol{a}^{3}+\boldsymbol{b}^{3}+\boldsymbol{c}^{3}-\boldsymbol{3} \boldsymbol{a} \boldsymbol{b} \boldsymbol{c} \)
Subject: Chemistry
On the basis of the following thermochemical data
\( \boldsymbol{H}_{2} \boldsymbol{O}_{(\boldsymbol{g})} \longrightarrow \boldsymbol{H}_{(a q)}^{+}+\boldsymbol{O} \boldsymbol{H}_{(a q)}^{-} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( \mathbf{5 7 . 3 2 k J} \)
\( \boldsymbol{H}_{2(g)}+\frac{1}{2} \boldsymbol{O}_{2(g)} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -286.2 k J \)
The value of enthalpy of formation of
\( O H^{-} \) ion at \( 25^{\circ} C \) is:
\( \mathbf{A} \cdot+288.88 k J \)
в. \( -343.52 k J \)
c. \( -22.88 k J \)
D. \( -228.88 k J \)
Subject: Chemistry
(i) What type of isomerism is shown by
the complex \( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3} ? \)
(ii) On the basis of crystal field theory, write the electronic configuration for \( 4 d \)
ion if \( \Delta_{0}>P \)
(iii) Write the hybridization and shape of \( \left[\boldsymbol{C o F}_{6}\right]^{3-} \) (Atomic number of \( \mathrm{Co}=27 \) ).
Subject: Chemistry
Instantaneous rate of reaction for the
reaction \( 3 A+2 B \rightarrow 5 C \) is
A \( \cdot+\frac{1}{3} \frac{d[A]}{d t}=-\frac{1}{2} \frac{d[B]}{d t}=+\frac{1}{5} \frac{d[C]}{d t} \)
B. \( -\frac{1}{3} \frac{d[A]}{d t}=-\frac{1}{2} \frac{d[B]}{d t}=+\frac{1}{5} \frac{d[C]}{d t} \)
C \( \cdot-\frac{1}{3} \frac{d[A]}{d t}=+\frac{1}{2} \frac{d[B]}{d t}=-\frac{1}{5} \frac{d[C]}{d t} \)
D. \( +\frac{1}{3} \frac{d[A]}{d t}=-\frac{1}{2} \frac{d[B]}{d t}=-\frac{1}{5} \frac{d[C]}{d t} \)
Subject: Chemistry
For which of the following reactions
\( k_{310} / k_{300} \) would be maximum?
A \( \cdot A+B \rightarrow C ; E_{a}=50 k J \)
в. \( X+Y \rightarrow Z ; E_{a}=40 k J \)
c. \( P+Q \rightarrow R ; E_{a}=60 k J \)
D. \( E+F \rightarrow G ; E_{a}=100 k J \)
Subject: Physics
A body weighs \( 900 \mathrm{N} \) on the earth. Find its weight on a planet whose density is \( \mathbf{1}^{s} \)
\( \frac{1}{3} \) the density of earth and radius is 1
\( t h \)
\( \frac{1}{4} \) that of the earth.
A . \( 75 \mathrm{N} \)
в. 500 N
c. 62 N
D. 320N
Subject: Maths
Let \( n \) and \( r \) be two positive integers such that \( n \geq r+2 . \) Suppose \( \Delta(n, r)= \)
\( \left|\begin{array}{ccc}n & C_{r} & ^{n} C_{r+1} & ^{n} C_{r+2} \\ ^{n+1} C_{r} & ^{n+1} C_{r+1} & ^{n+1} C_{r+2} \\ ^{n+2} C_{r} & ^{n+2} C_{r+1} & ^{n+2} C_{r+2}\end{array}\right| \) Show that
\( \Delta(n, r)=\frac{n+2}{n+2} C_{3} \Delta(n-2, r-1) \) Hence
or otherwise,
A \( \cdot \frac{\left(^{n+2} C_{3}\right)\left(^{n+1} C_{3}\right) \ldots . .\left(^{n-r+3} C_{3}\right)}{\left.\left(r+2 C_{3}\right)\left(r+1 C_{3}\right) \ldots . .^{3} C_{3}\right)} \)
B. \( -\frac{\left(^{n+2} C_{3}\right)\left(^{n+1} C_{3}\right) \ldots . .\left(^{n-r+3} C_{3}\right)}{\left(r+2 C_{3}\right)\left(^{r+1} C_{3}\right) \ldots\left(^{3} C_{3}\right)} \)
c. \( \frac{(n+3}{(r+3)}(\sqrt[n+2]{(r+2)}) \ldots . .\left(^{n-r+3} C_{3}\right) \)
D. \( -\frac{\left.\left(^{n+3} C_{3}\right)(n+2)_{3}\right) \ldots . .\left(^{n-r+3} C_{3}\right)}{\left(r+3 C_{3}\right)\left(r+2 C_{3}\right) \ldots\left(^{3} C_{3}\right)} \)
Subject: Maths
Of a certain sum, \( \frac{1}{3} r d \) is invested at \( 3 \%, \frac{1}{6} t h \) at \( 6 \% \) and the rest at \( 8 \% \). If the
81 for 2 years from all these
investments amounts to Rs. 600. Then
the original sum was
A. Rs. 2000
B. Rs. 3000
c. Rs. 4000
D. Rs. 5000
Subject: Physics
An electron collides with a free
molecule initially in its ground state. The collision leaves the molecule in an
excited state that is metastable and
does not decay to the ground state by radiation. Let \( K \) be the sum of the
initial kinetic energies of the electron and the molecule, the \( \vec{P} \) the sum of their initial momenta. Let \( K^{\prime} \) and \( \vec{P} \)
represent the same physical quantities after the collision. Then.
\( \mathbf{A} \cdot K=K^{\prime}, \vec{P}=\vec{P} \)
B . \( K^{\prime}<K, \vec{P}=\vec{P}^{\prime} \)
C . \( K=K^{\prime}, \vec{P} \neq \vec{P}^{\prime} \)
D . \( K^{\prime} \neq K, \vec{P} \neq \vec{P}^{\prime} \)
Subject: Chemistry
Reactivity order for SN1
(i) \( C H_{3}-\underset{C l}{C} H-C H_{2}-C H_{3} \)
(ii) \( \boldsymbol{P h}-\boldsymbol{C H}_{3}-\underset{C l}{\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}_{3}} \)
(iii) \( C H_{3}-\quad \begin{array}{c}C l \\ \ \\ 0 \\ 0 C H_{3}\end{array}-C H_{3} \)
(iv) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \)
A. \( i>i i>i i i>i v \)
в. \( i i>i> \) ii \( i>i v \)
c. \( i i>i i>i>i v \)
D . \( i v>i i i>i i>i \)
Subject: Chemistry
Calculate the order of reaction from the
following data:
\[
\begin{array}{l}
\qquad \mathbf{2} N \boldsymbol{H}_{3} \rightarrow \boldsymbol{N}_{2}+\mathbf{3} \boldsymbol{H}_{2} \text { (reaction) } \\
\text { Pressure }(\mathbf{m m} \mathrm{Hg}) \quad \mathbf{5 0} \quad 100 \quad 200 \\
\text { Half lives }(\min ) \quad \text { 3.52 } \quad 1.82 \quad 0.93
\end{array}
\]
Subject: Physics
Read the given statements and mark
the correct option
Statement 1: If an earth satellite is on a
lower orbit, the speed of satellite increases
Statement 2: The speed of satelite is a constant quantity for all orbits of earth
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. both statements 1 and 2 are true but statement 2 is not correct explanation of statement
c. statement 1 is true but statement 2 is false
D. Both statements 1 and 2 are false
Subject: Maths
The principal value of \( \tan ^{-1}\left(\cot \frac{43 \pi}{4}\right) \) is
A \( \cdot-\frac{3 \pi}{4} \)
B. \( \frac{3 \pi}{4} \)
\( c \cdot-\frac{\pi}{4} \)
\( D \cdot \frac{\pi}{4} \)
Subject: Physics
The force 'F' acting on a particle of mass \( \mathrm{m}^{\prime} \) is indicated by the force-time graph shown below. The change in momentum
of the particle over the time interval
from zero to 8 s is
A. 24 Ns
B. 20 Ns
\( c \cdot 12 \mathrm{Ns} \)
\( D \cdot 6 \mathrm{Ns} \)
Subject: Chemistry
The geometry and hybridisation of \( \boldsymbol{X} \boldsymbol{e} \)
in \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) is:
A . see-saw, \( s p^{3} d \)
B. octahedral, \( s p^{3} d^{2} \)
C. planar, \( s p^{3} d^{2} \)
D. T-shaped, \( s p^{3} d^{3} \)
Subject: Maths
Differentiate the following function with
respect to \( x \)
\( \boldsymbol{x}^{5}\left(\boldsymbol{3}-\boldsymbol{6} \boldsymbol{x}^{-\boldsymbol{9}}\right) \)
A. \( 15 x^{-4}+24 x^{-5} \)
B \( \cdot 15 x^{5}+24 x^{-5} \)
\( \mathbf{c} \cdot 15 x^{4}+24 x^{-4} \)
D. \( 15 x^{4}+24 x^{-5} \)
Subject: Maths
What is the result when you add the \( \operatorname{matrix}\left[\begin{array}{ll}\mathbf{4} & \mathbf{5}\end{array}\right] \) to the matrix \( \left[\begin{array}{ll}\mathbf{7} & -\mathbf{3}\end{array}\right] \)
and multiply the result by \( 2 ? \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}2 & 6\end{array}\right] \)
в. \( \left[\begin{array}{ll}11 & 2\end{array}\right] \)
c. \( \left[\begin{array}{ll}22 & 4\end{array}\right] \)
D. \( [28 \quad-15] \)
E . \( \left[\begin{array}{ll}54 & -30\end{array}\right] \)
Subject: Physics
A small linear object of length \( b \) is
placed at a distance \( u \) from the pole of the concave mirror along the axis away from the mirror. The focal length of the mirror is \( f . \) The length of image will
then be?
A \( \cdot \quad b\left(\frac{f}{u-f}\right)^{2}\left(\frac{f}{u-f+b}\right)^{2} \)
в. \( \quad b\left(\frac{f}{u-f}\right)^{2}\left(\frac{f}{u-f+b}\right) \)
c. \( b\left(\frac{f}{u-f}\right)\left(\frac{f}{u-f+b}\right)^{2} \)
D. \( b\left(\frac{f}{u-f}\right)\left(\frac{f}{u-f+b}\right) \)
Subject: Maths
ff \( P(x, y) \) is equidistant from \( A(a+ \) \( \boldsymbol{b}, \boldsymbol{b}-\boldsymbol{a}) \) and \( \boldsymbol{B}(\boldsymbol{a}-\boldsymbol{b}, \boldsymbol{a}+\boldsymbol{b}), \) show that
\( \boldsymbol{b} \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y} \)
Subject: Maths
\( \mathbf{A B A}^{-1}=\mathbf{X} \) then \( \mathbf{B}^{\mathbf{2}}= \)
A \( \cdot x^{2} \)
B. AxA \( ^{-1} \)
c. \( A x^{2} A^{-1} \)
D. \( A^{-1} x^{2} A \)
Subject: Maths
When the determinant \( \left|\begin{array}{lll}\cos 2 x & \sin ^{2} x & \cos 4 x \\ \sin ^{2} x & \cos 2 x & \cos ^{2} x \\ \cos 4 x & \cos ^{2} x & \cos 2 x\end{array}\right| \) is expanded in
powers of \( \sin x, \) then the constant term in that expression is
\( A \)
B.
\( c \cdot-1 \)
D.
Subject: Physics
A particle of mass \( m_{1} \) collides elastically with a stationary particle of
\( \operatorname{mass} \boldsymbol{m}_{2}\left(\boldsymbol{m}_{1}>\boldsymbol{m}_{2}\right) . \) The maximum
angle through which the striking particle may deviate as a result of the collision is given as \( \sin \theta_{1 \max }=\frac{x m_{2}}{m_{1}} \)
Find \( \boldsymbol{x} \)
Subject: Physics
The energy equivalent to a substance of
mass \( 1 \mathrm{g} \) is?
A \( \cdot 18 \times 10^{13} \) 」
В. \( 9 \times 10^{13} \) j
C \( .18 \times 10^{6} \mathrm{J} \)
D. \( 9 \times 10^{6} \),
Subject: Maths
STATEMENT - 1: If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.

STATEMENT - 2 : If in two triangles,
corresponding angles are equal, then their corresponding sides are in the
same ratio and hence the two triangles
are similar.
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement -
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: Chemistry
Two metals \( X \) and \( Y \) have 3 and 2
electrons in their valence shells \( ^{\prime} M^{\prime} \)
and ' \( N^{\prime} \) respectively. These metals can
form binary compounds \( A \) and \( B \) with the same non-metal carbon. Both \( A \) and
\( B \) can undergo hydrolysis forming
hydrocarbons \( C \) and \( D \). Identify \( C \) and
\( D \)
A. \( C_{6} H_{6}, C_{3} H_{4} \)
в. \( C_{3} H_{6}, C_{3} H_{4} \)
c. \( C H_{4}, C_{2} H_{2} \)
D. \( C_{4} H_{10}, C_{3} H_{6} \)
Subject: Chemistry
The standard molar heats of formation
of ethane, \( C O_{2} \) and \( H_{2} O(l) \) are
respectively -21.1,-94,1 and \( -68.3 k c a l . \) The standard molar heat of
combustion of ethane will be:
A. \( -372 k c a l \)
В. \( -240 k c a l \)
c. \( 162 k c a l \)
D. \( 183.5 k c a l \)
Subject: Chemistry
What is the electron configuration of
\( \boldsymbol{V}^{2+} ? \)
\( \mathbf{A} \cdot[A r] 4 s^{2} 3 d^{3} \)
B . \( [A r] 4 s^{1} 3 d^{4} \)
\( \mathbf{c} \cdot[A r] 3 d^{3} \)
D \( \cdot[A r] 4 s^{2} 3 d^{1} \)
Subject: Chemistry
For a given reaction of first order, it takes 20 minutes for the concentration
to drop from \( 1.0 \mathrm{M} \) to \( 0.6 \mathrm{M} \). The time
required for the concentration to drop from \( 0.6 ~ M \) to \( 0.36 M \) will be:
A. more than 20 minutes
B. less than 20 minutes
c. equal to 20 minutes
D. infinite time
Subject: Chemistry
In which of the following compounds the carbon marked with asterisk is most
electronegative?
\( \mathbf{A} \cdot C H_{3}-C H_{2}-\dot{C} H_{2}-C H_{3} \)
в. \( C H_{3}-\dot{C H}=C H-C H_{3} \)
c. \( C H_{3}-C H_{2}-C \equiv \dot{C} H \)
D. \( C H_{3}-C H_{2}-C H=\dot{C} H_{2} \)