Complete the reactions with
appropriate products.
(i) \( C H_{3} C H O+N H_{2} O H \rightarrow X \)
(ii) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{P d C l}_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\boldsymbol{C u C l}_{2}}{\longrightarrow} \boldsymbol{Y} \)
(iii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \frac{C r \boldsymbol{O}_{3}-\boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{\lambda}} \boldsymbol{Z} \)
A. \( X=C H_{3} C H=N O H, Y=C H_{3} C H O, Z= \)
\( C H_{3} C H_{2} C H_{2} C O O H \)
B. \( X=C H_{3} C H_{2} N H_{2}, Y=C H_{3} C H_{2} C H O, Z= \)
\( C H_{3} C H_{2} C H_{2} C O O H \)
c. \( X=C H_{3} C O N H_{2}, Y=H C H O, Z=C H_{3} C O C H_{3} \)


Inside water, an air bubble behaves
A. Always like a flat plate
B. Always like a concave lens
C. Always like a convex lens
D. Always like a concave mirror


Blood of Pheretima is
A. Red
в. Вlue
c. colourless
D. None of the above


In the matrix, write:
\( A=\left[\begin{array}{ccc}2 & 5 & 19-7 \\ 35-2 & \frac{5}{2} & 12 \\ \sqrt{3} & 1 & -517\end{array}\right] \)
(i) The order of the matrix
(ii) The number of elements
(iii) Write the elements \( a_{13}, a_{21}, a_{33}, a_{24}, a_{23} \)


A toroid has a core(non-ferromagnetic) of inner radius \( 25 \mathrm{cm} \) and outer radius
\( 26 \mathrm{cm}, \) around which 3500 turns of a
wire are wound. If the current in the wire
is \( 11 A \), the magnetic field inside the core of the toroid is?


The maximum safe speed for a vehicle taking a turn on a curved banked road, does not depend upon
A. acceleration due to gravity
B. mass of the vehicle
c. angle of inclination with the horizontal
D. radius of curvature of the track


The ratio of value of gravitational constant \( G \) between Earth and Moon
system and Earth and Sun system is-
\( A \cdot>1 \)
в. \( <1 \)
c. 1
D. can't be calculated


An electric oven of \( 2 \mathrm{kW} \) power rating is operated in a domestic electric circuit
that has a current rating of 5A. If the supply voltage is \( 220 \mathrm{V} \), what result do you expect?
A . circuit will be breaked
B. fuse will blow
\( c . \) both
D. none


On increasing temperature from \( 200 \mathrm{K} \) to \( 220 \mathrm{K} \) rate of reaction \( \boldsymbol{A} \) increases by
3 times and rate of reaction \( B \)
increases by 9 times then correct relationship between activation energy of \( A \) and \( B \) is:
A. \( E_{A}=3 E_{B} \)
B \( .3 E_{A}=E_{B} \)
\( \mathbf{c} \cdot E_{B}=2 E_{A} \)
D. \( E_{A}=2 E_{B} \)


In a square box, a glass is to be surrounded by a \( 2 \mathrm{cm} \) glass border. If
the total area of the square is \( 121 \mathrm{cm}^{2} \) Find the dimension of the glass box.
A. \( 5 \mathrm{cm} \)
в. \( 6 \mathrm{cm} \)
\( c \cdot 7 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)


Account for the following:
(i) \( B i(V) \) is a stronger oxidizing agent
\( \operatorname{than} \boldsymbol{S b}(\boldsymbol{V}) \)
(ii) \( N-N \) single bond is weaker than
\( \boldsymbol{P}-\boldsymbol{P} \operatorname{single} \) bond
(iii) Noble gases have very low boiling points.


By dissolving 0.35 mole of sodium
chloride in water, \( 1.30 l \) of salt solution
is obtained. The molarity of the resulting solution should be reported
as:
A . 0.3
B. 0.269
c. 0.27
D. 0.2692


The flux of magnetic field through closed conducting loop of resistance 0.4 Whanges with time according to the
equation \( \phi=0.20 t^{2}+0.40 t+0.60 \) where
is time in seconds. Find
(i) the induced
emf at \( t=2 s . \) (ii) the average induced emf in \( t=0 \) to \( t=5 \) s. (iii) change passed through the loop in \( t=0 \) to \( t=5 s . \) (iv) average current in time interval \( t=0 \) to
\( t=5 s \)
(v) heat produced in \( t=0 \) to \( t=5 s \)


When is the virtual image formed?
A. when the rays of light after reflection or refraction appear to meet at a point
B. when the rays of light after reflection or refraction meet at a point
C. when the rays of light after deflection appear to meet at a point
D. when the lens rays after reflection or refraction meet at a point


\( A B C D \) is a quadrilateral in which \( A B \)
and \( C D \) are smallest and longest sides
respectively.
Prove that \( \angle A>\angle C a n d \angle B>\angle D \)


On a planet where \( \boldsymbol{g}_{\text {planet}}=\mathbf{0 . 2} \boldsymbol{g}_{\text {earth}} \)
What will be the difference in the height of column filled with mercury in a closed end manometer when the gas is
filled withe pressure of \( 2 a t m \) on earth (Assuming:outside pressure to be 1 atm on both planet; Volume of gas remain constant)
A . \( 30.4 \mathrm{cm} \)
в. \( 760 \mathrm{cm} \)
c. \( 380 c m \)
D. 152 ст


The material for making permanent magnets should have
A. high retentivity, high coercivity
B. high retentivity, low coercivity
c. low retentivity, high coercivity
D. low retentivity, low coercivity


Which metabolite is common in
respiration mediated breakdown of fats, carbohydrates and proteins?
A. Acetyl CoA
B. Glucose 6-phosphate
c. Fructose 1, 6-biphosphate
D. Pyruvic acid


The variable in the quadratic
polynomial \( t^{2}+4 t+5 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 4
\( c \cdot t \)
D. 5


initial speed of \( 25 \mathrm{m} / \mathrm{s} \) at an angle \( \boldsymbol{\theta} \)
with the horizontal as shown in figure. Write down the equation of the
projectile of the football when the ball is
7 m (along x-axis) away from the
footballer.
A \( \cdot y=7 \tan \theta-\frac{49 g}{1350 \cos ^{2} \theta} \)
B. \( y=\tan \theta-\frac{9 g}{1350 \cos \theta} \)
c. \( y=7 \cot \theta-\frac{49 g}{1350 \cos ^{2} \theta} \)
D. \( y=7 \tan \theta-\frac{41 g}{1350 \cos 2 \theta} \)


\( \int e^{x}\left[f(x)+f^{\prime}(x)\right] d x \) is equal to
\( \mathbf{A} \cdot e^{x} f(x)+c \)
B \( \cdot e^{x}+c \)
\( \mathbf{c} \cdot e^{x} f^{\prime}(x)+c \)
D. None of these


Figure shows equi-potential surfaces
for a two charges system. At which of
the labeled points point will an electron
have the highest potential energy?
A. Point \( A \)
B. Point \( B \)
\( c . \) Point \( C \)
D. Point \( D \)


The conductivity of \( 0.20 \mathrm{M} \) solution of
\( K C l \) at \( 298 \mathrm{K} \) is \( 0.0248 S c m^{-1} \)
Calculate its molar conductivity.
A \( \cdot 112 \operatorname{Scm}^{2} m o l^{-1} \)
B. \( 124 S c m^{2} m o l^{-1} \)
\( \mathbf{c} \cdot 136 S c m^{2} m o l^{-1} \)
D. 148 Scm \( ^{2} \) mol \( ^{-1} \)


Let \( \boldsymbol{A}=\boldsymbol{R} \times \boldsymbol{R} \) and \( * \) be a binary
operation on \( A \) defined by \( (a, b) * \) \( (c, d)=(a+c, b+d) . \) Show that \( * \) is
commutative and associative. Find the
identity element for \( * \) on \( A, \) if any


The difference between the wavelengths of the Stokes line and Anti-Stokes lines
in the Raman spectrum of \( \boldsymbol{H}-\boldsymbol{B} \boldsymbol{r} \)
molecule is \( 100 \dot{A} \). If the wavelength of the Anti-Stokes line is \( 5000 A \) the
wavelength of the incident radiation is:
В . \( 4950 \AA \)
c. \( 5100 \hat{h} \)
D. 4900 音


Water absorbs light. As depth increases intensity of light decreases linearly. At
13.5 feet, water absorbs 50 percent of
light which strikes the surface. At what depth would the light at noon be
reduced by \( \frac{1}{3.00,000} \) of the noon light.


A photon of wavelength \( 300 \mathrm{nm} \) interacts with a stationary hydrogen atom in ground state. During the interaction,whole energy of the photon is transferred to the electron of the
atom. State which possibility is correct (Consider,Plancks constant \( =\mathbf{4} \times \mathbf{1 0}^{-1 \mathbf{1}} \)
\( \mathrm{eVs}, \) velocity of light \( =3 \times 108 \mathrm{m} / \mathrm{s} \)
ionization energy of hydrogen \( =13.6 \mathrm{e} \)
A. Electron will be knocked out of the atom
B. Electron will go to any excited state of the atom
c. Electron will go only to first excited state of the atom
D. Electron will keep orbiting in the ground state of ato


Solve \( : 3^{1} \times^{10} C_{1}+3^{2} \times^{10} C_{2}+3^{3} \times^{10} \)
\( C_{3}+\ldots .+3^{10} \times^{10} C_{10}=? \)


An equilateral triangle has area \( A \sqrt{3} \) Three circles are drawn with their
centres at the vertices of the triangle. Diameter of each circle is equal to the
length of each side of the triangle. The area of the triangle NOT included in any
of the three circles is
A \( \cdot A\left(\sqrt{3}-\frac{\pi}{6}\right) \)
B . \( A(\pi-\sqrt{3}) \)
c. \( A(3 \pi-\sqrt{3}) \)
D. \( A\left(\sqrt{3}-\frac{\pi}{2}\right) \)


The atomic masses of three elements \( \boldsymbol{A} \)
\( B \) and \( C \) having similar chemical
properties are 7,23 and 39 respectively.
(a) Calculate the average atomic mass of elements \( A \) and \( C \)
(b) Compare the average atomic mass with atomic mass of \( \boldsymbol{B} \)
(c) What could the elements \( A, B \) and \( C \)
be?


In the figure given above, the position
time graph of a particle of mass \( 0.1 k g \)
is shown. The impulse at \( t=2 \sec \) is:
A \( .0 .2 k g m s e c^{-} \)
B. - \( 0.2 k g m \) sec \( ^{-1} \)
c. \( 0.1 k \) gmsec \( ^{-1} \)
D. - \( 0.4 k g \) msec\( ^{-} \)


ATP was discovered by
A. Lipmann
B. Lohmann
c. Blackman
D. Bowman


A satellite moves in a circular orbit
around the earth at height \( \boldsymbol{R} / 2 \) from
earth's surface where \( R_{e} \) is the radius
of the earth. Calculate its period of
revolution. Given \( \boldsymbol{R}_{e}=\mathbf{6 . 3 8} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m} \)


Is \( 1.0 \mathrm{M} \boldsymbol{H}^{+} \) solution under \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) at
1.0atm capable of oxidising silver metal
in the prescence of \( 1.0 \mathrm{M} A g^{+} \) ion?


Among the Lanthanoids, the one obtained by synthetic method is:
A . \( L u \)
в. \( P r \)
c. \( P m \)
D. \( G d \)


The total pressure in a mixture of 8 g of dioxygen and 4 g of dihydrogen confined in a vessel of \( 1 d m^{3} \) at \( 27^{\circ} C \) is :
\( \left(R=0.083 \text { bar } d m^{3} K^{-1} m o l^{-1}\right) \)
A . 44.02 bar
B . 35.35 bar
c. 56.025 bar
D. 42.39 bar


Standard electrode potential for \( \mathrm{Fe} \)
electrode are given as \( F e^{++}+2 e^{-} \rightarrow F e \)
\( E^{0}=-0.44 V F e^{3+}+e^{-} \rightarrow F e^{++} E^{0}= \)
\( +0.77 V F e^{++}, F e^{+++} \) and Fe block are
kept together then:
A \( \cdot\left[F e^{+++}\right] \) decreases
B . \( \left[F e^{+++}\right] \) increases
C \( \cdot\left[F e^{++} F e^{+++}\right] \) remains unchanged
D. \( \left[F e^{++}\right] \) decreases


tood
yo


What is the systematic position of funaria?


A 5 m \( 60 \mathrm{cm} \) high vertical pole casts a
shadow \( 3 m 20 \mathrm{cm} \) long. Find at the
same time (i) the length of the shadow cast by another pole 10 m \( 50 \mathrm{cm} \) high
(ii) the height of a pole which casts a shadow 5 m long.


Hydroboration-oxidation of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}= \)
\( \boldsymbol{C H}_{2} \) produces:
A. \( C H_{3} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H(O H) C H_{3} \)
c. \( C H_{3} C H(O H) C H_{2} O H \)
D. \( C H_{3} C O C H_{3} \)


\( \left[\boldsymbol{P T B r} \boldsymbol{C l}\left(\boldsymbol{N O}_{2}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)\right] \boldsymbol{I} \) complex on
ionization gives the ion?
A \( \cdot C l^{-} \)
B. \( B r \)
\( c \cdot I^{-} \)
D. \( N O_{2}^{-} \)


Starting from rest,a car moves with
uniform acceleration and attains a
velocity of \( 72 k m / h r \) in \( 2 s . \) It then
moves with uniform speed for \( 25 s \) and
is then brought to rest in \( 10 s \) under
uniform retardation.Find the total
distance travelled using velocity time graph.


Describe any two types of cartilaginous joints giving examples.


According to the Arrhenius equation,
This question has multiple correct options
A. A high activation energy usually implies a fast reaction.
B. Rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
C. Higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant
D. The pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy.


A closed box made of steel of uniform
thickness has length, breadth and
height \( 12 \mathrm{dm}, 10 \mathrm{dm} \) and \( 8 \mathrm{dm} \)
respectively. If the thickness of the steel sheet is \( 1 \mathrm{dm}, \) then the inner
surface area is
\( \mathbf{A} \cdot 456 \mathrm{dm}^{2} \)
B. \( 376 \mathrm{dm}^{2} \)
\( \mathbf{c} \cdot 264 \mathrm{dm}^{2} \)
D. \( 696 \mathrm{dm}^{2} \)


The set of all points of discontinuities of
fofofof, \( g \) where \( f \) and \( g \) are given by


Two proton beams are moving in the
parallel direction. Which of the following
statements are correct.
This question has multiple correct options
A. Force between the proton beams will be attractive
B. Magnetic force between proton beams will be attractive
C. Repulsive force will be greater than attractive forces
D. Magnetic and electrostatic forces will cancel each other


Prove that \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{1}|+|\boldsymbol{x}-\mathbf{1}|+ \)
\( |x-3| \) is continuous on \( R \) but not
differentiable at \( x=1,2 \) and 3 only.


Evaluate the integral \( \int_{0}^{1} \cos ^{-1} x d x \)
A .
B. -
c. \( \frac{\pi}{2} \)
D.


Which of the following orbital overlapping will form Pi bond?
\( \underbrace{1}_{s}+\underbrace{\bigcup_{s}}_{s} \)
в.
\( c \)
\( \underbrace{S_{p_{v}}}^{y}+\underbrace{V_{p_{y}}}_{V_{V}} \)
D.


A \( 200 M e V \) proton enters a region of the magnetic field of intensity 5 T. The
magnetic field points from south to north and the proton in moving along the vertical. The value of the force
acting on the proton will be
A. zero
В. \( 1.8 \times 10^{-10} N \)
c. \( 3.2 \times 10^{-18} N \)
D. \( 1.6 \times 10^{-6} N \)


The cost of an article is decreased by 15
\%. If the original cost is Rs. \( 80, \) find the
new cost.
\( \mathbf{A} \cdot 68 \)
B. 65
c. 57
D. 55


\( \int_{0}^{\pi}|\cos x| d x=? \)
\( A \cdot 2 \)
B. \( \frac{3}{2} \)
c. 1
D.


An object of mass \( 1 k g \) is dropped from
a height of 20 m. It hits the ground and
rebounds with the same speed. Find the change in momentum. (Take \( \boldsymbol{g}= \)
\( \left.10 m / s^{2}\right) \)


Ohm's law is true:
A. For metallic conductor at low temperature
B. For metallic conductor at high temperature
C. For electrolytes, when current passes through them
D. For diode when current flows


In the figure, \( \angle A C B=90^{0} \) and radius
of big circle \( =2 c m, \) then the radius of
small circle is (in \( c m) \)
\( A \cdot 3-2 \sqrt{2} \)
B. \( 4-2 \sqrt{2} \)
c. \( 7-4 \sqrt{2} \)
D. \( 6-4 \sqrt{2} \)


Assertion
The focal length of a lens does not
depend on the medium in which it is submerged
Reason \( \frac{1}{\boldsymbol{f}}=\frac{\boldsymbol{\mu}_{2}-\boldsymbol{\mu}_{1}}{\boldsymbol{\mu}_{1}}\left(\frac{1}{\boldsymbol{R}_{1}}-\frac{1}{\boldsymbol{R}_{2}}\right) \)
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


Find the mean variance and standard
deviation using short-cut method
\( \begin{array}{ll}\begin{array}{l}\text { Height } \\ \text { in cms }\end{array} & \text { No. of children } \\ \text { 70-75 } & 3 \\ \text { 75-80 } & 4 \\ 80-85 & 7 \\ \text { 85-90 } & \text { 7 } \\ \text { 90-95 } & 15 \\ \text { 95-100 } & 9 \\ \text { 100-105 } & 6 \\ \text { 105-110 } & 6 \\ \text { 110-115 } & \text { 3 }\end{array} \)


Q Type your question.
1811 Iclicucu ny a pian
4
B
\( c \)
\( D \)


Recall that two circles are congruent if
they have the same radius then equal chords of congruent circles subtend equal angles at their centres.
A . True
B. False


Identify if the given Lewis structure is
correct
If correct enter 1 , else enter 0 .


The pKa values for the three groups
\( P, Q, R \) are 4.3,9.7 and 2.2 respectively Calculate the isoelectric point of the
amino acid rounded to the nearest
integer?


Coulomb of charge contains
\( \overline{\mathbf{2 5}} \)
electrons
\( \mathbf{A} \cdot 10^{15} \)
В. \( 10^{18} \)
\( c \cdot 10^{20} \)
D. None of these


Two wires of different material and
radius have their length in ratio of 1: 2
if these were stretched by the same force, the strain produced will be in the
ratio.
A . 4: 1
B. 1: 1
c. 2: 1
D. 1: 2


Solve the equation:cos \( ^{-1}\left(\frac{x^{2}-1}{x^{2}+1}\right)+ \)
\( \sin ^{-1}\left(\frac{2 x}{x^{2}+1}\right)+\tan ^{-1}\left(\frac{2 x}{x^{2}-1}\right)= \)
3
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \cot 20^{\circ} \)
\( c \cdot \frac{-1}{\sqrt{3}} \)
D. \( \tan 20 \)


IR region lies between.
A. Radio waves and microwave regions
B. Microwave and visible
C. Visible and UV region
D. UV rays and X-ray region


Which of the following weights less when weighted in magnetic field?
A. \( S r C l_{3} \)
в. \( F e C l_{3} \)
c. \( T i C l_{3} \)
D. \( V C l_{3} \)


A full-wave p-n diode rectifier uses a load resistor of \( 1500 \Omega \). No filter is used.
The forward bias resistance of the diode
is \( 10 \Omega . \) the efficiency of the rectifier is
A . \( 81.2 \% \)
B . \( 40.6 \% \)
c. \( 80.4 \% \)
D. \( 40.2 \% \)


Fill in the blank:
charges collect near the upper edges of the clouds.
A. Negative
B. Positive
c. Neutral
D. No


A neutron breaks into a proton and an electron. Calculate the energy produced in this reaction is MeV. Mass of an
electron \( =9 \times 10^{-31} k g, \) mass of proton
\( =1.6725 \times 10^{-27} k g, \) mass of neutron
\( =1.6747 \times 10^{-27} k g, \) and speed of light
\( =3 \times 10^{8} m s^{-1} \)


Water flows out through a circular pipe whose internal diameter is \( 2 \mathrm{cm} \), at the
rate of 6 metre per second into a cylindrical tank, the radius of whose base is \( 60 \mathrm{cm} \). By how much will the
level of water rise in 30 minutes?
A \( .2 m \)
в. \( 3 m \)
\( c .4 m \)
D. \( 5 m \)


During an \( \alpha \) -decay, the atomic number of parent element
and mass number
4


Q Type your question
by \( \boldsymbol{S}_{N} \mathbf{1} \) IS \( \boldsymbol{3}^{v}>\boldsymbol{Z}^{v} \mathbf{1}^{v} \boldsymbol{K} \boldsymbol{X} \) and \( \mathbf{b} \mathbf{y} \boldsymbol{\nabla} \boldsymbol{V}^{-} \)
path is \( 1^{\circ}>2^{\circ}>3^{\circ} R X \)
Which of the following statements are
correct for the above energy diagras of
\( \boldsymbol{S}_{N} \mathbf{1} \) and \( \boldsymbol{S}_{N} \mathbf{2} \) reactions?
\( (a) \)
Fig. \( (\mathbf{b}) \)
This question has multiple correct options
\( \mathbf{A} \cdot(I) \) is Fig (a) and \( (I V) \) in Fig. (b) represent \( S_{N} 1 \) reaction
B. \( (I I) \) is Fig (a) and \( (I I I) \) in Fig. (b) represent \( S_{N} 2 \) reaction
\( \mathbf{C} \cdot \) Fig.
(a) and Fig. (b) are the energy diagrams for \( 1^{\circ} R X \)
and \( 3^{\circ} R X \) respectively
\( D \cdot F i g \)
(a) and Fig. (b) are the energy diagrams for \( 3^{\circ} \) RX
and \( 1^{\circ} R X \) respectively


Mohan lends Rs.4,800 to John for \( 4 \frac{1}{2} \) years and Rs.2,500 to Shyam for 6 years and receives a total sum of Rs.2,196 as
interest. Find the rate per cent per annum, it being the same in both the
cases.
A . २\%
B. 5\%
c. \( 6 \% \)
D. 9\%


The D.E whose solution is \( y=c \sin x \) is:
This question has multiple correct options
A \( \cdot \frac{d y}{d x}=y \cot x \)
\( \mathbf{B} \cdot y_{2}+y=0 \)
C \( \cdot \frac{d y}{d x}=y \cos x \)
D. \( \frac{d y}{d x}=y \csc x \)


Commercial silk is obtained from
A. Cocoon or pupa
B. Caterpillar
c. Adult moth
D. Both egg and adult moth


Which of the following quantities do not change when a resistor connected to a
battery is heated due to the current?
A . Resistance
B. Resistivity
c. Drift velocity
D. Free electron density


Calculate the weight of \( F e O \) produced
from 6.7 g of \( V O \) and 4.8 g of \( F e_{2} O_{3} \) \( 2 V O+3 F e_{2} O_{3} \rightarrow 6 F e O+V_{2} O_{5} \)
(Given that the atomic weight of \( V \) is 51
amu and of \( F e \) is 56 amu.
A .4 .32
B. 7.755
c. 2.585
D. 0.0718


Stars, in a constellation form:
A. no shape
B. any arbitrary shape
c. a recognisable shape
D. a straight line always


While opening a tap with two fingers, the forces applied are :
A. Equal in magnitude
B. Parallel to each other
c. opposite in direction
D. All the above


A variable line is such that its distance
from origin always remains 2 units. Minimum value of the length of
intercept made by it between coordinate axis is
A \( \cdot 12 \)
B. 4
\( c \cdot 8 \)
D. 16


Solve: \( (\boldsymbol{x}+\boldsymbol{y})(\boldsymbol{d} \boldsymbol{x}-\boldsymbol{d} \boldsymbol{y})=\boldsymbol{d} \boldsymbol{x}+\boldsymbol{d} \boldsymbol{y} \)


Calculate the angle of minimum deviation of ray of light passing through an equilateral prism of refractive index \( \mathbf{1 . 7 3 2} \)


Sum of atomic masses of all atoms in a
formula unit of an ionic compound is known as:
A. molecular mass
B. formula mass unit
c. atomic mass
D. None of the above


A long string under tension of \( 100 N \) has one end at \( x=0 . \) A sinusoidal wave
is generated at \( x=0 \) whose equation is
given by
\( \boldsymbol{y}= \)
\( (0.01 c m) \sin \left[\left(\frac{\pi x}{10} m\right)-50 \pi t(s e c)\right] \)
Sketch the shape of the string at \( t= \) \( \frac{1}{50} s e c \)


Gold does not occur in the combined
form. It does not react with air or water.
It is in the \( _{\text {一一一十日 }} \)
A. native
B. combined
c. original
D. liquid


Check whether the following are Quadratic equations
\( (x+2)^{3}=2 x\left(x^{2}-1\right) \)


Study the given figure carefully.
Which of the following reactions explains the above change most appropriately?
A. \( Z n S O_{4}+C u \rightarrow C u S O_{4}+Z n \)
в. \( C u S O_{4}+F e \rightarrow F e S O_{4}+C u \)
c. FeSO\( _{4}+C u \rightarrow \) CuSO\( _{4}+ \) Fe
D. \( C u S O_{4}+Z n \rightarrow Z n S O_{4}+C u \)


The equiconvex lens has a focal length
'f. If the lens is cut along the line perpendicular to principal axis and passing through the pole, what will be the focal length of any half part?
A \( \cdot \frac{f}{2} \)
B . \( 2 f \)
\( c \cdot \frac{3 f}{2} \)
D. \( f \)


Consider the following half-cell
reactions and associated standard half-
cell potentials and determine the
maximum voltage that can be obtained by combination resulting in
spontaneous processes:
\( \boldsymbol{A u} \boldsymbol{B r}_{4}^{-}(\boldsymbol{a q})+\boldsymbol{3} \boldsymbol{e}^{-} \rightarrow \boldsymbol{A u}(\boldsymbol{s})+ \)
\( 4 B r^{-}(a q) ; E^{\circ}=-0.86 V \)
\( \boldsymbol{E} \boldsymbol{u}^{3+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{e}^{-} \rightarrow \boldsymbol{E} \boldsymbol{u}^{2+}(\boldsymbol{a} \boldsymbol{q}) ; \boldsymbol{E}^{\circ}= \)
\( -0.43 V \)
\( \boldsymbol{S} \boldsymbol{n}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{S} \boldsymbol{n}(\boldsymbol{s}) ; \boldsymbol{E}^{\circ}= \)
\( -0.14 V \)
\( \boldsymbol{I O}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O}(l)+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \)
\( \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) ; \boldsymbol{E}^{\circ}=+\mathbf{0 . 4 9} \boldsymbol{V} \)
\( \mathbf{A} \cdot+0.72 \)
B. +1.54
c. +1.00
D. +1.35


The unit of electron affinity is:
A. kcal/mole
B. erg-sec
\( c \cdot A^{c} \)
D. no unit


Cell in \( G_{0} \) phase of cell cycle
A. Exit cell cycle
B. Enter cell cycle
c. suspend cell cycle
D. Terminate cell cycle


Four cows are tethered at four corners of
a square plot of side \( 50 \mathrm{m} \) as shown in
figure. What area will be left ungrazed?


In the given figure, \( \boldsymbol{A B} \perp \boldsymbol{B C}, \boldsymbol{F G} \perp \)
\( B C \) and \( D E \perp A C . \) Prove that \( \triangle A D E \)
\( \sim \triangle G C F \)


A school has five houses \( A, B, C, D \) and \( E \)
A class has 23 students, 4 from house
A, 8. from house B, 5 from house C, 2
from house 0 and rest from house \( \mathrm{E} \)
A single student is selected at random ,to be the class monitor. The probability that the selected student is not from \( A \),
Band C is?
\( \mathbf{A} \cdot \frac{4}{23} \)
B. \( \frac{6}{23} \)
\( c \cdot \frac{8}{23} \)
D. \( \frac{17}{23} \)


n \( N i(C O)_{4}, \) the oxidation state of Ni is:
\( A \cdot 4 \)
B.
\( c \cdot 2 \)
D. 8


The order in which the following oxides are arranged to decreasing basic
nature is \( C u O, N a_{2} O, M g O, A l_{2} O_{3} \)


Which of the states Snell's law?
A. Incident ray, refracted ray and the normal at the point of incidence all lies in the same plane
B. \( \frac{\sin i}{\sin r}= \) constant (for a given media)
C. Angle of incidence \( = \) Angle of refraction
D. All


If an equilateral triangle, having centroid at the origin, has a side along
the line, \( x+y=2 \), then the area (in
sq.units) of this triangle is:
\( \mathbf{A} \cdot \mathbf{6} \)
B. \( 6 \sqrt{3} \)
c. \( \frac{9}{2} \sqrt{3} \)
D. \( 3 \sqrt{6} \)


I. Ethanol
II. Acetic acid
III. Phenol
IV. Acetonitrile
The acidity of compounds I-IV in water follows the order:
A. \( I V<I<I I I<I I \)
в. \( I<I I<I I I<I V \)
c. \( I V<I<I I<I I I \)
D. \( I V<I I I<I<I I \)


Observe the relationship between the
first two words and then fill in the fourth
place
(a) Angiosperms: roots :: Rhodophyta
(b) Fern: prothallus :: moss:
(c) Moss : capsule :: fern:
(d) Angiosperms: flowers :: conifers


What are isotonic solutions? Give an
example.


A positive charge \( Q \) is uniformly distributed along a circular ring of radius R. A small test charge q is placed
at the center of the ring figure. Then which statement is incorrect:
A. If \( q>0 \) and is displaced away from the centre in the plane of the ring,it will be pushed back towards the centr
B. if \( q<0 \) and is displaced away from the centre in the plane of the ring,it will never return towards the centre and will continue moving till it hits the ring
C. ifif q>0, it will perform SHM for small displacement along the axis
D. \( q \) at the centre of the ring is in an unstable equilibrium within the plane of the ring \( q>0 \)


The side of a rhombus is \( 26 m \) and
length of one of its diagonal is 20 m. The
area of the rhombus is
A \( \cdot 120 m^{2} \)
В. \( 240 \mathrm{m}^{2} \)
c. \( 480 m^{2} \)
D. None


The conditions favourable for the
reaction: \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g) ; \triangle H^{\circ}=-198 K J \) are
A. low temperature,high pressure
B. any value of T and P
c. low temperature and low pressure
D. high temperature and high pressure


From the given figure, we can find that
\( \angle A B C=47^{\circ} \)
A. True
B. False


In borex bead test which compound is formed:
A. ortho borate
B. meta borate
c. dDouble oxide
D. tetra borate


Find \( a \) so that roots of \( x^{2}+2(3 a+ \)
5) \( x+2\left(9 a^{2}+25\right)=0 \) are real.


In a moving coil galvanometer, the magnetic pole pieces are made cylindrical and a soft iron core is placed at the centre of the coil,the purpose for doing so is:
A. to make the magnetic field strong
B. to make the magnetic field strong and radial
c. to make the magnetic field uniform
D. to make the magnetic field strong and uniform


A particle of mass \( m \) is executing
oscillations about the origin on the \( x- \) axis. It's potential energy is \( \boldsymbol{U}(\boldsymbol{x})= \)
\( \boldsymbol{k}|\boldsymbol{x}|^{3}, \) where \( \boldsymbol{k} \) is a positive constant. If
the amplitude of oscillation is \( a \), then
its time period \( \boldsymbol{T} \) is:
A . proportional to \( \frac{1}{\sqrt{a}} \)
B. independent of \( a \)
c. proportional to \( \sqrt{a} \)
D. proportional to \( a^{3 / 2} \)


In a hydrogen atom, an electronjumps from the second orbit to the first orbit
Find out
The wavelength of the radiation is :
A \( \cdot 1.325 \times 10^{3} \mathrm{A} \)
в. \( 2.430 \times 10^{3} \) А
c. \( 1.215 \times 10^{3} \) A
D. \( 2.255 \times 10^{3} \) A


A point source of light at the surface of a sphere causes a parallel beam of light to emerge from the opposite surface of the sphere. The refractive index of the material of the sphere is?
A . 5
В. \( 5 / 3 \)
c. 2
D. 2.5


Match list A and list B accurately:
List \( \mathbf{A} \) List B
a) spherical wave front
e) linear
source
b) plane wave front
f) point light source
c) cylindrical wave front
g) at infinite distance
\( A \cdot(a, f) ;(b, g) ;(c, e) \)
B. ( a, f); (b, e); (c, g)
\( c \cdot(a, g) ;(b, f) ;(c, e) \)
D. \( (a, e) ;(b, g) ;(c, f) \)


For the path \( P Q R \) in a conservative
force field, the amount of work done in
carrying a body from \( P \) to \( Q \& \) from \( Q \) to
\( R \) are \( 5 J \& 2 J \) respectively. The work
done in carrying the body from \( \boldsymbol{P} \) to \( \boldsymbol{R} \)
will be-
в. 3 J
c. \( \sqrt{21} J \)
D. Zer


Assertion
Ascomycetes fungi produce asexual spore which are called ascospore.
Reason
Ascospores are produced endogenously in sac like asci.
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 and Reason are correct


An electron and a photon have same wavelength of \( 10^{-9} \mathrm{m} . \) If \( \mathrm{E} \) is the energy
of the photon and p is the momentum of the electron, the magnitude of E/p in \( \mathrm{S} \) units is?
A. \( 1.00 \times 10^{-9} \)
B. \( 1.50 \times 10^{8} \)
c. \( 3.00 \times 10^{8} \)
D . \( 1.20 \times 10^{7} \)


A small ring of mass \( m \) is connected
with a particle of same mass by an ideal string \( \& \) the whole system is released as shown in figure. Coefficient of friction between ring \( A \) and wire is 3/5. Ring A will start sliding when connecting string will make an angle \( (5 \times x)^{0} \) with the vertical. Find \( x \)
(particle is free to move and ring can slide only)


A complex number is represented by an
ordered pair \( z:(3,4), \) which of the
following is true for \( z ? \)
A. \( z=3+4 i \)
В. \( z=4+3 i \)
\( \mathbf{c} \cdot z=3+4 \)
D. None of these


The primary dentition in human differs from permanent dentition in not having one of the following type of teeth
A. Canine
B. Premolars
c. Molars
D. Incisors


Explain how animals in Vertebrata are classified into further subgroups.


Observe the following picture and
answer the following question:
What is corrosion?


Nucleic acid in chromosomes of
bacteria are
A. Of two types DNA and RNA
B. Linear DNA
c. circular DNA
D. Linear RNA


Which is the correct decreasing order of nucleophilic addition of carbonyl
compound?
A. aldehyde, ketone, ester, acid, amide
B. acid, aldehyde, ketone, ester, amide
c. amide, aldehyde, ketone, ester, acid,
D. ketone, aldehyde, ester, acid, amide


Which of the following do not exist?
A. \( N C l_{5} \)
в. \( P H_{5} \)
\( \mathbf{c} \cdot\left[B C l_{6}\right]^{3-} \)
D. All of these


The temperature of a thin uniform rod
increases by t. Its moment of inertia about an axis perpendicular to its length increases by:
A .
B. \( \alpha I t \)
\( c \cdot 2 \alpha I \)
D. \( \alpha^{2} I \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{0}\end{array}\right], \) then \( \boldsymbol{A}^{2} \) is equal to
\( A \cdot\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \)
B. \( \left[\begin{array}{ll}1 & 0 \\ 1 & 0\end{array}\right] \)
c. \( \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}0 & 1 \\ 0 & 1\end{array}\right] \)


The yield of the products in the reaction, \( \boldsymbol{A}_{2(\boldsymbol{g})}+\mathbf{2} \boldsymbol{B}_{(\boldsymbol{g})} \rightleftharpoons \boldsymbol{C}_{(\boldsymbol{g})}+\boldsymbol{Q} \boldsymbol{k} \boldsymbol{J} \) would be
higher at :
A. high temperature and high pressure
B. high temperature and low pressure
C. low temperature and high pressure
D. low temperature and low pressure


Splenic artery arises from?
A. Anterior mesenteric artery
B. Coeliac artery
c. Posterior mesenteric artery
D. Intestinal artery


A charge of \( 20 \mu C \) is placed on the
positive plate of an isolated parallelplate capacitor of capacitance \( 10 \mu F \) Calculate the potential difference developed between the plates.


For an electron in the second orbit of
Bohr's hydrogen atom, the moment of linear momentum is:
\( A \cdot \pi h \)
в. \( 2 \pi r h \)
\( c \cdot \frac{h}{\pi} \)
D. \( \frac{2 h}{\pi} \)


pumps deoxygenated blood to the
lungs.
A. Right auricle
B. Right ventricle
c. Left auricle
D. Left ventricle


One end of a rod of length \( L \) is fixed to a
point on the circumference of a wheel of radius R. The other end is sliding freely
along a straight channel passing
through the centre 0 of the wheel as
shown in the figure. The wheel is
rotating with a constant angular velocity \( \omega \) about \( 0 . \) Taking \( T=\frac{2 \pi}{P \omega} \) the
motion of the rod is?
A. Simple harmonic with a period of \( T \)
B. Simple harmonic with a period of \( T / 2 \)
c. Not simple harmonic but periodic with a period of \( T \)
D. Not simple harmonic but periodic with a period of \( T / 2 \)


The length of perpendicular from the
point (7,14,5) to the plane \( 2 x+4 y- \)
\( z=2 \) is
A \( \cdot 21 \sqrt{3} \)
is
B. \( 3 \sqrt{21} \)
c. \( \sqrt{321} \)
D. \( 5 \sqrt{2} \)


What will be the pH value of a solution of \( 500 m L \) containing \( 5 g \) acetic acid
and \( 7.2 g \) of sodium acetate? \( K_{a}= \)
\( 1.8 \times 10^{-5} \) at \( 25^{\circ} C \)


Assertion
In the human body the heart acts as the
pump that circulates blood through different parts of the body, transferring
heat by forced convection.
Reason
In forced convection,material is forced
to move by a pump or by some other
physical means.
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


A reaction involving two different
reactants:
A. can never be a second order reaction.
B. can never be a unimolecular reaction
c. can never be a bimolecular reaction
D. can never be a first order reaction


An object may have
This question has multiple correct options
A. Varying speed without having varying velocity
B. Varying velocity without having varying speed
C. Non zero acceleration without having varying velocity
D. Non zero acceleration without having varying speed


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


For how many real values of \( ^{\prime} m^{\prime} \) the points \( \boldsymbol{A}(\boldsymbol{m}+\mathbf{1}, \mathbf{1}), \boldsymbol{B}(\boldsymbol{2 m}+\mathbf{1}, \boldsymbol{3}) \) and
\( C(2 m+2,2 m) \) are collinear.


To which type of reaction, Le Chatelier's principle can always be applied?
A . Reversible
B. Elementary
c. synthesis
D. Decomposition
E. Double Replacement


Which of the following symbol represents a universal gate?
\( A \)
в.
\( c \)
D.


Angles forming a linear pair can both be acute angles.
A. True
B. False
c. Ambiguous
D. Data Insufficient


Wavelength of gamma rays are:
\( \mathbf{A} \cdot 10^{-10} m \) to less than \( 10^{-14} m \)
B. \( 10^{-14} \mathrm{m} \) to less than \( 10^{-10} \mathrm{m} \)
C \( \cdot 10^{-11} \mathrm{m} \) to less than \( 10^{-14} \mathrm{m} \)
D. \( 10^{-14} \mathrm{m} \) to less than \( 10^{-6} \mathrm{m} \)


After balancing and reducing the coefficients to lowest whole number
terms, What is the coefficient of \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
\( \boldsymbol{H} \boldsymbol{C l}+\boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{K} \boldsymbol{C l}+ \)
\( M n C l_{2}+C l_{2} \)
\( A \cdot 1 \)
B. 2
\( c .5 \)
D. 8
E . 16


If \( p-\frac{1}{p}=4, \) find the value of \( p^{4}+\frac{1}{p^{4}} \)
A . 16
B. 18
c. 324
D. 322


Light years is the unit of:
A. time
B. length
c. mass
D. none of these


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. \( \quad B=\frac{\mu_{0} I a^{2}}{4 \pi c\left(b^{2}-a^{2}\right)} \)
\( \mathbf{D} \cdot B=z e r o \)


f the equilibrium constant for reaction
(i) is \( 2, \) what is the equilibrium constant for reaction (ii)?
\( C O_{2} \rightleftharpoons C O+\frac{1}{2} O_{2 \cdots \cdots}(i) \)
\( 2 C O+O_{2} \rightleftharpoons 2 C O_{2} \dots( \) ii)
A.
в.
c. 1
D.


A spot light \( S \) rotates in a horizontal
plane with a constant angular velocity of \( 0.1 \mathrm{rad} / \mathrm{s} \). The spot of light \( \boldsymbol{P} \) moves
along the wall at a distance \( 3 m \). What is
the velocity of the spot \( \boldsymbol{P} \) when \( \boldsymbol{\theta}=\mathbf{4 5}^{o} \) ?
A. \( 0.6 \mathrm{m} / \mathrm{s} \)
B. \( 0.5 \mathrm{m} / \mathrm{s} \)
\( c .0 .4 m / s \)
D. \( 0.3 \mathrm{m} / \mathrm{s} \)


Reverse saturation current of a diode:
A. is independent of temperature
B. increases with increase in temperature
C. decreases with increase in temperature
D. may increase or decrease with increase in temperature depending on the semiconductor


Two vectors \( \vec{A} \) and \( \vec{B} \) have magnitude 3 each. \( \vec{A} \times \vec{B}=-5 \hat{k}+2 \hat{i} . \) Find the
angle between \( A \) and \( B \)
A \( \cdot \cos ^{-1} \frac{\sqrt{29}}{9} \)
B. \( \tan ^{-1}\left(\frac{-5}{2}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{2}{5}\right) \)
D. \( \sin ^{-1}\left(\frac{\sqrt{29}}{9}\right) \)


An element \( A \) has electronic
configuration \( 2,8,13,2 . \) The number of electrons in the element having \( l=0 \)
is:
A . 6
B. 8
\( c .5 \)
D. 4


In coupling reactions, diazonium ion
acts as:
A. nucleophile
B. electrophile
c. solvent
D. none of the above


A card is down \& replaced in ordinary pack of 52 playing cards. Minimum number of times must a card be drawn
so that there is atleast an even chance
of drawing a heart, is
A . 2
B. 3
\( c \cdot 4 \)
D. more than four


To find the standard potential of \( M 3^{+} / M \) electrode, the following cell is constituted :
\( \boldsymbol{P t} / \boldsymbol{M} / \boldsymbol{M}^{3+}\left(\mathbf{0 . 0 0 1 m o l} \boldsymbol{L}^{-1}\right) / \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{0 . 0 1} \)
The emf of the cell is found to be 0.421
volt at \( 298 \mathrm{K} \) The standard potential of
half reaction \( M^{3}+3 e^{-} \rightarrow M \) at \( 298 \mathrm{K} \)
will be :
(Given \( \boldsymbol{E}_{A g^{+} / A g}^{e} \) at \( 298 \mathrm{K}=0.80 \) Volt
A. 0.32 volt
B. 0.66 Volt
c. 1.28 volt
D. 0.38 Volt


Assertion
Adsorption is exothermic and spontaneous inspite of the fact that
adsorption is accompained with decrease in entropy.
Reason
The factor \( T \Delta S \) is lesser than \( \Delta H \)
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


Which statement regarding translation
is out of order first?
A. Ribosomal subunits bind to mRNA
B. Ribosome comes to a stop codon on the mRNA
C. As a tRNA leaves the ribosome it passes its amino acid to the growing polypeptide
D. The messenger RNA codon binds to the tRNA anticodon


(Concentration/Molarity) is the amount of solute present in a given amount of solution.


Identify the correct order.
1. Mineral absorption zone.
2. Meristematic zone.
3. Maturation zone.
4. Water absorption zone.
в. 4,3,2,1
c. 2,4,1,3
D. 1,2,3,4


In the circuit shown in figure, the
voltage drop between \( A \) and \( D \) is
A . \( 10 v \)
B. 5 v
\( c \cdot 4 v \)
0.6


Which one of the following elements reduces \( N a O H \) to \( N a ? \)
A . \( S i \)
в. \( P b \)
\( c . c \)
D. \( s n \)


The equation of the circle which passes through the point (3,-2) and (-2,0) and centre line \( 2 x-y=3, \) is
A \( \cdot x^{2}+y^{2}-3 x-12 y+2=0 \)
B. \( x^{2}+y^{2}-3 x+12 y+2=0 \)
c. \( x^{2}+y^{2}+3 x+12 y+2=0 \)
D. None of these


Consider following three halides:
(।) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \)
(II) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C l} \)
\( (\| I) \quad C_{6} H_{5} C l \)
Arrange \( C-C l \) bond length of these
compounds in decreasing order
A \( . I>I I>I I I \)
в. \( I>I I I>I I \)
c. \( I I I>I I>I \)
D. \( I I>I I I>I \)


Arrange \( C C l_{3}\left(C H_{2}\right)_{3} N H_{2}(\mathrm{a}) \)
\( C C l_{3}\left(C H_{2}\right) N H_{2}(\mathrm{b}), \) and \( C C l_{3} C H_{2} N H_{2} \)
(c) in order of decreasing basic nature
\( A \cdot C>B>A \)
B. \( C>A>B \)
\( c \cdot A>c>B \)
D. \( B>A>C \)


Gas constant \( (\boldsymbol{R}) \) equals to
A \( \cdot \frac{C_{p}}{C_{v}} \)
B.
c. \( C_{v}-C_{p} \)
D. \( C_{p}-C_{v} \)


Linnaeus published his concept of binomial nomenclature first in
A. Systema Naturae
B. Species Plantarum
c. Genera Plantarum
D. Philosophia Botanica


Resistivity of a material depends on
A . Area
B. Length
c. Either A or B
D. None of the above


ABCD is a quadrilateral. If \( A C \) and \( B D \) bisect each other then ABCD must be a
A. triangle
B. cylinder
c. parallelogram
D. pyramid


Which organism are called primitive
and how are they different from the socalled advanced organisms?


The points \( A(4,5,10), B(2,3,4) \) and \( C(1, \) 2,-1) are three vertices of a
parallelogram ABCD. Find the vector
equations of the sides \( A B \) and \( B C \) and also find the coordinates of point \( D \)


A force of \( 10^{3} \mathrm{N} \) stretches the length of a
hanging wire by 1 millimeter. The force required to stretch a wire of same material and length but having four
times the diameter by 1 millimeter is :
\( \mathbf{A} \cdot 4 \times 10^{3} \mathrm{N} \)
В \( \cdot 16 \times 10^{3} \mathrm{N} \)
c. \( \frac{1}{4} \times 10^{3} \mathrm{N} \)
D. \( \frac{1}{16} \times 10^{3} \mathrm{N} \)


Given the relation \( \boldsymbol{R}=\{(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{3})\} \)
on the set \( A=\{1,2,3\} \), the minimum
number of ordered pairs which when added to \( R \) make it an equivalence
relation is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 6
\( c \cdot 7 \)
\( D \)


The product is:
\( A \)
B.
\( c \)
D.


Read the statements regarding muscle proteins and identify the correct
statements
i. Actin is a thin filament and is made
up of two F-actins
ii. Complex protein, tropomyosin is distributed at regular intervals on the
troponin
iii. Myosin is a thick filament which is
also a polymerized protein
iv. Globular head of meromyosin consists of light meromyosin (LMN)
A. i, iii and iv are correct
B. i and iii are correct
c. i, ii and iii are correct
D. i, ii and iv are correct
E. ii and iv are correct


\( \int \frac{e^{x} d x}{\cosh x+\sinh x}= \)
\( A \cdot \log \cosh x+c \)
B. \( \tan x+\cot x+c \)
C \( \cdot \frac{1}{2} e^{2 x}+c \)
D. \( x+c \)


In the figure above, line \( \iota \) (not shown) is
perpendicular to segment \( A B \) and
bisects segment \( A B \). Which of the
following points lies on line \( \iota \) ?
A \( \cdot(0,2) \)
В \( \cdot(1,3) \)
\( c .(3,1) \)
D. (3,3)
E. 6,6


Given the equilibrium constants:\( \boldsymbol{C I}^{-}+\boldsymbol{H} \boldsymbol{g} \boldsymbol{C I}^{+} \rightleftharpoons \boldsymbol{H} \boldsymbol{g} \boldsymbol{C I}_{2} \)
\( \boldsymbol{K}_{\mathbf{1}}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{6}} \)
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{C} \boldsymbol{I}_{2}+\boldsymbol{C} \boldsymbol{I}^{-} \rightleftharpoons \boldsymbol{H} \boldsymbol{g} \boldsymbol{C} \boldsymbol{I}_{3}^{-} ; \boldsymbol{K}_{2}=\boldsymbol{8} . \boldsymbol{9} \)
The equilibrium constants for the disproportionation equilibrium
\( 2 H g C I_{2} \rightleftharpoons H g C I^{+} H g C I_{3}^{-} \) is :
\( \mathbf{A} \cdot 3 \times 10^{-6} \)
В. \( 4 \times 10^{-6} \)
c. \( 3.5 \times 10^{-6} \)
D. \( 4.5 \times 10^{-6} \)


In the double helix model of DNA as
proposed by Watson and Crick, each base pair is how far from the next base
pair?
\( A \cdot 0.034 \mathrm{nm} \)
B. 0.34 nm
\( c .3 .4 \mathrm{nm} \)
D. 34 nm


Which of the following is a component of dynamo?
B. Armature coil
c. Slip Rings
D. All of the above


Ultraviolet light of wavelength \( \lambda_{1} \) and \( \lambda_{2} \) when allowed to fall on hydrogen atoms in their ground state is found to liberate electron with kinetic energy \( 1.8 e V \) and 4.0 \( e V \) respectively. Find the value of \( \frac{\lambda_{1}}{\lambda_{2}} \)
A \( -\frac{7}{8} \)
B. \( \frac{8}{7} \)
c. \( \frac{9}{20} \)
D. \( \frac{20}{9} \)


Name the most abundant elements
which occur in nucleic acid
macromolecules
A. \( C, H, O, N, S, \)
в. \( C, O, N, S \)
c. \( C, O, P, S \)
D. \( C, H, O, N, P \)
ह. \( H, O, P \)


In a sample of semi conductor
mobilities of electrons and holes are
\( 24 \times 10^{3} c m^{2} V^{-1} S^{-2} \) and \( 0.2 \times \)
\( 10^{3} \mathrm{cm}^{2} V^{-1} S^{-1} \) respectively. If the
density electrons is \( 0.8 \times 10^{14} \mathrm{cm}^{-3} \)
and that of holes is \( 0.4 \times 10^{14} \mathrm{cm}^{-3} \)
Find the nature of semi conductor and
its conductivity


The number \( 4^{n}+15 n-1 \) is a
multiple of 9 for any natural \( n \)
A. True
B. False


The shunt required to send \( 10 \% \) of the main current through a moving coil galvanometer of resistance \( 99 \Omega \) is
\( \mathbf{A} \cdot 99 \Omega \)
в. \( 9.9 \Omega \)
c. \( 9 \Omega \)
D. \( 10 \Omega \)
E . \( 11 \Omega \)


Monera is divided into
A. Archaebacteria and Eubacteria
B. Animalia and Plantae
c. chordata and Hemichordata
D. None of the above


The ability of the lens in human eye to
change the power of the lens to be able to see the near and far off distances is
called the power of


Simplify \( [38 \div(-57)] \)


Non-essential components of ecosystem
A. Producer
B. Carbon dioxide
c. secondary produces
D. Transformers


Give nomenclature of the following
compound.


Choose the correct answer from the
following
This question has multiple correct options
A. An area of one square centimetre is \( 10^{4} \) times greater
than one square metre.
B. 1 hour 18 min is equal to 3618 seconds
C. Sl unit of volume is cubic metres.
D. Metre is the standard unit to measure length.


The process of acquiring information about an object or phenomenon without making actual physical contact within, as opposed to onsite observation is called :
A. Remote Sensing
B. Actuation
c. Transducing
D. None of the above


The nucleic acid base having two possible binding sites is:
A. thymine
B. cytosine
c. guanine
D. adenine


A pair of opposite sides of a cyclic quadrilateral are equal. Prove that its diagonal are also equal


Factorise the expressions and divide them as directed.
\( 12 x y\left(9 x^{2}-16 y^{2}\right) \div 4 x y(3 x+4 y) \)
A. \( 3(3 x-4 y) \)
B. \( 3(3 x+4 y) \)
c. \( 4(3 x-4 y) \)
D. \( 3(4 x-3 y) \)


Unreacted sodium metal can be
removed from liquid ammonia safely by
A. distilling the mixture
B. adding oil and then heating to convert ammonia to gas
c. adding ammonium chloride
D. none of the above


A plant with parallel venation is
A. castor
B. Grass
c. colocasia
D. Mustard


A direct vision spectroscope is
constructed on the principle of :
A. Deviation with dispersion
B. Dispersion without deviation
c. Selective absorption
D. Diffusion


If \( |x|<1 \) then the coefficient of \( x^{5} \) in the expansion of \( \frac{3 x}{(x-2)(x-1)} \) is
A \( \cdot \frac{33}{32} \)
в. \( -\frac{33}{32} \)
c. \( \frac{31}{32} \)
D. \( -\frac{33}{34} \)


The last common ancestor between the
African apes and hominids lived during epoch.
A. Oligocene
B. Pliocene
c. Miocene
D. Pleistocene


In a gaseous reaction of the type, \( a A+ \) \( b B \rightarrow c C+d D, \) which is wrong?
A. a litres of A combines with b litres of B to give C and
B. a mol of A combines with b mol of B to give C and
c. a g of A combines with b g of B to give C and D
D. a molecules of A combines with b molecules of B to give \( C \) and \( D \)


Choose the correct statement regarding the physical properties of carbonyl compound.
A. All aldehydes are insoluble in benzene
B. Higher aldehydes are more fragrant
c. n-Butane has more boiling point than acetone
D. Methanal and propanone are immiscible with water in all proportions


Find the volume of a sphere of radius
given below:
\( \mathbf{A} \cdot 1,706.25 f t^{3} \)
B. \( 1,766.15 f t^{3} \)
\( c \cdot 1,866.25 f t^{3} \)
D. \( 1,766.25 \mathrm{ft}^{3} \)


A hormone that increases deposition of
\( C a^{+2} \) in bones by decreasing blood calcium level. It is antagonistic to a hormone secreted from a gland located at back side of the most famous gland
of body identify it.
A. Parathyroid hormone
B. Thyrocalcitonin hormone
c. Aldosterone hormone
D. Calcitriol hormone


One of most common solvent used for
crystallization is:
A. syrup
B. normal saline
c. water
D. sulphuric acid


If \( y=\sin \left(m \sin ^{-1} x\right) \) then
\( \left(1-x^{2}\right) y^{\prime \prime}-x y^{\prime} \) is equal to
A \( \cdot m^{2} y \)
в. \( m y \)
c. \( -m^{2} y \)
D. None of these


If \( \boldsymbol{x}=\cos t \) and \( \boldsymbol{y}=\ln t ; \) then at \( \boldsymbol{t}=\frac{\boldsymbol{\pi}}{2} \)
\( \left(\frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right) \) is equal to
A . 0
B. - -
\( c .1 \)
\( D \)


Oxidation state of oxygen in \( K O_{2} \) is :
A . 0
B. -
\( c \cdot-\frac{1}{2} \)
D. -


Which of the following sets belongs to
the same period:
A. \( L i, N a, K \)
в. \( L i, M g, C a \)
c. \( N i, C u, Z n \)
D. \( F, C l, B r \)


The ratio of the length of the parallel
sides of a trapezium is 5: 3 and the
distance between then is 16 cm. If the
area of the trapezium is \( 960 \mathrm{cm}^{2} \), find the length of the parallel sides.
\( \mathbf{A} \cdot 45 \mathrm{cm} \) and \( 65 \mathrm{cm} \)
B. \( 35 \mathrm{cm} \) and \( 75 \mathrm{cm} \)
c. \( 45 \mathrm{cm} \) and \( 75 \mathrm{cm} \)
D. \( 55 \mathrm{cm} \) and \( 75 \mathrm{cm} \)


The distance of the point (1,-5,9) from the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) measured
along the line \( x=y=z \) is:
\( A \cdot 3 \sqrt{10} \)
в. \( 10 \sqrt{3} \)
c. \( \frac{10}{\sqrt{3}} \)
D. \( \frac{20}{3} \)


A convex lens of focal length \( 40 \mathrm{cm} \) is in contact with a concave lens of focal
length \( 25 \mathrm{cm} . \) The power of the
combination is:
A . - 6.5 \( \mathrm{D} \)
\( B .+6.5 D \)
\( c \cdot+6.67 \)
D . - 1.5 D


The perimeter of a rhombus is \( 40 \mathrm{cm} \)
and the measure of an angle is \( 60^{\circ} \)
then the area of it is -
B \( \cdot 75 \sqrt{3} \mathrm{cm}^{2} \)
D. \( 50 \sqrt{3} \mathrm{cm}^{2} \)


An acidic buffer solution can be
prepared by mixing the solution of \( ? \)
A. sodium acetate and acetic acid
B. ammonium acetate and ammonium hydroxide
C. sodium chloride and sodium hydroxide
D. potassium sulphate and sulphuric acid.


The IUPAC name of \( N C-C H_{2}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C O O H} \) is:
A. 3 - carboxy propanenitrile
B. 4- cyanobutanoic acid
c. 2 - cyanomethane Carboxylic acid
D. 3- cyanopropanoic acid


A man saves \( 20 \% \) of his monthly salary.
If on account of increase in prices, he is to increase his monthly expenses by \( 20 \%, \) he is only able to save Rs 800 per month. His monthly salary is
A. Rs 40,000
B. Rs 28,000
c. Rs 24,000
D. Rs 20,000


The variance of first 20 - natural
numbers is?
A \( \cdot \frac{399}{4} \)
в. \( \frac{379}{12} \)
c. \( \frac{133}{2} \)
D. \( \frac{133}{4} \)


Verify Rolle's theorem for the following
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\mathbf{9}, \boldsymbol{x} \varepsilon[\mathbf{1}, \boldsymbol{4}] \)


Find the minimum distance of any point on the curve \( x^{2}+y^{2}+2 x y=8 \) from
the origin.


A point charge \( q \) is situated at a
distance \( r \) on axis from one end of a
thin conducting rod of length \( L \) having a
charge \( Q \) (Uniformly distributed along its length). The magnitude electric force between the two is
A \( \cdot \frac{k q^{2}}{r(r+L)} \)
в. \( \frac{K Q q}{r^{2}} \)
c. \( \frac{K Q q}{r(r-L)} \)
D. \( \frac{K Q q}{r(r+L)} \)


How much heat energy in joules must be supplied to 14 gms of nitrogen at
room temperature to rise its
temperature by \( 40^{\circ} \mathrm{C} \) at constant
pressure? (Mol.wt.of \( \left.N_{2}=28 g m, R=c o n s t a n t\right) \)
A \( .50 R \)
в. \( 60 R \)
\( c .70 R \)
D. \( 80 R \)


Statues and painting coated with white
lead turn black on long exposure to atmosphere. The original color can be
restored by treating them with \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) The reason behind this is?
A. blackened statues get coated with \( P b S \) which on reaction with \( H_{2} O_{2} \) is oxidised to while \( P b S O_{4} \)
B. \( H_{2} O_{2} \) dissolves the coating of white lead and exposses the inner surface
c. White lead reacts with \( H_{2} O_{2} \) to form white \( P b S O_{4} \)
D. Blackened statues get coated with lead sulphate which reacts with \( H_{2} O_{2} \) to give \( P b S \).


Two identical conductors of copper and
aluminium are placed in an identical electric field. What is the magnetic of induced charge in the aluminium?
A. Less than in copper
B. Equal to that in copper
c. Greater than in copper
D. zero


The cubes of the natural numbers are
\( \operatorname{grouped~as} 1^{3},\left(2^{3}, 3^{3}\right),\left(4^{3}, 5^{3}, 6^{3}\right) \dots \)
then sum of the numbers in the nth
group is
A \( \cdot \frac{n^{2}}{12}\left(n^{2}+1\right)\left(n^{2}+4\right) \)
B \( \frac{n^{3}}{8}\left(n^{2}+1\right)\left(n^{2}+3\right) \)
c. \( \frac{n^{3}}{8}\left(n^{2}+1\right)\left(n^{2}+4\right) \)
D \( \frac{n^{2}}{16}\left(n^{2}+1\right)\left(n^{2}+4\right) \)


If current in the coil decreases, then strength of the magnetic field
A. decreases
B. increases
c. sometimes decreases and sometimes increases
D. remains unchanged


Which of the following factor generally favours electrovalency? This question has multiple correct options
A. Low charge on ions
B. High charge on ions
c. Large cation and small anion
D. Small cation and large anion


The aromatic compounds present in the middle oil fraction are :
A. Benzene, Napthalene, Anthracene
B. Naphthalene, Pyridine, Phenol
c. Naphthalene, Pyridine
D. Toluene, Cresol


The compound \( N H_{3}-B F_{3} \) can be
easily separated into its compounds because
\( \mathbf{A} \cdot B F_{3} \) is highly reactive
B. \( N H_{3} \) is highly reactive
C. \( B F_{3} \) and \( N H_{3} \) are unstable
D. \( B F_{3} \) and \( N H_{3} \) have their independent existence


Which substance is wrongly paired
with the bonding found between the
molecules of that substance?
\( \mathbf{A} \cdot N H_{3}- \) hydrogen bonding
B. \( F_{2} \) -van der waals (dispersion) forces
c. \( H C l \) - dipoles
D. \( C H_{4} \) - dipoles
E . \( N a C l(a q) \) - molecule-ion attraction


In which of the following Lanthanoids oxidation state +2 is most stable?
A . \( \mathrm{c} \)
B. Eu
\( c \cdot T b \)
\( D \cdot D y \)


A circle is inscribed in an equilateral
triangle of side \( a . \) What is the area of any square inscribed in the circle?
A \( \cdot \frac{a^{2}}{3} \)
в. \( \frac{a^{2}}{4} \)
c. \( \frac{a^{2}}{6} \)
D. \( \frac{a^{2}}{8} \)


item \( \| \) is
A Item I \( \quad \) Item II
\( (A) \)
(B) Allosteric
effect
\( (C) \)
(D)
\( \mathbf{A} \)
\( (A) \rightarrow(P) ;(B) \rightarrow(R) ;(C) \rightarrow(S) ;(D) \rightarrow(Q) \)
B \( .(A) \rightarrow(R) ;(B) \rightarrow(P) ;(C) \rightarrow(S) ;(D) \rightarrow(Q) \)
\( \mathbf{c} \cdot(A) \rightarrow(P) ;(B) \rightarrow(R) ;(C) \rightarrow(Q) ;(D) \rightarrow(S) \)
D. \( (A) \rightarrow(R) ;(B) \rightarrow(P) ;(C) \rightarrow(Q) ;(D) \rightarrow(S) \)


State the various postulates of Dalton's atomic theory of matter


Which of the following species has (have) five unpaired electrons?
This question has multiple correct options
A . cs
в. мп
\( c \cdot M n^{2+} \)
D. \( \mathrm{Fe}^{2} \)


Which of the following(s) are called fossil fuel?
A. Mineral Coal
B. Petroleum
c. Natural Gas
D. All of the above


Identify the correct sequence represents a infinite geometric
sequence.
A .3,6,12,24,48
B. \( 1+2+4+8+\ldots \)
c. 1,-1,1,-1,1
D. \( 1,3,4,5,6 \dots \)


What is the speed of the component wave?
A. \( 120 \mathrm{cm} / \mathrm{s} \)
B. 240 cm/s
c. \( 143 \mathrm{cm} / \mathrm{s} \)
D. \( 287 \mathrm{cm} / \mathrm{s} \)


PQRS is a parallelogram whose diagonals intersect at \( \mathrm{M} \)
If \( \angle P M S=54^{\circ}, \angle Q S R=25^{\circ} \) and
\( \angle \boldsymbol{S} \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{3} \boldsymbol{0}^{\circ}: \) find \( \angle \boldsymbol{R} \boldsymbol{P} \boldsymbol{S} \)
A \( .86^{\circ} \)
B. \( 96^{\circ} \)
\( c \cdot 92^{\circ} \)
D. \( 100^{\circ} \)


Expand each of the following, using suitable identities:
\( (-2 x+5 y-3 z)^{2} \)


answer the question. A student in 1895 prepared three
coordination compounds containing chromium with the following properties:
\( C l^{-} \) ions \( \begin{array}{ll}\text { Formula } & \text { Colour } \\ & \text { in } \\ & \text { solution } \\ & \text { per } \\ & \text { formula } \\ & \text { units }\end{array} \)
(A) \( \mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O} \quad \) violet 3
(B) \( ^{C r} C_{3,6 H_{2} O} / \begin{array}{l}\operatorname{ligh}_{\operatorname{gre} n} \\ 2\end{array} \)
\( (C) \)
\( \mathrm{CrCl}_{3} .6 \mathrm{H}_{2} \mathrm{O} \quad \begin{array}{l}\text { Dark } \\ \text { green }\end{array} \)
IUPAC name of the complex \( A \) is
A. Hexaaquatrichlorochromium(III)
B. Hexaaquachromium(III) chloride.
C. Pentaaquachlorochromium(III) chloride.
D. Tetraaquadichlorochromium(III) chloride


\( \boldsymbol{a} \boldsymbol{A}+\boldsymbol{b} \boldsymbol{B} \rightarrow \operatorname{Product}, \boldsymbol{d} \boldsymbol{x} / \boldsymbol{d} \boldsymbol{t}=\boldsymbol{k}[\boldsymbol{A}]^{\boldsymbol{a}}[\boldsymbol{B}]^{b} \)
If concentration of \( \boldsymbol{A} \) is doubled, rate is
four times. If concentration of \( B \) is
made four times, rate is doubled. What
is relation between rate of
disappearance of \( A \) and that of \( B ? \)
\( \mathbf{A} \cdot-\{d[A] / d t\}=-\{d[B] / d t\} \)
B . \( -\{d[A] / d t\}=-\{4 d[B] / d t\} \)
\( \mathbf{c} \cdot-\{4 d[A] / d t\}=-\{d[B] / d t\} \)
D. None of these


Deforestation causes
A. Soil erosion
B. Soil pollution
c. water pollution
D. Noise pollution


Match the following and choose the
correct answer.
\begin{tabular}{lll|l}
& table A & & table B \\
a. & Earthquake & 1. & Prevent leakage \\
b. & Lightning & 2. & Faultzone \\
c. & Insulation & 3. & Detection of charges \\
d. & Electroscope & 4. & Earthing
\end{tabular}
A. \( a-2, b-4, c-1, d-3 \)
B. \( a-3, b-4, c-2, d-1 \)
c. \( a-4, b-3, c-2, d-1 \)
D. \( a-1, b-2, c-3, d-4 \)


\( A l+M n O_{4}^{-} \rightarrow A l(O H)_{4}^{-}+M n O_{2} \)
For this reaction, element \( X \) is reduced
and element Y is oxidised. Then \( X \) and
\( Y \) are respectively:
A. \( A l \) and \( M n \)
B. \( M n \) and \( A l \)
c. \( A l \) and \( A l \)
D. Mn and \( M n \)


What initial kinetic energy (in joule and in \( M e V \) ) did the \( \alpha \) - particle have?
A . 36.3
B. 0.36
c. 3.63
D. 2.63


A box contain card number 11 to \( 123 . \) A
card is drawn at random from the find
the probability that the number on the drawn card is
(ii) a multiple of 7


If \( A \) and \( B \) are events such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 6}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B})=\mathbf{0 . 2}, \) find \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) \) and \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \)


The sum of 10 terms of the series \( 0.7+ \)
\( .77+.777+\ldots \ldots \ldots \) is
A \( \cdot \frac{7}{9}\left(89+\frac{1}{10^{10}}\right) \)
в. \( \frac{7}{81}\left(89+\frac{1}{10^{10}}\right) \)
c. \( \frac{7}{81}\left(89+\frac{1}{10^{9}}\right) \)
D. \( \frac{7}{9}\left(89+\frac{1}{10^{9}}\right) \)


A thin metallic spherical shell contains
a charge \( Q \) on its surface. A point
charge \( q_{1} \) is placed at the centre of the
shell and another charge \( q_{2} \) is placed
outside the shell. All the three charges
are positive. Then, the force on charge \( \boldsymbol{q}_{1} \)
is
A. Towards left
B. Towards right
D. zero


The radius of curvature of a spherical mirror is :
A. equal to half its focal length
B. equal to one-fourth of its focal length
c. equal to its focal length
D. twice its focal length


Form the differential equation by eliminating arbitrary constants from the relation \( \boldsymbol{A x}^{2}+\boldsymbol{B y}^{2}=1 \) or \( \frac{\boldsymbol{x}^{2}}{\boldsymbol{a}^{2}}+ \)
\( \frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=\mathbf{1} \)


ff \( P(x)=\left[\begin{array}{cc}\cos x & \sin x \\ -\sin x & \cos x\end{array}\right] \) then
\( \boldsymbol{P}(\boldsymbol{x}) \cdot \boldsymbol{P}(\boldsymbol{y})= \)
This question has multiple correct options
A \( . P(x) . P(y)=P(x+y) \)
в. \( P(x) . P(y)=P(x y) \)
c. \( P(x) . P(y)=P(y) . P(x) \)


Which of the following is/are polar
dielectric molecules?
This question has multiple correct options
A \( . N H_{3} \)
B. Benzene
c. Methane
D. \( H C L \)


Expression for \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{H} \boldsymbol{g}_{2}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) is:
\( \mathbf{A} \cdot\left[H g^{+}\right]^{2}\left[N O_{3}^{-}\right]^{2} \)
B \( \cdot\left[H g_{2}^{+}\right]^{2}\left[N O_{3}^{-}\right]^{2} \)
\( \mathbf{c} \cdot\left[H g_{2}^{2+}\right]\left[N O_{3}^{-}\right]^{2} \)
\( \mathbf{D} \cdot\left[H g_{2}^{2+}\right]^{2}\left[N O_{3}^{-}\right]^{2} \)


The messenger satellite launched by NASA was to study
A. Mars
B. Mercury
c. venus
D. Saturn


Which is used for ending charge on colloidal solutions?
A. Electrons
B. Electrolysis
c. Positively charged ions
D. compounds


The point of intersection of the lines \( \overrightarrow{\boldsymbol{r}}=(-\overrightarrow{\boldsymbol{i}}+\mathbf{2} \overrightarrow{\boldsymbol{j}}+\boldsymbol{3} \overrightarrow{\boldsymbol{k}})+\boldsymbol{t}(-\boldsymbol{2} \overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{j}}+\overrightarrow{\boldsymbol{k}}) \)
and \( \vec{r}=(2 \vec{i}+3 \vec{j}+5 \vec{k})+s(\vec{i}+2 \vec{j}+ \)
\( \mathbf{3} \overrightarrow{\boldsymbol{k}}) \) is:
A \( .(1,1,2) \)
в. (2,1,1)
c. (1,1,1)
D. (1,2,1)


Two long, thin, parallel conductors, separated by a distance d carry
currents \( i_{1} \) and \( i_{2} . \) The force acting on unit length of any one conductor is \( \mathrm{F} \) :
This question has multiple correct options
A . F is attractive, if \( i_{1} \) and \( i_{2} \) flow in the same directions
B. F is attractive, if \( i_{1} \) and \( i_{2} \) flow in the opposite directions
c. F is the same for both conductors
D. F is the different for the two conductors


Ethylamine is not soluble in water
whereas aniline is.

If this is true enter 1 , if false enter 0 .


The value of \( K_{c} \) is 0.50 for the reaction
\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3}, \) at \( 400^{\circ} C \)
Calculate the value of \( K_{p} \) for the given
reaction at the same temperature. \( (R=0.082 \text { atm deg mole }) \)


\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{S O}_{4}\right] \boldsymbol{B r} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{B r}\right] \boldsymbol{S} \boldsymbol{O}_{4} \) are a pair of
isomers.
A . ionisation
B. ligand
c. coordination
D. hydrate


The enthalpies of formation of \( A l_{2} O_{3} \)
and \( C r_{2} O_{3} \) are \( -1596 \mathrm{kJ} \) and \( -1134 \mathrm{kJ} \)
respectively. \( \Delta H \) for the reaction,
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}+\boldsymbol{C r}_{2} \boldsymbol{O}_{3} \rightarrow \boldsymbol{2} \boldsymbol{C r}+\boldsymbol{A l}_{2} \boldsymbol{O}_{3} \) is :
B . -462 kJ
c. -1365 kJ
D. +2730 kJ


\( X e F_{6} \) on partial hydrolysis with water
produces a compound \( X \). The same
compound \( X \) is formed when \( X e F_{6} \)
reacts with silica. The compound \( \boldsymbol{X} \) is:
A. \( X e F_{2} \)
в. \( X e F_{4} \)
\( \mathrm{c} \cdot_{X e O_{3}} \)
D. \( X e O F_{4} \)


Why is it advised to tie any luggage
kept on the roof of a bus with a rope?
A. While the bus is moving, luggage tends to remain in inertia of motion state
B. When the bus stops, the luggage tends to resist the change and due to inertia of motion it move forward and may fall off
C. Both a and b are true
D. None of them is True


Solve \( (1+i)^{4}+(1-i)^{4}= \)


If equal concentrations are mixed (of products \( \& \text { reactants }) \) then will the reaction proceed to the right or left?
\[
H_{2} \operatorname{sO}_{4}(\text { aq })+N H_{3}(\text { aq }) \mapsto N H_{4}^{+}(\text {aq })+H \mathrm{SO}_{4}^{-}(\text {аๆ })
\]


A rubber rope of length \( 8 m \) is hung
from the ceiling of a room. What is the increase in length of rope due to its own weight? (Given : Young's modulus of elasticity of rubber \( =\mathbf{5} \times \mathbf{1 0 6} N / \boldsymbol{m} \)
and density of rubber \( =1.5 \times \) \( \left.\mathbf{1 0}^{3} \mathbf{k g} / \boldsymbol{m}^{3} . \text { Take } \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A \( .1 .5 \mathrm{mm} \)
B. \( 6 m m \)
c. \( 24 m m \)
D. \( 96 m m \)


Use the given figure to find \( : \boldsymbol{n}\left(\boldsymbol{B}^{\prime} \cap \boldsymbol{A}\right) \)
Given, \( n(\xi)=52, n(A)=43 \) and
\( \boldsymbol{n}(\boldsymbol{B})=\mathbf{2 7} \)


In moss, antheridia and archegonia occur at the tips of two different branches of the same plant. The condition is called
A. Monoecious and autoicous
B. Monoecious and paroicous
c. Monoecious and synoicous
D. Dioecious


One metal which is not ductile at room
temperature is:
A. \( C u \)
в. \( S n \)
\( c \cdot P b \)
D. \( H g \)


Stomata of CAM plants
A. Are always open
B. Open during the day and close at night
C . Open during the night and close during the day
D. Never open


The freezing point depression of a \( 0.109 M a q . \) solution of formic acid is
\( -0.21^{\circ} \mathrm{C} . \) The equilibrium constant for
the reaction is \( 1.44 \times 10^{-x} \)
\( \boldsymbol{H} \boldsymbol{C O O H}(\boldsymbol{a q}) \rightleftharpoons \boldsymbol{H}^{+}(\boldsymbol{a q})+ \)
\( H C O O^{\ominus}(a q) \)
\( \boldsymbol{K}_{f} \) for water \( =\mathbf{1 . 8 6} \boldsymbol{k g} \boldsymbol{m o l}^{-1} \boldsymbol{K} \)
Value of \( x \) is:


The formula for volume of cube is
A \( \cdot l^{3} \)
B. \( 6 l^{2} \)
c. \( 4 l^{3} \)
D. \( 6 l^{3} \)


The apparent weight of a body, weighing M kg-wt, during free fall is
A. less than Mkg wt
B. more than M kg w
c. equal to Mkg wt
D. zero


What will be the effect of refraction on a
lemon, when it is placed in a glass tumbler filled with water?
A. It will appear smaller than the actual size
B. It will appear bigger than the actual size
c. It will be invisible
D. It will appear raised


A geometry box is marked for Rs. \( 45 . \) If the rate of sales tax is \( 7 \% \), find the
amount a customer has to pay for it.


The EMF of the cell;
\( \mathbf{M g}\left|\mathbf{M g}^{2+}(\mathbf{0 . 0 1} \mathbf{M}) \| \mathbf{S n}^{2+}(\mathbf{0 . 1} \mathbf{M})\right| \mathbf{S} \mathbf{n} \)
is:
\( \left(\text { Given: } \mathbf{E}_{\mathbf{M g}^{2+}, \mathbf{M g}}^{\circ}=-\mathbf{2 . 3 4} \mathbf{V}, \mathbf{E}_{\mathbf{S n}^{2+}, \mathbf{S n}}^{\circ}=\right. \)
\( -0.14 V) \)
\( \mathbf{A} \cdot 2 \cdot 17 V \)
в. \( 2.23 \mathrm{V} \)
c. \( 2.51 V \)
D. \( 2.45 V \)


Write down the structures of the
stereoisomers formed when cis-2-
butene is treated with bromine.


Proteins are composed of :
A. amino acids
B. carbohydrates
C. vitamins
D. mineral salts


The value of \( \lim _{n \rightarrow \infty} \Sigma_{i=1}^{n} \log \left(2+\frac{5 i}{n}\right) \frac{5}{n} \)
is equal to?
A \( \cdot \int_{2}^{5} \ln (x) d x \)
B. \( \int_{3}^{7} \ln (x) d x \)
c. \( \int_{2}^{7} \ln (x) d x \)
D \( \cdot \int_{2}^{7} \ln \left(x^{2}\right) d x \)


A person with myopic vision see objects only up to a distance of \( 0.25 \mathrm{m} . \) To be able to read a book placed at the distance of \( 0.50 \mathrm{m} \) from the eyes, the
spectacles needed by this person have
power of
A . -1.00
B . -1.5
c. - 2.0 \( D \)
D. +2.00


A student measure the height h of a convex mirror using spherometer. The legs of the spherometer are \( 4 \mathrm{cm} \) apart and there are 10 divisions per cm on its linear scale and circular scale has 50
divisions. The student takes 2 as linear
scale division and 40 as circular scale
division. What is the radius of curvature
of the convex mirror?
A. \( 9.06 \mathrm{cm} \)
в. \( 20.66 \mathrm{cm} \)
\( c .5 .66 \mathrm{cm} \)
D. \( 9.66 \mathrm{cm} \)


A car \( A \) is going north-east at \( 80 \mathrm{km} / \mathrm{h} \) and another car \( B \) is going south-east at
\( 60 \mathrm{km} / \mathrm{h} . \) Then the direction of the velocity
of \( A \) relative to \( B \) makes with the north
an \( \alpha \) angle such that \( \tan \alpha \) is :
A \( \cdot \frac{1}{7} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{3}{5} \)


If \( \mathbf{A}=\left\{\begin{array}{ll}\mathbf{2} & \mathbf{2} \\ \mathbf{- 3} & \mathbf{2}\end{array}\right\}, \mathbf{B}=\left\{\begin{array}{ll}\mathbf{0} & -\mathbf{1} \\ \mathbf{1} & \mathbf{0}\end{array}\right\} \)
\( \operatorname{then}\left(\boldsymbol{B}^{-\mathbf{1}} \boldsymbol{A}^{-1}\right)^{-\mathbf{1}_{=}} \)
\( \mathbf{A} \cdot\left\{\begin{array}{ll}2 & -2 \\ 2 & 3\end{array}\right\} \)
в. \( \left\{\begin{array}{ll}3 & -2 \\ 2 & 2\end{array}\right\} \)
c. \( \frac{1}{10}\left\{\begin{array}{ll}2 & 2 \\ -2 & 3\end{array}\right\} \)
D \( \cdot \frac{1}{10}\left\{\begin{array}{ll}3 & 2 \\ -2 & 2\end{array}\right\} \)


\( P \) and \( Q \), respectively are the sodium salts of:
A. hypochlorous and chloric acids
B. hypochlorous and chlorous acids
c. chloric and perchloric acids
D. chloric and hypochlorous acids


List the elements of the solution set of
the inequation \( -3<x-2 \leq 9-2 x \)
\( \boldsymbol{x} \in \boldsymbol{N} \)


Find the area of circle in sq. cms, in which the chord of length \( 18 \mathrm{cm} \) is at the distance of half of the radius of circle
from the centre of circle:
A . \( 108 \pi \)
B. \( 54 \pi \)
c. \( 27 \pi \)
D. \( 81 \pi \)


Find the number of 5 letter words that
can be formed using the letter of the
word NATURE that begin with N when repetitions allowed.


Primary circuit of potentiometer is as shown in the diagram. Find potential
drop across the wire AB.


Convert the given measurement into the bigger unit. Then, multiply by the second number and find the products. \( 7 k m 63 m \) and 4


find the coordinate of the tip of the position vector which is equivalent to \( \overrightarrow{A B}, \) where the coordinates of \( A \) and \( B \) \( \operatorname{are}(-1,3) \) and (-2,1) respectively
\( A \cdot(+1,+2) \)
B . (+1,-2)
c. (-1,+2)
D. (-1,-2)


The number of unpaired electrons in
nickel carbonyl is:
A . zero
B. one
c. four
D. five


If \( \left(\sin ^{-1} x\right)^{2}+\left(\sin ^{-1} y\right)^{2}+\left(\sin ^{-1} z\right)^{2}= \)
\( \frac{3 \pi^{2}}{4}, \) then find the minimum value of
\( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \)


Which is an alicyclic compound?
A. benzene
B. cyclohexane
c. pyridine
D. pyrrole


Which of the following are isomers?
A. ethane and propane
B. ethane and ethene
c. ethene and ethyne
D. butane and isobutane


What percent of length of a wire will
increase by applying a stress of \( 1 k g \)
wt/mm on it.
\( \left[Y=1 \times 10^{11} \mathrm{Nm}^{-2} \text {and } 1 k g w t=9.8 \mathrm{N}\right] \)
A. \( 0.0078 \% \)
в. \( 0.0088 \% \)
c. \( 0.0098 \% \)
D. \( 0.0067 \% \)


What type of wave is represented by density-distance graph?
A. Transverse wave
B. Longitudinal wave
c. water waves
D. Light waves


Rice is now being sold at Rs 30 per \( \mathrm{kg} \)
During last month its rate was Rs26 per
kg. Find by how much percentage must a family reduce its consumption to keep the expenditure fixed?


Typological concept of species was given by
A. Mendel
B. Aristole and Plato
c. John Ray
D. Hutchinson


Six equal capacitors each of
capacitance \( C \) are connected as shown
in the figure. The equivalent
capacitance between points \( A \) and \( B \) is :
A \( .1 .5 \mathrm{c} \)
\( B \)
\( c \cdot 2 c \)
D. \( 0.5 \mathrm{c} \)


Two billiard balls each of mass \( 0.05 k g \)
moving in opposite directions with speed \( 6 m s^{-1} \) collide and rebound with
the same speed. What is the impulse imparted to each ball due to the other?


Current efficiency in electroplating is usually:
A . 99\%
B. 90 to 98\%
c. 70 to \( 80 \% \)
D. 50 to 60\%


In the given figure, \( O \) is the centre of
circle, \( \angle A E C=40^{\circ}, \) then find the value
of \( a+b+c \)


A piece of wire \( 22 \mathrm{cm} \) long is bent into the form of an arc of a circle subtending an angle of \( 60^{\circ} \) at its center. Find the radius of the circle \( \left[\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)


If the points whose position vectors are \( \mathbf{2} \overline{\mathbf{i}}+\overline{\boldsymbol{j}}+\overline{\boldsymbol{k}}, \mathbf{6} \overline{\mathbf{i}}-\overline{\boldsymbol{j}}+\mathbf{2} \overline{\mathbf{k}} \) and \( \mathbf{1 4} \overline{\mathbf{i}}-\mathbf{5} \overline{\mathbf{j}}+ \)
\( p \bar{k} \) are collinear then the value of \( \mathbf{p} \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8


If \( 200 \mathrm{J} \) of heat is added during the time
interval from \( \mathrm{B} \) to \( \mathrm{C} \), the specific heat of
the substance is.
A \( \cdot 200 J / k g^{o} C \)
в. \( 100 \mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C} \)
c. \( 60 J / k g^{o} C \)
D. \( 17 J / k g^{o} C \)
ह \( \cdot 1.67 \mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C} \)


For real \( x, \) the value of expression \( \frac{x^{2}-2 x+2}{2 x-2} \) cannot lis in the interval
A. (infinity,- -1)
B. (-1,1)
c. (1,2)
D. (2, infinity)


\( (x-6)+(3 x-4)+(x-1) \)


Carbon has three isotopes with atomic
mass no.
A \( . \) 10, 11,12 2 1,1,22 ?
B. 13, 14, 15
c. 12,13,14
D. 14,15,16


Assertion
Solids in finely divided state act as
good adsorbents.
Reason
Adsorption is a surface phenomenon.
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


Which set helps in tearing food?


White phosphorus exists as:
A . \( P \) molecule
B. \( P_{2} \) molecule
c. \( P_{6} \) molecule
D. \( P_{4} \) molecule


Out of starch and ferric hydroxide sol which one can easily be coagulated and
why?


Which facts are revealed from
Avogadro's law for ideal gases?
This question has multiple correct options
A. The distance between molecules is much large than the actual dimension of molecules
B. Equal number of molecules of different gases under identical conditions of temperatures and pressure occupy the same volume.
C. Saturated vapours obey gas laws
D. 1 mole of a gas contains \( 6.023 \times 10^{23} \) molecules of
gases.


In the given figure, the area of \( \triangle A B C \)
is \( 64 \mathrm{cm}^{2} . \) State giving means:
\( \operatorname{ar}(\| \operatorname{gm} A B C D) \)


Two objects \( A \) and \( B \) are moving towards
each other with velocities \( 10 \mathrm{m} / \mathrm{s} \) and
12 \( \mathrm{m} / \mathrm{s} \) respectively as shown. Find the velocity of A with respect to B.
\( \mathbf{A} \)
A. \( 22 \mathrm{m} / \mathrm{s} \)
в. \( -22 \mathrm{m} / \mathrm{s} \)
c. \( 12 m / s \)
D. \( 40 \mathrm{m} / \mathrm{s} \)


In hydrogen bomb we use the process of
A. Fusion
B. Fission
\( c . \) Both (1)\( \&(2) \)
D. None of these


Which of the following non-metal is commonly used as pesticides and photography?
A. Bromine
B. Helium
c. Selenium
D. lodine


Find the sixth term in the expansion of
\( \left(2 x^{2}-\frac{3}{7 x^{3}}\right)^{11} \)
A \( \cdot-^{11} C_{5} \frac{2^{6} 3^{5}}{7^{5}} x^{3} \)
В \( \cdot \quad^{11} C_{5} \frac{2^{6} 3^{5}}{7^{5}} x^{-3} \)
c. \( _{-11} C_{5} \frac{2^{6} 3^{5}}{7^{5}} x^{-3} \)
D. None of these


\( \sin \left(\frac{\pi}{2}-x\right)=\cos x \)


Calculate the \( p H \) after the addition of
\( 90 m l \) and \( 100 m l \) respectively of
\( \mathbf{0 . 1} N \) NaOH to
\( 100 m l 0.1 N C H_{3} C O O H \)
(Given \( \left.p K_{a} \text { for } C H_{3} C O O H=4.74\right) \)


Consider the situation shown in figure.
The elevator is going up with an acceleration of \( 2.00 m / s^{2} \) and the focal
ength of the mirror is \( 12.0 \mathrm{cm} . \) All the
surfaces are smooth and pulley is light.
The mass-pulley system is released from rest (with respect to the elevator)
at \( t=0 \) when the distance of \( B \) from
the mirror is \( 42.0 \mathrm{cm} \). Find the distance
between the image of the block \( B \) and
the mirror at \( t=0.200 s . \) Take \( g= \)
\( 10 m / s^{2} \)


A person decides to use his bath tub
water to generate electric power to run a 40 watt bulb. The bath tub is located at a height of \( 10 \mathrm{m} \) from the ground \& it
holds 200 litres of water. If we install a
water driven wheel generator on the
ground, at what rate should the water
drain from the bath tub to light bulb? How long can we keep the bulb on, if the bath tub was full initially? The
efficiency of generator is \( 90 \% .(g= \)
\( 10 m / s^{-2} \)


Shape of \( S e O_{2} \) molecule is
A. Triangular
B. Angular
c. Linear
D. pyramidal


If there is a nonzero net force acting on an object for some time, which of the following must be true?
I. The object is gaining kinetic energy
II. The object experiences displacement
III. There is work being done on the object
A. I only
B. I and II only
c. I and III only
D. Il and III only
E . I, II, and III


A point charge \( q \) is rotated along a circle in the electric field generated by another point charge \( Q \). The work done by the electric field on the rotating charge in one complete revolution
is
A . zero
B. positive
c. negative
D. zero if the charge \( Q \) is at the center and nonzero otherwise


State the laws of refraction. What is the
meaning of "the refractive index of crown glass is \( 1.52 " ? \)


Resistance and conductivity of a cell containing \( 0.001 \mathrm{M} \) KCl solution at 298
\( \mathrm{K} \) are \( 1500 \Omega \) and \( 1.46 \times 10^{-4} \mathrm{S.cm}^{-1} \)
respectively. What is the cell constant?
\( \mathbf{A} \cdot 0.219 \mathrm{cm}^{-1} \)
B. \( 0.319 \mathrm{cm}^{-1} \)
c. \( 0.419 c m^{-1} \)
D. None of these


The value of \( \Delta \) S is negative for the
process
A. Burning of rocket fuel
B. Dissolution of sugar
C. Sublimation of iodine
D. Freezing of water


A uniform rod \( A B \) which is free to swing
in the vertical plane about a horizontal axis through \( A, \) is hanging freely. \( A \) particle of equal mass strikes the rod
with a velocity \( V_{0} \) and gets stuck to it.Find the angular velocity of the combination immediately after the
collision.


Atomic reactor is based on
A. controlled chain reaction
B. uncontrolled chain reaction
c. nuclear fission
D. nuclear fusion


For maintaining sustained chain
reaction, the following is required
A. protons
B. electrons
c. neutrons
D. positrons


Which is the correct representation of
the net force \( f_{n e t} \) on the mass?
(k is the constant of oscillation and \( x \) is
the displacement about the mean
position)
A \( \cdot f_{n e t}=-k x+b v \)
B. \( f_{n e t}=k x+b v \)
C \( \cdot f_{n e t}=-k x-b v \)
\( \mathbf{D} \cdot f_{n e t}=k x-b v \)


Assertion
Colloidal solutions are stable but
colloidal particles do not settle down.
Reason

Brownian movement counters the force
of gravity actively on colloidal particles.
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


Explain the phenomenon of total internal reflection with one or two
activities.


If \( \mathbf{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{3}\end{array}\right] \) and \( \mathbf{B}=[\mathbf{3}-\mathbf{1}], \) then
\( \mathbf{B A}= \)
A. \( \left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right] \)
B. \( \left[\begin{array}{ll}3 & 0\end{array}\right] \)
\( \begin{array}{ll}\text { c. }[3 & 3]\end{array} \)
D. \( [0-3] \)


The acceleration due to gravity on the moon is one sixth that on the earth. \( A \)
high jumper canjump \( 2 \mathrm{m} \) on earth. What distance can he jump on the moon?
\( A \cdot 2 m \)
B. \( 6 \mathrm{m} \)
\( c \cdot 12 m \)
D. 18


Two communicable diseases prevalent in developing countries caused by unsafe drinking water and bad sanitation are
A. Acute diarrhoea and cancer
B. Diarrhoea and schistosomiasis
c. onchocerciasis and leukaemia
D. Rheumatism and malaria


The nature of the chemical bond in MgO
is:
A. electrovalent
B. covalent
c. dative
D. polar covalent


The reaction \( : 2 A \rightarrow 2 B+C \) occurs by
the mechanism:
\( \boldsymbol{A} \stackrel{\boldsymbol{k}_{1}}{\longrightarrow} \boldsymbol{B}+\boldsymbol{x}(\boldsymbol{s} \boldsymbol{l} \boldsymbol{o} \boldsymbol{w}) \)
(1)
\( \boldsymbol{x} \stackrel{\boldsymbol{k}_{2}}{\longrightarrow} \boldsymbol{B}+\boldsymbol{C}(\text {fast}) \)
(2)
Which of the following step is incorrect?
A. molecularity of the reaction is one
B. the order of the reaction with respect to A is two
C . the rate law is : \( v=k_{1}[A] \)
D. \( k_{2}>k_{1} \)


A tuning fork of unknown frequency makes three beats per second with a
standard fork of frequency 384 Hz. The beat frequency decreases when a small piece of wax is put on a prong of the first fork. What is the frequency of this fork ? \( (\text { in } \mathrm{Hz}) \)


If \( \Delta H_{f}^{o}\left(N H_{3}\right)=-46.1 k J \) and \( \Delta H^{o} \)
of the reaction \( N_{2} H_{4}(g) \rightarrow \)
\( 2 N H_{3}(g) i s-187.6 k J, \) then
\( \Delta H_{f}^{o}\left(N_{2} H_{4}\right) \) is:
A. \( -95.4 k J \)
в. \( +95.4 k J \)
c. \( -141.5 k J \)
D . \( -233.7 k J \)


(a) Give two names of artificial
sweeteners.
(b) Give definition of antibiotic and one
example
(c) Give definition of antihistamine
drug with name and uses.


Choose the correct answers from the
alternatives given. \( \frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{x^{2}+1}-\frac{4}{x^{4}+1} \)
be equal to
A \( \cdot \frac{4}{x^{4}-1} \)
в. \( \frac{4}{x^{4}+1} \)
c. \( \frac{8}{x^{8}-1} \)
D. \( \frac{8}{x^{8}+1} \)


toppr
-०६
Q Type your question
the object's velocity as a function of
time. The data points are shown on the
graph below, along with a best-fit line that has been inserted to extrapolate data for the entirety of the object's
motion.

In using the graph to analyze the object's motion, several different
quantities about the best fit line can be
calculated.

Which quantities would be equal to the object's initial velocity, and to the object's displacement, during its slowing motion?
A. Initial Velocity: Slope
Displacement: Area under line
B. Initial Velocity: x-intercept
Displacement: Slope
c. Initial Velocity: y-intercept
Displacement: Area under line
D. Initial Velocity: Slope
Displacement: y-intercept


The prefixes \( n a n o(n), m i c r o(\mu) \) and pico \( (p) \) are often used with units.
Which row shows their correct values?
A \( \cdot n=10^{-6}, \mu=10^{-9}, p=10^{-12} \)
B . \( n=10^{-6}, \mu=10^{-12}, p=10^{-9} \)
C \( . n=10^{-9}, \mu=10^{-6}, p=10^{-12} \)
D . \( n=10^{-12}, \mu=10^{-9}, p=10^{-6} \)


The de Broglie wavelength \( (\lambda) \) associated with a photoelectron varies
with the frequency ( \( v \) ) of the incident
radiation as, \( \left[v_{0} \text { is thrshold frequency }\right] \)
A \( \cdot \lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{3}{2}}} \)
B. \( \lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{1}{2}}} \)
c. \( a \lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{1}{4}}} \)
D. \( \lambda \propto \frac{1}{\left(v-v_{0}\right)} \)


The probability that a number selected at random from the numbers
\( \mathbf{1}, \mathbf{2}, \mathbf{3} \dots \dots \mathbf{1 5} \) is a multiple of \( \mathbf{4} \) is
A \( \cdot \frac{4}{15} \)
в. \( \frac{2}{15} \)
c. \( \frac{1}{15} \)
D.


Name the disease in which there is
reduced renal reabsorption of water with consequent elimination of a large volume of very dilute urine.


Out of 48 cricket matches between
India and England, India won toss 12 times. How many times England won
toss?
A . 12
B . 24
\( c .36 \)
D. 48


If a rigid body is subjected to two forces \( \vec{F}_{1}=2 \hat{i}+3 \hat{j}+4 \hat{k} \) acting at (3,3,4)
and \( \vec{F}_{2}=-2 \hat{i}-3 \hat{i}-4 \hat{k} \) acting at (1
0, 0) then which of the following is (are)
true?
A. The body maybe in equilibrium
B. The body is under the influence of a torque only
c. The body is under the influence of a single force.
D. The body is under the influence of a force together with torque


what is the ratio of Youngs modulus \( \boldsymbol{E} \)
to shear modulus \( G \) in terms of
poissons ratio?
\( \mathbf{A} \cdot 2(1+\mu) \)
B . \( 2(1-\mu) \)
C \( \cdot \frac{1}{2}(1-\mu) \)
D \( \cdot \frac{1}{2}(1+\mu) \)


A rectangular plot \( 85 ~ m \) long and \( 60 m \)
broad is to be covered with grass leaving \( 5 m \) all around. Find the area to
be laid with grass.
A. 3750 sq. \( \mathrm{m} \)
B. 5750 sq. \( \mathrm{m} \)
c. 4750 sq. \( \mathrm{m} \)
D. 6750 sq.


A particle in SHM has a period of 4 sec.
It takes time \( t_{1} \) to start from mean
position and reach half the amplitude in
another case it takes a time \( t_{2} \) to start
from extreme position and reach half
the amplitude, then
A \( \cdot \frac{t_{1}}{t_{2}}=1 \)
в. \( \frac{t_{1}}{t_{2}}=\frac{1}{2} \)
c. \( \frac{t_{1}}{t_{2}}=2 \)
D. \( \frac{t_{1}}{t_{2}}=3 \)


Structures called beads on string are
A. Nucleosomes
B. Base pairs
c. Genes
D. Nucleotides


Tissue level of organization is found in:
A. Sea cucumber
B. Glass sponge
c. Sea anemone
D. comb jelly


Let \( a, b, c \) are \( 7^{t h}, 11^{t h} \) and \( 13^{t h} \) terms of
non constant AP. If \( a, b, c \) are also in GP, then find \( \frac{\boldsymbol{a}}{\boldsymbol{c}} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


A point is moving on \( y=4-2 x^{2} \). The \( x \)
coordinate of the point is decreasing at the rate of 5 units per second. Then the rate at which y-coordinate of the point
is changing when the point is at (1,2)
is.
A . 5 units/sec
B. 10 units/sec
c. 15 units/sec
D. 20 units/sec


Benzene sulphonic acid is:
\( A \). basic
B. acidic
c. neutral
D. both A and B


In mature mammalian erythrocytes, the respiration is
A. Aerobic
B. Anaerobic
c. Sometimes aerobic and sometimes anaerobic
D. Absent


A saturn year is 29.5 times the earth
year. How far is saturn from the moon
\( (M) \) if the earth is \( 1.5 \times 10^{8} k m \) away
from the sun?


\( \lim _{\boldsymbol{n} \rightarrow \infty} \frac{\mathbf{1}^{\boldsymbol{p}}+\boldsymbol{2}^{\boldsymbol{p}}+\ldots+\boldsymbol{n}^{\boldsymbol{p}}}{\boldsymbol{n}^{\boldsymbol{p}+1}} \) is
A. \( \frac{1}{p+1} \)
B. \( \frac{1}{1-p} \)
c. \( \frac{1}{p}-\frac{1}{p-1} \)
D. \( \frac{1}{p+2} \)


In amphibian, the heart has
A. Two auricles and two ventricle
B. Two auricles and one ventricle
c. one auricle and two ventricles
D. One auricle and one ventricle


In which of the following states is the
potential energy of an electric dipole
maximum?
\( A \)
B.
\( c \)
D.


Assertion
Van der Waals' forces are responsible
for chemisorption.
Reason
High temperature is favorable for chemisorption.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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


\( R \)
\( -\square-(A) \)
\begin{tabular}{l}
\( ^{R} \) \\
\hline\( (D \) \\
\( Q \) \\
\( \sqrt{ } \)
\end{tabular}
\begin{tabular}{l}
\( n \) \\
\hline
\end{tabular}


For \( \boldsymbol{r}=\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots, \mathbf{1 0}, \) let \( \boldsymbol{A}_{r}, \boldsymbol{B}_{r}, \boldsymbol{C}_{\boldsymbol{r}} \)
denote respectively the coefficient of \( x^{r} \)
in the expansions of \( (1+x)^{10},(1+x)^{20} \)
and \( (1+x)^{30} . \) Then \( \sum_{r=1}^{10} A_{r}\left(B_{10} B_{r}-\right. \)
\( \left.C_{10} A_{r}\right) \) is equal to
\( \mathbf{A} \cdot B_{10}-C_{10} \)
B . \( A_{10}\left(B_{10}^{2}\right)-C_{10} A_{10} \)
c.
D. \( C_{10}-B_{10} \)


A convex lens forms a real image of a
point object at a distance of \( 50 \mathrm{cm} \) from the convex lens. A concave lens is
placed. \( 10 \mathrm{cm} \) behind the convex lens on the image side. On placed a plane mirror an the image side and facing the concave lens. It is observed that the
final image now coincides with the
object itself. The focal length of the concave lens is:
A. \( 50 \mathrm{cm} \)
B. 20 cm
\( c .40 \mathrm{cm} \)
D. 25 cm


When \( N a N O_{3} \) is heated in a closed
vessel, \( O_{2} \) is liberated and \( N a N O_{2} \) is left behind. At equilibrium:
A. addition of \( N a N O_{2} \) favours reverse reaction
B. addition of \( N a N O_{3} \) favours forward reaction
c. increasing temperature favours forward reaction
D. increasing pressure favours forward reaction


If \( S \) is a sample space \( P(A)=\frac{1}{3} P(B) \)
and \( S=A \cup B \) where \( A \) and \( B \) are two
mutually exclusive events, then
\( \boldsymbol{P}(\boldsymbol{A})= \)
A \( \cdot \frac{1}{4} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.


The number of incisors, molars, premolars and canines in the buccal cavity is
A. 8,4,8,8
B. 8,4,8,4
c. 4,8,8,8
D. 8,8,8,4


Phalangeal formula of hand of man is
A. 1,2,2,2,2
B. 2, 1,1,1,1
c. 2,3,3,3,3
D. 2, 3, 3, 2, 2


Q Type your question
Which out of the following statements
is incorrect regarding this?
\( =\sqrt{3} \)
\( =11 \)
A. A continuous high osmotic concentration is maintained in region \( \mathrm{P} \), which loads a sieve tube element by passively transporting solute molecules into it
B. R shows the movement of \( H_{2} O \) into sieve tube
elements from nearby xylem vessels by osmosis
C. Translocation of organic solutes take place from region P with high turgor pressure to region Q with low turgor pressure
D. In region \( Q \), material is either consumed or is converted into insoluble storage forms resulting in decreased osmotic pressure


Using elementary tansormations, find
the inverse of each of the matrices, if it
exists in \( \left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right] \)


Find the inverse of the following matrix by using elementary row transformation
\( \left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right] \)


Which of the following acid occurs in polymeric form?
A. \( H P O_{3} \)
в. \( H_{4} P_{2} O_{7} \)
c. \( H_{3} P O_{4} \)
D. none of these


Find the particular solution of the differential equation \( \left(1+x^{2}\right) \frac{d y}{d x}= \)
\( \left(e^{m \tan ^{-1 x}}-y\right), \) given that \( y=1 \) when \( x= \)
0


In which of the following reactions the inversion of configuration takes place?
(I) pentan\( -2-o l+S O C l_{2} \rightarrow \)
(II) pentan\( -2-o l+C O C l_{2} \longrightarrow \)
(III) pentan \( -2-o l+(A)+S O C l_{2} \)
Pyridine
(IV) pentan\( -2-o l+ \)COCl\( _{2} \stackrel{\text {Pyridine}}{ } \)
\( \mathbf{A} \cdot(I),(I I I) \)
в. \( (I),(I I) \)
c. \( (I I I),(I V) \)
D. \( (I),(I V) \)


Assertion
Most amplifiers use common emitter circuit configuration
Reason
Its input resistance is comparatively higher
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


The first terms of a G.P. is 1. The sum of
the third and fifth term is \( 90 . \) Find the
common ratio.


Electrons can jump from one orbit to
other orbits. They cannot flow from one
orbit to another
A. True
B. False


Which of the following is not a nitrogenous fertilizer?
A. Calcium cyanamide
B. CAN
c. Super phosphate of lime
D. urea


The value of the sum \( \sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right) \) where \( i=\sqrt{-1}, \) equals
\( \mathbf{A} \cdot i \)
B . \( i-1 \)
\( c \cdot-i \)
\( D \)


Assertion
Systematics is the branch of biology
that deals with classification of living organisms.
Reason
The aim of classification is to group the
organisms in an orderly manner
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


What are the functional groups present in the given compound?
A. Ester and ether
B. Ester and amine
c. Ester and carboxylic acid
D. Ether and carboxylic acid
E. Ether and ketone


Two cells of same emf are connected in
series. Their internal resistances are \( r_{1} \)
and \( r_{2} \) respectively and \( r_{1}>r_{2} . \) When
this combination is connected to an
external resistance \( R \) then the potential difference between the terminals of first
cell becomes zero. In this condition the
value of R will bw
A \( \cdot \frac{r_{1}-r_{2}}{2} \)
B. \( \frac{r_{1}+r_{2}}{2} \)
c. \( r_{1}-r_{2} \)
D. \( r_{1}+r_{2} \)


The oxidation number of Mn in the
product of alkaline oxidative fusion of
\( M n O_{2} \) is:


Bentham and Hooker classified dicots
into
A. Polypetalae, gamopetale and glumiflorae
B. Polypetalae, gamopetalae and monochlamydae
C. Archichlamydae, monochalmydae and glumiflorae
D. Lignosae and herbaceae


A stone tied at the end of string \( 80 \mathrm{cm} \) long is whirled in a horizontal circle
with a constant speed. If the stone makes 25 revolutions in 14 s, what is
the magnitude of acceleration of the
stone?
A \( .90 m s^{-2} \)
B. \( 100 \mathrm{ms}^{-2} \)
\( \mathbf{c} \cdot 110 m s^{-2} \)
D. \( 120 \mathrm{ms}^{-2} \)


The quantity of heat required by 1 gram of a substance to raise its temperature by \( 1 \mathrm{K} \) is called its specific heat. State whether given statement is True/False
A. True
B. False


Two organisms are present in the same class but not in the same family. They may belong to same.
A. Genus
B. species
c. Variety
D. Order


In a circle of radius \( 5 \mathrm{cm}, \mathrm{AB} \) and \( \mathrm{AC} \) are
two chords. such that \( A B=A C= \)
\( 6 \mathrm{cm} . \) Find the length of chord BC.


Determine the shape of the following molecules using the VSEPR model.
\( B e C l_{2}, B C l_{3}, S i C l_{4}, A s F_{5}, H_{2} S a n d \)


Copper dissolves in hydrochloric acid.
State the given statement is True or False:
A. True
B. False


The current I in the circuit shown below
is
\( \mathbf{A} \)
\( B \cdot \frac{1}{15} A \)
\( c \cdot \frac{1}{10} A \)
\( D \cdot \frac{1}{2} \)


If the determinant \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{t}-\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{t}-\boldsymbol{c} \\ \boldsymbol{2} & \boldsymbol{1} & \boldsymbol{0}\end{array}\right|=0 \)
if \( a, b, c \) are in
A. \( A . P \)
в. G.Р.
c. \( H . P \)
D. \( k=1 / 2 \)


The maximum load a wire can
withstand without breaking, when its length is reduced to half of its original length, will
A. be double
B. be half
c. be four times
D. remains same


The minimum value of \( \boldsymbol{f}(\boldsymbol{x})= \) \( 2^{\log _{8}^{3} \cos ^{2} x}+3^{\log _{8}^{2} \sin ^{2} x} \)
A \( \cdot 2^{1-\log _{8} \sqrt{3}} \)
B \( \cdot 2^{\log _{8} \sqrt{3}} \)
c. \( 3^{\log _{8} \sqrt{2}} \)
D. \( 2^{1+\log _{8}} \sqrt{3} \)


A train travels from one station \( X \) to
another station \( Y \) at a rate of \( 20 \mathrm{km} / \mathrm{hr} \)
and returns at the rate of \( 30 \mathrm{km} / \mathrm{hr} \). The
average speed of the total journey is
\( \mathbf{A} \cdot 25 \mathrm{km} / \mathrm{hr} \)
B. \( 24 \mathrm{km} / \mathrm{hr} \)
\( \mathbf{c} .35 \mathrm{km} / \mathrm{hr} \)
D. \( 40 \mathrm{km} / \mathrm{hr} \)


Find the volume of hemisphere of
radius \( 3.5 \mathrm{cm} \)


Fleming's left hand rule tells us about
direction of magnetic force due to
current in magnetic field, but what is its magnitude?


The product in the following reaction is:
\( \boldsymbol{P h}-\boldsymbol{C l}+\boldsymbol{F e} / \boldsymbol{B r}_{2} \longrightarrow \) Product
A . o-bromo-chloro benzene
B. p-bromo-chloro benzene
c. both of the above
D. 2,4,6-tribromo chloro benzene


A solution contains \( \boldsymbol{H} \boldsymbol{C l} \)
\( C l_{2} H C C O O H \) and \( C H_{3} C O O H \) at
concentrations \( 0.09 M \) in \( H C l, 0.09 M \)
in \( C l_{2} H C C O O H \) and \( 0.1 M \) in
\( C H_{3} C O O H, p H \) for the solution is 1
lonization constant of \( C H_{3} C O O H= \)
\( 10^{-5} . \) What is the magnitude of \( K \) for
dichloroacetic acid?
A \( \cdot k a_{2}=1.25 \times 10^{-2} \)
В . \( k a_{2}=1.25 \times 10^{-1} \)
D. \( k a_{2}=1.25 \times 10^{-3} \)


The distance between the plates of a charged parallel plate capacitor is \( 5 \mathrm{cm} \) and electric field inside the plates is
\( 200 V c m^{-1} . \) An uncharged metal bar of width \( 2 \mathrm{cm} \) is fully immersed into the
capacitor. The length of the metal bar is same as that of capacitor. The voltage across capacitor after the immersion of the bar is:
A. zero
B. \( 400 \mathrm{V} \)
c. \( 600 V \)
D. \( 100 V \)


If \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{2} & \mathbf{3} \\ \mathbf{3} & \mathbf{5} & \mathbf{7}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{3} & \mathbf{7} \\ \mathbf{2} & \mathbf{4} & \mathbf{1}\end{array}\right] \)
if \( \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{5} & \mathbf{1 0} \\ \mathbf{5} & \boldsymbol{k} & \mathbf{8}\end{array}\right] \)
Find the value of \( \mathbf{k} \)
\( A \cdot 9 \)
B. 4
\( c \cdot 5 \)
\( D \)


Rashmi bought a CD player for Rs. 2200
and sold it for Rs. \( 1980 . \) Find her loss
and loss \%.


Angle of dip is \( 90^{\circ} \) at:
A. Equator
B. Middle point
c. Poles
D. None of these


If \( S=1^{2}-2^{2}+3^{2}-4^{2} \dots \) upto \( n \)
terms and \( n \) is even, then \( S \) equals
A \( \cdot \frac{n(n+1)}{2} \)
B. \( \frac{n(n-1)}{2} \)
c. \( \frac{-n(n+1)}{2} \)
D. \( \frac{-n(n-1)}{2} \)