AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A cyclist comes to skidding stop in \( 10 \mathrm{m} \) During this process, the force on the cycle due to the road is \( 200 \mathrm{N} \) and is directly opposed to the motion.(a) how much work does the road do on the
cycle?
(b) How much work does the
cycle do on the road?
A. -2000,,20000
B. - 2000 J,1000 J by each tyre
c. 0.2000
D . -2000 J,0 J
Subject: Chemistry
From the rate expression for the following reactions, determine their order of reaction and the dimensions of
the rate constants.
(i) \( 2 N O(g) \rightarrow N_{2} O(g) ; \quad \) Rate \( = \)
\( \boldsymbol{k}[\boldsymbol{N} \boldsymbol{O}]^{2} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{3} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{H}^{+} \rightarrow \)
\( 2 H 2 O(I)+3 I ; \quad R a t e=k\left[H_{2} O_{2}\right]\left[I^{-}\right] \)
(iii) \( \boldsymbol{C H}_{3} \boldsymbol{C H O}(\boldsymbol{g}) \rightarrow \boldsymbol{C H}_{4}(\boldsymbol{g})+ \)
\( \boldsymbol{C O}(\boldsymbol{g}) ; \quad \boldsymbol{R} \boldsymbol{a} \boldsymbol{t e}=\boldsymbol{k}\left[\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C H O}\right]^{3 / 2} \)
(iv) \( C_{2} H_{5} C l(g) \rightarrow C_{2} H_{4}(g)+ \)
\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) ; \quad \boldsymbol{R} \boldsymbol{a} \boldsymbol{t} e=\boldsymbol{k}\left[\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C l}\right] \)
Subject: Chemistry
Which of the following is a displacement reaction?
\( A \cdot \operatorname{cacos} \rightarrow c a 0+c O \)
B . Ca0+2HCI \( \rightarrow \) CaCl \( _{2}+H_{2} \) O
\( \mathrm{c} \cdot \mathrm{Fe}+\mathrm{CuSO}_{4} \rightarrow \mathrm{FeSO}_{4}+\mathrm{Cu} \)
D. NaOH+HCI \( \rightarrow \) Nacl \( +H_{2} \) 0
Subject: Maths
7th term of \( \frac{1}{2}, \frac{1}{4}, \frac{1}{6} \dots \dots \) is
\( A \cdot \frac{1}{10} \)
в. \( \frac{1}{12} \)
c. \( \frac{1}{14} \)
D. \( \frac{1}{16} \)
Subject: Physics
A current of 1 A flows in a length \( 0.1 \mathrm{m} \) placed in a magnetic field of \( 0.5 \mathrm{T} \) Calculate the force acting on the wire when the wire makes an angle of
(i) \( 90^{\circ} \) and
(ii) \( 0^{\circ}, \) with respect to the magnetic field.
Subject: Maths
\( A \) and \( B \) are events with \( P(A)= \)
\( \mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3} \)
Find the probability that
i) A does not occur
ii) neither A nor B occurs
Subject: Physics
In Young's double slit experiment with
sodium vapour lamp of wavelength 589 tun and the slits 0.689 min apart, the
half angular width of the central maximum is
A \( \cdot \sin ^{-1}(0.01) \)
B. \( \sin ^{-1}(0.0001) \)
c. \( \sin ^{-1}(0.001) \)
D. \( \sin ^{-1}(0.1) \)
Subject: Chemistry
A mixture of volatile components \( A \) and B has total vapour pressure (in torr) as \( \boldsymbol{P}=\mathbf{2 5 4}-\mathbf{1 1 9} \chi_{A}, \) where \( \chi_{A} \) is the
mole fraction of \( A \) in the mixture. Hence,
\( P_{A}^{o} \) and \( P_{B}^{o} \) respectively are (in torr):
A. 254,119
в. 119,254
C. 135,254
D. 154, 119
Subject: Chemistry
\( 5 g \) of an unknown solute is dissolved in 295 g solvent. If molarity and density of solution are \( 0.05 \mathrm{M} \) and \( 1.5 \mathrm{g} / \mathrm{cc} \) respectively. The molecular weight of unknown solute is:
A . 375
в. 425
\( c .400 \)
D. 500
Subject: Maths
\( \boldsymbol{y}=\boldsymbol{A} \cos \boldsymbol{n} \boldsymbol{x}+\boldsymbol{B} \sin \boldsymbol{n} \boldsymbol{x} \)
Prove that \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{n}^{2} \boldsymbol{y}=\mathbf{0} \)
Subject: Physics
What is the moment of intertia for a
solid sphere w.r.t. a tangent touching to its surface?
\( ^{\mathbf{A}} \cdot \frac{2}{5} M R^{2} \)
B. \( \frac{7}{5} M R^{2} \)
c. \( \frac{2}{3} M R^{2} \)
D. \( \frac{5}{3} M R^{2} \)
Subject: Biology
toppr LOGIN JOIN NOW
\( \widehat{n} \)
Q Type your question
\( - \)
\( A \cdot A-p, B-q, C-r, D-t, E-s \)
B. \( A-r, B-p, C-t, D-s, E-q \)
\( \mathbf{C} \)
1 \( \alpha \) - \( r, C-s, D-p, E-t \)
3- \( t, C-q, D-r, E-p \)
\( D \)
-1
\( E \cdot A-t, B-s, C-p, D-q, E- \)
Subject: Chemistry
Basic stregth of \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{N H}_{2} \) is
to that of \( \boldsymbol{C} \boldsymbol{H}_{2}= \)
\( \boldsymbol{C H} \boldsymbol{N} \boldsymbol{H}_{2} \)
A. stronger
B. weaker
c. equal
D. none of the above
Subject: Maths
Assertion
The differential equation of the family of
curves represented by \( \boldsymbol{y}=\left(\boldsymbol{a}+\boldsymbol{b} e^{c}\right) \boldsymbol{x} \)
is \( x \frac{d y}{d x}-y=0, \) where \( a, b \) and \( c \) are
constant.
Reason
In general, a differential equation of \( n \) th
order is obtained on eliminating \( n \) arbitrary constants.
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
A ladder of length I and mass m is placed against a smooth vertical wall, but the ground is not smooth. Coefficient of friction between the
ground and the ladder is \( \mu . \) The angle \( \theta \)
at which the ladder will stay in equilibrium is:
A \( \cdot \theta=\tan ^{-1}(\mu) \)
B . \( \theta=\tan ^{-1}(2 \mu) \)
c. \( \theta=\tan ^{-1}\left(\frac{\mu}{2}\right) \)
D. none of these
Subject: Maths
If \( f(x) \) is continuous and \( f\left(\frac{9}{2}\right)=\frac{2}{9} \) then \( \lim _{x \rightarrow 0} f\left(\frac{1-\cos 3 x}{x^{2}}\right) \) is equal to:
A \( \cdot \frac{9}{2} \)
в. \( \frac{2}{9} \)
\( c \cdot 0 \)
D. \( \frac{8}{9} \)
Subject: Physics
topp
Q Type your question
the same wire as shown in figure.
\( A E F D \) is a square of side \( 1 m \) and
\( \boldsymbol{E B}=\boldsymbol{F C}=\mathbf{0 . 5 m .} \) The entire circuit is
placed in a steadily increasing, uniform magnetic field directed into the plane of paper and normal to it. The rate of
change of the magnetic field is \( 1 T s^{-1} \)
The resistance per unit length of the
wire is \( 1 \Omega m^{-1} \). Find the magnitude ano
direction of the current in the segment \( A E, B E \) and \( E F \)
\( ^{\mathbf{A}} \cdot \frac{6}{22} A, E \) to \( A ; \frac{7}{22} A, B \) to \( E ; \frac{1}{22} A, F \) to \( E \)
B. \( \frac{1}{22} A, \) E to \( A ; \frac{6}{22} A, E \) to \( B ; \frac{7}{22} A, F \) to \( E \)
c. \( \frac{7}{22} A, \) E to \( A ; \frac{6}{22} A, B \) to \( E ; \frac{1}{22} A, F \) to \( E \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by
\( \boldsymbol{f}(\boldsymbol{x})=(\mathbf{1}-\boldsymbol{x})^{\frac{1}{3}} \) is :
A. one-one and onto
B. many one and onto
c. one-one and into
D. many one and into
Subject: Biology
An adaptation in the structure and
function of loop of Henle to xerophytic
environment is
A. A short loop of Henle, which allows more filtrate to be removed from the blood
B. A short loop of Henle, which allows less water to be removed from the filtrate
C. A long loop of Henle, which allows more filtrate to be removed from the blood
D. A long loop of Henle, which allows more water to be removed from the filtrate
E. A long loop of Henle, which allows less filtrate to be removed from the blood
Subject: Physics
A particle is kept at rest at a distance \( \boldsymbol{R} \) (earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is
A \( \cdot \sqrt{\frac{G M}{4 R}} \)
в. \( \sqrt{\frac{G M}{2 R}} \)
c. \( \sqrt{\frac{G M}{R}} \)
D. \( \sqrt{\frac{2 G M}{4 R}} \)
Subject: Maths
An open box is made of 3cm thick. Its
external length, breadth, and hights are \( 1.48 \mathrm{m}, 1.16 \mathrm{m}, 8.3 \mathrm{dm} . \) Find the cost of
painting the inner surface at 50 p per \( 100 \mathrm{cm}^{2} \)
Subject: Chemistry
The correct order for decreasing atomic radius of the five atoms \( \mathrm{H}, \mathrm{Br}, \mathrm{I}, \mathrm{He} \) and
Sis?
\( A \cdot \mid>B r>S>H e>H \)
\( \mathbf{B} \cdot \mid>S>B r>H>H e \)
\( \mathrm{c} \cdot \mid>\mathrm{S}>\mathrm{Br}>\mathrm{He}>\mathrm{H} \)
\( \mathbf{D} \cdot \mathbf{B r}>\mid>\mathbf{S}>\mathrm{He}>\mathbf{H} \)
Subject: Maths
If \( P \) is (-3,4) and \( M y M x(P) \) shows the reflection ofthe point \( P \) in the \( x \) -axis and then the reflection of the image in the \( y \) -
axis, then \( M_{y} M_{x}(P) \) is
\( A \cdot(3,4) \)
B. (-3,-4)
c. (-3,4)
D. (3,-4)
Subject: Chemistry
A \( 1-k W \) radio transmitter operates at a
frequency of 880 Hz. How many photons per second does it emit?
A. \( 1.71 \times 10^{21} \)
the \( 1.71 \times 10^{1.11} \)
B . \( 1.71 \times 10^{30} \)
c. \( 6.02 \times 10^{23} \)
D. \( 2.85 \times 10^{26} \)
Subject: Chemistry
In which of the following reactions,
\( \Delta \boldsymbol{H}>\boldsymbol{\Delta} \boldsymbol{U} ? \)
This question has multiple correct options
\( \mathbf{A} \cdot H_{2}(g)+I_{2}(g) \rightarrow 2 H I(g) \)
B \( \cdot P C l_{5}(g) \rightarrow P C l_{3}(g)+C l_{2}(g) \)
\( \mathbf{c} \cdot 2 H_{2} O_{2}(l) \rightarrow 2 H_{2} O(l)+O_{2}(g) \)
\( \mathbf{D} \cdot C(s)+O_{2}(g) \rightarrow C O_{2}(g) \)
Subject: Maths
Calculate mean deviation about for the
following data.
\( \begin{array}{lllll}\text { Class } & \begin{array}{l}0- \\ 10\end{array} & \begin{array}{l}10 \\ 20\end{array} & \begin{array}{l}\text { 20- } \\ 30\end{array} & \begin{array}{l}\text { 30- } \\ 40\end{array}\end{array} \)
Frequence 6.7 15 16
Subject: Chemistry
Select the incorrect reaction from the
following.
\( \mathbf{A} \cdot 2 N a_{2} C r O_{4}+H^{+} \rightarrow N a_{2} C r_{2} O_{7}+2 N a^{+}+H_{2} O \)
B. \( 4 M n O_{2}+4 K O H+O_{2} \rightarrow 4 K M n O_{4}+2 H_{2} O \)
\( \mathbf{c} \cdot 2 M n O_{4}^{-}+5 C_{2} O_{4}^{2}+16 H^{+} \rightarrow 2 M n^{2+}+10 C O_{2}+8 H_{2} O \)
D. \( M n O_{4}^{-}+8 H^{+}+5 F e^{2+} \rightarrow 5 F e^{3+}+M n^{2+}+4 H_{2} O \)
Subject: Maths
Solve the following system of equations
\( |\boldsymbol{x}-\mathbf{1}|+|\boldsymbol{y}-\mathbf{2}|=\mathbf{1} \)
\( \boldsymbol{y}=\mathbf{2}-|\boldsymbol{x}-\mathbf{1}| \)
A \( \cdot x=\frac{1}{2}, \frac{5}{2} \) and \( y=\frac{3}{2} \)
B. \( x=\frac{3}{2}, \frac{5}{2} \) and \( y=\frac{7}{2} \)
c. \( x=\frac{5}{2}, \frac{7}{2} \) and \( y=\frac{5}{2} \)
D. \( x=\frac{1}{2}, \frac{3}{2} \) and \( y=\frac{3}{2} \)
Subject: Chemistry
Assertion
Pure water obtained from different
sources such as river, well, spring, sea etc. always contain hydrogen and oxygen combined in the ratio 1: 8 by
mass.
Reason
A chemical compound always contains elements combined together in same proportion by mass, it was discovered by French chemist, Joseph Proust (1799)
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
Effective capacitance of parallel
combination of two capacitors \( C_{1} \) and
\( C_{2} \) is \( 10 \mu F \). when these capacitors are individually connected to a voltage
source of \( 1 V \), the energy stored in the capacitor \( C_{2} \) is 4 times that of \( C_{1} \). If
these capacitors are connected in series, their effective capacitance will be:
\( \mathbf{A} \cdot 8.4 \mu F \)
в. \( 3.2 \mu F \)
c \( .1 .6 \mu F \)
D. \( 4.2 \mu F \)
Subject: Physics
Angle of dip at a place is \( 60^{0} \) and earth's magnetic field is \( 8 \mu T . \) Its horizontal
component \( \boldsymbol{B}_{\boldsymbol{H}} \) is :
A \( .4 \sqrt{3 \mu} T \)
в. \( 4 \mu T \)
c. \( \frac{8}{\sqrt{3}} \mu T \)
D. \( 8 \sqrt{3 \mu} T \)
Subject: Chemistry
A sample of wustite \( F e_{x} O \) contains one \( \boldsymbol{F} e(\boldsymbol{I} \boldsymbol{I} \boldsymbol{I}) \) for every three \( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{I} \boldsymbol{I}) . \) The
value of \( x \) is:
\( \mathbf{A} \cdot 9 / 8 \)
в. \( 8 / 9 \)
c. \( 3 / 4 \)
D. \( 4 / 3 \)
Subject: Maths
If the points \( \boldsymbol{A}(1,2,-1), B(2,6,2) \) and
\( C(\lambda,-2,-4) \) are collinear, then \( \lambda \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c .-2 \)
\( D \)
Subject: Chemistry
The \( K_{s p} \) for a sparingly soluble \( A g_{2} C r O_{4} \) is \( 4 \times 10^{-12} . \) The molar
solubility of the salt is:
\( \begin{array}{lll}\text { A } \cdot 2.0 \times 10^{-6} & \text {mol } & L^{-1}\end{array} \)
\( \begin{array}{lll}\text { В. } 1.0 \times 10^{-4} & \text {тод } L^{-1}\end{array} \)
\( \begin{array}{lll}\text { C. } 2.0 \times 10^{-12} & \text {mol } & L^{-1}\end{array} \)
D. \( 1.0 \times 10^{-15} \) mol \( L^{-1} \)
Subject: Chemistry
Assertion
Only one out of every 12000 alpha particles rebound in Rutherford's experiment.
Reason
Most of the space in the atom is empty.
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: Biology
If the sign was nailed to the side of a tree \( 5^{\prime} \) above the ground in \( 1997 . \) How high would the sign be in 2007 if the tree grew 4" taller each year?
A. \( 5^{\text {'high }} \)
B. 8'highh
c. 4'8" high
D. 9'4" high
Subject: Physics
A rigid body in the shape of a \( V \) has two equal arms made of uniform rods.What must the angle between the two rods be so that when the body is suspended from one end, the other arm is horizontal?
\( ^{A} \cdot \cos ^{-1}\left(\frac{1}{3}\right) \)
B. \( \cos ^{-1}\left(\frac{1}{2}\right) \)
c. \( \cos ^{-1}\left(\frac{1}{4}\right) \)
D. \( \cos ^{-1}\left(\frac{1}{6}\right) \)
Subject: Maths
Choose the quadratic equation in \( \boldsymbol{p} \)
whose solutions are 1 and 7
A \( \cdot p^{3}-p x+6=0 \)
B . \( p^{2}-p x+6=0 \)
c. \( p^{2}-8 p+7=0 \)
D. \( p^{2}-5 p+7=0 \)
Subject: Chemistry
Cane sugar underoges the inversion as
follow:
\( \boldsymbol{C}_{12} \boldsymbol{H}_{22} \boldsymbol{O}_{11}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}+ \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\mathbf{1 2}} \boldsymbol{O}_{\boldsymbol{6}} \)
If solution of 0.025 moles of sugar in \( 200 \mathrm{gm} \) of water show depression in
freezing point \( 0.372^{\circ} \mathrm{C}, \) then what \( \% \)
sucrose has inverted. \( \left(\boldsymbol{K}_{f}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=\right. \)
1.86 \( \left.K k g m o l^{1}\right) \)
Subject: Maths
In a final examination in Statistics the
mean marks of a group of 150 students
were 78 and the \( S . D \) was \( 8.0 . \ln \)

Economics, however, the mean marks
were 73 and the S.S was \( 7.6 . \) The
variability in the two subjects
respectively is
A. \( 10.3 \%, 10.4 \% \)
\( \% \)
B. \( 95 \%, 7.9 \% \)
c. \( 11.2 \%, 10.1 \% \)
D. none of these
Subject: Chemistry
Zn gives \( \mathrm{H}_{2} \) gas with \( \mathrm{H}_{2} \mathrm{SO}_{4} \) \& HCl but
not with HNO \( _{3} \) because:
A. \( Z n \) act as oxidising agent when react with \( H N O_{3} \)
B. \( H N O_{3} \) is weaker acid then \( H_{2} \) SO \( _{4} \) \& \( H C l \)
C. in electrochemical series \( Z n \) is above hydrogen
D. \( N O_{3}^{\Theta} \) is reduced in prefference to hydronium ion
Subject: Chemistry
Ratio of solubilities of \( \operatorname{gases} N_{2} \& O_{2} \)
in water from air at \( 25^{\circ} \& 1 \) atm will be
if air is \( 20 \% \) by volume of \( O_{2} \) and \( 80 \% \) by
volume of \( \boldsymbol{N}_{2} \)
\[
\begin{aligned}
\operatorname{Given} &: \boldsymbol{K}_{\boldsymbol{H}}\left(\boldsymbol{N}_{2}\right)=\boldsymbol{2} \times \mathbf{1 0}^{4} \boldsymbol{a t m} \\
\boldsymbol{K}_{\boldsymbol{H}}\left(\boldsymbol{O}_{2}\right) &=\mathbf{1 0}^{4} \boldsymbol{a t m}
\end{aligned}
\]
A . 8: 1
B. 1: 8
\( c \cdot 1: 2 \)
D. 2: 1
Subject: Chemistry
Which of the following reaction represent the decrease in entropy?
I. \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
Il. \( \boldsymbol{F e}^{2+}(\boldsymbol{a q})+\boldsymbol{S}^{2-}(\boldsymbol{a q}) \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{S}(\boldsymbol{s}) \)
III. \( 2 S O_{3}(g) \leftrightharpoons 2 S O_{2}(g)+O_{2}(g) \)
A. I only
B. I and II only
c. ॥ and III only
D. III only
E . I, II, and III
Subject: Chemistry
Heat of dissociation of benzene to
elements is \( 5535 \mathrm{KJ} \) mol \( ^{-1} \). The bond
enthalpies of \( \boldsymbol{C}-\boldsymbol{C}, \boldsymbol{C}=\boldsymbol{C} \) and \( \boldsymbol{C}-\boldsymbol{H} \)
are 347.3,615.0 and \( 416.2 \mathrm{KJ} \)
respectively. Resonance energy of benzene is:
A. \( 1.51 \mathrm{KJ} \)
в. 15.1 К.
c. \( 151 \mathrm{KJ} \)
D. \( 1511 \mathrm{KJ} \)
Subject: Physics
The vibrations of a string of length
\( 60 \mathrm{cm} \) fixed at both ends are
represented by the equation \( \boldsymbol{y}= \) \( 4 \sin \left[\frac{\pi x}{15}\right] \cos (96 \pi t) \) where \( x \) and \( y \) are
in \( \mathrm{cm} \) and \( t \) in sec. The equation of
component waves whose superposition gives the above wave are
A \( \cdot y_{1}=2 \sin \left(96 \pi t+\frac{\pi x}{5}\right), y_{2}=-2 \sin \left(96 \pi t-\frac{\pi x}{5}\right) \)
B・ \( y_{1}=2 \sin \left(\frac{\pi \mathrm{x}}{5}+96 \pi t\right), y_{2}=-2 \sin \left(\frac{\pi \mathrm{x}}{5}-96 \pi t\right) \)
c. \( y_{1}=2 \operatorname{sm}\left(\frac{\pi \mathrm{x}}{15}+96 \pi t\right), y_{2}=-2 \sin \left(96 \pi t-\frac{\pi x}{15}\right) \)
D. \( y_{1}=2 \sin \left(\frac{\pi \kappa}{15}+96 \pi t\right) y_{2}=-2 \sin \left(\frac{\pi \mathrm{x}}{15}-96 \pi t\right) \)
Subject: Maths
Evaluate \( \int_{0}^{\pi / 4} \frac{\cos x-\sin x}{10+\sin 2 x} d x \)
A \( \cdot \frac{1}{3}\left(\tan ^{-1} \frac{\sqrt{2}}{3}+\tan ^{-1} \frac{1}{3}\right) \)
B. \( \frac{1}{3}\left(\tan ^{-1} \frac{\sqrt{1}}{3}-\cot ^{-1} \frac{2}{3}\right) \)
c. \( \frac{1}{3}\left(\tan ^{-1} \frac{\sqrt{2}}{3}-\tan ^{-1} \frac{1}{3}\right) \)
D. \( \frac{1}{3}\left(\tan ^{-1} \frac{\sqrt{1}}{3}-\cot ^{-1} \frac{1}{3}\right) \)
Subject: Maths
In the following table, given that \( a \) is the
first term, \( d \) the common difference and
\( a_{n} \) the \( n t h \) term of the \( A P \)
(i)
(ii) \( \begin{array}{ccccc}a & d & n & a_{n} \\ 7 & 3 & 8 & \dots \\ -18 & \dots & 10 & 0 \\ \dots & -3 & 18 & -5 \\ -18.9 & 2.5 & \dots & 3.6 \\ 3.5 & 0 & 105 & \dots\end{array} \)
(iii)
(iv)
\( (v) \)
A. \( (i) a_{n}=13(i i) d=1(i i i) a=46(i v) n=9(v) a_{n}=3.5 \)
B. \( (i) a_{n}=36(i i) d=7(i i i) a=46(i v) n=13(v) a_{n}=3.5 \)
C \( \cdot(i) a_{n}=18(i i) d=3(i i i) a=46(i v) n=4(v) a_{n}=3.5 \)
D \( \cdot(i) a_{n}=28(i i) d=2(i i i) a=46(i v) n=10(v) a_{n}=3.5 \)
Subject: Chemistry
\( \boldsymbol{Y} \stackrel{\boldsymbol{\Delta}, 205^{\circ} \boldsymbol{C}}{\boldsymbol{C}} \boldsymbol{C a S} \boldsymbol{O}_{4} \cdot \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\boldsymbol{\Delta}, \mathbf{1 2 0}^{\circ} \boldsymbol{C}}{\longrightarrow} \boldsymbol{X} \)
\( X \) and \( Y \) are respectively
A. plaster of paris, dead burnt plaster
B. dead burnt plaster, plaster of paris
c. \( C a O \), plaster of paris
D. plaster of paris, mixture of gases
Subject: Physics
\( \mathbf{A} \)
\( \mathbf{5 0 0} \Omega \) resistor and a capacitor \( C \) are
connected in series across \( 50 H z . A C \)
supply mains. The r.m.s potential
difference recorded on voltmeter \( V_{1} \) and
\( V_{2} \) are \( V_{1}=120 V \) and \( V_{2}=160 \mathrm{V} . \) The
power taken from the mains is:
4. \( 480 \mathrm{W} \)
В. 240 И
c. \( 28.8 W \)
D. \( 14.4 \mathrm{W} \)
Subject: Physics
elevated ends and a flat central part as shown in the Figure below. The flat portion BC has a length \( l=3.0 m . \) The
curved portions of the track are
frictionless. For the flat part the
coefficient of kinetic friction is \( \mu_{k}= \)
\( 0.20, \) the particle is released at point \( A \)
which is at height \( h=1.5 m \) above the
flat part of the track. Where does the
particle finally comes to rest?
B. The particle comes to rest at \( \frac{1}{4} \) th distance from the point B of the flat part.
C. The particle comes to rest at \( \frac{3}{4} \) th distance from the
point B of the flat part.
D. The particle comes to rest at point
Subject: Physics
On a hypothetical scale \( A \) the ice point
is \( 42^{\circ} \) and the steam point is \( 182^{\circ} \) For
another scale \( \mathrm{B} \), the ice point is \( -10^{\circ} \)
and steam point in \( 90^{\circ} \) ) If \( \mathrm{B} \) reads \( 60^{\circ} \) the reading of \( A \) is,
\( \mathbf{A} \cdot 160^{\circ} \)
B. \( 140^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 110^{\circ} \)
Subject: Maths
The monthly salaries in rupees of 30
workers in a factory are given below:
\( \mathbf{5 0 0 0}, \mathbf{7 0 0 0}, \mathbf{3 0 0 0}, \mathbf{4 0 0 0}, \mathbf{4 0 0 0}, \mathbf{3 0 0 0}, \mathbf{3} \)
4000,9000,3000,5000,4000,4000,3
\( 8000,3000,3000,6000,7000,7000, \)
Find the mean of monthly salary.
Subject: Maths
For \( a>0 \) the value of \( \int_{-\pi}^{\pi} \frac{\sin ^{2} x}{1+a^{x}} d x \)
A \( \cdot \frac{\pi}{2} \)
B. \( \pi \)
c. \( \frac{a \pi}{2} \)
D. \( a \pi \)
Subject: Chemistry
If the solubility of \( A g C l \) (formula mass
\( =143) \) in water at \( 25^{\circ} \mathrm{C} \) is \( 1.43 \times 10^{-4} \)
g/100 mL of solution then the value of
\( \boldsymbol{K}_{s p} \) will be:
A \( \cdot 1 \times 10^{-5} \)
В. \( 2 \times 10^{-5} \)
c. \( 1 \times 10^{-10} \)
D. \( 2 \times 10^{-10} \)
Subject: Maths
The value of
\( \lim _{x \rightarrow a} \frac{\sqrt{x-b}-\sqrt{a-b}}{x^{2}-a^{2}}(a>b) \) is
A \( \cdot \frac{1}{4 a} \)
B. \( \frac{1}{a \sqrt{a-b}} \)
c. \( \frac{1}{2 a \sqrt{a-b}} \)
D. \( \frac{1}{4 a \sqrt{a-b}} \)
Subject: Chemistry
Which process of purification is represented by the following scheme?
\( \underset{\text { impure }}{\boldsymbol{T i}}+\mathbf{2 I}_{\mathbf{2}} \stackrel{\mathbf{2 5 0}^{\circ} \boldsymbol{C}}{\boldsymbol{\pi} \boldsymbol{i} \boldsymbol{I}_{4}} \frac{\mathbf{1 4 0 0}^{\boldsymbol{o}} \boldsymbol{C}}{\boldsymbol{p} \boldsymbol{p} \boldsymbol{i}}+ \)
\( 2 I_{2} \)
A. Cupellation
B. Electrolytic refining
c. zone refining
D. Van-Arkel process
Subject: Chemistry
NaOH can also be prepared by electrolysis of aqueous NaCl. Amount of NaOH formed when 0.445 L of \( \mathrm{NaCl} \) (aq) is electrolysed for 137 s with a current of
\( 1.08 A, \) is :
A . \( 0.09 g \)
B. \( 0.12 g \)
c. \( 0.06 g \)
D. amount of NaCl has not been given
Subject: Maths
Prove that \( x^{2}-y^{2}=c\left(x^{2}+y^{2}\right)^{2} \) is the
general solution of differential equation
\( \left(x^{3}-3 x y^{2}\right) d x=\left(y^{3}-3 x^{2} y\right) d y \)
where \( c \) is a parameter
Subject: Maths
A circle and a parabola intersect at four points \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right) \) and
\( \left(x_{4}, y_{4}\right) . \) Then \( y_{1}+y_{2}+y_{3}+y_{4} \) is equal
to
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3/2
\( c \cdot 2 \)
D.
Subject: Maths
The solution of the equation \( |z| z=1+2 i \)
is
A \( \cdot \frac{-2}{5^{0.25}}+\frac{4}{5^{0.25}} \)
B. \( \frac{1}{5^{0.25}}+\frac{2}{5^{0.25}} \)
c. \( \frac{0.5}{5^{0.25}}-\frac{1}{5^{0.25}} \)
D. \( \frac{0.25}{5^{0.25}}-\frac{0.5}{5^{0.25}} \)
Subject: Physics
Consider a circuit which contains a
resistance free battery and a single
resistance \( R . \) If a second resistance is
added in parallel with \( \boldsymbol{R} \)
A. The voltage across \( R \) will decrease
B. The current through \( R \) will increase
C. The total current drawn from the battery will increases
D. The power dissipated in \( R \) will decrease current drawn from battery will increase