AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \int x \sqrt{\frac{a^{2}-x^{2}}{a^{2}+x^{2}}} d x \) is equal to
A \( \cdot \frac{a^{2}}{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}-x^{4}}+C \)
B \( \cdot \frac{a^{2}}{2} \tan ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}-x^{4}}+C \)
C \( \cdot \frac{a^{2}}{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{3}{2} \sqrt{a^{2}-x^{2}}+C \)
D \( \frac{a^{2}}{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{2}-x^{2}}+C \)
Subject: Biology
Choose the correct combination
\begin{tabular}{cccc} 
Hormone & Source & Functic \\
A. & Vasopressin & Posterior pituitary & Increas of wate through \\
B. & Norepinephrine & Adrenal medulla & Increas heart be respirat and ale \\
C. & Glucagon & \( \beta \) -cells of islet of Langerhans & Stimula glycoge \\
D. & Prolactin & Posterior pituitary & Regulat growth mamm glands milk formati females \\
\hline
\end{tabular}
\( A \cdot A \)
\( B . \quad B \)
\( c \cdot c \)
D.
Subject: Chemistry
Select the correct order of bond angle.
This question has multiple correct options
\( \mathbf{A} \cdot O s F_{2}<O s C l_{2}<O s B r_{2} \)
B \( \cdot S b C l_{3}<S b B r_{3}<S b I_{3} \)
\( \mathbf{C} \cdot P I_{3}>A s I_{3}>S b I_{3} \)
\( \mathbf{D} \cdot P I_{3}<A s I_{3}<S b I_{3} \)
Subject: Physics
A circular copper disc \( 10 \mathrm{cm} \) in diameter rotates at 1800 revolution per minute about an axis through its centre and at right angles to disc. A uniform
field of induction \( B \) of 1 Wh \( m^{2} \) is
perpendicular to disc. What potential difference is developed between the axis of the disc and the rim?
A. 0.023 v v vas
B. 0.23
\( c \cdot 23 v \)
D. 230 V
Subject: Physics
The velocity of electromagnetic radiation in a medium of permittivity \( \varepsilon_{0} \)
and permeability \( \mu_{0} \) is given by :
A \( \cdot \sqrt{\frac{\varepsilon_{0}}{\mu_{0}}} \)
B . \( \sqrt{\mu_{0} \varepsilon_{0}} \)
c. \( \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} \)
D. \( \sqrt{\frac{\mu_{0}}{\varepsilon_{0}}} \)
Subject: Chemistry
How many electrons flow when a current
of 5 amperes is passed through a conductor for 200 seconds?
A \( \cdot 6.25 \times 10^{21} \)
B. \( 6.025 \times 10^{21} \)
c. \( 6.25 \times 10^{22} \)
D. \( 6.025 \times 10^{22} \)
Subject: Chemistry
\( \boldsymbol{C a} \boldsymbol{C}_{2} \frac{\boldsymbol{H y d r o l y s i s}}{\boldsymbol{A}} \boldsymbol{A} \frac{\boldsymbol{R e d} h_{o t}}{\boldsymbol{C u} \boldsymbol{t u b e}} \)
\( \frac{\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}-\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}}{\boldsymbol{5} \boldsymbol{0}-\boldsymbol{6} \boldsymbol{0}^{0} \boldsymbol{C}} \boldsymbol{C} \stackrel{\boldsymbol{F} \boldsymbol{e}+\boldsymbol{H} \boldsymbol{C l}}{\longrightarrow} \)
\( \boldsymbol{D} \stackrel{\boldsymbol{N a N O}_{2}+\boldsymbol{H C l}, \mathbf{0}^{0} \boldsymbol{C}}{\longrightarrow} \boldsymbol{E} \)
In the reaction sequence given above, \( \boldsymbol{E} \)
is:
A. aniline
B. benzene diazonium chloride
c. phenyl osazone
D. benzoyl chloride
Subject: Physics
Two stones are dropped from the top of a tower at half a second apart. The time after dropping the first stone at which
the distance between the two stones is
\( 20 \mathrm{m} \) is \( \left(g=10 m s^{-2}\right) \)
A \( .4 \mathrm{s} \)
B. 3.75 s
c. 4.25 s
D. 0.53 s
Subject: Chemistry
The energy required for the electron to jump from \( n=2 \) to \( n=3 \) will be:
\( \mathbf{A} \cdot 5 x k J \)
в. \( \frac{36 x}{5} k J \)
c. \( \frac{5 x}{36} k J \)
D. \( \frac{9 x}{4} k J \)
Subject: Maths
\( \boldsymbol{x}^{2}-(\boldsymbol{m}-\mathbf{3}) \boldsymbol{x}+\boldsymbol{m}=\mathbf{0}(\boldsymbol{m} \in \boldsymbol{R}) \) be a
quadratic equation. Find the value of \( \boldsymbol{m} \)
for which, both the roots lie in the
interval of (1,2)
A. \( (10, \infty) \)
)
в. \( (-\infty, 0) \)
\( c \cdot(-\infty, \infty) \)
D. None of the above
Subject: Physics
The de-Broglie wavelength of a proton \( \left(\text {mass}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}\right) \) accelerated
through a potential difference of \( 1 \mathrm{kV} \) is :
B . \( 0.9 \times 10^{-12} \mathrm{m} \)
\( c .7 \dot{h} \)
D. \( 0.9 \times 10^{-19} n m \)
Subject: Maths
\( \int \frac{x+1}{x\left(1+x e^{x}\right)} d x=0 \)
\( ^{\mathbf{A}} \cdot \log \left|\frac{1+x e^{x}}{x e^{x}}\right|+C \)
\( ^{\mathbf{B}} \cdot \log \left|\frac{x e^{x}}{1+x e^{x}}\right|+C \)
\( \mathbf{c} \cdot \log \left|x e^{x}\left(1+x e^{x}\right)\right|+C \)
\( \mathbf{D} \cdot \log \left(1+x e^{x}\right)+C \)
Subject: Chemistry
Assertion
The Daniell cell becomes dead after
some time.
Reason
Oxidation potential of zinc anode decreases and that of copper increases.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Four rays, 1,2,3 and 4 are incident normally on the face \( P Q \) of an isosceles
prism PQR with apex angles \( \angle Q=120^{\circ} \)
The refractive indices of the material of
the prism for the above rays 1,2,3 and 4 are 1.85,1.96,2.05 and \( 2.15, \) respectively and the surrounding medium is air. Then the rays emerging from the face QR are :
A. 4 only
B. 1 and 2 only
c. 3 and 4 only
D. 1,2,3 and 4
Subject: Physics
The dimensional formula for viscosity is
\( \left[M L^{-1} T^{-1}\right] . \) One poise, i.e, C.G.S. unit of viscosity is:
A \( \cdot 10^{-1} \) M.K.S.
B. \( 10^{0} \) M.K.S.
c. \( 10^{1} \) M.K.S.
D . \( 10^{-2} \) M.K.S
Subject: Maths
f \( \boldsymbol{f}:[\mathbf{0}, \boldsymbol{\pi}] \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=\cos \boldsymbol{x}, \) then \( \boldsymbol{f} \) is
A. one-one onto
B. one-one into
c. many-one onto
D. many-one into
Subject: Physics
In an oscillating \( L C \) circuit, the total
stores energy is \( U \) and the maximum
charge on the capacitor is \( Q . \) When the charge on the capacitor is \( Q / 2, \) the energy stored in the inductor is :
A. \( U / 2 \)
в. \( U / 4 \)
c. \( (4 / 3) U \)
D. \( 3 U / 4 \)
Subject: Chemistry
What is the electronic configuration for \( \operatorname{an} F e(I I I) \) ion in its ground state?
\( \mathbf{A} \cdot[A r] 3 d^{5} \)
B . \( [A r] 3 d^{6} \)
\( \mathbf{c} \cdot[A r] 4 s^{2} 3 d^{3} \)
D \( \cdot[A r] 4 s^{2} 3 d^{6} \)
Subject: Physics
A person trying to lose weight by burning fat lifts a mass of \( 10 k g \) upto a
height of \( 1 m 1000 \) times. Assume that
the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work dine only when the weight is lifted up? Fat supplies \( 3.8 \times 10^{7} J \) of energy
per kg which is converted to
mechanical energy with a \( 20 \% \) efficiency rate. Take \( g=9.8 m s^{-2} \)
A \( \cdot 6.45 \times 10^{-3} k g \)
в. \( 9.89 \times 10^{-3} k g \)
c. \( 12.89 \times 10^{-3} k g \)
D. 2.45 \( \times 10^{-3} k g \)
Subject: Physics
Q Type your question-
less than \( \mathbf{U}^{\mathbf{v}} \) ( . If the tnickness or the lce
layer formed on the surface grows from
\( 2 c m \) to \( 4 c m \) in 1 hour, the atmosphere temperature will be (Thermal
conductivity of ice, \( \boldsymbol{K}=\mathbf{4} \times \)
\( 10^{-3} \) cal \( c m^{-1} s^{-1 o} C^{-1}, \) density of ice
\( =0.9 g c c^{-1} . \) Latent heat of fusion of ice
\( =80 \mathrm{cal} g^{-1} \) Neglect the change of
density during the state change. Assume that the water below the ice
has \( 0^{\circ} \mathrm{C} \) temperature every where.)
Formed ice
\( --- \)
A. \( -20^{\circ} \mathrm{C} \)
B. \( 0^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot-30^{\circ} C \)
D. \( -15^{\circ} \mathrm{C} \)
Subject: Chemistry
Isomerisms exhibited by
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{2} \boldsymbol{C l}_{2}\right]^{+} \) are:
A. ionisation, optical
B. hydrate, optical
c. geometrical, optical
D. coordinate, geometrical
Subject: Physics
The wrong unit conversion among the
following is
\( \mathbf{A} \cdot 1 \) angstrom \( =10^{-10} m \)
B. 1 fermi \( =10^{-15} \mathrm{m} \)
C \( . \) 1 light year \( =9.46 \times 10^{15} \mathrm{m} \)
D. 1 astronomical unit \( =1.496 \times 10^{-11} \mathrm{m} \)
Subject: Chemistry
In a particular process, the concentration of a solution that is
initially 0.24 M is reduced to 0.12 M in 10 hr and \( 0.06 \mathrm{M} \) in \( 20 \mathrm{hr} \)
\( 6.93 \times 10^{-x} h r^{-1} \) is the rate constant
for the reaction?
value of \( x \) is
Subject: Physics
Potential energy function describing the interaction between two atoms of a
diatomic molecule is \( U(r)=\frac{a}{r^{12}}-\frac{b}{r^{6}} \)
Force acting between them will be zero
when the distance between them would
be
A
B. \( \quad\left(\frac{b}{2 a}\right)^{\frac{1}{6}} \)
\( \left(\frac{a}{b}\right)^{\frac{1}{6}} \)
D. \( \quad\left(\frac{b}{a}\right)^{\frac{1}{6}} \)
Subject: Physics
A particle executes S.H.M. of period
\( 6.28 s \) and amplitude \( 3 \mathrm{cm} . \) Its maximum acceleration is
A \( .2 .14 \mathrm{cm} / \mathrm{s}^{2} \)
в. 3 ст / \( s^{2} \)
c. \( 9.42 \mathrm{cm} / \mathrm{s}^{2} \)
D. \( 1.5 \mathrm{cm} / \mathrm{s}^{2} \)
Subject: Maths
Prove that \( \frac{\left(\boldsymbol{a}^{\boldsymbol{p}+\boldsymbol{q}}\right)^{2}\left(\boldsymbol{a}^{\boldsymbol{q}+\boldsymbol{r}}\right)^{2}\left(\boldsymbol{a}^{\boldsymbol{r}+\boldsymbol{p}}\right)^{\mathbf{2}}}{\left(\boldsymbol{a}^{\boldsymbol{p}} \cdot \boldsymbol{a}^{\boldsymbol{q}} \boldsymbol{a}^{\boldsymbol{r}}\right)^{\boldsymbol{4}}}=\mathbf{1} \)
Subject: Physics
Two cell of emf \( 6 V \) and \( 4 V \) having
internal resistance \( 3 \Omega \) and \( 2 \Omega \)
respectively are connected in parallel so
all to send a current through extend
resistance of \( 8 \Omega \) in the same direction.
Find the current through the cells and
the potential difference across \( 8 \Omega \)
Resistor.
Subject: Chemistry
Which of the following order of root
mean square speed of different gases
at the same temperature is true?
A \( \cdot\left(U_{r m s}\right)_{H_{2}}>\left(U_{r m s}\right)_{C H_{4}}>\left(U_{r m s}\right)_{N H_{3}}>\left(U_{r m s}\right)_{C O} \)
B . \( \left(U_{r m s}\right)_{H_{2}}<\left(U_{r m s}\right)_{C H_{4}}<\left(U_{r m s}\right)_{N H_{3}}<\left(U_{r m s}\right)_{C O} \)
C. \( \left(U_{r m s}\right)_{H_{2}}<\left(U_{r m s}\right)_{C H_{4}}>\left(U_{r m s}\right)_{N H_{3}}>\left(U_{r m s}\right) \) Co \( _{2} \)
D. \( \left(U_{r m s}\right)_{H_{2}}>\left(U_{r m s}\right)_{C H_{4}}<\left(U_{r m s}\right)_{N H_{3}}<\left(U_{r m s}\right)_{C O} \)
Subject: Chemistry
How much amount of \( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O} \)
required for liberation of \( 2.54 g I_{2} \) when titrated with \( K \) I?
A . \( 2.5 \mathrm{gm} \)
в. \( 4.99 \mathrm{gm} \)
c. \( 2.4 \mathrm{gm} \)
D. \( 1.2 \mathrm{gm} \)
Subject: Maths
\( \operatorname{Let} a_{i}=i+\frac{1}{t} \) for \( i=1,2, \dots \dots, 20 \) put
\( \boldsymbol{p}=\frac{\mathbf{1}}{\mathbf{2 0}}\left(\boldsymbol{a}_{1}+\boldsymbol{a}_{2}+\ldots \ldots+\boldsymbol{a}_{20}\right) \) and \( \boldsymbol{q}= \)
\( \frac{1}{20}\left(\frac{1}{a_{1}}+\frac{1}{a_{2}}+\ldots . .+\frac{1}{a_{20}}\right) . \) Then
A \( \cdot q \epsilon\left(0, \frac{22-p}{21}\right) \)
В \( \cdot_{q \epsilon}\left(\frac{22-p}{21}, \frac{2(22-p)}{21}\right) \)
c. \( _{q \epsilon}\left(\frac{2(22-p)}{21}, \frac{22-p}{7}\right) \)
D. \( q \epsilon\left(\frac{22-p}{7}, \frac{4(22-p)}{21}\right) \)
Subject: Maths
\( \frac{\boldsymbol{x}^{2}+\mathbf{5}}{\left(\boldsymbol{x}^{2}+\mathbf{2}\right)^{2}}=\frac{\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{2}}+\frac{\boldsymbol{k}}{\left(\boldsymbol{x}^{2}+\mathbf{2}\right)^{2}} \Rightarrow \)
\( \boldsymbol{k}= \)
\( A \)
B.
\( c \cdot 3 \)
D. 5
Subject: Chemistry
\( \boldsymbol{K}_{c} \) for \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} \) is \( \mathbf{1 0} \) at \( \mathbf{2 5}^{\boldsymbol{o}} \boldsymbol{C} . \) If
a container contains 1,2,3 and 4 mole per litre of \( A, B, C \) and \( D \) respectively
\( \operatorname{at} 25^{\circ} C, \) the reaction shall:
A. Proceed from left to right
B. Proceed from right to left
c. Be at equilibrium
D. None of these
Subject: Physics
A uniform solid sphere is placed on a
smooth horizontal surface. An impulse
\( I \) is given horizontally to the sphere at a height \( h=\frac{4 R}{5} \) above the centre line. \( m \)
and \( R \) are mass and radius of sphere
respectively.
(a) Find angular velocity of sphere \( \& \) linear velocity of centre of mass of the
sphere after impulse.
(b) Find the minimum time after which
the highest point \( B \) will touch the
ground
(c) Find the displacement of the centre of mass during this interval.
Subject: Physics
A particle having a mass of 1.0 mg has
a velocity of \( 3600 k m / h \). Calculate the wavelength of the particle:
\( \left(h=6.626 \times 10^{-27} e r g-s e c\right) \)
A \( \cdot 6.626 \times 10^{-28} \mathrm{cm} \)
B. \( 6.626 \times 10^{-29} \mathrm{cm} \)
C. \( 6.626 \times 10^{-30} \mathrm{cm} \)
D. \( 6.626 \times 10^{-31} \mathrm{cm} \)
Subject: Physics
What is fractional change in the
resistance of a filament of \( \boldsymbol{\alpha}=\mathbf{1 0} \times \)
\( 10^{-4} /^{\circ} \mathrm{C}, \) when temperature changes
from \( 25^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} ? \)
Subject: Physics
If the density of earth increases by \( 20 \% \) and radius decreases by \( 20 \% \) then the new value of "g" on the surface of earth will be:
A. \( 0.8 \mathrm{g} \)
B. \( 0.90 \mathrm{g} \)
c. \( 0.96 \mathrm{g} \)
D.
Subject: Chemistry
For a gaseous phase reaction \( \boldsymbol{A}+ \) \( \mathbf{2} \boldsymbol{B} \rightleftharpoons \boldsymbol{A} \boldsymbol{B}_{2}, \boldsymbol{K}_{C}=\mathbf{0 . 3 4 7 5} \boldsymbol{L}^{2} \boldsymbol{m o l} \boldsymbol{e}^{-\mathbf{2}} \mathbf{a} \)
\( 200^{\circ} \mathrm{C} \). When 2 moles of \( B \) are mixed
with one mole of \( A \), what total pressure
is required to convert \( 60 \% \) of \( A \) in \( A B_{2} \) ?
A \( . P=1.8 a t m \)
B. \( P=63 \) atm
c. \( P=181.5 \) atm
\( D . P=34 a t m \)
Subject: Chemistry
\( M Y \) and \( N Y_{3}, \) two nearly insoluble
salts, have the same \( \boldsymbol{K}_{s p} \) values of
\( 6.2 \times 10^{-13} \) at room temperature
Which statement would be true in
regards to \( M Y \) and \( N Y_{3} ? \)
A. The molar solubilities of \( M Y \) and \( N Y_{3} \) in water are identical.
B. The molar solubility of \( M Y \) in water is less than that of \( N Y_{3} \)
C. The salts \( M Y \) and \( N Y_{3} \) are more soluble in \( 0.5 M K Y \) than in pure water.
D. The addition of the salt of KY to solution of \( M Y \) and
\( N Y_{3} \) will have no effect on their solubilities
Subject: Physics
An electric dipole of moment p is kept along an electric field E. The work done
in rotating it from an equilibrium
position by an angle \( \boldsymbol{\theta} \) is :
\( A \cdot P E(1-\cos \theta) \)
B. PE(1 - \( \sin \theta \) )
c. \( P E \cos \theta \)
D. PE sin \( \theta \)
Subject: Chemistry
The six most common atoms in organic
molecules are
A. \( c, H, 0, \) He, \( \operatorname{ca} \) and \( s \)
B. C, H, 0, N, P and S
c. \( c, H, 0, c a, M g, \) and \( s \)
D. C, 0, N, S, P and Mg
Subject: Maths
Let \( A B C \) be a right triangle in which
\( A B=3 c m, B C=4 c m \) and \( \angle B= \)
\( 90^{\circ} . B D \) is the perpendicular from \( B \) on
\( A C . \) The circle through \( B, C, D \) is drawn. Construct the tangents from \( \boldsymbol{A} \) to this circle.
Subject: Chemistry
The correct order of increasing bond length of \( C-H, C-O, C-C \) and
\( \boldsymbol{C}=\boldsymbol{C} \) is :
A. \( C-H<C-O<C-C<C=C \)
в. \( C-H<C=C<C-O<C-C \)
c. \( C-C<C=C<C-O<C-H \)
D. \( C-O<C-H<C-C<C=C \)
Subject: Maths
The area bounded by the curve \( y=e^{x} \)
and the lines \( y=|x-1|, x=2 \) is given
by:
\( \mathbf{A} \cdot e^{2}+1 \)
B \( \cdot e^{2}-1 \)
c. \( e^{2}-2 \)
D. \( e-2 \)
Subject: Maths
Which of the following number lines represents only natural numbers?
\( A \)
\( \begin{array}{lllllllllll}\nwarrow & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\end{array} \)
B.
\( c \)
D.
\( \frac{1}{10} \frac{2}{10} \frac{3}{10} \frac{4}{10} \frac{5}{10} \frac{6}{10} \frac{7}{10} \frac{8}{10} \frac{9}{10} \frac{10}{10} \)
Subject: Physics
A particle executes SHM whose instantaneous displacement is given by \( \boldsymbol{x}=\boldsymbol{A} \cos (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\pi} / 2) . \) What will be its
acceleration at \( t=T / 4 \)
\( \mathbf{A} \cdot a=0 \)
B . \( a=2 \omega^{2} A \)
\( \mathbf{c} \cdot a=\omega^{2} A \)
D. \( a=\omega^{2} A / 2 \)
Subject: Chemistry
The IUPAC name of the compound
\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H C} \equiv \boldsymbol{C H} \) is :
A. pent-4-yn-2-ene
B. pent-3-en-1-yne
c. pent-2-en-4-yne
D. pent-1-yn-3-ene
Subject: Maths
In the figure, \( m \angle P O Q=30^{\circ} \) and radius
OP \( =12 \mathrm{cm} . \) Find the given area of sector O-PRQ (Given \( \pi=3.14) \)
A. \( 37.68 \mathrm{cm}^{2} \)
\( \mathbf{B} \cdot 57.68 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 47.68 \mathrm{cm}^{2} \)
D. none of these
Subject: Physics
If the vectors \( \vec{P}=a \tilde{i}+a \hat{j}+ \) 3 \( \hat{k} \) and \( \vec{Q}=a \hat{i}-2 \hat{j}-\hat{k} \) are
perpendicular to each other then the positive value of a is
A . zero
в.
\( c \cdot 2 \)
D. 3
Subject: Maths
Find the equation whose roots are the
reciprocals of the roots of \( 3 x^{2}-5 x+ \)
\( \mathbf{7}=\mathbf{0} \)
A \( \cdot 7 x^{2}-5 x+3=0 \)
B . \( 7 x^{2}+5 x+3=0 \)
c. \( 4 x^{2}-5 x+3=0 \)
D. \( 7 x^{2}-5 x+7=0 \)
Subject: Physics
adjacent circuit. With the resistors
\( P=50 \Omega \) and \( Q=100 \Omega, \) the null point
is obtained at \( C \) where \( A C=33 \mathrm{cm} \)
When the resistors are interchanged, the null point is found at \( C \) with \( A C= \)
\( 67 \mathrm{cm} . \) The systematic error in this
experiment seems to be due to non-
coincidence of \( A \) and \( B \) with 0 cm mark
and \( 100 \mathrm{cm} \) mark respectively. If these
and errors are equivalent to \( ^{\prime} a^{\prime} c m \) and
\( b^{\prime} c m \) respectively, then they are.
A. 0 and 1
B. 1 and 0
c. 0.33 and 0.33
D. 1 and 1
Subject: Chemistry
Find the sum of the coefficients when
given equation is balanced.
\( \boldsymbol{A l}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{C a}(\boldsymbol{O H})_{2} \rightarrow \boldsymbol{A l}(\boldsymbol{O H})_{3}+ \)
\( \boldsymbol{C} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} \)
A . 5
B. 6
\( c \cdot 7 \)
D. 8
E . 9
Subject: Chemistry
All minerals are not the ore but all ores
are minerals. The extraction of a
particular metal depends upon several
factors and overall it has to be
convenient and economical.
Which of the following statement is
true?
A. Na-ethyl xanthate is used as frother exclusively.
B. Levigation cannot be applied for sulphide in any condition.
C. Froth floatation can be applied for non-sulphide ore also using suitable activator
D. Impurities like \( S \) and \( A \) s are removed as elemental vapor in roasting.
Subject: Physics
A body starts moving with an initial velocity of \( 5 m s^{-1} \) and an acceleration
of \( 1 m s^{-2} . \) The distance travelled by it in
the 5 th second is
\( \mathbf{A} \cdot 9.5 \mathrm{m} \)
B. \( 22.5 \mathrm{m} \)
c. \( 50 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Physics
In the following circuit the values of
\( \boldsymbol{L}, \boldsymbol{C}, \boldsymbol{R} \) and \( \boldsymbol{E}_{\mathbf{0}} \) are \( 0.01 \mathrm{H}, \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{F}, \mathbf{2 5 \Omega} \)
and 220 volt respectively. The value of current flowing in the circuit at \( \boldsymbol{f}=\mathbf{0} \)
and \( \boldsymbol{f}=\infty \) will respectively be
\( A \cdot 8 A \) and \( 0 A \)
B. \( 0 A \) and \( 0 A \)
\( c \cdot 8 A \) and \( 8 A \)
D. o \( A \) and \( 8 A \)
Subject: Chemistry
The electron in a hydrogen atom makes
a transition \( n_{1} \rightarrow n_{2} \) where \( n_{1} \) and \( n_{2} \)
are principal quantum numbers of two states. Assume the Bohr model to be
valid. The time period of the electron in the initial state is eight times that in
the final state. Then the possible value
of \( n_{1} \) and \( n_{2} \) is/are:
\( \mathbf{A} \cdot n_{1}=2, n_{2}=1 \)
B \( . n_{1}=1, n_{2}=2 \)
\( \mathbf{c} \cdot n_{1}=4, n_{2}=2 \)
D \( . n_{1}=6, n_{2}=3 \)
E \( . n_{1}=6, n_{2}=4 \)
Subject: Chemistry
Arrange the following compounds in increasing order of boiling points.
: 3-methyl pentane II: 3chloropentane
III: 3-bromopentane IV: 3,3dichloropentane
A. \( I<I I I<I I<I V \)
в. \( I<I V<I I I<I I \)
c. \( I<I I<I I I<I V \)
Subject: Physics
Assertion
Light nuclei are most stable if \( \boldsymbol{N}=\boldsymbol{Z} \)
while heavy nuclei are more stable if \( N>Z .(N \rightarrow \) number of neutrons
\( Z \rightarrow \) number of protons
Reason
As the number of protons increases in a nucleus, the Coulomb's repulsive force increases, which tends to break the
nucleus apart. So, to keep the nucleus stable, more number of neutrons are needed which are neutral in nature.
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
Given \( \boldsymbol{P}(\boldsymbol{x})=\boldsymbol{x}^{4}+\boldsymbol{a} \boldsymbol{x}^{3}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}+\boldsymbol{d} \)
such that \( x=0 \) is the only real root of
\( \boldsymbol{P}^{\prime}(\boldsymbol{x})=\mathbf{0} . \) If \( \boldsymbol{P}(-1)<\boldsymbol{P}(1), \) then in the
interval [-1,1]
A. \( P(-1) \) is not minimum but \( P(1) \) is the maximum of \( P \)
B. \( P(-1) \) is the minimum but \( P(1) \) is not the maximum of \( P \)
c. neither \( P(-1) \) is the minimum nor \( P(1) \) is the maximum of \( P \)
\( D(-1) \) is the minimum and \( P(1) \) is the maximum of \( P \)
Subject: Maths
The inverse of the statement "lf a
number is divisible by 4 then it is also divisible by \( 2^{\prime \prime} \) is -
A. If a number is divisible by 4 , then it is always divisible by 2
B. If a number is not divisible by 4 , then it is divisible by
2.
c. If a number is not divisible by \( 4, \) then it is not divisible by 2.
D. None of the above
Subject: Physics
A ball of radius \( \boldsymbol{R}=\mathbf{1 0 . 0} \) cm rolls
without slipping on a horizontal plane
so that its centre moves with constant
acceleration \( a=2.50 \mathrm{cm} / s^{2} ; t=2.00 s \)
after the beginning of motion its
position corresponds to that shown in
Fig. Find:
(a) the velocities of the points \( A, B \) and
\( O \)
(b) the accelerations of these points.
Subject: Chemistry
For the system \( 3 A+2 B \rightarrow 2 C \), the
expression for equilibrium constant \( \boldsymbol{K} \)
is:
A \( \cdot \frac{[3 A] \times[2 B]}{[C]} \)
B. \( \frac{[A]^{3} \times[B]}{[C]} \)
c. \( \frac{[C]^{2}}{[A]^{3} \times[B]^{2}} \)
D. \( \frac{[C]}{[3 A] \times[2 B]} \)
Subject: Chemistry
The \( p H \) of a \( 10 m l \) aqueous solution of \( H C l \) is \( 4 . \) The amount of water to be
added to this solution in order to
change its \( p H \) from 4 to 5 is?
A. \( 30 m \)
в. \( 60 \mathrm{ml} \)
\( c .90 m l \)
D. \( 120 m l \)
Subject: Chemistry
The ionization enthalpies, \( (I E)_{1} \) and
the \( (I E)_{2} \) in \( \mathrm{kJ} \mathrm{mol}^{-1} \) of a few elements designated by Roman numerals are shown below:
\( \begin{array}{lll}\text { Element } & (I E)_{1} & (I E)_{2} \\ \text { A } & \text { 2372 } & 5251 \\ \text { B } & 520 & 7300 \\ \text { c } & 900 & \text { 1760 } \\ \text { D } & \text { 1680 } & \text { 3380 }\end{array} \)
Which of the above elements form a
stable binary halide of the formula
\[
\boldsymbol{M} \boldsymbol{X}_{2} ?
\]
A. \( A \)
в. \( B \)
c. \( C \)
D. \( D \)