Among the three types of velocities, which has greater value at a given
temperature?
A. Most probable velocity
B. RMS velocity
c. Average velocity
D. All the three have same value


How many electrons constitute a current of one microampere?
\( \mathbf{A} \cdot 6.25 \times 10^{6} \)
B. \( 6.25 \times 10^{12} \)
C. \( 6.25 \times 10^{9} \)
D. \( 6.25 \times 10^{15} \)


A person standing near the edge of the top of a building throws two balls \( A \) and
B. The ball \( A \) is thrown vertically
upward and \( B \) is thrown vertically downward with the same speed. The ball
\( A \) hits the ground with a speed \( v_{A} \) and
the ball \( B \) hits the ground with a speed
\( \boldsymbol{v}_{B} . \) We have:
В . \( v_{A}<v_{B} \)
c. \( v_{A}=v_{B} \)
D. the relation between \( v_{a} \) and \( v_{b} \) depends on height of the building above the ground


The radii of two circles are in the ratio
\( 3: 8 . \) If the difference between their
areas is \( 2695 \pi \mathrm{cm}^{2}, \) find the area of the
smaller circle.
A \( \cdot 1386 \mathrm{cm}^{2} \)
B. \( 1280 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 1187 \mathrm{cm}^{2} \)
D. \( 1546 \mathrm{cm}^{2} \)


Solve for \( r: \)
\( \mathbf{4 1}=\mathbf{4 0 0}\left[\left[\frac{100+r}{100}\right]^{2}-\mathbf{1}\right] \)


Which of the following process under desired conditions show endothermic
change? This question has multiple correct options
A \( \cdot N_{2}+\frac{1}{2} O_{2} \rightarrow N_{2} O \)
в. \( N_{2}+O_{2} \rightarrow 2 N O \)
\( \mathbf{c} \cdot F_{2}+\frac{1}{2} O_{2} \rightarrow F_{2} O \)
D. \( C+\frac{1}{2} O_{2} \longrightarrow C O \)


The value of \( \sum_{r=1}^{n} \int_{0}^{1} f(r-1+x) d x \) is equal to (if function has period 1 )
A \( \cdot \int_{0}^{1} f(x) d x \)
B. \( _{n \int_{0}}^{1} f(x) d x \)
c. \( (n-1) \int_{0}^{1} f(x) d x \)
D. \( \int_{0}^{n} f(x) d x \)


If \( n \) is a positive integer and \( n \in[5,100] \)
then the number of integral roots of the equation \( x^{2}+2 x-n=0 \) are
A . 4
B. 6
c. 8
D. 10


The carbohydrates are classified on the
basis of:
This question has multiple correct options
A. sugars and non-sugars
B. reducing character
c. optical activity
D. hydrolysis


Describe an activity to show that sound is produced by vibration of materials.


A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \( 15 \mathrm{cm} \) from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is :
A. \( 5 \mathrm{cm} \)
B. -10 cm
c. \( 20 \mathrm{cm} \)
D. -30 cm


A sphere contracts in volume by \( 0.01 \% \) when taken to the bottom of lake \( 1 k m \)
deep. If the density of water is \( 1 g m / c c \)
the bulk modulus of water is
A \( \cdot 9.8 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} \)
B. \( 9.8 \times 10^{8} \mathrm{N} / \mathrm{m}^{2} \)
c. \( 9.8 \times 10^{10} \mathrm{N} / \mathrm{m}^{2} \)
D. 9.8 \( \times 10^{6} \mathrm{N} / \mathrm{m}^{2} \)


The sum of magnitudes of two forces
acting at a point is \( 16 N . \) If the
resultant force is \( 8 N \) and its direction
is perpendicular to smaller force, then the forces are:
A 6 Nand \( 10 N \) n
B. \( 8 N \) and \( 8 / N \)
c. \( 4 N \) and \( 12 N \)
D. \( 2 N \) and \( 14 N \)


The final product is formed followed by
the formation of
carbocation


Solve the equations using cross
multiplication method: \( x-y=12 \) and
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{1 4} \)
A . \( x=13, y=1 \)
В. \( x=13, y=-1 \)
c. \( x=-13, y=-1 \)
D. \( x=-13, y=1 \)


If for any \( A . P, d=5 \) then \( t_{18}-t_{13} \)
\( = \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 20
c. 25
D. 30


The direction of current in the coil at
one end of an electromagnet is clockwise. This end of
the electromagnet is.
A. north pole
B. south pole
c. east pole
D. west pole


What is the basic structural difference
between starch and cellulose?


Two free charges \( q \) and \( 4 q \) are placed at a distance d apart. A third charge \( Q \) is placed between them at a distance \( x \) from charges q such that the system is in equilibrium.Then
\( A \cdot Q=\frac{4 q}{9} \)
B . \( Q=\frac{7 q}{9} \)
c. \( Q=-\frac{3 q}{9} \)
D \( \cdot Q=-\frac{2 q}{9} \)


The allowed energy for the particle for a particular value of \( n \) is proportional to
A \( \cdot a^{-2} \)
B \( \cdot a^{-3 / 2} \)
\( c \cdot a^{-1} \)
D. \( a^{2} \)


No of \( \sigma \) and \( \pi \) bonds in \( C_{2}(C N)_{4} \) are
respectively:
\( \mathbf{A} \cdot 9 \sigma, 9 \pi \)
в. \( 8 \sigma, 7 \pi \)
c. \( 1 \sigma, 1 \pi \)
D. \( 9 \sigma, 8 \pi \)


When \( \frac{1}{10} \) percent of 5000 is subtracted from \( \frac{1}{10} \) of \( 5000, \) the difference is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 50
\( c .450 \)
D. 495
E. 500


write a general expression for the wave
function
\( y=(15 \mathrm{cm}) \sin \left[\left(16 \pi s^{-1}\right) t-\left(\frac{\pi \mathrm{rad}}{20 \mathrm{cm}}\right) x+\frac{\pi}{2}\right] \)
\( y=(30 \mathrm{cm}) \sin \left[\left(16 \pi s^{-1}\right) t-\left(\frac{\pi r a d}{20 \mathrm{cm}}\right) x+\frac{\pi}{2}\right] \)
\( y=(15 \mathrm{cm}) \sin \left[\left(8 \pi s^{-1}\right) t-\left(\frac{\pi \mathrm{rad}}{20 \mathrm{cm}}\right) x+\frac{\pi}{2}\right] \)
\( y=(15 \mathrm{cm}) \sin \left[\left(16 \pi s^{-1}\right) t-\left(\frac{\pi r a d}{10 \mathrm{cm}}\right) x+\frac{\pi}{2}\right] \)


The reagent with which the following
reaction is best accomplished is:
\( \mathbf{A} \cdot H_{3} P O_{2} \)
В. \( H_{3} P O_{3} \)
\( \mathbf{c} \cdot H_{3} P O_{4} \)
D. \( N a H S O_{3} \)


\( \mathbf{1 . 4}+\mathbf{2 . 5}+\ldots+\mathbf{n}(\mathbf{n}+\mathbf{3})= \)
A. \( \frac{n(n+3)(n+5)}{9} \)
в. \( \frac{n(n+1)(n+5)}{3} \)
c. \( \frac{n(n+5)(n+7)}{6} \)
D. \( \frac{n(n+3)(n+9)}{12} \)


Evaluate the following limit :
\( \lim _{x \rightarrow 0} \frac{\sin ^{2} 3 x}{x^{2}} \)
\( A \)
B. 3
\( c \cdot 9 \)
D.


Find the value of \( x \) :
\( \sec ^{2} 2 x=1-\tan 2 x \)


Describe the work-energy relationship by giving a suitable example


What is the distribution of electrons in
a magnesium atom?
\( A \cdot(2,8,1) \)
B. (2,8,2)
\( c \cdot(2,8,3) \)
D. (2,8,4)


Two examples of non-luminous objects
are:
A. stars, the moon
B. a burning candle, a glowing bulb
c. the moon, a spoon
D. stars, a spoon


The efficiency of carnot's engine is \( 50 \% \)
The temperature of its \( \operatorname{sink} \) is \( 7^{\circ} \mathrm{C} \). To
increase its efficience \( 70 \% \). What is the
increase in temperature of the source?


Match the following
\begin{tabular}{lll|l}
& Column I & & Column II \\
a. & Adrenaline & 1. & Myxoederna \\
b. & Hyperparathyroidism & 2. & Accelerates heartbeat \\
c. & Oxytocin & 3. & Water balan \\
d. & Hypothyroidism & 4. & Childbirth \\
e. & Aldosterone & 5. & Demineraliz
\end{tabular}
\( \mathbf{A} \)
\( a-2, b-5, c-4, d-1, e-3 \)
B. \( a-5, b-3, c-2, d-4, e-1 \)
\( 3, b-4, c-5, d-1, e-2 \)
\( C \cdot a-3 \)
D. \( a-2, b-3, c-4, d-5, e-1 \)


Wire bound resistors are made by.
A. Winding the wires of an alloy viz, \( \mathrm{Cu} \), Al, \( \mathrm{Ag} \)
B. Winding the wires of an alloy viz, Si, Tu, Fe
C. Winding the wires of an alloy viz, Ge, Au, Gr
D. Winding the wires of an alloy viz, manganin, constantan, nichrome


Identify the oxidation states of titanium \( (Z=22) \) and copper \( (Z=29) \) in their colourless compounds:
A \( \cdot T i^{3+}, C u^{2+} \)
B. \( T i^{2+}, C u^{2+} \)
c. \( T i^{4+}, C u^{+} \)
D. \( T i^{4+}, C u^{2+} \)


The distance between two points (1,1) and \( \left(\frac{2 t^{2}}{1+t^{2}}, \frac{(1-t)^{2}}{1+t^{2}}\right) \) is
\( A \cdot 4 t \)
B. 3t
\( c \)
D. none of these


The electric charge, in uniform motion, produces
A. electric field only
B. magnetic field only
c. both 'a' and 'b'
D. neither 'a' or 'b'


Inverse circular functions,Principal values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y}
\]
\( x y<1 \)
\( \boldsymbol{\pi}+\boldsymbol{\operatorname { t a n }}^{-1} \frac{\boldsymbol{x}+\boldsymbol{y}}{1-\boldsymbol{x} \boldsymbol{y}}, \quad \boldsymbol{x} \boldsymbol{y}>1 \)
(a) If \( \tan ^{-1} \frac{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}{\sqrt{\left(1+x^{2}\right)}+\sqrt{\left(1+x^{2}\right)}}= \)
\( \alpha . \) then prove that \( x^{2}=\sin 2 \alpha \)
(b) If \( \frac{\operatorname{mtan}(\alpha-\theta)}{\cos ^{2} \theta}=\frac{n \tan \theta}{\cos ^{2}(\alpha-\theta)} \)
then prove that \( \boldsymbol{\theta}= \) \( \frac{1}{2}\left[\alpha-\tan ^{-1}\left(\frac{n-m}{n+m} \tan \alpha\right)\right] \)
(c) \( \cos ^{-1} \frac{\cos \alpha+\cos \beta}{1+\cos \alpha \cos \beta}= \)
\( 2 \tan ^{-1}\left(\tan \frac{\alpha}{2} \tan \frac{\beta}{2}\right) \)


\( H_{2} \) gas is liberated at cathode and
anode both by electrolysis of the following aq. solution except in:
A. \( N a H \)
в. \( H C O O N a \)
c. \( N a C l \)
D. LiH


Two identical parallel plate capacitors are connected in series and then joined
with a battery of \( 100 ~ V . A \) sheet of
dielectric constant 4.0 is inserted
between the plates of second capacitor. The potential difference across the
capacitors will be respectively.
\( \mathbf{A} \cdot 50 V, 50 V \)
B . \( 80 \mathrm{V}, 20 \mathrm{V} \)
c. \( 20 V, 80 V \)
D. \( 75 V, 25 V \)


Form the differential equation representing the family of ellipses having centre at the origin and foci on \( x \) axis.


Which of the following compound is obtained on heating potassium
ferrocyanide with concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) ?
A \( \cdot C O_{2} \)
в. \( C O \)
\( \mathbf{c} \cdot C_{2} H_{2} \)
D. \( (C N)_{2} \)


Which of the following has a 3 chambered heart?
A. Salamander
B. Fish
c. crocodile
D. Dolphin


Assertion
Alveoli are the primary sites for
exchange of gases.
Reason
All factors in our body are favourable for
the diffusion of \( O_{2} \) from alveoli to
tissues and that of \( \mathrm{CO}_{2} \) from tissues to
alveoli.
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


There are various arsenic drugs
(containing arsenic compounds), such as Salvarsan, Atoxyl, and Tryparsamide. Their main use is in the treatment of:
A. Syphilis
B. Typhoid
c. Jaundice
D. Cholera


\( \mathbf{f} \mathbf{f}_{\mathbf{3}}=\left[\begin{array}{ccc}\mathbf{0} & \mathbf{1} & \mathbf{- 1} \\ \mathbf{2} & \mathbf{1} & \mathbf{3} \\ \mathbf{3} & \mathbf{2} & \mathbf{1}\end{array}\right], \) then
\( \left[\boldsymbol{A}(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}) \boldsymbol{A}^{-1}\right] \boldsymbol{A}= \)
\( \mathbf{A} \cdot\left[\begin{array}{lll}6 & 0 & 0 \\ 0 & 6 & 0 \\ 0 & 0 & 6\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{lll}4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right] \)
D. \( I \)


according to Ruther-fordis atomic
model, the mass of the atom is evenly distributed throughout the atom
A. True
B. False


Two strips of metal are riveted together at their ends by four rivets, each of
diameter 6 m \( m \). Assume that each rivet
is to carry one quarter of the load. If the shearing stress on the rivet is not to exceed \( 6.9 \times 10^{7} P a \), the maximum
tension that can be exerted by the riveted strip is then
A \( \cdot 2 \times 10^{3} N \)
B. \( 3.9 \times 10^{3} N \)
c. \( 7.8 \times 10^{3} N \)
D. \( 15.6 \times 10^{3} N \)


Solve the following pair of equations:
\( \frac{5 y}{2}-\frac{x}{3}=8 \)
\( \frac{y}{2}+\frac{5 x}{3}=12 \)
\( \mathbf{A} \cdot x=2 ; y=7 \)
B. \( x=4 ; y=3 \)
\( \mathbf{c} \cdot x=6 ; y=4 \)
D. \( x=7 ; y=3 \)


Find the zeroes of polynomial \( \boldsymbol{p}(\boldsymbol{x})= \)
\( 6 x^{2}-3 \)


What is the number of molecules
present in 0.5 mole of hydrogen?
A. \( 3.011 \times 10^{22} \) molecules
B. \( 3.011 \times 10^{23} \) molecules
c. \( 6.022 \times 10^{23} \) molecules
D. \( 3.011 \times 10^{33} \) molecules


A sigma bond may be formed by the
overlap of 2 atomic orbitals of atoms \( \boldsymbol{A} \)
and \( B \). If the bond is formed along the
\( x- \) axis, which of the following overlaps
is acceptable?
\( \mathbf{A} \cdot s \) orbital of \( A \) and \( p_{z} \) orbital of \( B \)
B. \( p_{x} \) orbital of \( A \) and \( p_{y} \) orbital of \( B \)
C . \( p_{z} \) orbital of \( A \) and \( p_{x} \) orbital of \( B \)
D. \( p_{x} \) orbital of \( A \) and \( s \) orbital of \( B \)


A smooth ball of mass \( m \) strikes a
horizontal surface with a velocity \( v \) in a
direction making an angle \( 30^{\circ} \) with the
normal to the surface as shown in
figure. If the coefficient of restitution for
the collision between the ball and the
surface is \( e \) and the ball was in contact
with the surface for a small time \( \Delta t, \) the
average force acting on the ball during
collision is
\( \mathbf{A} \cdot m g \)
B. \( \frac{m v(1+e)}{2 \Delta t} \)
c. \( \sqrt{3} \frac{m v(1-e)}{2 \Delta t} \)
D. \( \sqrt{3} \frac{m v(1+e)}{2 \Delta t} \)


A mutually beneficial relationship between two different organisms for nutrition is called as
A. Symbiotic Nutrition
B. Parasitic Nutrition
c. Saprobiotic Nutriton
D. Detritivores


The term 'biosystematics' was coined by
A. Gaspard Bauhin
B. Camp and Gilly
c. Karl Prantl
D. Robert Brown


\( 0.6 \mathrm{g} \) of an organic compound when dissolved in 21.7 g water freezes at 272.187 K. The molar mass of the
organic compound is close to:
\( \left(K_{f} \text { of water is } 1.86 \) deg/molality; \right. freezing point is \( 273 \mathrm{K} \) )
A. \( 61 \mathrm{g} \) mol \( ^{-1} \)
B. \( 63 \mathrm{g} \) mol \( ^{-1} \)
\( \mathbf{c} \cdot 65 \mathrm{g} m o l^{-1} \)
D. \( 67 \mathrm{g} \) mol \( ^{-1} \)


Out of the elements with atomic
numbers given below which one would be a halogen?
A . 25
B. 35
c. 45
D. 55


Calculate the charge on the capacitor in coulombs if a 20 -F capacitor has a \( 30-v \) potential difference across it.
A. \( 6.7 \times 10^{-7} \mathrm{c} \)
В. \( 6.0 \times 10^{-4} \mathrm{C} \)
\( c \cdot 1.5 c \)
D. \( 6.0 \times 10^{2} \mathrm{C} \)
E . \( 1.5 \times 10^{6} \mathrm{C} \)


After attaining the puberty girls develop
voice.
A . Low
B. High pitched
c. Deep
D. Low pitched


A radio nuclide \( A_{1} \) with decay constant
\( \lambda_{1} \) transforms into a radio nuclide \( A_{2} \)
with decay constant \( \lambda_{2} \). Assuming that at the initial moment, the preparation
contained only the radio nuclide \( \boldsymbol{A}_{\mathbf{1}} \)
(a) Find the equation describing
accumulation of radio nuclide \( A_{2} \) with
time.
(b) Find the time interval after which
the activity of radio nuclide \( A_{2} \) reaches
its maximum value.


If the current in a wire is directed east
wards and it is kept in a magnetic field directed northwards, the direction of
force on the wire is:
A. due west
B. due south
c. vertically upwards
D. vertically downwards


A transformer consists of a coil of 1200
turns and another coil, with a total of
120 turns, which can be tapped at various places. Primary voltage is \( 240 \mathrm{V} \) At which pair of terminals would you connect to a \( 12 \mathrm{V}, 24 \mathrm{V} \) lamp for it to be
lit normally?


Find the coordinates of a point \( A, \) where
\( A B \) is the diameter of a circle whose
centre is (2,-3) and \( B \) is (1,4)


\begin{tabular}{|ccc}
If \( \boldsymbol{f}(\boldsymbol{x})= \) & \\
\( \mathbf{1} \) & \( \boldsymbol{x} \) & \( \boldsymbol{x} \) \\
\( \boldsymbol{2} \boldsymbol{x} \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( (\boldsymbol{x}-1) \) \\
\( \boldsymbol{3} \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2}) \) & \( (\boldsymbol{x}+\mathbf{1}) \)
\end{tabular}
then \( f(100) \) is equal to
A.
B.
\( c \cdot 100 \)
D. -100


Which of the following is the most basic oxide?
A. \( S e O_{2} \)
в. \( A l_{2} O_{3} \)
\( \mathbf{c} \cdot S b_{2} O_{3} \)
D. \( B i_{2} O_{3} \)


All atoms contain neutrons in their
nuclei except:
A. Protium
B. Helium
c. Neon
D. Chlorine


Two blocks are arranged as shown in
the figure. Find the ratio of \( a_{1} / a_{2} .\left(a_{1} \) is \right.
acceleration of \( \boldsymbol{m}_{1} \) and \( \boldsymbol{a}_{1} \) that of \( \boldsymbol{m}_{2} \) ).


\( f \int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x= \)
\( \sin ^{-1}\left(\frac{\boldsymbol{A}}{\mathbf{4} \mathbf{2 6}}(\sin \boldsymbol{x}+\cos \boldsymbol{x})\right)+\boldsymbol{C} \) then
A is equal to


Differentiate between streamline and
turbulent flow.


Find the cube root of the following number by prime factorization method:
\( \mathbf{1 3 3 1} \)


Thyroxin is responsible for


For \( \boldsymbol{x} \in \boldsymbol{R} \) let \( \boldsymbol{f}(\boldsymbol{x})=|\sin \boldsymbol{x}| \) and
\( g(x)=\int_{0}^{x} f(t) d t . \) Let \( p(x)=g(x)-\frac{2}{\pi} x \)
Then
A. \( p(x+\pi)=p(x) \) for all \( x \)
B . \( p(x+\pi) \neq p(x) \) for all least one but finitely many \( x \)
c. \( p(x+\pi) \neq p(x) \) for infinitely many \( x \)
D. \( p \) is a one-one function


Find the area bounded by the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) and the ordinates \( x=0 \)
and \( x=a e, \) where \( b^{2}=a^{2}\left(1-e^{2}\right) \) and
\( e<1 \)


\( \int \frac{d x}{(x-b) \sqrt{(x-a)(b-x)}}= \)
A \( -\frac{(b-a)}{2} \sqrt{\frac{b-x}{x-a}}+c \)
В. \( -(b-a) \sqrt{(b-x)(x-a)}+c \)
c. \( -\frac{2}{(b-a)} \sqrt{\frac{x-a}{b-x}}+c \)
D. \( (b-a) \sqrt{(x-b)(x-a)}+c \)


If \( A \) is a \( 3 \times 3 \) skew symmetric matrix,
then trace of \( A \) is equal to
A . -1
B. 7
c. \( |A| \)
D. None of these


If \( f(x) \) is the integral of \( \frac{2 \sin x-\sin 2 x}{x^{3}}, x \neq 0 . \) Find
\( \lim _{x \rightarrow 0} f^{\prime}(x), \) where \( f^{\prime}(x)=\frac{d f(x)}{d x} \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{3} \)
\( D \)


Simple interest on a certain sum is \( \frac{\mathbf{9}}{\mathbf{1 6}} \)
of the sum. Find the rate percent and the time if both are numerically equal


Draw a labelled diagram of 'Standard Hydrogen Electrode'.


A man weight \( W \) on the surface of the
earth and his weight at a height \( \boldsymbol{R} \) from
surface of the earth is \( (R \) is radius of
the earth)
A \( \cdot \frac{W}{4} \)
в. \( \frac{W}{2} \)
c. \( W \)
D. \( 4 W \)


Genetic material of TMV is
\( \mathbf{A} \cdot \operatorname{RNA} \)
B. DNA
C. DNA and RNA
D. None of the above


Assertion: Enzymes have active sites that hold substrate molecule for a
chemical reaction
Reason : Drugs compete with natural substrate by attaching covalently to the active site of enzyme
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct and Reason is NoT the correct explanation for Assertion
c. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct
F. Answer reqiured


n Fig. \( D \) is a point on hypotenuse \( A C \)
of \( \triangle A B C, \) such that
\( B D \perp A C, D M \perp B C \) and \( D N \perp A B \)
Prove that:
(i) \( D M^{2}=D N \cdot M C \)
(ii) \( D N^{2}=D M \cdot A N \)


A train of length 200 m travelling at 30 \( m s^{-1} \) overtakes another train of length
\( 300 \mathrm{m} \) travelling at \( 20 \mathrm{ms}^{-1} \). The time
taken by the first train to pass the second is
A . 30 sec
B. 40 sec
c. \( 50 \mathrm{sec} \)
D. 60 sec


The standard reduction potential \( E^{\circ} \) for half reaction are:
\( Z n \rightarrow Z n^{2+}+2 e^{-} ; E^{o}=+0.76 V \)
\( \boldsymbol{F e} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} ; \boldsymbol{E}^{o}=+\boldsymbol{0 . 4 1} \boldsymbol{V} \)
The EMF of the cell reaction is:
\( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{Z} \boldsymbol{n}^{2+}+\boldsymbol{F} \boldsymbol{e} \)
A. \( -0.35 V \)
в. \( +0.35 V \)
\( \mathrm{c} \cdot+1.17 V \)
D. -1.17V


Regarding dipole-dipole attractions the
incorrect statement is:
This question has multiple correct options
A. dipole-dipole attractions are more, if the molecules have height dipole moment values.
B. in liquid \( H B r \) dipole-dipole attractions are present
C. dipole-dipole interaction energy between stationary polar molecules as in solids \( \propto r^{-3} \)
D. dipole-dipole interaction energy between rotating molecules \( \propto r^{6} \)


A cell phone tower has a safety light and it blinks once in every 2.5 seconds to warn airplanes of its location. If \( f(\boldsymbol{m}) \) is the total number of times this light blinks in \( m \) minutes, then \( f(m) \) is defined by
A. \( f(m)=2.5 m \)
B. \( f(m)=\frac{3.5 m}{60} \)
\( \mathrm{c} \cdot f(m)=\frac{60 m}{2.5} \)
D. \( f(m)=210 m \)


The dissociation constant of \( N H_{4} O H \)
can be given as
\( ^{\mathbf{A}} \cdot_{K_{b}}=\frac{\left(c_{3}\right)^{2}}{\left(c_{2}-c_{3}\right)} \)
B. \( \quad K_{b}=\frac{\left(c_{3}\right)^{2}}{c_{2}} \)
\( ^{\mathbf{c}} \cdot_{K_{b}}=\frac{c_{3}}{\left(c_{2}-c_{3}\right)} \)
D. \( _{K_{b}}=\frac{c_{3}}{\left(c_{1}-c_{2}\right)} \)


How many grams of potassium chloride \( (K C l) \) must be added to make \( 500 \mathrm{mL} \)
of \( 1.00 \mathrm{M} K C l \) solution?
A \( .1 .00 \mathrm{g} \)
B. 18.6 \( g \)
c. \( 37.3 \mathrm{g} \)
D. 74.5 g
E. \( 149 \mathrm{g} \)


With reference to periodic table,
indicate:
First transition element of the fourth
period.


How can we consider green algae similar to plant world?


Which statement is correct for all
metals?
A. Conduct electricity when molten
B. Gain electrons when they form ions
c. Have a low density
D. Have a low melting point


What is the path difference for destructive interference?
A \( \cdot \frac{(2 n+1) \lambda}{2} \)
B. \( \frac{(n+1) \lambda}{2} \)
c. \( n(\lambda+1) \)
D. \( n \lambda \)


Why are interhalogen compounds more
reactive that halogens?


The output power in step-up transformer used in practice is
A. Greater than the input power
B. Equal to the input power
c. Less than the input power
D. None of the above


Read the following statements carefully
(1) In fishes the heart pumps out deoxygenated blood which is oxygenated by the gills and supplied to the body parts from where deoxygenated blood is returned to the
heart
(2) The openings of the right and the left ventricles into the pulmonary artery and the aorta respectively are provided with the mitral valves.
(3) The nodal musculature has the ability to generate action potential without any external stimuli, i.e., it is auto-excitable
(4) The T-wave of ECG represents depolarization of the ventricles Which of the given two statements are correct?
A. 1 and 3
B. \( 2 \& 4 \)
c. 1 and 2
D. 3 \& 4


Compute the value of \( x \) in each of the
following figures


Find the modulus and the principal
argument of the complex number
\( (\tan 1-i)^{2} \)
\( \mathbf{A} \cdot|z|=(\tan 1)^{2}+1, z \) lies in 4 rd quadrant, \( \arg (z)=2- \)
\( \pi / 2 \)
B \( \cdot|z|=(\tan 1)^{2}+1, z \) lies in 4 rd quadrant, \( \arg (z)=2-\pi \)
\( \mathbf{C} \cdot|z|=(\tan 1)^{2}+1, \mathbf{z} \) lies in \( 3 \mathrm{rd} \) quadrant, \( \arg (z)=2- \)
\( \pi / 2 \)
D \( \cdot|z|=(\tan 1)^{2}+1, z \) lies in 3rd quadrant, \( \arg (z)=2-\pi \)


An object \( 2.4 ~ m \) in front of a lens forms
a sharp image on a film \( 12 \mathrm{cm} \) behind
the lens. A glass plate \( 1 \mathrm{cm} \) thick of
refractive index 1.50 is interposed between lens and film with its plane
faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?
\( \mathbf{A} \cdot 7.2 m \)
B. \( 2.4 m \)
c. \( 3.2 m \)
D. \( 5.6 m \)


State whether given statement is True or False.
The motion of the moon around the
earth is a curvilinear motion
A. True
B. False


Find the smallest number which when
subtracted from 9761 , the difference is
a perfect cube


BOD (biological oxygen demand) is
A. Amount of oxygen consumed by microorganisms for decaying organic matter per unit volume of water
B. Amount of \( C O_{2} \) consumed by microorganisms per
unit of sewage water
C. Amount of oxygen required by aquatic plants for survival
D. None of the above


A: Radio wave can diffract at the edges
of buildings
B: X-rays can diffract at the interiors of a crystal
A. A is true, B is false
B. Both A and B are true
c. A is false, B is true
D. Both A and B are false


ADP \( \longrightarrow \) ATP reaction occurs when two
protons \( \left(\boldsymbol{H}^{+}\right) \) are passed from
A. Thylakoid to cytosol
B. Thylakoid to lumen
c. Lumen of thylakoid to stroma
D. Stroma to thylakoid lumen.


The function \( \boldsymbol{f}:(\boldsymbol{R}-\mathbf{0}) \rightarrow \mathbf{R} \) given by
\( f(x)=\frac{1}{x}-\frac{2}{e^{2 x}-1} \) can be made
continuous at \( x=0 \) by defining \( f(0) \) as
A . 2
B. - -
c. 0
\( D \)


The short range attractive nuclear forces that are responsible for the binding of nucleons in a nucleus are supposed to be caused by the role played by the particles called
A. Positron
B. m-Meson
c. K-Meson
D. \( \pi \) - Meson


The areas under the I-H hysteresis loop and B-H hysteresis loop are denoted by \( A_{1} \) and \( A_{2}, \) then the ratio of \( \frac{A_{2}}{A_{2}} \) is given by
\( A \cdot \mu_{0} \)
в. \( \frac{1}{\mu_{0}} \)
\( c \cdot 1 \)
D. \( \sqrt{\mu_{0}} \)


Three uniform spheres, each having mass \( \mathrm{m} \) and radius \( \mathrm{r}, \) are kept in such a way that each touches the other two.
The magnitude of the gravitational
force on any sphere due to the other two is?
A \( \cdot \frac{G m^{2}}{r^{2}} \)
в. \( \frac{G m^{2}}{4 r^{2}} \)
c. \( \sqrt{2} \frac{G m^{2}}{4 r^{2}} \)
D. \( \sqrt{3} \frac{G m^{2}}{4 r^{2}} \)


A circular ring is fixed in a gravity free
space and one point of the ring is earthed. Now a magnet is placed along
axis of the ring at a distance from its
centre such that the nearer pole is north pole as shown in figure. A sharp impilse is applied on the magnet so that it
starts to move towards the ring. Then,
A. Initially magnet experiences an acceleration and then it retards to come to an instantaneous rest.
B. Magnet starts to oscillate about centre of the ring
C. Magnet continues to move along the axis with constant velocity
D. The magnet retards and comes to rest finally


Find the cube root of the given number through estimation:
\( \mathbf{2 1 9 7} \)


A virtual image of magnification \( =1 \) is formed by a ........ (convex, plane) mirror.


Which of the following is used as standard for determination of atomic
mass?
\( \mathbf{A} \cdot O^{16} \)
B. \( C^{12} \)
\( c \cdot H^{1} \)
D. \( O^{1} \)


Consider the following equilibrium
system; \( \boldsymbol{S O}_{2}(\boldsymbol{g})+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
set up in a cylinder fitted with a piston. Some inert gas is added and the piston is moved outwards to keep the total
gaseous pressure constant. Predict which of the following is true?
A. Addition of inert gas does not affect the equilibrium.
B. Less \( S O_{3}(g) \) is produced
c. More \( S O_{3}(g) \) is produced
D. The system moves to new equilibrium position which cannot be predicted theoretically.


The Young's modulus of a wire of length and radius \( r \) is \( Y N / m^{2} . \) If the length
is reduced to \( L / 2 \& \) radius to \( r / 2 \), then its Young's modouls will be-
A \( \cdot \frac{Y}{2} \)
B. Y
c. 2 y
D. 4Y


The solution of the given D.E \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{\boldsymbol{y}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{y}^{2}}}{\boldsymbol{x}} \) is
A \( \cdot y+\sqrt{x^{2}+y^{2}}=c x^{2} \)
B . \( x+\sqrt{x^{2}+y^{2}}=c y^{2} \)
c. \( y+\sqrt{x^{2}+y^{2}}=c x \)
D. \( x+\sqrt{x^{2}+y^{2}}=c y \)


A siphon has a uniform circular base of
diameters \( 8 / \sqrt{\pi} \mathrm{cm} \) with its crest \( \boldsymbol{A} \)
1.8 \( m \) above the water level vessel \( B \) is
of large cross section \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
and atmosphere pressure \( \boldsymbol{P}_{0}= \)
\( \mathbf{0}^{\mathbf{5}} \mathbf{N} / \mathbf{m}^{\mathbf{2}} \mathbf{)} \)
This question has multiple correct options
A. Velocity of flow through pipe is \( 6 \sqrt{2} \mathrm{m} / \mathrm{s} \)
B. Discharge rate of flow through pipe is \( 96 \sqrt{2} \times \) \( 10^{-4} m^{3} / s \)
C. Velocity of flow through pipe is \( 6 \mathrm{m} / \mathrm{s} \)
D. Pressure of \( A \) is \( 0.46 \times 10^{-5} \mathrm{N} / \mathrm{m}^{2} \)


Assertion
Molarity of an aqueous solution at \( 0^{\circ} \mathrm{C} \)
is less than the molarity of the same
solution at \( 4^{\circ} \mathrm{C} \)
Reason
Molarity increases with an increase of
temperature
A. Both Assertion and Reason are correct and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
C. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect but the Reason is correct


Electroscope is used
A. to detect and test small electric charges
B. to calculate the amount of electric charge flowing through the conductor in the given interval of time
C. to find out the presence of antimatter
D. to test the presence of magnetic field


Period of adolescence means the
Period between
A . 12 to 18 years age
B. 15 to 45 years age
c. 15 to 24 years age
D. 45 to 80 years age


A shopkeeper gave a discount of \( 12 \frac{1}{2} \% \) on the marked price of all items during
Diwali. What was the selling price of an
item whose marked price 1250


Primary process in photosynthesis leads to the conversion of light energy
into chemical energy. Discuss the statement.


Which of the following is a property of
nonmetals?
A. Low densities
B. Low melting points
c. Poor conductor of electricity
D. All the three


Substrates bind to the active sites of an
enzyme by interactions like:
A. ionic bonding
B. hydrogen bonding
c. van Der Waals' interactions
D. All of the above


The first mammal clone dolly was created by
A . lan wilmut
B. T.H. Morgan
c. Robert Briggs
D. Thomas King


A string tied on a roof can bear a maximum tension of 50kgwt. The
minimum acceleration that can be
acquired by a man of \( 98 k g \) to descend
will be (Take \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \) )
A \( \cdot 9.8 m / s^{2} \)
в. \( 4.9 m / s^{2} \)
c. \( 4.8 m / s^{2} \)
D. \( 5 m / s^{2} \)


The heat of combustion of carbon to
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) \) is \( -\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} . \boldsymbol{5} \boldsymbol{k} \boldsymbol{J} \quad \boldsymbol{m} \boldsymbol{o l}^{-1} \)
Calculate the heat released upon
formation of \( 35.2 g \) of \( C O_{2}(g) \) from
carbon and oxygen gas.
\( \mathbf{A} \cdot-315 k J \)
в. \( 315 J \)
c. \( 215 k J \)
D. \( -215 . J \)


Vapour phase refining of nickel is carried out using:
\( \mathbf{A} \cdot I_{2} \)
в. \( C l_{2} \)
c. \( H C l \)
D. \( C O \)


A long curved conductor carrier a current \( \overrightarrow{\boldsymbol{I}}(\overrightarrow{\boldsymbol{I}} \) is a vector). A small current element of length \( d \vec{l} \), on the wire,
induces a magnetic field at a point, away from the current element. If the
position vector between the current
element and the point is \( \vec{r}, \) making an
angle \( \theta \) with current element then, the induced magnetic field density, \( d \vec{B} \) at
the point is \( \left(\mu_{0}= \) permeability of free \right. space
\( \frac{\mu_{o} I(d \vec{l} \times \vec{r})}{4 \pi r^{3}} \) perpendicular to the current element \( d \vec{l} \)
B. \( \frac{\mu_{o} I \times \vec{r} . d \vec{l}}{4 \pi r^{2}} \) perpendicular to the current element \( d \vec{l} \)
\( \frac{\mu_{o} I \times d \vec{l}}{r} \) perpendicular to the plane containing the current element and position vector \( \vec{r} \)
D. \( \frac{\mu_{o} I \times d \vec{l}}{4 \pi r^{2}} \) perpendicular to the plane containing current element and position vector \( \vec{r} \)


The energy releasing process in which the substrate is oxidised without an
external electron acceptor is called as
A. Aerobic respiration
B. Glycolysis.
C. Fermentation.
D. Photorespiration.


The polymer used in making handles of
cookers and frying pans is :
A. bakelite
B. nylon-2-nylon-6
c. orlon
D. polyvinyl chloride


State uses of nitrogen


Curie temperature is the temperature
above which
A. a ferromagnetic material becomes paramagnetic
B. a paramagnetic material becomes diamagnetic
C . a ferromagnetic material becomes diamagnetic
D. a paramagnetic material becomes ferromagnetic


If 'p' and 'q' are the coefficients of \( x^{a} \) and
\( x^{b} \) respectively in \( (1+x)^{a+b}, \) then
A. \( 2 p=q \)
В. \( p+q=0 \)
c. \( p=q \)
D. \( p=2 q \)


'The motion of a particle with a restoring force gives oscillatory motion". Which of the following forces can be a restoring force for the oscillatory motion.
A. Frictional force
B. A constant force
c. A time varying force opposite to direction of motion
D. Force due to a spring


Linear velocity of the \( C M \) of rod is
\( \mathbf{A} \cdot \frac{<F>(\Delta t)}{2 m}(\sqrt{3 \hat{i}}+\hat{j}) \)
B. \( \frac{<F>(\Delta t)}{2 m}(\sqrt{5 \hat{i}}+2 \hat{j}) \)
\( \mathbf{c} \cdot \underline{\leq F>(\Delta t)}(\sqrt{3 \hat{i}}+\hat{j}) \)
\( \mathbf{D} \cdot \frac{<F>(\Delta t)}{2 m}(\sqrt{5 \hat{i}}+\hat{j}) \)


Suppose a girl throws a die. If she gets 1 or \( 2, \) she tosses a coin three times and notes the number of tails. If she gets
3,4,5 or \( 6, \) she tosses a coin once and
notes whether a 'head' or 'tail' is
obtained. If she obtained exactly one
tail', what is the probability that she
threw 3,4,5 or 6 with the die?


Select the missing number from the
given matrix:
\( \begin{array}{ccc}5 & 2 & 4 \\ 4 & 4 & 7 \\ 2 & 5 & 3 \\ 18 & 30 & ?\end{array} \)
A . 43
B. 42
\( c .33 \)
D. 32


The foci of the ellipse \( \frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1 \) and the hyperbola \( \frac{x^{2}}{144}-\frac{y^{2}}{81}=\frac{1}{25} \) coincide
Then, the value of \( b^{2} \) is :
A . 5
B. 7
c. 9
D.


In the adjoining figure, find the
measure of \( \angle B A C, \) if \( \angle A B D=\angle C A D \)
and \( \angle B A D=\angle A C D \)
A \( \cdot 120^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 75^{\circ} \)
D. \( 90^{\circ} \)


Explain why iron, cobalt, nickel do not show the expected highest oxidation states of +8,+9 and +10 respectively?


A straight tunnel is dug into the earth
as shown in figure at a distance \( b \) from
its center. A ball of mass \( m \) is dropped
from one of its ends. Find the time it
takes to reach the other end is
approximately.


Differentiate with respect to \( x \) :
\( \frac{2^{x} \cos x}{\left(x^{2}+3\right)^{2}} \)


\( \ln I C I_{4}^{64} \) the shape is square planar.The number of bond pair-long repulsion at \( 90 \mathrm{re} \)
\( A \cdot 6 \)
B. 8
\( c \cdot 12 \)
D. 4


The radius of a wheel is 0.25 m. How
many rounds will it take to complete the distance of \( 11 k m ? \)
A. 7000
в. 8000
c. 9000
D. 6000


Express the following fractions as
percents:
\( (i) \frac{1}{2} \)
\( (i i) \frac{17}{25}(i i i) \frac{3}{8} \)
(iv) \( 2 \frac{7}{16}(v) \frac{14}{75} \)


Find the domain of definition and the
range of the following function:
\( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\boldsymbol{x}-\mathbf{1}}+\mathbf{2} \sqrt{\mathbf{3}-\boldsymbol{x}} \)


How is nuclear energy released in a
fission process? How is this energy converted into electric energy?


Calculate pH of a buffer prepared by adding \( 10 m L \) of \( 0.10 M \) acetic acid to
\( 20 m L \) of \( 0.1 M \) sodium acetate
\( \left[\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}\left(\boldsymbol{C H}_{3} \boldsymbol{C O O H}\right)=\boldsymbol{4 . 7 4}\right] \)
A . 3.00
в. 4.44
c. 4.74
D. 5.04


Radiations of intensity \( 0.5 W / m^{2} \) are
striking a metal plate. The pressure on the plate is
A \( \cdot 0.166 \times 10^{-8} \mathrm{N} / \mathrm{m}^{2} \)
B . \( 0.332 \times 10^{-8} \mathrm{N} / \mathrm{m}^{2} \)
c. \( 0.111 \times 10^{-8} \mathrm{N} / \mathrm{m}^{2} \)
D. \( 0.083 \times 10^{-8} N / m^{2} \)


If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( |\vec{a}|=|\vec{c}|=1,|\vec{b}|=4,|\vec{b} \times \vec{c}|=2 \)
and \( 2 \vec{b}=\vec{c}+\lambda \vec{a} \) then \( \lambda \) is
A \( \cdot \sqrt{65-8 \sqrt{3}} \)
B. \( \sqrt{17} \)
\( c \cdot \sqrt{3} \)
D. \( \sqrt{\frac{17}{2}(2+\sqrt{3})} \)


In a single toss of a coin the events \( \{\mathrm{H}\} \)
\( \{T\} \) are mutually exclusive.
Write 1 if true and 0 if false


Which of the following is the correct order of relative sizes?
\( \mathbf{A} \cdot I^{-}>I^{+}>I \)
B . \( I^{-}>I>I^{+} \)
C \( \cdot I>I^{+}>I^{-} \)
D. \( I^{+}>I^{-}>I \)


For the galvanic cell, \( \boldsymbol{C u}\left|\boldsymbol{C u}^{2+} \| \boldsymbol{A} \boldsymbol{g}^{+}\right| \boldsymbol{A} \boldsymbol{g} \)
Which of the following observations is
not correct?
A. Cu acts as anode and Ag acts as cathode
B. Ag electrode loses mass and Cu electrode gains mass
C. Reaction at anode, \( C u \rightarrow C u^{2+}+2 e^{-} \)
D. copper is more reactive than silver


\( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{x} & \mathbf{2} & \mathbf{3} \\ \mathbf{1} & \mathbf{2}+\boldsymbol{x} & \mathbf{3} \\ \mathbf{1} & \mathbf{2} & \mathbf{3}+\boldsymbol{x}\end{array}\right|=\mathbf{0} \operatorname{then} \boldsymbol{x}= \)
\( A \)
B. -1
\( c .-6 \)
\( D \)


If \( A=\left\{x: x^{2}+5 x+6=0, x \quad \epsilon \quad N\right\} \)
then \( n(A)=\dots \dots \dots \)


The diameter of a wheel is \( 2.8 m . \) How
far will travel in 1000 revolution?


At what rate \% per annum will a sum of
\( R s 13,700 \) invested for 3 years
amounts to \( \boldsymbol{R} \boldsymbol{s} \mathbf{1 6}, \mathbf{5 7 7} \)


If a line makes angles \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) with
coordinate axes, find
\( \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma+1 \)


Between a square of perimeter \( 44 \mathrm{cm} \) and a circle of circumference \( 44 \mathrm{cm} \) which figure has a larger area and by how much?
A. Square, \( 33 \mathrm{cm}^{2} \)
B . Circle, \( 33 \mathrm{cm}^{2} \)
c. Both have equal areas
D. square, \( 95 \mathrm{cm}^{2} \)


Moon has no atmosphere because:
A. it is far away from the surface of the earth
B. its surface temperature is \( 10^{0} C \)
C. the \( r m s \) velocity of all the gas molecules is more then the escape velocity of the moon's surface
D. the escape velocity of the moon's surface is more than the \( r m s \) velocity of all molecules


In which ship Charles Darwin went for his expedition?
A. siboga
B. Beagle
c. sea gull
D. Atlantic


Find the radius of a sphere whose
surface area is \( 154 \mathrm{cm}^{2} \)


Which of the following molecules has the shortest hydrogen-to-carbon bond?
A. \( C_{2} H_{4} \)
в. \( C_{2} H_{6} \)
c. \( C_{2} H_{2} \)
D. all are same


The pressure difference across a pipe of length \( 5 c m \) is \( 2 \times 10^{3} \) Pa. Work done by
the pressure in forcing \( 2 m^{3} \) of water through the pipe in joule is :
A \( \cdot 4 \times 10^{5} \)
B . \( 2 \times 10^{5} \)
\( c \cdot 2 \times 10^{4} \)
D. \( 4 \times 10^{3} \)


Two bodies of different masses have
same K.E. The one having more momentum is
A. Heavier body
B. Iighter body
c. both none
D. both


Select incorrect pair from the following.
A. Porifera - Choanocytes
B. Coelenterata - Nematocysts
c. Annelida - Segmentation
D. Monera - Eukaryote


Which of the following orders is not
correct with respect to the property indicated against each?
\( \mathbf{A} \cdot F>C l>B r>I \rightarrow \) electron gain enthalpy
B \( \cdot F^{-}>C l^{-}>B r>I^{-} \rightarrow \) enthalpy of hydration
\( \mathbf{C} \cdot F_{2}>C l_{2}>B r_{2}>I_{2} \rightarrow \) bond dissociation energy
\( \mathbf{D} \cdot F_{2}<C I_{2}<B r_{2}<I_{2} \rightarrow X-X \) bond lenght


The electronic configuration of bivalent europium and trivalent cerium are:
[Atomic number: \( \boldsymbol{X} \boldsymbol{e}=\mathbf{5 4}, \boldsymbol{C} \boldsymbol{e}= \)
\( \mathbf{5 8}, \boldsymbol{E u}=\mathbf{6 3}] \)
A \( \cdot[X e] 4 f^{7} 6 s^{2} \) and \( [X e] 4 f^{2} 6 s^{2} \)
B \( \cdot[X e] 4 f^{4} \) and \( [X e] 4 f^{9} \)
C \( \cdot[X e] 4 f^{2} \) and \( [X e] 4 f^{7} \)
\( \mathbf{D} \cdot[X e] 4 f^{7} \) and \( [X e] 4 f^{1} \)


Find the equation of normal to the curve \( x^{2}=4 y \) passing through the point
(1,2)
A \( . x+y=3 \)
B. \( x-y=3 \)
c. \( 2 x-y=4 \)
D. \( 2 x-3 y=1 \)


The average velocity of a body moving
with uniform acceleration after
travelling a distance of \( 3.06 m \) is \( \mathbf{0 . 3 4} \boldsymbol{m} / \boldsymbol{s} . \) The change in velocity of the body is \( 0.18 m / s . \) During this time, its acceleration is
A \( \cdot 0.01 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 0.02 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 0.03 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 0.04 \mathrm{m} / \mathrm{s}^{2} \)


Example of primary pollutant:
This question has multiple correct options
\( A \cdot S O_{2} \)
в. \( C O_{2} \)
c. Hydrocarbon
D. \( C O \)


Silk contains a protein known as
A. Fibroin
B. casein
c. Sericin
D. Both A and C


The induced emf in the smaller loop is
\( A \)
B.
\( ^{\mathbf{c}} \cdot \frac{_{3 \mu_{0} \pi i} R^{2} r_{r}^{2}}{2} \)
\( D \)
E . none


\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) is triprotic. Prove.


The only methyl halide which is a liquid is at room temperature is :
A. iodomethane
B. bromomethane
c. chloromethane
D. fluoromethane


Number of pairs of spiracles in cockroach are
A . 4
B. 6
\( c \cdot 8 \)
D. 10


Which of the following criteria does not pertain to facilitated transport?
A. High selectivity
B. Transport saturation
c. Uphill transport
D. Requirement of special membrane proteins


By selling a bouquet for \( R s 322 \), a florist
gains \( 15 \% . \) At what price should he sell, it to gain \( 25 \% ? \)


Calculate the maximum value of
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{3}-(\boldsymbol{x}+\boldsymbol{2})^{2} \)
A . -3
B. -
c. 1
D. 3
E. 5


Evaluate :
\( \int \frac{\left(x^{4}-x\right)^{1 / 4}}{x^{5}} d x \)


An athlete with \( 3 \mathrm{m} \) long iron rod in hand runs towards east with a speed of 30 kmph. The horizontal component of earth's magnetic field is \( 4 \times \)
\( 10^{-5} W b / m^{2} . \) If he runs with the rod in
horizontal and vertical positions then the induced emf generated in the rod in two cases will be
A. zero in vertical position and volt in horizonta
position.
B. 1 \( \times 10 \) volt in vertical position and zero volt in in horizontal position
c. zero in both positions
D. \( 1 \times 10^{-3} \) volt in both positions


In the right triangle, \( A B \) is twice \( B C \)
What is the length of \( \overline{B C} \) ?
A \( \cdot \sqrt{5} \)
B. \( 2 \sqrt{5} \)
\( c \cdot 3 \sqrt{5} \)
\( D \)


A proton and an \( \alpha \) -particle are accelerated through the same potential difference. The ratio of their De Broglie
wavelength is:
A. \( \sqrt{2} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot 2 \sqrt{2} \)
D. 2


The value of \( \sum_{r=1}^{n} \frac{n P_{r}}{r !} \)
\( \mathbf{A} \cdot 2^{n} \)
B . \( 2^{n}-1 \)
\( c \cdot 2^{n-1} \)
D. \( 2^{n+1} \)


The parabolas \( y^{2}=4 x \) and \( x^{2}=4 y \)
divide the square region bounded by the lines \( x=4, y=4 \) and the coordinate axes.
f \( S_{1}, S_{2}, S_{3} \) are respectively the areas of
these parts numbered from top to
bottom(Example: \( S_{1} \) is the area
bounded by \( y=4 \) and \( x^{2}=4 y \) ); then
\( \boldsymbol{S}_{1}, \boldsymbol{S}_{2}, \boldsymbol{S}_{3} \) is
A . 1: 2: 1
B. 1: 2: 3
c. 2: 1: 2
D. 1: 1: 1


If a ball fallen freely from 'h' height reaches in time 't' at ground, then what
will be the time when it reaches at height \( \frac{h}{2} ? \)


The expression for kinetic energy is :
A \( \cdot \frac{1}{2} m v \)
в. \( \frac{1}{3} m v^{2} \)
c. \( \frac{1}{2 m} v^{2} \)
D. \( \frac{1}{2} m v^{2} \)


In Duman's method of estimation of
nitrogen, 0.35 g of an organic compound gave 55 mL of nitrogen collected at \( 300 \mathrm{K} \) temperature and \( 715 \mathrm{mm} \) pressure. The percentage composition of nitrogen in the compound would be:
(Aqueous tension at \( 300 K=15 \mathrm{mm} \) )
A . 15.45
B. 16.45
c. 17.45
D. 14.45


The table below shows recorded
concentration data for the following chemical reaction:
\[
\begin{array}{l}
\boldsymbol{C a C l}_{2}(\boldsymbol{a q})+\mathbf{2 A g} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{a q}) \rightarrow \\
\boldsymbol{C a}\left(\boldsymbol{N O}_{3}\right)_{2}(\boldsymbol{a q})+\boldsymbol{2 A g} \boldsymbol{C l}(\boldsymbol{s})
\end{array}
\]
Use the data to determine the
exponents \( x \) and \( y \) in the rate law:
\[
0.100
\]
\[
0.050
\]
\( 6.66 \times 10^{-} \)
100 100
\( 13.32 \times 10 \)
A \( . x=2, y=3 \)
B. \( x=1, y=2 \)
c. \( x=1, y=1 \)
D. \( x=2, y=2 \)


There are 8 men and 10 women and you
need to form a committee of 5 men and
6 women. In how many ways can the committee be formed?
A . 10420
B. 11420
c. 11760
D. None of these


In the given figure, \( \triangle A B C \) is an isosceles right angled triangle with
\( \angle B=90 \) such that \( P Q \perp A C, S T \perp A C \)
where Plies on AB and S lies on BC. Then
prove that \( \triangle A Q P \sim \triangle C T S \)


Find the solution of system of
equations:
\( -24-8 j=12 k \) and \( 3+\frac{5}{3} k=-\frac{7}{6} j \)
A. (6,-6)
в. (3,0)
c. (0,2)
(年. \( 0,2,2) \)
D. (-4,1)


\( A B C D \) is a trapezium in which \( A B \| \) \( D C, D C=7 c m \) distance between \( A B \)
and \( D C \) is \( 4 c m \). Find \( A B \).


Observe the following statements:
1. Heavy water is harmful to the growth of animals.
2. Heavy water reacts with \( A l_{4} C l_{3} \) and
forms deuterated acetylene.
3. \( B a C l_{2} .2 D_{2} O \) is an example of interstitial deuterate
The correct statements are:
A. 1 and 3
B. 1 and 2
c. 1,2 and 3
D. 2 and 3


Fill in the blank:
Vrishchika is the Indian name for
constellation.
A. Virgo
B. Gemini
c. Leo
D. Scorpio


Describe the formation of
Acetyl Coenzyme A


The perimeter of two similar triangle
are \( 30 \mathrm{cm} \) and \( 20 \mathrm{cm} . \) If one side of first
triangle is \( 12 \mathrm{cm} \) determine the corresponding side of second triangle.
A. \( 8 \mathrm{cm} \)
в. \( 4 \mathrm{cm} \)
\( \mathrm{c} .3 \mathrm{cm} \)
D. \( 16 \mathrm{cm} \)


Assuming the balls to be identical except for difference in colors, the number of ways in which one or more
balls can be selected from 10 white, 9
green and 7 black balls is
A. 880
в. 629
\( c .630 \)
D. 879


The process of protecting iron by coating with zinc is called:
A. smelting
B. galvanising
c. rusting
D. corrosion


A/An \( _{-}--_{-}- \) is the smallest particle of a substance which can take part in a chemical reaction.
\( A \). atom
B. molecule
c. both \( A \) and \( B \)
D. none of the above


The nature of the roots of the equation \( x^{2}-5 x+7=0 \) is
A. No real roots
B. 1 real root and 1 imaginary
c. Real and unequal
D. Real and equal


A magnet of moment \( 4 \mathrm{Am}^{2} \) is kept
suspended in a magnetic field of induction \( 5 \times 10^{-5} T . \) The workdone in
rotating it through \( 180^{0} \) is
\( \mathbf{A} \cdot 4 \times 10^{-4} J \)
В. \( 5 \times 10^{-4} J \)
c. \( 2 \times 10^{-4} J \)
D. \( 10^{-4} J \)


Deduce an equation \( U=\frac{1}{2} L I^{2} \) for an
inductor.


An oil drop of 10 excess electrons is
held stationary under a constant electric field of \( 3.65 \times 10^{4} N C^{-1} \) in
Millikan's oil drop experiment. The density of oil is \( 1.26 g c m^{-3} . \) Radius of
the oil drop is
(Take \( \left.g=9.8 m s^{-2}, e=1.6 \times 10^{-19} C\right) \)
A \( \cdot 1.04 \times 10^{-6} \mathrm{m} \)
в. \( 4.8 \times 10^{-5} \mathrm{m} \)
\( \mathbf{c} \cdot 4.8 \times 10^{-18} m \)
D. \( 1.13 \times 10^{-18} \mathrm{m} \)


A cell of emf \( E \) volts with no internal
resistance is connected to a wire of
uneven cross-sectional area. The wire
has three sections of equal length. The radius of the middle section is \( a \)
and the other are \( 2 a \). The ratio of the
potential difference across the middle section to any other section is
A .2: 1
B . 4: 1
c. 1: 2
D. 1: 4


The area enclosed between the velocitytime sketch and the time axis gives
A. acceleration of a body
B. displacement of a body
c. distance travelled by a body
D. nothing specifically


In an ellipse, the distance between its focii is 6 and minor axis is \( 8 . \) Then its
eccentricity is
A \( \cdot \frac{3}{5} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{4}{5} \)
D. \( \frac{1}{\sqrt{5}} \)


Casparian strips occur in
A. Radial walls of endodermis
B. Radial walls of phellem cells
C. Radial walls of epidermal cells
D. None of the above


Height of atmosphere is about \( \boldsymbol{k m} \)
A. 3000
в. 300
c. 30
D. 30000


Temperature at which the equilibrium
water vapour pressure is 1.00 bar.
\( \mathbf{A} \cdot 107^{0} \mathrm{C} \)
B \( .380^{0} \mathrm{C} \)
\( \mathbf{C} \cdot 215^{0} \mathrm{C} \)
D. \( 240^{\circ} \mathrm{C} \)


In a reaction carried out at \( 400 \mathrm{K} \)
\( 0.0001 \% \) of the total number of
collisions are effective. The energy of
activation of the reaction is:
A . zero
B. 7.37 k cal/mol
c. \( 9.212 \mathrm{k} \) cal/mol
D. 11.05 k cal/mol


The distance between the line \( r=2 \hat{i}- \) \( 2 \hat{j}+3 \hat{k}+\lambda(\hat{i}-\hat{j}+4 \hat{k}) \) and the plane
\( r \cdot(\hat{i}+5 \hat{j}+\hat{k})=5 \) is
A \( \cdot \frac{10}{9} \)
в. \( \frac{10}{3 \sqrt{3}} \)
c. \( \frac{10}{3} \)
D. None of these


Which of the following is not characteristic of coke?
A. Hard
B. Porous
c. High carbon content
D. soft


At \( 30^{\circ} C, \) the degree of dissociation of
\( \mathbf{0 . 0 6 6} \boldsymbol{M} \boldsymbol{H} \boldsymbol{A} \) is \( \mathbf{0 . 0 1 4 5 .} \) The degree of
dissociation of \( 0.02 M \) solution of acid
at the same temperature is \( x, \) then find
the value of \( x \times 100 \) to the nearest
integer


By Rolles theorem for \( f(x)=(x- \)
\( a)^{m}(x-b)^{n} \) on \( [a, b] ; m, n \) being
positive integer. Find the value of \( c \) which lies between \( a \)
\& b.
A \( \cdot c=\frac{m b+n a}{m+n} \)
в. \( c=\frac{m b-n a}{m+n} \)
c. \( _{c}=\frac{n b+m a}{m+n} \)
D. \( c=\frac{n b-m a}{m+n} \)


Drive the following relation:
\( \boldsymbol{K} \boldsymbol{p}=\boldsymbol{K} \boldsymbol{c}(\boldsymbol{R} \boldsymbol{T})^{n} \)


Fermentation is an
A. Aerobic respiration
B. Incomplete oxidation
c. Excretory process
D. None of the above


A wire of resistance \( 10.0 \Omega \) is stretched
and increases its length by \( 20 \% \). Its resistance then would be: ( neglect any
change in volume or resistivity
A . \( 10.0 \Omega \)
B. \( 12.0 \Omega \)
c. \( 14.4 \Omega \)
D. \( 10.2 \Omega \)


If \( d \) is the determinant of a square
matrix A of order \( n \), then the
determinant of its adjoint is:
A . \( d^{n} \)
B. \( d^{n-1} \)
\( c \cdot d^{n-2} \)
D. \( d \)


An example of hydrocarbon:
A. Phorone
B. Mesitylene
c. Metaldeyhde
D. chloretone


For a liquid which is rising in a
capillary, the angle of contact is
A. obtuse
B. Acute
\( c \cdot 180^{\circ} \)
D. \( 90^{\circ} \)


toppr 'ОGा
Q Type your question_
but represents path from each of the
two slits to the third "bright fringe"
formed as part of the interference
pattern.
In the diagram how much longer is path
1 than path \( 2 ? \)
\( \mathbf{A} .400 n m \)
B. \( 1200 n m \)
\( \mathbf{c} \cdot 1600 n m \)
D. \( 1000 n m \)
E . \( 600 n m \)


\( f(x)=\left\{\begin{array}{l}k-2 x, \text { if } x \leq-1 \\ 2 x+3, \text { if } x>-1\end{array}\right\}, \) if \( f \) has
a local minimum at \( x=-1, \) then \( k= \)


Write the dimensional formula of
pressure.


Prove the following:
If \( \tan A=\frac{3}{4}, \) then \( \sin A \cos A=\frac{12}{25} \)


The breakdown of complex components of food into simple ones is called as
A. Respiration
B. Digestion
c. Excretion
D. Absorption


Degree of hydrolysis for a salt of strong
acid and weak base is:
A. independent of dilution
B. increases with dilution
C . increases with decrease in \( K_{b} \) of the bases
D. decreases with decrease in temperature.


The field of view is maximum for
A. Plane mirror
B. Concave mirror
c. convex mirror
D. plano concave mirror


A boy walks on a straight road from his home to a market \( 2.5 \mathrm{km} \) with a speed
of \( 5 \mathrm{km} h^{-1} \). Finding the market closed
he instantly turns and walks back with
a speed of \( 7.5 \mathrm{km} h^{-1} . \) What is the
average speed and average velocity of the boy between \( t=0 \) to \( t=50 \) min?
\( A \cdot 0,0 \)
B. \( 6 \mathrm{km} h^{-1} \), o
\( c \cdot 0,6 \mathrm{km} h^{-1} \)
\( \mathbf{D} \cdot 6 \mathrm{km} h^{-1}, 6 \mathrm{km} h^{-1} \)


National population policy was declared
in the year
A. 2000
B . 1999
\( c .200 \)
D. 1998


What is the electronic configuration for \( \operatorname{an} F e(I I I) \) ion in its ground state?
\( \mathbf{A} \cdot[A r] 3 d^{5} \)
B . \( [A r] 3 d^{6} \)
\( \mathbf{c} \cdot[A r] 4 s^{2} 3 d^{3} \)
D \( \cdot[A r] 4 s^{2} 3 d^{6} \)


An open vessel at \( 27^{\circ} \mathrm{C} \) is heated until
\( \left.\frac{2}{5}\right) \) th of the air in it has been expelled. Assuming that the volume of the vessel
remains constant. Which of the
following option is correct?
A. Final temperature is 500 \( \mathrm{K} \)
B. Final volume is 2 times the initial volume
C. Final pressure is 1 atm
D. None of the above


Sprinkling of water reduces
temperature of a closed room because
A. the temperature of water is less than that of room.
B. the specific heat of water is high.
C. the water has large latent heat of vaporization.
D. water is bad conductor of heat.


The minute hand of a clock is \( 10 \mathrm{cm} \)
long. Find the area of the face of the
clock described by the minute hand between 9 A.M. and 9.35 A.M.


The area of the portion of the circle
\( x^{2}+y^{2}=1, \) which lies inside the
parabola \( \boldsymbol{y}^{2}=\mathbf{1}-\boldsymbol{x}, \) is
A \( \cdot \frac{\pi}{2}-\frac{2}{3} \)
B. \( \frac{\pi}{2}+\frac{2}{3} \)
c. \( \frac{\pi}{2}-\frac{4}{3} \)
D. \( \frac{\pi}{2}+\frac{4}{3} \)


Fission of nuclei is possible because binding energy per nucleon in them:
A. increases with mass number at low mass number
B. increases with mass number at high mass number
c. decreases with mass number at low mass number
D. decreases with mass number at high mass number


The thickness of depletion region is of the order of
A. \( 0.1 \mu m \)
в. \( 1 \mu \) т
c. \( 0.1 m m \)
D. \( 1 \mathrm{mm} \)


\( k_{c} \) for the reaction \( N_{2} O_{4}(g) \leftrightharpoons 2 N O_{2} \) is
\( 4.63 \times 10^{-3} \) at \( 25^{\circ} C \)
a. what is the value of \( \boldsymbol{K}_{\boldsymbol{p}} \) at this
temperature
b. \( A t ~ 25^{\circ} C, \) if the partial pressure of
\( N_{2} O_{4}(g) \) at equilibrium is 0.2 at \( m \) calculate equilibrium pressure of
\( N O_{2}(g) \)


If the resistance in parallel with a
parallel resonant circuit is reduced, the bandwidth
A. disappears
B. becomes sharper
c. increases
D. decreases


Statement-1:
The point \( A(1,0,7) \) is the mirror image of the point \( B(1,6,3) \) in the line \( \frac{x}{1}= \) \( \frac{y-1}{2}=\frac{z-2}{3} \)
Statement-2:
The line: \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) bisects the
line segment joining \( A(1,0,7) \) and \( B(1,6,3) \)
A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for statement- -1
B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true


Increase in frequency of urination is
A. Uremia
B. Proteinuria
c. Polyurea
D. Glycosuria


If \( \tan \alpha=2, \) then the value of
\( \frac{\sin \alpha}{\sin ^{3} \alpha+\cos ^{3} \alpha} \) is
\( A \cdot \frac{2}{9} \)
в. \( \frac{5}{9} \)
c. \( \frac{10}{9} \)
D. \( \frac{5.5}{9} \)


The quantum theory is a suggestion that heat, light, electricity or any other form of energy.
A. Cab be if any size
B. Exist in discrete bundles
c. Is continuous
D. Is transfered in as small amount as one could imagine


The value of \( \sin ^{-1}(\sin 10) \) is
A . 10
в. \( 10-3 \pi \)
\( c .3 \pi-10 \)
D. none of these


Correct order of boiling points among following is:
\( \boldsymbol{C H}_{3}\left(\boldsymbol{C H}_{2}\right)_{3} \boldsymbol{C H}_{3}, \quad \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O C}_{2} \boldsymbol{H}_{5} \)
\( (\boldsymbol{X}) \)
\( (Y) \)
\( A \cdot x>Y>z \)
B. \( Y>X>Z \)
\( c \cdot z>x>r \)
D. \( z>Y>x \)


Give the path of movement of \( C O_{2} \) from
air to a mesophyll cell of the leaf


There are 6 red, 6 brown, 6 yellow, and 6 gray scarves packaged in 24 identical, unmarked boxes, 1 scarf per box. What
is the least number of boxes that must
be selected in order to be sure that
among the boxes selected 3 or more contain scarves of the same color?
A . 3
B. 6
\( c .7 \)
D.
\( E \)


Sodium sulphate is added to washing powders to
A. keep dirt suspended in water
B. keep washing powders dry
c. maintain alkalinity to remove dirt
D. produce whiteness in clothes


Two cars are moving in the same direction with the same speed \( 30 \mathrm{km} / \mathrm{h} \) They are separated by a distance of 4 km. What is the speed of a car moving in the opposite direction if it meets these two cars at an interval of 5 min?


Four spheres \( A, B, C \) and \( D \) of different metals but of same radius are
kept at same temperature.The ratios of their densities and specific heats are 2: 3: 5: 1 and \( 3: 6: 2: 4 . \) Which
sphere will show the fastest rate of
cooling (initially)?
A. \( A \)
в. \( B \)
\( c . c \)
D. \( D \)


Which among the following salts will give basic solution on hydrolysis? This question has multiple correct options
A. \( N a H_{2} P O_{4} \)
в. \( N H_{4} C l \)
c. \( N a C l \)
D. \( K_{2} C O_{3} \)


If for the following half-cell reactions:
\( \boldsymbol{C u}^{2+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}^{\oplus} \)
\( \boldsymbol{E}^{\oplus}=\mathbf{1 . 7 7} \boldsymbol{V} \)
\( \boldsymbol{C u}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{C u} \)
\( \boldsymbol{E}^{\ominus}=-\mathbf{0 . 3 4} \)
The \( E^{\ominus} \) of the half-cell reaction will be
\( (\text { in } V) \)
\( \boldsymbol{C u}^{\oplus}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u} \)


An \( \alpha- \) particle and a proton have their
masses in the ratio 4: 1 and charges
in the ratio 2: 1

Find ratio of de-Broglie wavelengths
when both have equal momentum.
\( \mathbf{A} \cdot 2: 1 \)
B. 1: 1
\( \mathbf{c} \cdot 4: 1 \)
D. 1: 4
E .1: 4


The path difference between two wavefronts emitted by coherent sources \( o \)
of wavelength \( 5460 A \) is 2.1 micron. The phase difference between the wavefronts at that point is
A. 7.962
в. 7.962 \( \pi \)
c. \( \frac{7.962}{\pi} \)
D. \( \frac{7.962}{3 \pi} \)


Choose the correct answer among the alternatives given:

Which of the following contraceptives are implanted under the skin?
\( A \)
в.
\( c \)
D.


toppr LoGıN
Q Type your question
the combustion reaction is
\( \boldsymbol{C}_{8} \boldsymbol{H}_{18}+\mathbf{1 2 . 1} \boldsymbol{O}_{2} \rightarrow \mathbf{0 . 8} \boldsymbol{C O}+ \)
\[
\mathbf{7} . \mathbf{2} \boldsymbol{C} \boldsymbol{O}_{\mathbf{2}}+\mathbf{9} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}
\]
Calculate the temperatures of the Gases just at the time of maximum compression and Write sum of these two temperatures. Exhaust gases leaving the cylinder if
the final pressure in the cylinder is
\( 200 k p a \)
Relevant data neede for one burn cycle
is given below:
Compound \( \boldsymbol{\Delta} \boldsymbol{H}_{f}\left(\boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1}\right) \) mol
\( N_{2}(g) \) 0.0
\( O_{2}(g) \) 0.0
\( \mathcal{P}(g) \) -110.53
\( \mathcal{P} O_{2}(g) \)
-395.51
-241.82 \( H_{2} O(g) \)
sooctane -187.82


Spongy parenchyma is arranged in
A. One layer
B. Loosely arranged
c. Compactly arrangedd
D. Regularly arranged around large cavities


Structure containing a ketone group is:
A \( \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-C-O H \)
॥
О
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
I
O
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)


The potential difference between two
parallel plates is \( 10^{4} V . \) If the plates are
separated by \( 0.5 \mathrm{cm}, \) the force on an electron between the plates is :
A . \( 32 \times 10^{-13} N \)
В. \( 0.32 \times 10^{-13} N \)
D. \( 3.2 \times 10^{-13} \) \( N \)


Naturally occurring argon (Ar) consists of three isotopes the atoms of which occur in the abundances as given in the table The atomic weight of argon is:
Isotopes Abundance
\( ^{36} A r \) 0.34\%
\( ^{38} A r \) 0.07\%
\( \begin{array}{ll}40 & \text { 99.59\% }\end{array} \)
A. 38.45 u
в. 37.20
c. 39.98 и
D. 40.98 u


\( M g_{2} C_{3} \) reacts with water to form
propyne \( C_{3} H_{4} \) has:
A. six sigma and two pi bonds
B. three sigma and one pi bond
c. two sigma and one pi bond
D. two sigma and three pi bonds


A body which is uniformly accelerated,
changes its velocity from \( 36 k m / h r \) in
one direction to \( 18 k m / h r \) in the
opposite in 6 seconds. The total distance traveled by the body during this time interval is


A small linear object of length \( b \) is
placed at a distance \( u \) from the pole of the concave mirror along the axis away from the mirror. The focal length of the mirror is \( f . \) The length of image will
then be?
A \( \cdot \quad b\left(\frac{f}{u-f}\right)^{2}\left(\frac{f}{u-f+b}\right)^{2} \)
в. \( \quad b\left(\frac{f}{u-f}\right)^{2}\left(\frac{f}{u-f+b}\right) \)
c. \( b\left(\frac{f}{u-f}\right)\left(\frac{f}{u-f+b}\right)^{2} \)
D. \( b\left(\frac{f}{u-f}\right)\left(\frac{f}{u-f+b}\right) \)


In a parallel combination, the reciprocal of the equivalent resistance is
A. the sum of resistances.
B. the sum of the reciprocal of individual resistances.
c. the largest resistance among them.
D. none of above.


Chlorophyll \( a \), Chlorophyll \( d \) and
phycoerythrin occur in
A. Chlorophyceae
B. Bacillariophyceae
c. cyanophyceae
D. Rhodophyceae


An elevator is moving upwards with
constant acceleration. The dashed
curve in figure. shows the position y of the ceiling of the elevator as a function of time t. At the instant indicated by the
point \( P \) a bolt breaks loose and drops
from the ceiling. Which of the solid curves shown best describes the
position of the bolt as a function of time?
\( A \)
B.
\( c \)
D. IV


\[
\operatorname{ftg}\left[\begin{array}{ccc}
3 & 2 & -1 \\
2 & -2 & 0 \\
1 & 3 & 1
\end{array}\right], B\left[\begin{array}{ccc}
-3 & -1 & 0 \\
2 & 1 & 3 \\
4 & -1 & 2
\end{array}\right]
\]
and \( X=A+B \) then find \( X \)


A flask contains a mixture of isohexane
and 3-methylphentane. One of the
liquids boils at \( 63^{\circ} \mathrm{C} \) while the other
boils at \( 60^{\circ} \mathrm{C} \). What is the best way to
separate the two liquids and which one will be distilled out first?
A. fractional distillation, 3-methylpentane
B. simple distillation, isohexane
c. fractional distillation, isohexane
D. simple distillation, 3-methylpentane


Considering \( B e C l_{2}, M g C l_{2}, C a C l_{2} \) and
\( B a C l_{2} \) predict which of the following
statement is true?
\( \mathbf{A} \cdot B e C l_{2} \) is least ionic out of the given chlorides
B. Covalent character increases as the atomic number of the metal atom increases
\( \mathrm{c} \cdot \mathrm{BeCl}_{2} \) has the lowest melting point among the given chlorides
D. All are highly ionic compounds


A particle has a rectilinear motion and
the figure gives its displacement as a function of time. Which of the following
statements is false with respect to the
motion?
A. Between O and A the velocity is positive and acceleration is negative
B. Between A and B the velocity and acceleration are positive
c. Between B and C the velocity is negative and acceleration is positive
D. Between C and D the acceleration is positive


The oxide of a metal contains \( 40 \% \) of
oxygen. The valency of metal is 2. What is the atomic weight of the metal?
A .24
B. 12
\( c \cdot 40 \)
D. 36


Below point 'A' FeO can
A. be reduced by carbon monoxide only
B. be reduced by both carbon monoxide and carbon
c. be reduced by carbon only
D. not be reduced by both carbon monoxide and carbon


Which of the following represents the use(s) of cement?
A. All of these
B. Blocks
c. Pillar
D. Pipes


Choose the correct answer from the
alternatives given

Sugars and amino acids are carried
into the cell by the sodium- potassium pump by means of
A. Facilitated transport
B. Active transport
c. simple diffusion
D. Endocytosis


\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ccc}|\boldsymbol{x}-\mathbf{2}|+\mathbf{1} & \boldsymbol{i} \boldsymbol{f} & \boldsymbol{x}<\mathbf{2} \\ \mathbf{2} & \boldsymbol{i} \boldsymbol{f} & \boldsymbol{x}=\mathbf{2} \\ |\boldsymbol{x}-\mathbf{2}|-\mathbf{1} & \boldsymbol{i} \boldsymbol{f} & \boldsymbol{x}>\mathbf{2}\end{array}\right\} \)
If \( \lim _{x \rightarrow a} f(x) \) exists then
A \( . a=2 \)
\( \mathbf{B} \cdot a \epsilon R \)
\( \mathbf{c} \cdot a \epsilon R-\{2\} \)
D \( \cdot a \epsilon R-\{1,2\} \)


Why is the motion of a body moving with a constant speed around a circular path said to be accelerated?


Which of the following is an organic acid?
A. Sulphurous acid
B. Nitric acid
c. Hydrochloric acid
D. Formic acid


Which among the following are the indian breed sheeps?
A. Vembur sheep
B. Nilgiri sheep
c. Macheri sheep
D. All of the above


In the tigure shown water Is thled in a
symmetrical container. Four pistons of
equal area \( A \) are used at the four
opening to keep the water in
equilibrium. Now an additional force \( \boldsymbol{F} \)
is applied at each piston. The increase
in the pressure at the centre of the
container due to this addition is
\( \mathbf{A} \cdot \frac{F}{A} \)
B. \( \frac{2 F}{A} \)
\( c \cdot \frac{4 F}{A} \)
\( D \)


Which of the following statements is
not correct regarding Lanthanoids and
Actinoids?
A. Oxidation state +3 is predominant in both theseries.
B. In both the series f-orbitals are being progressively filled
C. the elements of both the series are radioactive
D. Both series show contraction as Lanthanide
contraction and actinide contraction.


The perpendicular bisector of the line segment joining \( \boldsymbol{P}(1,4) \) and \( \boldsymbol{Q}(\boldsymbol{k}, \boldsymbol{3}) \)
has \( \boldsymbol{y}- \) intercept \( -4 . \) Then a possible
value of \( k \) is \( ? \)
A . -2
B. -4
c.
D. 2


Describe briefly the structure of a nerve
cell.


The modulus of elasticity \( (\boldsymbol{E}) \) and modulus of rigidity \( (C) \) are related by(m is the poissons ratio)
\( ^{A} \cdot C=\frac{E}{3(m-2)} \)
в. \( c=\frac{E}{2(m+1)} \)
\( c \cdot c=\frac{3(m-2)}{m E} \)
D. \( c=\frac{2(m+1)}{m E} \)


The ovary ripens to form fruit.
A. True
B. False


Given below is the cascade of events
following deforestation. Select the option which arrange them in the
correct sequence.
\( P: \) Erosion of top soil
Q: River channel become shallow.
R : Eroded soil gets deposited on the river bed as silt
S : Destruction of crops leads to starvation.
T : Shallow channels cannot hold excess
water during rain and hence cause
flood
U: Floods damage agricultural crops.
A. \( P \rightarrow Q \rightarrow R \rightarrow S \rightarrow T \rightarrow U \)
в. \( P \rightarrow R \rightarrow Q \rightarrow T \rightarrow U \rightarrow S \)
\( c \cdot Q \rightarrow R \rightarrow P \rightarrow S \rightarrow T \rightarrow U \)
D. \( P \rightarrow T \rightarrow U \rightarrow Q \rightarrow R \rightarrow S \)


Mark the incorrect statement
(I) Fractionating column is a long tube.
(II) Fractionating column is provided
with obstructions to the passage of vapours upwards and to the liquids
downward.
(III) Column itself is fitted with a
thermometer.
A . ।, ॥।, ॥।
B. ।,।
\( c \cdot \) ।, ॥
D. None of the above


A uniform solid sphere is placed on a
smooth horizontal surface. An impulse
\( I \) is given horizontally to the sphere at a height \( h=\frac{4 R}{5} \) above the centre line. \( m \)
and \( R \) are mass and radius of sphere
respectively.
(a) Find angular velocity of sphere \( \& \) linear velocity of centre of mass of the
sphere after impulse.
(b) Find the minimum time after which
the highest point \( B \) will touch the
ground
(c) Find the displacement of the centre of mass during this interval.


The study of the interrelationships between structure and reactivity in organic molecules is called:
A. physical organic chemistry
B. analytical chemistry
c. stereo chemistry
D. none of the above


A radioactive substance after 48 days
remains \( 25 \% \) of initial. Find
disintegration constant
A \( \cdot 2.89 \times 10^{-2} T^{-1} \)
В. \( 3.89 \times 10^{-3} T^{-1} \)
c. \( 4.89 \times 10^{-2} T^{-1} \)
D. none of these


The phase angle between current and voltage in a purely inductive circuit is :
A . zero
в. \( \pi \)
\( c \cdot \pi / 4 \)
D. \( \pi / 2 \)


Specific heat and equivalent wt. of a
metal are \( =0.057 \) cal \( g^{-1} \) and 38.24
respectively. It's exact atomic weight
is?
A . \( 114.72 g \)
в. \( 38.297 g \)
c. \( 110.9 g \)
D. uncertain


A physical quantity \( x \) can be dimensionally represented in terms of \( M, L \) and \( T \) that is \( x=M^{a} L^{b} T^{c} . \) The
quantity time
A. may be dimensionally represented in terms of \( x, M \) and \( L \) if \( c \neq 0 \)
B. may be dimensionally represented in terms of \( x, M \) and \( L \) if \( c=0 \)
c. may be dimensionally represented in terms of \( x, M \) and \( L \), irrespective of value of \( c \)
D. can never be dimensionally represented in terms of \( x, M \) and \( L \)


Which of the following statements
is/are not true?
A. Blood is positively charged sol
B. Soap solution contains ionic micelles as the colloidal particles
C. Blood is purified by the process of dialysis
D. \( C a^{2+} \) and \( K^{+} \) cause coagulation of blood if added in
excess


Mark the wrong statement
A. Zinc is a cofactor for proteolytic enzyme carboxypeptidase
B. \( K_{m} \) (Michaelis Constant) is numerically equivalent to \( 1 / 2 \mathrm{Vmax} \)
C. Strands of DNA appear like a helical staircase. At each
step of ascent, strand turns \( 36^{\circ} \)
D. Tyrosine, Phenylalanine and Tryptophan are aromatic amino acids


Roots of plants take up air from
A. The air spaces present between the soil particles
B. The bacteria surrounding the roots
C. The leaves
D. The stem tissues


An a.c. generator consists of a coil of
10,000 turns and of area \( 100 \mathrm{cm}^{2} . \) The
coil rotates at an angular speed of 140 rpm in a uniform magnetic field of
\( 3.6 \times 10^{-2} \mathrm{T} . \) Find the maximum value
of the emf induced.


For a material \( \sigma=-0.25 \) under an
external stress, the longitudinal strain
is \( 10^{-2} \). The percentage change in the diameter of the wire is
A . \( +1 \% \)
B. -1\%
c. \( +0.25 \% \)
D. - 0.25\%


Find the variance for an ungrouped data
\( \mathbf{5}, \mathbf{1 2}, \mathbf{3}, \mathbf{1 8}, \mathbf{6}, \mathbf{8}, \mathbf{2}, \mathbf{1 0} \)


Which is the correct sequence of the
components of a reflex arc?
A. Receptors \( \rightarrow \) muscles \( \rightarrow \) sensory neuron \( \rightarrow \) motor neuron \( \rightarrow \) spinal cord
B. Receptors \( \rightarrow \) motor neuron \( \rightarrow \) spinal cord \( \rightarrow \) sensory neuron \( \rightarrow \) muscle
C. Receptors \( \rightarrow \) spinal cord \( \rightarrow \) sensory neuron \( \rightarrow \) motor neuron \( \rightarrow \) muscle
D. Receptors \( \rightarrow \) sensory neuron \( \rightarrow \) spinal cord \( \rightarrow \) motor neuron \( \rightarrow \) muscle


represents the solution set to which of
the following systems of inequalities?
A \( \cdot\left\{\begin{array}{l}y<-x+2 \\ (x-1)^{2}+(y-2)^{2}<9\end{array}\right. \)
B \cdot \( \left\{\begin{array}{l}y>-x+2 \\ (x-1)^{2}+(y-2)^{2}<9\end{array}\right. \)
c. \( \left\{\begin{array}{l}y>-x+2 \\ (x-1)^{2}+(y-2)^{2}>9\end{array}\right. \)
D \cdot \( \left\{\begin{array}{l}y<-x+2 \\ (x-1)^{2}+(y-2)^{2}>9\end{array}\right. \)
E \( \left\{\begin{array}{l}(y-2)<3 \\ (x-1)>3\end{array}\right. \)


\( \int(1-x) \sqrt{x} d x \)


Fibrous proteins and globular proteins can be differentiated on the basis of:
A. primary and secondary structures
B. secondary structures only
c. tertiary structures
D. primary structures only


An alkali used for removing grease stains is:
A. \( H C l \)
в. \( A l(O H)_{3} \)
c. \( N H_{4} O H \)
D. \( N a_{2} S O_{4} \)


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}\} \) and let \( \boldsymbol{R}= \)
\( \{(a, b): a, b \in A \text { and } b=a+1\} . \) Show
that \( R \) is not reflexive.


Determine the domain and range of the relation R defined by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{x}+\mathbf{5}) \)
\( \boldsymbol{x} \in\{\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\}\} \)


If \( 1, \omega, \omega^{2} \) are two cube roots of unity
then \( \Delta=\left|\begin{array}{ccc}1 & \omega^{n} & \omega^{2 n} \\ \omega^{2 n} & 1 & \omega^{n} \\ \omega^{n} \omega^{2 n} & 1\end{array}\right| \) has the value
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \omega^{2} \)
D.


In those plants whose pulp is of economical importance, they are generally propagated by vegetative means because
A. It is cheaper
B. It is more economical
c. The pulp quality remains same
D. The pulp quality becomes better


A student performed the experiment of
determination of focal length of a
concave mirror by u v method using an optical bench of length 1.5 meter. The focal length of the mirror used is \( 24 \mathrm{cm} \) The maximum error in the location of
the image can be \( 0.2 \mathrm{cm} . \) The 4 sets of (u, v) values recorded by the student(in
\( \mathrm{cm} \) ) are: \( (42,56),(48,48),(66,33),(78, \)
39). The data set(s) that cannot come
from experiment and is (are) incorrectly recorded, is (are):
This question has multiple correct options
A . (42, 56)
B. (48,48)
C. (66,33)
D. (78, 39)


Express the \( 150^{0} \) in radians:


In how many ways can a football team of 11 players be selected from 16 players? How many of these will Include 2
particular players?
\( \mathbf{A} \cdot 4638,2020 \)
B. 4658,2001
c. 4368,2002
D. None of these


Assuming Z-axis as molecular axis, the molecular orbitals formed by the combination of atomic orbitals is
labeled as \( 2 p_{x}+2 p_{x} \) is :
A \( \cdot \pi 2 p_{x} \)
В . \( \pi p_{x} \)
c. \( \pi / 2 p_{x} \)
D. \( \pi p_{y} \)


Assertion
In an inelastic collision between two
bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason
In an elastic collision, the linear momentum of the system is conserved.
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


Match the following


The mass of \( N a_{2} C O_{3} \) required to
prepare \( 500 \mathrm{ml} \) of \( 0.1 \mathrm{M} \) solution is:
A . 10.6 g
B. \( 5.3 \mathrm{g} \)
c. \( 2.65 \mathrm{g} \)
D. 7.95


The Sum of three numbers in AP is 75
and product of extremities is \( 609 . \) The numbrs and AM of 1st two numbers is
\( \mathbf{A} \cdot\{21,25,29\}, \) АМ \( =23 \)
B. \( \{13,17,21\}, \) АМ \( =22 \)
c. \( \{21,25,29\}, \) АМ \( =25 \)
D. \( \{21,22,29\}, \) АМ \( =23 \)


Two different types of rubber are found
to have the stress-strain curve as
shown. Then
A. \( A \) is suitable for shock absorber
B. \( B \) is suitable for shock absorber
\( \mathrm{c} . B \) is suitable for car types
D. None of these


An air filled balloon is at a depth of \( 2 \mathrm{km} \)
below the water level in an ocean.
Determine the normal stress on the
balloon [atmospheric pressure \( =10^{5} \) Pa \( ] \)
A \( .190 \times 10^{5} P a \)
В. \( 196 \times 10^{5} \mathrm{Pa} \)
c. \( 190 \times 10^{7} P a \)
D. \( 196 \times 10^{7} P a \)


State the following statement is True or
False

The sum of a natural number \( x \) and its
eciprocal is \( \frac{37}{6}, \) then the equation is \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\frac{\mathbf{3 7}}{\mathbf{6}} \)
A. True
B. False


A magnet is moved towards a coil (i) quickly (ii) slowly, then the induced e.m.f. is
A. larger in case (i)
B. smaller in case (i)
c. equal in both the cases
D. larger or smaller depending upon the radius of the coil


Each thoracic segment of Periplaneta americana is enclosed by four
skeletal scleries: a dorsal
ventral and two lateral
The \( \quad \) of the
prothorax is also called pronotum,
which covers the neck and a part of the
head.
Complete the above paragraph by
selecting the correct sequence of words.
A. Chitinous, tergum, sternum, pleura, tergum
B. Proteinaceous, sternum, tergum, pleura, tergum
C. Chitinous, sternum, tergum, pleura, sternum
D. Proteinaceous, tergum, pleuron, sternum, tergum


How many times the calvin cycle occur to produce two molecules of sucrose
\( \mathbf{A} \cdot \mathbf{6} \)
B. 12
c. 18
D. 24


Sulphur combines with oxygen in the ratio 2: 3 to form the oxides of sulphur
Find the formula of its oxide.


Find the value of \( \int \frac{\boldsymbol{d}\left(\boldsymbol{x}^{2}+\mathbf{1}\right)}{\sqrt{\left(\boldsymbol{x}^{2}+\mathbf{2}\right)}} \)


What is the refractive index of a prism
whose angle \( A=60^{\circ} \) and angle of
minimum deviation \( \boldsymbol{d}_{m}=\mathbf{8 0}^{o} ? \)
A \( \cdot \sqrt{2} \)
B. \( \sin ^{-1}(\sqrt{3}) \)
\( \mathbf{c} \cdot \tan ^{-1}(\sqrt{2}) \)
D. \( \tan ^{-1}(\sqrt{3}) \)


Sum to 20 terms of the series \( 1.3^{2}+ \)
\( 2.5^{2}+3.7^{2}+\ldots \) is
A . 178090
B. 168090
c. 188090
D. None of these


Formula of Freon is:
A \( \cdot C C l_{2} F_{2} \)
в. \( \mathrm{COCl}_{2} \)
\( \mathrm{c} \cdot \mathrm{SO}_{2} \mathrm{Cl}_{2} \)
D. none of these


Three sets of English, Hindi and Mathematics books have to be stacked
in such a way that all the books are
stored topic-wise and the height of each stack is the same. The number of
English books is \( 96, \) the number of Hindi books is 240 and the number of
Mathematics books is \( 336 . \) Assuming
that the books are of the same
thickness, determine the number of
stacks of English, Hindi and Mathematics books.


In a nuclear reactor, it is desirable to
use reactor core in the form of
A. cubical or cylindrical
B. cubical or spherical
c. cylindrical or spherical
D. spherical


A coil of inductive reactance \( 1 / \sqrt{3} \Omega \) and resistance \( 1 \Omega \) is connected to
\( 200 V, 50 H z \) A.C. supply. The time lag
between maximum voltage and current
is
A \( \cdot \frac{1}{600} s \)
в. \( \frac{1}{200} s \)
c. \( \frac{1}{300} s \)
D. \( \frac{1}{500} s \)


Assertion
\( C O_{2} \) molecule is linear in shape.
Reason
Any atom bonded to two other atoms
should be linear.
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


How much resistance should be
connected to \( 15 \Omega \) resistor shown in the
circuit in adjoining figure below so that the points \( \mathrm{M} \) and \( \mathrm{N} \) are at the same
potential


At what temperature does the average transnational kinetic energy of a molecule in a gas become equal to kinetic energy of an electron accelerated from rest through a
potential difference of 1 volt? \( (k= \)
\( \left.1.38 \times 10^{-23} J / K\right) \)
A . \( 3770 K \)
в. \( 7370 K \)
c. \( 7730 K \)
D. \( 7330 K \)


In order to meet the ever-increasing demand in factories and for shelter,
trees are being continually cut. Is it justified to cut trees for such projects? Discuss and prepare a brief report.


IUPAC name of \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{C H}= \)
\( \boldsymbol{C H}-\boldsymbol{C H O} \)
A. 4,4,4 -trimethyl but- - -en- -1-al
B. 4, 4-Dimethylpent-2-enal
c. 2, 2-dimethylpent-3- 3n-4-al
D. 3-tert. butyl prop-2-en-1-al


Which of the following is a recently originated problem of environment?
A. Ozone layer depletion
B. Green house effect
c. Global warming
D. All of the above


Which of the following ores can be concentrated by froth floatation method and why?
\( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}, \boldsymbol{Z} \boldsymbol{n} \boldsymbol{S}, \boldsymbol{A} \boldsymbol{I}_{2} \boldsymbol{O}_{3} \)


A balanced reaction between \( F e \) and \( O_{2} \)
to give magnetic oxide is :
A \( \cdot 2 F e+O_{2} \rightarrow 2 F e O \)
B. \( 2 F e+2 O_{2} \rightarrow F e_{2} O_{3} \)
\( \mathrm{c} \cdot 3 \mathrm{Fe}+2 \mathrm{O}_{2} \rightarrow \mathrm{Fe}_{3} \mathrm{O}_{4} \)
D. \( F e+2 O_{2} \rightarrow F e_{3} O_{4} \)


\( |f(x)|=\left[\begin{array}{ccc}\sin x & \operatorname{cosec} x & \tan x \\ \sec x & x \sin x & x \tan x \\ x^{2}-1 & \cos x & x^{2}+1\end{array}\right] \)
then \( \ldots \int_{-a}^{a}|\boldsymbol{f}(\boldsymbol{x})| \boldsymbol{d} \) equals
\( A \)
в.
\( c \cdot 2 a \)
\( D \)


Assertion
The mechanical energy between consecutive node and antinode will
remain conserved in standing wave.
Reason

The mechanical energy does not flow between node and antinode in standing
wave.
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


Drinking of mineral water with very low level of pesticides (about 0.02 ppm) for long periods may
A. Produce immunity against mosquito.
B. Cause leukemia (blood cancer) in most people.
c. Cause cancer of the intestine
D. Lead to accumulation of pesticide residues in body fat


Claw is found in the petals of
A . Cruciferae
B. Fabaceae
c. Liliaceae
D. Solanaceae


A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two
others is:
A . 4
B. 5
\( c \cdot 6 \)
D.


Find the number of ways of permuting the letters of the word PICTURE so
that
(i) All vowels come together
(ii) No two vowels come together
(iii) The relative positions of vowels and consonants are not disturbed


Certain perfect gas is found to obey
\( P V^{3 / 2}= \)constant during an adiabatic
process. If such a gas at initial temperature \( T \) is adiabatically compressed to half the initial volume,
its final temperature will be
A \( \cdot \sqrt{2} T \)
в. 27
c. \( 2 \sqrt{2} T \)
D. 47


Two rods \( P \) and \( Q \) are considered such
that Young's modulus of elasticity of rod \( P \) is twice that of the other while the
density of rod \( Q \) is eighteen times that of rod P. If a sound wave is allowed to
transverse \( 2 \mathrm{m} \) distance through each rod, then by how many times the time taken through \( P \) is less than that of \( Q ? \)
A. 2 times
B. 3 times
c. 4 times
D. 5 times


At any particular time, different particles in the gas:
A. have same speed and kinetic energy
B. have same speed but different kinetic energies
c. have different speeds but same kinetic energy
D. have different speeds and hence different kinetic energies


Which of the following behaviour is true regarding the coefficient of viscosity \( (\eta) \) of a liquid?
A. Plot of \( \eta \) versus \( T \) is linear
B. Plot of \( \eta \) versus \( \frac{1}{T} \) is linear
c. \( \eta=\frac{E}{R T} \)
D. Plot log of \( \eta \) versus \( \frac{1}{T} \) is linear


If \( Z=\frac{1-\sqrt{3} i}{1+\sqrt{3} i} \) then find \( \arg (z) \)
\( \mathbf{A} \cdot-\frac{2 \pi}{3} \)
B. \( \frac{2 \pi}{5} \)
\( \mathbf{C} \cdot \frac{\pi}{3} \)
D. \( \frac{2 \pi}{3} \)


How many functional group are present in above compound?
\( \boldsymbol{C H}_{3}-\boldsymbol{O}-\underset{d}{_{\|}}-\underset{\boldsymbol{o}_{H}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}=\boldsymbol{C} \boldsymbol{H}- \)
\( C-\stackrel{N}{C}-O H \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


If \( f(x)=x^{3}-10 x^{2}+200 x-10, \) then
\( (x) \) is
A. decreasing \( (-\infty, 10] \) and increasing in \( (10, \infty) \)
B. increasing \( (-\infty, 10] \) and decreasing in \( (10, \infty) \)
c. increasing for every value of \( x \)
D. decreasing for every value of \( x \)


If \( g(x)=7 x^{2} e^{-x^{2}} \forall x \in R, \) then \( g(x) \) has
This question has multiple correct options
A. local maximum at \( x=0 \)
B. local minima at \( x=0 \)
c. local maximum at \( x=1 \)
D. two local maxima and one local minima


The pitch or frequency of the siren of the coming train appears to be increasing because of:
A. Big-bang theory
B. Doppler's effect
c. charle's law
D. Archemedies' principle


What is true about the breakdown
voltage in a zener diode?
A. It decreases when current increases.
B. It destroys the diode.
c. It equals the current times the resistance.
D. It is approximately constant.


Consider the arithmetic sequence 9,15
21
a) Write the algebraic form of this
sequence.
b) Find the twenty fifth term of this
sequence.
c) Find the sum of terms from twenty
fifth to fiftieth of this sequence.
d) Can the sum of some terms of this
sequence be \( 2015 ? \) Why?


The value of \( \int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin \theta}{2+\sin \theta}\right) d \theta \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of these


Mouth part of cockroach are suited for
A. Piercing
B. Absorbing
c. Cutting and chewing
D. Drinking


The ore that can be concentrated by magnetic separation method is:
A \( \cdot \) bauxite \( \left(A l_{2} O_{3} \cdot x H_{2} O\right) \)
B . pyrolusite \( \left(M n O_{2}\right) \)
C . cuprite \( \left(C u_{2} O\right) \)
D. zincite \( (Z n O) \)


If the length of the tangent at any point on the curve \( y=f(x) \) intercepted
between the point of contact and \( x \) -axis
is of length \( 1, \) the equation of the curve
¡s:
This question has multiple correct options
\( \mathbf{A} \cdot \sqrt{1-y^{2}}+\ln |(1-\sqrt{1-y^{2}}) / y|=\pm x+c \)
B \( \cdot \sqrt{1-y^{2}}-\ln |(1-\sqrt{1-y^{2}}) / y|=\pm x+c \)
\( \mathbf{c} \cdot \sqrt{1-y^{2}}+\ln |(1+\sqrt{1-y^{2}}) / y|=\pm x+c \)
D. None of these


Whenever the magnetic flux linked with a coil changes, then there is an induced emf in the circuit. This emf lasts:
A. for a short time
B. for a long time
\( c . \) for ever
D. so long as the change in the flux takes place


Structural isomerism and
stereoisomerism should be considered
when answering this question. The molecular formula of compound \( x \)
is \( C_{5} H_{12} O \)
Compound \( X: \)
reacts with alkaline aqueous iodine
can be dehydrated to form two alkenes only. What could be the identify of compound
X?
A. \( C H_{3} C H_{2} C H\left(C H_{3}\right) C H_{2} O H \)
B. \( C H_{3} C H_{2} C H(O H) C H_{2} C H_{3} \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C H C H(O H) C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C H(O H) C H_{3} \)


For a series LCR circuit at resonance,
the statement which is not true is
A. Peak energy stored by a capacitor = peak energy stored by an inductor
B. Average power = apparent power
C. Wattless current is zero
D. Power factor is one


An example of micelle is:
\( \mathbf{A} \cdot A s_{2} O_{3} \operatorname{sol} \)
B. Ruby glass
\( \mathrm{C} \cdot \mathrm{Na}_{2} \mathrm{SO}_{3} \) solution
D. Sodium stearate concentrated solution


Two bodies \( A \) and \( B \) of equal masses are
kept at height of h and \( 2 h \) respectively. ratio of their potential energy?


For the given reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{S}(\boldsymbol{s}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}_{\boldsymbol{T}}= \)
\( \mathbf{1 0 0} k J / \) mol and \( \Delta S_{T}= \)
\( 400 J / m o l / K \)
Temperature at which above reaction
occurs reversibly is (Assuming \( \Delta \boldsymbol{H}_{\boldsymbol{T}} \)
and \( \Delta S_{T} \) are independent of
temperature)
\( \mathbf{A} \cdot 200 K \)
B . \( 250 K \)
c. \( 400 K \)
D. None


In glycolysis, enzyme enolase produces
A. Phosphoglyceric acid
B. Phosphoenol pyruvate
c. Phosphoglyceraldehyde
D. Pyruvate


A square plate of edge \( a / 2 \) is cut out
from a uniform square plate of edge \( ^{\prime} a^{\prime} \) as shown in figure. The mass of the
remaining portion is \( M . \) The moment of inertia of the shaded portion about an axis passing through' \( O^{\prime} \) (center of the square of side a) and perpendicular to
plane of the plate is:
\( ^{A} \cdot \frac{9}{64} M a^{2} \)
в. \( \frac{3}{16} M a^{2} \)
c. \( \frac{5}{12} M a^{2} \)
D. \( \frac{M a^{2}}{6} \)


fthe matrix \( \left(\begin{array}{cc}\mathbf{6} & -\boldsymbol{x}^{2} \\ \mathbf{2} \boldsymbol{x}-\mathbf{1 5} & \mathbf{1 0}\end{array}\right) \)
symmetric, find the value of \( x \)


What is the mass of \( C O_{2} \) in grams?
\( A \cdot 11 g m \)
B. 44 gm
c. \( 22 \mathrm{gm} \)
D. 8 gm


Find the Cartesian equation of \( \vec{r} \) \( (2 \hat{i}+3 \hat{j}-4 \hat{k})=1 \)


Solve the set of equations: \( 3(2 u+v)= \)
\( \mathbf{7} \boldsymbol{u} \boldsymbol{v} \) and \( \boldsymbol{3}(\boldsymbol{u}+\boldsymbol{3} \boldsymbol{v})=\mathbf{1 1} \boldsymbol{u} \boldsymbol{v} \)
A \( \cdot u=1 ; v=\frac{3}{2} \)
в. \( u=2 ; v=\frac{1}{2} \)
c. \( u=2 ; v=\frac{5}{4} \)
D. \( u=5 ; v=\frac{7}{4} \)


Acetamide is treated separately with
following reagents. Which one of these
would give methylamine?
A \( \cdot P C l_{5} \)
B. Sodalime
c. \( N a O H+B r_{2} \)
D. Hot concentrated \( H_{2} S O_{4} \)


Classify \( B=\{y \mid y \text { is a factor of } 13\} \) as
'finite' or 'infinite'.
A . Infinite
B. Finite
c. Data insufficient
D. None of these


The principle of limiting factor was given by
A. Hill
B. F. F Blackman
c. will statter
D. Calvin


How many geometrical isomers are possible in the following coordination
entities?
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C l}_{3}\right] \)


A small magnet is suspended freely by a vertical string. The horizontal and vertical components of Earth's field is \( 20 \mu T \) and \( 30 \mu T \) respectively. Find the
angle from horizontal at which magnet will stay in equilibrium.
A \( \cdot \tan ^{-1}\left(\frac{3}{2}\right) \)
B \( \cdot \tan ^{-1}\left(\frac{2}{3}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{2}{3}\right) \)
D. \( \cos ^{-1}\left(\frac{2}{3}\right) \)


Primary amines have higher boiling points than tertiary amines If this is true enter 1 , if false enter 0 .


An example of the even number of terms
in an arithmetic progression written in a symmetrical format is?
A. \( a-d, a+d, a+2 d, a+4 d \)
B. \( a-2 d, a+d, a+2 d, a+3 d \)
c. \( a-3 d, a-d, a+d, a+3 d \)
D. \( a-2 d, a-d, a, a+d, a+2 d \)


One of the roots of
\( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{x}+\boldsymbol{c}\end{array}\right|=\mathbf{0} \) is
A \( . a b c \)
B. \( a+b+c \)
c. \( -(a+b+c) \)
D. \( -a b c \)


The velocity \( v \) of a particle at timet is given by \( v=a t+\frac{b}{t+c} \) where \( a, b \) and \( c \) are constants. The dimensions of \( a, b \) and \( c \) are respectively:
\( \mathbf{A} \cdot L T^{-2}, L \) and \( T \)
B. \( L^{2}, T \) and \( L T^{2} \)
c. \( L T^{2}, L T \) and \( L \)
D. \( L, L T \) and \( T^{2} \)


Write IUPAC name of the complex
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)(\boldsymbol{C} \boldsymbol{N})\right]^{2+} \)


A die is tossed twice. Getting an odd number is termed a success. The
probability distribution of number of successes \( (X) \) is formed. Then its mean,
variance are
A \( \cdot 1, \frac{1}{2} \)
B. \( \frac{1}{2}, 1 \)
c. \( \frac{1}{2}, \frac{1}{2} \)
D. 1,1


Curie temperature is the temperature
above which
A. a ferromagnetic material becomes paramagnetic
B. a paramagnetic material becomes diamagnetic
C . a ferromagnetic material becomes diamagnetic
D. a paramagnetic material becomes ferromagnetic.


(a) \( A \) tiger from wildlife sanctuary was shifted in a Zoological garden. Where do you think the tiger will be happier
(b) What is the difference between a
Zoological garden and a wildlife
sanctuary


A disc of mass \( 2 k g \) and diameter \( 2 m \) is
performing rotational motion. Find the work done, if the disc is rotating from \( 300 r p m \) to \( 600 r p m \)
A . \( 1479 J \)
в. \( 147.9 J \)
c. \( 14.79 J \)
D. \( 1.479 J \)


The properties which are not common to
both groups 1 and 17 elements in the
periodic table are:
A. electropositive character increases down the groups
B. reactivity decreases from top to bottom in these groups
c. atomic radii increases as the atomic number increases
D. electronegativity decreases on moving down group


A small steel ball falls through a syrup at a constant speed of \( 10 \mathrm{cm} / \mathrm{sec} \). If the steel ball is pulled upwards with a force equal to twice its effective weight; how fast will it move upwards?
A. \( 10 \mathrm{cm} / \mathrm{sec} \)
в. \( 20 \mathrm{cm} / \mathrm{sec} \)
\( \mathrm{c} \cdot 5 \mathrm{cm} / \mathrm{sec} \)
D. \( 0 \mathrm{cm} / \mathrm{sec} \)


If \( \alpha \) and \( \beta \) are the roots of \( a x^{2}+b x+ \)
\( c=0, a \neq 0 \) then the wrong statement
is
\( ^{A} \cdot \alpha^{2}+\beta^{2}=\frac{b^{2}-2 a c}{a^{2}} \)
B . \( \alpha \beta=\frac{c}{a} \)
\( \mathbf{c} \cdot \alpha+\beta=\frac{b}{a} \)
D. \( \frac{1}{\alpha}+\frac{1}{\beta}=-\frac{b}{c} \)


If true then enter 1 and if false then
enter 0
Can two obtuse angles be
supplementary?


If \( \vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}, \vec{b}=b_{1} \hat{i}+b_{2} \hat{j}+ \)
\( b_{3} \hat{k}, \vec{c}=c_{1} \hat{i}+c_{2} \hat{j}+c_{3} \hat{k} \) and \( \vec{c} \) is a unit
vector orthogonal to the plane of \( \vec{a}, \vec{b} \) and the angle between \( \vec{a} \) and \( \vec{b} \) is \( \frac{\pi}{3} \)
then \( |\vec{c}|^{2}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( \frac{3}{4}\left(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}\right)\left(b_{1}^{2}+b_{2}^{2}+b_{3}^{2}\right) \)
D \( \cdot \frac{3}{4}\left(C_{1}^{2} a_{1}^{2}+b_{1}^{2}+\mathrm{X} a_{2}^{2}+b_{2}^{2}+c_{2}^{2}\right) \)


Why is more energy required to break a sigma bond than to break a pi bond?


The zig-zag random motion of colloidal particles in a dispersion medium is called:
A. brownian motion
B. tyndall effect
c. electrophoresis
D. electro-osmosis


The critical temperature of the gas is the
tem perature:
A. at which Charle's law is obeyed
B. at which Boyle's law is obeyed
C. above which the gas cannot be liquefied
D. at which all molecular motion ceases


Which of the following complex shows optical isomerism?
A \( \cdot\left[C d(C N)_{4}\right]^{2-} \)
B \( \cdot\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3} \mathrm{Cl}_{3}\right] .3 \mathrm{H}_{2} \mathrm{O} \)
\( \mathbf{c} \cdot\left[Z n(g l y)_{2}\right]^{\circ} \)
D \( \cdot\left[N i(d m g)_{2}\right]^{\circ} \)


Find the modulus of complex number \( -2+2 \sqrt{3} i \)


In which of the following circuit, there
may be no change in current with
increase in the frequency when same ac
current is passed through them:
\( A \)
B.
(b)
\( c \)
D.


The A.M. of two numbers exceeds their
G.M. by 15 and H.M. by 27 , find the bigger
of the two numbers.


In measuring the sides of a rectangle errors of \( 5 \% \) and \( 3 \% \) in excess are made. The error per cent in the calculated area
is
A . \( 8.35 \% \)
B . \( 7.15 \% \)
c. \( 8.15 \% \)
D. \( 6.25 \% \) \%


Find the moment of inertia of a uniform
sphere of mass \( m \) and radius \( R \) about a tangent if the sphere is hollow.


Write the IUPAC names of the given
compounds:
\[
\begin{array}{c}
\mathrm{cl}-\mathrm{CH}_{2}-\mathrm{c}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3} \\
\mathrm{O}
\end{array} \mathrm{CH}_{3}
\]


The correct sequence of human
evolution is
A. Australopithecus \( \rightarrow \) Homo-Habilis \( \rightarrow \) Homoerectus \( \rightarrow \) Homo-Neanderthalensis \( \rightarrow \) Cro-magnon
B. Australopithecus \( \rightarrow \) Homo-Habilis \( \rightarrow \) HomoNeanderthalensis \( \rightarrow \) Homoerectus \( \rightarrow \) Cro-magnin \( \rightarrow \) Homosapiens
C. Australopithecus \( \rightarrow \) Homo-Neander thalensis \( \rightarrow \) Homo-Habilis \( \rightarrow \) Homoerectus \( \rightarrow \) Cro-magnon \( \rightarrow \) Homosapiens
D. Homo-Habilis \( \rightarrow \) Homo-Neanderthalensis \( \rightarrow \) Australopithecus \( \rightarrow \) Homoerectus \( \rightarrow \) Cro-magnon \( \rightarrow \) Homosapiens


A batsman can score 0,1,2,3,4 or 6
runs from a ball. The number of different
sequences in which he can score
exactly 30 runs in an over of six balls is:
\( A \cdot 4 \)
B. 72
\( c .56 \)
D. 7


Define coefficient of restitution.


The amplitude (in mm)


Show that \( x y=a e^{x}+b e^{-x}+x^{2} \) is a
solution of the differential equation \( x \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}-x y+x^{2}-2=0 \)


Six charges are placed at the vertices of
a regular hexagon as shown in the
figure. Find the electric field on the line
passing through \( O \) and perpendicular
to the plane of the figure as a function
of distance \( x \) from point \( O \)
A .
B. 4
\( c .1 \)
D. 2


State whether given statement is True or False

Innermost electrons are free to move:
A. True
B. False


The other name for larynx is
A. voice processor
B. voice modulator
c. voice box
D. voice generator


Pick out the statement which is not
true.
A. Tetrazine is harmful edible colour
B. Alitame is an artificial sweetener
C. BHT is an antioxidant
D. Sodium alkyl sulphate is a cationic detergent


The number of pairs \( (a, b) \) of positive
real numbers satisfying \( a^{4}+b^{4}<1 \)
and \( a^{2}+b^{2}>1 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. More than 2


Assertion
Two thin blankets put together are warmer than a single blanket of double the thickness.
Reason
Air gets trapped between two blanket which is a bad conductor of heat.
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


By Simpson's rule, the value of \( \int_{-3}^{3} x^{4} d y \) by taking 6 sub-intervals, is
A . 98
B. 90
c. 80
D. 70


Why does Mathura refinery pose problems to the Taj Mahal?


When water is added to \( H_{2} S O_{4} \), the
reaction is exothermic. It is because of
formation of:
A. viscous nature of \( H_{2} S O_{4} \)
B. hydrates of \( H_{2} S O_{4} \)
c. corrosive nature of \( H_{2} S O_{4} \)
D. none of these


Unlike poles of two magnets
each other.
A . attract
B. repel
c. neutralize
D. exert no force on