AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Cards marked with the numbers 2 to
101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is a perfect square.
A \( \cdot \frac{9}{100} \)
в. \( \frac{5}{100} \)
c. \( \frac{4}{100} \)
D. \( \frac{7}{100} \)
Subject: Physics
The magnetic induction at 0 due to a current in conductor shaped as shown
in figure is:
A \( \cdot \frac{\mu_{0} i}{4 \pi}\left[\frac{3 \pi}{2 a}+\frac{\sqrt{2}}{b}\right] \)
В \( \cdot \frac{\mu_{0} i}{4 \pi}\left[\frac{3 \pi}{4 a}-\frac{\sqrt{2}}{b}\right] \)
\( ^{\text {c. }} \cdot \frac{\mu_{0} i}{2 \pi}\left[\frac{3 \pi}{4 a}-\frac{1}{\sqrt{2} b}\right] \)
D. \( \frac{\mu_{0}}{2 \pi}\left[\frac{1}{a}+\frac{1}{b}\right. \)
Subject: Physics
A source of constant potential
difference is connected across a
conductor having irregular cross-
section as shown in figure. Then :-
A. Electric field intensity at \( P \) is greater than at \( Q \).
B. Rate of electric current crossing per unit area of cross section at \( P \) is less than that at \( Q \)
C. The rate of generation of heat per unit length at \( P \) is greater than that at \( Q \).
D. Mean kinetic energy of free electron at \( P \) is greater than that at \( Q \)
Subject: Chemistry
Explain : When \( M n(O H)_{2} \) is made by adding an alkali to a solution
containing \( M n^{2+} \) ions, the ppt quickly darkens, and eventually goes black
A. The black colour is due to the manganese (VI) oxide \( M n_{2} O_{3} \)
B. The black colour is due to the manganese (VI) oxide \( M n O_{2} \)
C. The black colour is due to the manganese (VI) oxide \( M n_{2} O_{5} \)
D. None of these
Subject: Maths
If \( \boldsymbol{y}=|\cos \boldsymbol{x}|+|\sin \boldsymbol{x}|, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}= \)
\( \frac{2 \pi}{3} \) is
A \( \cdot \frac{1}{2}(\sqrt{3}+1) \)
B. \( 2(\sqrt{3}-1) \)
c. \( \frac{1}{2}(\sqrt{3}-1) \)
D. none of these
Subject: Physics
When \( 1 g \) of water at \( 100^{\circ} \mathrm{C} \) gets converted into steam at the same
temperature, the change in volume is approximately:
A \( .1 c c \)
в. \( 1000 \mathrm{cc} \)
\( c .1500 c c \)
D. \( 1670 c c \)
Subject: Physics
If the speed of longitudinal wave equals
10 times the speed of the transverse waves in a stretched wire of material
which has modulus of elasticity \( \mathrm{E} \), then the stress in the wire is
\( \mathbf{A} \cdot 100 E \)
в. \( \frac{E}{100} \)
c. \( \frac{E}{10} \)
D. \( 10 E \)
Subject: Biology
Match the names of the special cells
with the names of the organs / parts in which they occur. Choose the answer,
which gives the correct combinations of the alphabets of the two columns.
Cells
A. Cellsof Von \( \quad \) p. Small intestine Kupffer
q. Proximal convolutec
в. \( \beta \) cells \( \quad \) tubules
Brush border cells
D. Paneth cells
t. Islets of Langerhans
A. \( A-r, B-p, C-t, D-q \)
в. \( A-r, B-t, C-p, D-q \)
c. \( A-r, B-s, C-q, D-p \)
D. \( A-r, B-t, C-q, D-p \)
Subject: Physics
A ball is released from the top of a
height \( h \). It takes time \( T \) to reach the
ground. What is the position of the ball
(from ground) after time \( \frac{T}{3} \)
A \( \cdot \frac{h}{9} m \)
в. \( \frac{7 h}{9} m \)
c. \( \frac{8 h}{9} m \)
D. \( \frac{17 h}{18} \mathrm{m} \)
Subject: Chemistry
The \( \boldsymbol{H}-\boldsymbol{C}-\boldsymbol{H}, \boldsymbol{H}-\boldsymbol{N}-\boldsymbol{H}, \) and
\( H-O-H \) bond angles (in degrees) in
methane, ammonia and water are
respectively, closest to.
A. 109.5,104.5,107.1
в. 109.5,107.1,104.5
c. 104.5,107.1,104.5
D. 107.1,104.5,109.5
Subject: Physics
Assertion
The stress-strain behaviour varies from
material to material.
Reason
A rubber can be pulled to several times its original length and still returns to its
original shape.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Assertion
\( K_{p} \) can be equal to or less than or even
greater than the value of \( \boldsymbol{K}_{c} \)
Reason
\( \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{K}_{\boldsymbol{c}}(\boldsymbol{R} \boldsymbol{T})^{\boldsymbol{\Delta} \boldsymbol{n}} \)
the relation between \( \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{K}_{\boldsymbol{c}} \)
depends on the change in the number of moles of gaseous reactants and
products.
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
The general solution of the differential
equation \( (x+y) d x+x d y=0 \) is
A \( \cdot x^{2}+y^{2}=C \)
B . \( 2 x^{2}-y^{2}=C \)
c. \( x^{2}+2 x y=C \)
D. \( y^{2}+2 x y=C \)
Subject: Physics
For a longitudinal sound wave, \( (B \) is the engineering modulus of the medium
and \( \rho \text { is the density }) \)
A \( \cdot \frac{d^{2} y}{d x^{2}}=\frac{B}{\rho} \frac{d^{2} y}{d t^{2}} \)
в. \( \frac{d y}{d x}=\frac{B}{\rho} \frac{d y}{d t} \)
c. \( \frac{d^{2} y}{d t^{2}}=\frac{B}{\rho} \frac{d^{2} y}{d x^{2}} \)
D. \( \frac{d y}{d t}=\frac{B}{\rho} \frac{d y}{d x} \)
Subject: Maths
If \( A B C D \) is a parallelogram, \( A E \perp \)
DC and \( \boldsymbol{C F} \perp \boldsymbol{A D} \). If \( \boldsymbol{A B}=\mathbf{1 6 c m} \)
\( A E=8 c m \) and \( C F=10 \mathrm{cm}, \) find
\( A D \)
Subject: Maths
The area of the region bounded by \( y= \)
\( -1, y=2, x=y^{3} \) and \( x=0 \) is
A \( \cdot \frac{17}{4} \) sq. units
B. \( \frac{1}{4} \) sq. units
c. 4 sq. units
D. None of these
Subject: Maths
A man \( 1.5 \mathrm{m} \) tall walks away from a
lamp post \( 4.5 \mathrm{m} \) high at the rate of 4 km/hr. How fast is the farther end of
shadow moving on the pavement
A. \( 4 \mathrm{km} / \mathrm{hr} \)
B. \( 2 \mathrm{km} / \mathrm{hr} \)
c. \( 6 \mathrm{km} / \mathrm{hr} \)
D. None of these
Subject: Chemistry
At some temperature and under a
pressure of 4 atm, \( P C l_{5} \) is \( 10 \% \) dissociated. Calculate the pressure
at which \( P C l_{5} \) will be \( 20 \% \) dissociated,
temperature remaining same.
A. 1.84 atm
B. 0.97 atm
c. 2.87 atm
D. None of these
Subject: Physics
A moving coil galvanometer, having a
resistance \( G \), produces full scale
deflection when a current \( I_{g} \) flows
through it. This galvanometer can be
converted into (i) an ammeter of range
\( \mathbf{0} \operatorname{to} \boldsymbol{I}_{\mathbf{0}}\left(\boldsymbol{I}_{\mathbf{0}}>\boldsymbol{I}_{\boldsymbol{g}}\right) \) by connecting a shunt
resistance \( \boldsymbol{R}_{\boldsymbol{A}} \) to it and (ii) into a
voltmeter of range 0 to \( V\left(V=G I_{0}\right) \) by
connecting a series resistance \( \boldsymbol{R}_{\boldsymbol{V}} \) to it.
Then
\( \mathbf{A} \cdot_{R_{A} R_{V}}=G^{2}\left(\frac{I_{g}}{I_{0}-I_{g}}\right) \) and \( \frac{R_{A}}{R_{V}}=\left(\frac{I_{0}-I_{g}}{I_{g}}\right) \)
\( ^{\mathrm{B}} R_{A} R_{V}=G^{2} \) and \( \frac{R_{A}}{R_{V}}=\left(\frac{I_{g}}{I_{0}-I_{g}}\right)^{2} \)
\( ^{\mathbf{c}} \cdot_{R_{A} R_{V}}=G^{2} \) and \( \frac{R_{A}}{R_{V}}=\frac{I_{g}}{I_{0}-I_{g}} \)
\( ^{\mathrm{D}} R_{A} R_{V}=G^{2}\left(\frac{I_{0}-I_{g}}{I_{g}}\right) \) and \( \frac{R_{A}}{R_{V}}=\left(\frac{I_{g}}{I_{0}-I_{g}}\right)^{2} \)
Subject: Maths
If (1,-2,-2) and (0,2,1) are direction ratios of two lines, then the direction
cosines of a perpendicular to both the
lines are
\( ^{\mathrm{A}} \cdot\left(\frac{1}{3},-\frac{1}{3}, \frac{2}{3}\right) \)
в. \( \left(\frac{2}{3},-\frac{1}{3}, \frac{2}{3}\right) \)
\( ^{c} \cdot\left(-\frac{2}{3},-\frac{1}{3}, \frac{2}{3}\right) \)
D. \( \left(\frac{2}{\sqrt{14}},-\frac{1}{\sqrt{14}}, \frac{3}{\sqrt{14}}\right) \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\sin \boldsymbol{x}, \boldsymbol{x} \neq \boldsymbol{n} \boldsymbol{\pi} \\ \boldsymbol{2}, \boldsymbol{x}=\boldsymbol{n} \boldsymbol{\pi}\end{array}, \text { where } \boldsymbol{n} \boldsymbol{\epsilon} \mathbb{Z}\right. \)
and
\( \boldsymbol{g}(\boldsymbol{x})=\left\{\begin{array}{l}\boldsymbol{x}^{2}+\mathbf{1}, \boldsymbol{x} \neq \mathbf{2} \\ \boldsymbol{3}, \boldsymbol{x}=\mathbf{2}\end{array}\right. \)
Then \( \lim _{x \rightarrow 0} g(f(x)) \) is
\( A \)
B.
\( c \cdot 3 \)
D. none of these
Subject: Physics
place two substances, 1 and 2 in
contact with each other so that they exchange heat with each other only, until they come to the same temperature. The mass of substance 1
is twice as much as the mass of
substance 2. The temperature change for substance 2 is three times as much
as the temperature change for substance 1. How does the specific heat of substance 2 compare to the specific
heat of substance 1?
A. The specific heat of substance 2 is \( 3 / 2 \) as much as the specific heat of substance 1
B. The specific heat of substance 2 is \( 2 / 3 \) as much as the specific heat of substance 1
c. The specific heat of substance 2 is bigger than the specific heat of substance 1, but we cannot determine how much bigger
D. The specific heat of substance 2 is smaller than the specific heat of substance 1, but we cannot determine how much smaller
E. We cannot determine how the specific heat of substance 2 is related to the specific heat of substance
Subject: Physics
A converging lens of focal length \( f_{1} \) is placed in front of and coaxially with a
convex mirror of focal length \( f_{2} \). Their
separation is \( d \). A parallel beam of light
incident on the lens returns as a
parallel beam from the arrangement. This question has multiple correct options
A. The beam diameter of the incident and reflected beams must be the same
в. \( d=f_{1}-2 \mid f_{2} \)
c. \( d=f_{1}-\left|f_{2}\right| \)
D. If the entire arrangement is immersed in water, the conditions will remain unaltered
Subject: Physics
In an ac circuit the instantaneous
values of current and applied voltage are respectively \( i= \)
\( 2(A m p) \sin \left(250 \pi s^{-1}\right) t \) and \( \epsilon= \)
\( (10 V) \sin \left[\left(250 \pi s^{-1}\right) t+\frac{\pi}{3}\right] . \) Find the
instantaneous power drawn from the source at \( t=\frac{2}{3} m s \) and its average
value.
Subject: Physics
A heavy seesaw (i.e., not massless) is out of balance. A light girl sits on the
end that is tilted downward, and a heavy
body sits on the other side so that the
seesaw now balances. If they both move
forward so that they are one-half their original distance from the pivot point (the fulcrum) what will happen to the
seesaw?
A. The side the body is sitting on will tilt downward
B. The side the girl is sitting on will once again tilt downward
C. Nothing; the seesaw will still be balanced.
D. It is impossible to say without knowing the masses and the distances.
Subject: Maths
\( \frac{\boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}+\mathbf{7}}{(\boldsymbol{x}-\mathbf{3})^{3}}=\frac{\boldsymbol{A}}{\boldsymbol{x}-\mathbf{3}}+\frac{\boldsymbol{B}}{(\boldsymbol{x}-\mathbf{3})^{2}}+ \)
\( \frac{C}{(x-3)^{3}} \Rightarrow A= \)
\( A \cdot 2 \)
B . - -
\( c \)
\( D \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}}+\int_{0}^{1}\left(\boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{t} \boldsymbol{e}^{-\boldsymbol{x}}\right) \boldsymbol{f}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t} \)
then prove that \( f(x)=\frac{2(e-1)}{4 e-2 e^{2}} \cdot e^{x}+ \)
\( \frac{e-1}{4-2 e} \cdot e^{-x} \)
Subject: Physics
64 identical spheres of charge \( q \) and capacitance \( C \) each are combined to form a large sphere. The charge and capacitance of the large sphere is:
\( A \cdot 64 q, c \)
B. 169, 4C
\( c \cdot 649,4 c \)
D. \( 169,64 \mathrm{c} \)
Subject: Chemistry
An organic compound of molecular formula \( C_{4} H_{6},(A), \) forms precipitates with ammoniacal silver nitrate and
ammoniacal cuprous chloride.'A' has an isomer'B', one mol of which reacts
with one mol of \( B r_{2} \) to form 1.4 -dibromo-
2-butene. Another isomer of A is 'C', one
mole of \( C \) reacts with only 1 mol. of \( B r_{2} \) to give vicinal dibromide. A,B \& C are
\( A \)
сн \( _{3}- \) сн \( _{2}- \) с \( \equiv c \) н \( _{3} \) апа сн \( _{2}= \) сн \( - \) сн \( = \) си \( _{i} \)
B. \( C H_{3}-C \equiv C-C H_{3} \) and \( C H_{3}-C H=C= \)
\[
C H_{2} ; C H_{3}-C \equiv C-C H_{3}
\]
\( c \)
\[
\left.\left.\right|_{\mathrm{cH}_{2}} ^{\mathrm{cH}_{2}}\right\rangle\left._{\mathrm{c}=\mathrm{cH}_{2} \text { and }}\right|_{\mathrm{cH}_{2}-\mathrm{cH}} ^{\mathrm{cH}_{2}-\mathrm{cH}} ; \mathrm{cH}_{2}=\mathrm{cH}-\mathrm{cH}=\mathrm{cH}_{2}
\]
\( D \)
Subject: Physics
Two particles are executing SHM of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half of their magnitude.
What is the phase difference between them?
\( \mathbf{A} \cdot \pi / 6 \)
в. \( 4 \pi / 6 \)
c. \( \pi / 3 \)
D. 2\pi/6
Subject: Chemistry
Phosgene is formed by aerial oxidation
of \( \boldsymbol{C H} \boldsymbol{C l}_{3} \)
\( \boldsymbol{C H} \boldsymbol{C l}_{3}+\frac{1}{2} \boldsymbol{O}_{2} \longrightarrow \boldsymbol{C O C l}_{2}+\boldsymbol{H C l} \)
If true enter 1 , else enter 0 .
Subject: Maths
If \( D_{1} \) and \( D_{2} \) are two \( 3 \times 3 \) diagonal
matrices, then
A. \( D_{1} D_{2} \) is a diagonal matrix
B. \( D_{1}+D_{2} \) is a diagonal matrix
c. \( D_{1}^{2}+D_{2}^{2} \) is a diagonal matrix
D. 1,2,3 are correct
Subject: Physics
Two particles \( A \) and \( B \) initially at rest, move towards each other under a
mutual force of attraction. At the
instant when the speed of A is v and speed of \( \mathrm{B} \) is \( 2 \mathrm{v} \), the speed of centre of
mass of the system is :
A. zero
в.
\( c \cdot 1.5 v \)
D. 3
Subject: Physics
The displacement \( y \) in centimeters is
given in terms of time \( t \) in second by the
equation: \( y=3 \sin 3.14 t+4 \cos 3.14 t \)
then the amplitude of SHM is
\( A \cdot 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 5 \mathrm{cm} \)
D. \( 7 \mathrm{cm} \)
Subject: Chemistry
The correct order of acid strength of the
following substituted phenols in water
at \( 28^{\circ} C \) is:
A. p-nitrophenol<p-fluorophenol<p-chlorophenol
B. p-chlorophenol
D. p-fluorophenol<p-nitrophenol<p-chlorophenol
October 15, 2019
Q omuttam venkateshwarlu
(8) Share Save
Subject: Physics
A rectangular block is heated from \( 0^{\circ} C \)
to \( 100^{\circ} C \).
The percentage increase in its length is
\( 0.2 \% \).The percentage increase in its volume is:
A. \( 0.6 \% \)
B. \( 0.10 \% \)
\( c .0 .2 \% \)
D. \( 0.4 \% \)
Subject: Maths
True or False
A person stands at a point A due south of a tower and observes his elevation is
\( 60^{\circ} . \) He then walks westwards towards
where the elevation is \( 45^{\circ} . \) At a point \( C \)
on \( A B \) produced he finds it to be \( 30^{\circ} \)
then \( A B=2 B C \)
A. True
B. False
Subject: Chemistry
Assertion
Detergents with a straight chain of hydrocarbons are preferred over a branched chain
Reason
Detergents with branched chain hydrocarbon part are expensive.
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 transverse sinusoidal wave of
amplitude a, wavelength \( \lambda \) and frequency \( \boldsymbol{f} \) is travelling on a stretched string. The maximum speed of any point on the string is \( \frac{v}{10}, \) where \( v \) is the
speed of propagation of the wave. If \( \boldsymbol{a}= \)
\( 10^{-3} m \) and \( v=10 \mathrm{m} / \mathrm{s}, \) then \( \lambda \) is given
by This question has multiple correct options
\( \mathbf{A} \cdot \lambda=2 \pi \times 10^{-2} m \)
B. \( \lambda=10^{-3} m \)
C \( . \lambda=\pi \times 10^{-2} \)
D. \( \lambda=2 \pi \times 10^{-3} \)
Subject: Physics
A hollow cylinder has a charge \( \boldsymbol{q} \boldsymbol{C} \)
within it. If \( \phi \) is the electric flux in units
of \( V m \) associated with the curved
surface \( \mathrm{B} \), the flux linked with the plane
surface A in units of \( V m \) will be
A \( \cdot \frac{1}{2}\left(\frac{q}{\epsilon_{0}}-\phi\right) \)
B. \( \frac{q}{2 \epsilon_{0}} \)
\( c \cdot \frac{\phi}{3} \)
D. \( \frac{q}{\epsilon_{0}}-\phi \)
Subject: Physics
In a Young's double slit set-up, light from a laser source falls on a pair of
very narrow slits separated by 1.0 micrometer and bright fringes separated by 1.0 millmeter are observed on a distant screen. It the
frequency of the laser light is doubled, what will be the separation of the bright fringes?
A. \( 0.25 \mathrm{mm} \)
в. \( 0.5 \mathrm{mm} \)
c. \( 1.0 \mathrm{mm} \)
D. 2.0 \( m \) m
Subject: Chemistry
\( 1 \times 10^{-3} \mathrm{kg} \) of urea is present in 400
cubic centimetre solution at \( 310 \mathrm{K} \)
Calculate the approximate osmotic pressure of the solution. \( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}, \) molecular \right.
weight of urea \( =60 \) )
\( A \cdot 1 \) atm
B. 2 atm
\( c \cdot 4 a t m \)
\( D \cdot 5 \) atm
Subject: Physics
A vector perpendicular to \( \hat{i}+\hat{j}+\hat{k} \) is
\( \mathbf{A} \cdot \hat{i}-\hat{j}+\hat{k} \)
B. \( \hat{i}-\hat{j}-\hat{k} \)
c. \( -\hat{i}-\hat{j}-\hat{k} \)
D. \( 3 \hat{i}+2 \hat{j}-5 \hat{k} \)
Subject: Maths
\( \sum_{m=1}^{n} \tan ^{-1}\left(\frac{2 m}{m^{4}+m^{2}+2}\right) \) is equal
to
A \( \cdot \tan ^{-1}\left(n^{2}+n+1\right)-\frac{\pi}{4} \)
B \cdot \( \tan ^{-1}\left(n^{2}+n+1\right)+\frac{\pi}{4} \)
c. \( \tan ^{-1}\left(n^{2}+n-1\right)-\frac{\pi}{4} \)
D \( \cdot \tan ^{-1}\left(n^{2}-n-1\right)-\frac{\pi}{4} \)
Subject: Chemistry
During the process of electrorefining of \( C u, \) some metals present as impurity settle as anode mud. These are:
\( \mathbf{A} \cdot \operatorname{Sn} \) and \( A g \)
B. \( P b \) and \( Z n \)
c. \( A g \) and \( A u \)
D. Fe and \( N i \)
Subject: Chemistry
The following are the data for the reaction
\[
A+B \rightarrow \text { products }
\]
\( [A] \)
\( [\mathrm{B}] \)
Initial rate
\[
\begin{array}{l}
\left(\operatorname{mol} L^{-1} s^{-1}\right) \\
\begin{array}{llll}
\text { (i) } 0.1 \mathrm{M} & \text { 0.1 } \mathrm{M} & \text { 4. } 0 \times 10^{-4}
\end{array}
\end{array}
\]
(ii) \( 0.2 \mathrm{M} \quad 0.2 \mathrm{M} \)
\[
1.6 \times 10^{-3}
\]
(iii) \( 0.5 \mathrm{M} \)
\( 0.1 \mathrm{M} \)
\[
1.0 \times 10^{-2}
\]
(iv) \( 0.5 \mathrm{M} \quad 0.5 \mathrm{M} \)
\[
1.0 \times 10^{-2}
\]
The reaction rate when the
concentration of \( A \) and \( B \) are 0.4 M and
\( 0.7 \mathrm{M} \) respectively:
A \( \cdot 6.4 \times 10^{-2} \)
B. \( 6.4 \times 10^{-3} \)
c. \( 6.4 \times 10^{-4} \)
D. \( 6.4 \times 10^{-5} \)
Subject: Maths
Find the left and right hand limits of \( f(x)=\left\{\begin{array}{ll}\frac{3 x^{2}+2}{3 x-2} & x<1 \\ \frac{4 x^{2}-3}{4 x+3} & x>1\end{array} \text { at } x=1\right. \)
\( A \)
(a) 5 and \( \frac{1}{7} \)
B. \( (b)-\frac{1}{2} \) and -1
C \( \cdot(c)-\frac{7}{2} \) and 2
D \cdot (d) \( -\frac{9}{2} \) and 3
Subject: Chemistry
Which of the following reactions is an example of use of water gas in the synthesis of other compounds?
A \( \cdot C H_{4}(g)+H_{2} O_{(g)} \frac{\frac{1272 k}{N i}}{N} C O(g)+H_{2}(g) \)
B. \( C O_{4}(g)+H_{2} O_{(g)} \frac{673 k}{\text { Cactlyst }} C O_{2}(g)+H_{2}(g) \)
c. \( \left.C_{n} H_{2 n+2}+n H_{2} O_{(} g\right) \frac{1270 k}{N i} n C O+(2 n+1) H_{2} \)
D. \( C O(g)+2 H_{2}(g) \frac{\text { cobalt }}{\text { catalyst }} C H_{3} O H(l) \)
Subject: Maths
If \( \boldsymbol{O}=(\mathbf{0}, \mathbf{0}, \mathbf{0}), \mathbf{P}=(\mathbf{4}, \mathbf{3},-\mathbf{5}), \mathbf{Q}= \)
\( (-2,1,-8), \cos \angle P O Q=\frac{a}{\sqrt{b} \sqrt{c}} \) and
\( \mathbf{b}>\mathbf{c}, \) then \( \sqrt{\boldsymbol{b}}-\sqrt{\boldsymbol{c}} \) is
A . 19
B . \( \sqrt{69}-\sqrt{50} \)
c. -19
D. 17
Subject: Chemistry
Lanthanoids are:
A. 14 elements in the seventh period(At. no. 90 to 103 ) that are filling \( 5 f \) sublevel
B. 14 elements in the sixth period(At. No. 58 to 71 ) that are filling 4f sublevel.
C. 14 elements in the seventh period(At. No.58 to 71 ) that are filling 4f sublevel
D. 14 elements in the sixth period (At.No.90 to103)
Subject: Maths
Which one of the following is true for the
given triangle?
\( \mathbf{A} \cdot \angle 3=\angle 1+\angle 2 \)
B . \( \angle 1=\angle 3+\angle 2 \)
c. \( \angle 2=\angle 1+\angle 3 \)
D. Both (A) and (B)
Subject: Maths
Suppose \( \boldsymbol{f}:[-\mathbf{2}, \mathbf{2}] \rightarrow \boldsymbol{R} \) is defined by
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}-1 \text { for }-2 \leq x \leq 0 \\ x-1 \text { for } 0 \leq x \leq 2\end{array}\right. \)
then the \( \{x \in(-2,2): x \leq \)
\( \operatorname{Oand} f(|x|)=x\}= \)
A . \{-1\}
в. \{0\}
c. \( \left\{\frac{-1}{2}\right\} \)
D.
Subject: Physics
The number of turns in the coil of an AC
generator is 5000 and the area of the
coil is0.25 \( m^{2} . \) The coil is rotated at the
rate of 100 cycles /sec in the magnetic field of \( 0.2 W / m^{2} . \) then the peak value will be :
A. \( 786 \mathrm{kv} \)
B. 178 kV
c. \( 157 \mathrm{kv} \)
D. 123 kv
Subject: Physics
The mutual inductance of a pair of coils, each of \( \mathrm{N} \) turn, be M henry. If a current of i ampere in one of the coils is brought to zero in \( t \) second, the emf induced per turn in the other coil, in volt will be
A \( \cdot \frac{M i}{t} \)
в. \( \frac{N M i}{t} \)
c. \( \frac{M N}{i t} \)
D. \( \frac{M^{i}}{N t} \)
Subject: Physics
A coil of resistance \( 10 \Omega \) and 1000 turns
have the magnetic flux line of \( 5.5 \times \)
\( 10^{-4} W b . \) If the magnetic flux changed
to \( 5 \times 10^{-4} W \) b. in 0.1 sec, then the
induced charge in coil is
A. \( 50 \mu C \)
B. \( 5 \mu C C \)
\( c \cdot 2 \mu C \)
D. \( 20 \mu C \)
Subject: Physics
A long, straight metal has a long hole of
radius a drilled parallel to the rod axis
with cross-sectional view as shown. If
the rod carries a current \( I \), the value of
the magnetic field on the axis of the rod
is:
A \( \quad B=\frac{\mu_{0} I a^{2}}{2 \pi c\left(b^{2}-a^{2}\right)} \)
B. \( B=\frac{\mu_{0} I}{2 \pi c} \)
c. \( \quad B=\frac{\mu_{0} I a^{2}}{4 \pi c\left(b^{2}-a^{2}\right)} \)
\( \mathbf{D} \cdot B=z e r o \)
Subject: Chemistry
Substance \( A, C_{5} H_{8} \) is chiral When \( A \) is
treated with \( \boldsymbol{H}_{2} / \boldsymbol{P} \boldsymbol{t} \boldsymbol{B}, \boldsymbol{C}_{5} \boldsymbol{H}_{10}, \) is
produced \( B \) is achiral \( A \) can be:
A. 1- methylcyclobutene
B. 3-methylcyclobutene
c. trans-1,2-dimethylcyclopropane
D. cyclopentane
Subject: Chemistry
Which are acidic salts?
\( \mathbf{A} \cdot N a H_{2} P O_{2}, N a_{2} H P O_{3} \)
B \( \cdot N a_{2} H P O_{3}, N a_{2} H P O_{4} \)
\( \mathbf{c} \cdot N a H C O_{3}, N a H_{2} P O_{4} \)
D. all of these
Subject: Maths
\( \boldsymbol{y}=\tan ^{-1}\left[\frac{\log \left(\frac{\boldsymbol{e}}{\boldsymbol{x}^{2}}\right)}{\log \left(\boldsymbol{e} \boldsymbol{x}^{2}\right)}\right]+ \)
\( \tan ^{-1}\left(\frac{3+2 \log x}{1-6 \log x}\right), \) then \( \frac{d^{2} y}{d x^{2}}= \)
\( A \)
в.
\( c \cdot 0 \)
D. -
Subject: Chemistry
In the following redox reaction, number
of moles of \( C u(O H)_{2} \) reduced by one
mole of \( N_{2} H_{4} \) is :
\( \boldsymbol{C u}(\boldsymbol{O H})_{2}(\boldsymbol{s})+\boldsymbol{N}_{2} \boldsymbol{H}_{4}(\boldsymbol{a q}) \longrightarrow \)
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{N}_{2}(\boldsymbol{g}) \)
Subject: Physics
If the surface normal vector \( \hat{n} \) makes an
angle \( \theta \) with the electric field \( \vec{E} \), then
the electric flux through a surface of
\( \operatorname{area} d S \) is given by
A. \( \phi=E d S \sin \theta \)
\( \mathbf{B} \cdot \phi=E d S \cos \theta \)
c. \( \phi=d S \cos \theta \)
D. \( \phi=E \cos \theta \)