Which of the following equations
corresponds to the enthalpy of
combustion at \( 298 K ? \)
\( \mathbf{A} \cdot C_{2} H_{6}(g)+7 / 2 O_{2}(g) \longrightarrow 2 C O_{2}(g)+3 H_{2} O(g) \)
B \( \cdot 2 C_{2} H_{6}(g)+7 O_{2}(g) \longrightarrow 4 C O_{2}(g)+6 H_{2} O(g) \)
\( \mathbf{c} \cdot C_{2} H_{6}(g)+7 / 2 O_{2}(g) \longrightarrow 2 C O_{2}(g)+3 H_{2} O(l) \)
D. \( 2 C_{2} H_{6}(g)+7 O_{2}(g) \longrightarrow 4 C O_{2}(g)+6 H_{2} O(l) \)


In human body, the pressure exerted by the cells is the
atmospheric pressure.
A. equal to
B. more than
c. slightly greater than
D. greater than


Electromagnetic are made of soft iron
because soft iron has.
A. High susceptibility and low retentivity
B. Low susceptibility and high retentivity
c. Low susceptibility and low retentivity
D. High susceptibility and high retentivity


'Sexual selection' in Darwin theory was
the
A. Wearest parttttt
B. Strong part
c. strongest part
D. None of these


The maximum number of \( 90^{\circ} \) angles between the bond pair-bond pair of
electrons is observed in:
A \( \cdot d s p^{2} \)
B. \( s p^{3} d \) hybridization
c. \( d s p^{3} \) hybridization
D. \( s p^{3} d^{2} \) hybridization


Dialysis fluid contains all the constituents as in plasma except
A. Electrolytes
B. Proteins
c. Nitrogenous wastes
D. All the above


Solve:
\( \sin ^{-1} x+\sin ^{-1} \sqrt{1-x^{2}} \)


In the extraction of gold the gas used is
A. \( \mathrm{F}_{2} \)
в. \( \mathrm{H}_{2} \)
\( c \cdot \mathrm{Cl}_{2} \)
D. \( \mathrm{N}_{2} \)


Assertion
\( \mathbf{3 1 . 2 6} \) mL of \( \mathbf{0 . 1 6 5} \mathbf{~ M} \) solution of
\( B a(O H)_{2} \) is exactly neutralised by 25
mL of citric acid, \( C_{6} H_{8} O_{7} \) of molarity
\( \mathbf{0 . 1 3 8} \)
Reason
The acid is tribasic in nature.
A. Assertion is correct but Reason is wrong
B. Assertion is wrong but Reason is correct
c. Both Assertion and Reason are correct and Reason is correct explanation of Assertion
D. Both Assertion and Reason are correct but Reason is not correct explanation of Assertion


Which of the following is used as disinfectant :
A. Benzyl chloride
B. Toluene
c. Phenol
D. Benzene


Water pollination is best assessed by determining.
A. DO and BOD
B. BOD and turbidity
c. Do and acidity
D. BOD and alkalinity


Suppose you are given a circle. Give steps of construction to find its centre.


From the ECG of a normal human given
above, pick up the correct
interpretation.
A. The complex QRS- is one complete pulse.
B. Peak P- initiation of left atrial contraction only
C. Peak P and peak R together- systolic and diastolic blood pressures.
D. Peak T- initiation of total cardiac cycle.


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) where \( \left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}\right)^{2}=\boldsymbol{x} \boldsymbol{y} \)


In specific resistance measurement of
a wire using a meter bridge, the key k in the main circuit is kept open when we are not taking readings. The reason is
A. the emf of cell will decrease
B. the value of resistance will change due to joule heating effect
c. the galvanometer will stop working.
D. none of these


Select the correct statement(s):
A. The celsius scale is the fundamental unit of the
temperature scale.
B. Kelvin scale defined as 273.16 of the triple point (equilibrium among the solid, liquid, and gaseous phases) of pure water
C \( \cdot \) It is defined as \( \frac{1}{273.16} \) of the triple point (equilibrium among the solid, liquid, and gaseous phases) of pure water.
D. None of these


\( N_{1} \) atoms of a radioactive element emit
\( N_{2} \beta \) -particles per second. The decay
constant of the elements is \( \left(\operatorname{in} s^{-1}\right) \)
A \( \cdot \frac{N_{1}}{N_{2}} \)
B. \( \frac{N_{2}}{N_{1}} \)
c. \( N_{1} \ln (2) \)
D. \( N_{2} \ln (2) \)


Find the intersection of \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) and
represent it by Venn diagram:
\( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}\}, \boldsymbol{B}=\{\boldsymbol{b}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}\} \)
\( \mathbf{A} \cdot\{a, c, d, e\} \)
B \( \cdot\{d, e\} \)
\( \mathbf{c} \cdot\{a, b, c, d, e\} \)
D. None of these


The solution of the equation
\( (\sin x+\cos x)^{1+\sin 2 x}=2,-\pi \leq x \leq \pi \)
is
A \( \cdot \frac{\pi}{2} \)
B.
c. \( \frac{\pi}{4} \)
D. none of these


Two particles are executing simple harmonic motion of the same
amplitude \( A \) and frequency \( \omega \) along the x-axis. Their mean position is separated by distance \( \boldsymbol{X}_{\mathbf{0}}\left(\boldsymbol{X}_{\mathbf{0}}>\boldsymbol{A}\right) . \) If the
maximum separation between them is
\( \left(X_{0}+A\right), \) the phase difference between
their motion is
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 3 \)
c. \( \pi / 4 \)
D. \( \pi / 6 \)


For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number
2028


When equal volumes of the solutions
indicated are mixed, precipitation
should occur only for:
\( \left(\boldsymbol{K}_{s p} \) for \right.
\( \boldsymbol{M} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}, \boldsymbol{B} \boldsymbol{a} \boldsymbol{F}_{2}, \boldsymbol{C} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2}, \boldsymbol{P} \boldsymbol{b} \boldsymbol{S} \boldsymbol{O}_{4} \)
\( \operatorname{are} 7.1 \times 10^{-12}, 1 \times 10^{-6}, 5.5 \times \)
\( 10^{-6}, 1.6 \times 10^{-8} \) respectively
A \( \cdot 2 \times 10^{-3} M M g^{2+}+2 \times 10^{-3} M O H^{-} \)
B . \( 2 \times 10^{-3} M B a^{2+}+2 \times 10^{-3} M F^{-} \)
C \( \cdot 2 \times 10^{-3} M C a^{2+}+2 \times 10^{-2} M O H^{-} \)
D . \( 2 \times 10^{-3} M C a^{2+}+2 \times 10^{-3} M O H^{-} \)
E \( \cdot 2 \times 10^{-4} M P b^{2+}+2 \times 10^{-5} M S O_{4}^{2-} \)


The price of an article was increased by \( \boldsymbol{r} \% \). Later the new price was decreased by \( r \% \). If the latest price was Rs. 1 , then the original price was
A. Rs.
в.
Rs. \( \left(\frac{1-r^{2}}{100}\right) \)
c.
Rs. \( \frac{\sqrt{1-r^{2}}}{100} \)
D.
Rs. \( \frac{10000}{10000-r^{2}} \)


If salivary amylase is lacking in the saliva, which of the following events in the mouth cavity will be affected?
A. Proteins breaking down into amino acids.
B. Starch breaking down into sugars.
c. Fats breaking down into fatty acids and glycerol
D. Absorption of vitamins


Let \( x \) be non-empty set. \( P(x) \) be its power set. Let \( ^{*} \) be an operation defined on element of \( \boldsymbol{P}(\boldsymbol{x}) \boldsymbol{b} \boldsymbol{y}, \boldsymbol{A} * \boldsymbol{B}= \)
\( \boldsymbol{A} \cap \boldsymbol{B} \forall \boldsymbol{A}, \boldsymbol{B} \in \boldsymbol{P}(\boldsymbol{x}) . \) Then
(i) Prove that \( ^{*} \) is a binary operation in \( \boldsymbol{P}(\boldsymbol{x}) \)
(ii) is \( ^{*} \) associative?
(iii) Is \( ^{*} \) commutative?


Lizards reproduce by
A. Laying eggs
B. Roots
c. stems
D. seeds


Assume 100 pm \( X \) -ray beam is passed through YDSE. Interference pattern is observed on a photographic plate placed \( 40 \mathrm{cm} \) away from the slits. What should be the separation between the slits so that the separation between two successive maxima is \( 0.1 \mathrm{mm} \)
A \( .4 \mu m \)
в. \( 0.4 \mu m \)
\( c .4 n m \)
D. \( 40 \mu m \)


Match the following lists


The area of the region between the curve
\( \boldsymbol{y}=\boldsymbol{x}^{3} \) and the lines \( \boldsymbol{y}=-\boldsymbol{x} \) and \( \boldsymbol{y}=\mathbf{1} \)
is:
A. 5 sq. units
B. \( \frac{4}{5} \) sq. units
c. \( \frac{5}{4} \) sq. units
D. \( \frac{3}{5} \) sq. units


Assertion (A) : A large soap bubble expands while a small bubble shrinks, when they are connected to each other by a capillary tube. Reason (R): The excess pressure (due to surface tension) inside a spherical bubble is more due to its small volume.
A. Both Assertion
(A) and Reason
(R) are true and the Reason (R) is correct explanation of the Assertion(A)
B. Both Assertion
(A) and Reason (R) are true, but Reason
(R) is not correct explanation of the Assertion(A)
c. Assertion (A) is true, but the Reason
(R) is false
D. Assertrion
(A) is false, but the Reason (R) is true


Which statement(s) is/are correct?
This question has multiple correct options
A. Polarizing power refers to cation
B. Polarizability refers to anion
C. Small cation is more efficient to polarise anion
D. Molecules in which cation having pseudo inert gas configuration are more covalent


Which family plants are rich source of proteins?
A. Cruciferae
B. Leguminosae
c. Liliaceae
D. compositae


If magnetic flux through area \( 20 m^{2} \) at
point \( P \) in magnetic field is 50 Weber
then magnetic induction at point \( \boldsymbol{P} \) is :
A . \( 5 T \)
в. \( 200 T \)
c. \( 1000 T \)
D. \( 2.5 T \)


An aqueous solution of glucose is \( 10 \% \) (w/v). The volume in which 1 mole of glucose is dissolved, will be:
\( \mathbf{A} \cdot 180 \mathrm{L} \)
B. 91 L
c. \( 0.91 \mathrm{L} \)
D. 1.8 L


The incident ray and the reflected ray from a mirror is mutually perpendicular to each other. Find the angle of incidence.
A \( \cdot 0^{\circ} \)
B. 90
\( c \cdot 30 \)
D. 45


A number is increased by \( 10 \% \) an then the increased number is decreased by
\( 10 \% . \) Find the net increase or decrease
percent.


During fusion of ice, the entropy of system:
A. decreases
B. remains constant
c. increases
D. none of these


The reaction of \( X e F_{6} \) with silica \( \left(S i O_{2}\right) \) gives:
A. \( X e O_{3} \) and \( S i F_{4} \)
B. \( X e F_{4} \) and \( S i F_{4} \)
c. \( X e O F_{2} \) and \( S i F_{4} \)
D. \( X e O F_{4} \) and \( S i F_{4} \)


The halogen with the smallest covalent radius is:
A . \( I \)
в. \( C l \)
\( c \cdot B r \)
D. \( F \)


If \( \tan A=-\frac{1}{2} \) and \( \tan B=-\frac{1}{3} . \) (where
\( A, B>0), \) then \( A+B \) can be
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{3 \pi}{4} \)
c. \( \frac{5 \pi}{4} \)
D. \( \frac{7 \pi}{4} \)


Assertion
If mean \( \& \) median of an asymmetrical
distribution are 58 \& 61 respectively,
then Mode \( =\mathbf{6 7} \)
Reason
For an asymmetrical distribution Mode
\( =3 \) Median - 2 Mean
A. Both Assertion \&. Reason are individually true \& Reason is correct explanation of Assertion.
B. Both Assertion \& Reason are individually true but Reason is not the correct (proper) explanation of Assertion
c. Assertion is true Reason is false
D. Assertion is false Reason is true


The solubility of gases in liquids is not affected by the pressure because the vapor pressure of a substance is not a function of external pressure.
A . True
B. False


In the figure shown, a cubical block is held stationary against a rough wall by
applying force, ' \( \boldsymbol{F}^{\prime} \), then incorrect
statement among the following is
A. frictional force \( f=M g \)
B. \( F=N, N \) is normal reaction
C. \( F \) does not apply any toque
D. \( N \) does not apply any torque


Mean deviation from median of the data
90,100,125,115,110 is?
A . 10
B . 20
c. 30
D. None of these


When copper is reacted with conc.
sulphuric acid, which gas is evolved?
A. \( H_{2} \)
в. \( O_{2} \)
\( c \cdot S O_{2} \)
D. \( S O_{3} \)


Solve: \( 5 x-3<3 x+1, \) where \( x \) is an
integer.
\( \mathbf{A} \cdot\{-3,-2,-1,0,1,2,3\} \)
B . \{-5,-4,-3,-2,-1,0,1,2\}
c. \{-4,-3,-2,-1,0,1\}
D \( \cdot\{-2,-1,0,1,2\} \)


Which of the following oxides of nitrogen is a white solid?
A . \( N O \)
в. \( N O_{2} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{3} \)
D. \( N_{2} O_{5} \)


If \( (\sin \alpha) x^{2}-2 x+b \geq 2, \) for all rea
values of \( \boldsymbol{x} \leq \mathbf{1} \) and \( \boldsymbol{\alpha \epsilon}\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \cup\left(\frac{\boldsymbol{\pi}}{\mathbf{2}}, \boldsymbol{\pi}\right) \)
then possible real values of \( b \) is /are
This question has multiple correct options
A .2
B. 3
\( c \cdot 4 \)
D. 5


Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{\sqrt{a^{2}+x^{2}}-a}{x^{2}} \)
A \( \cdot \frac{1}{\sqrt{a}} \)
в. \( \frac{1}{\sqrt{2 a}} \)
\( c \cdot \frac{1}{a} \)
D. \( \frac{1}{2 a} \)


Match the following with the correct
answers.
(a) Scouring
(i) Yields silk
fibers
(b) Mulberry leaves
(ii) Cleaning sheared skin
(c) Sheep
(iii) Food of silk
worm.
(d) Cocoon
(iv) Wool yielding animal.
B . a - ->i, b- -> ii, c- -> iii, d- > iv
\( c \cdot a->-i v, b->>i i i, c-\rightarrow>i i, d->i \)
D. a->- ii, b- -> i, c- -> ii, d- - > iv


Which one of these muscles tires out
easily?
A. Cardiac
B. Unstriated
c. striated
D. All of the above


Explain why the electric field inside a conductor placed in an external electric field is zero.


From the following data at constant volume for combustion of benzene,
calculate the heat of this reaction at
constant pressure condition.
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(\boldsymbol{l})+\mathbf{1 5} / \mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{l}) \)
\( \Delta U \) at \( 25^{\circ} C=-3268.12 k J \)


Find the values of \( x, \) if \( \left|\begin{array}{cc}\mathbf{2 x} & \mathbf{5} \\ \mathbf{8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{ll}\mathbf{6} & \mathbf{5} \\ \mathbf{8} & \mathbf{3}\end{array}\right| \)


Form the given figure, find the values of
\( x \) and \( y \) respectively.
A \( \cdot 47^{\circ}, 66^{\circ} \)
B \( \cdot 66^{\circ}, 48^{\circ} \)
\( \mathbf{c} \cdot 68^{\circ}, 47^{\circ} \)
D. \( 47^{\circ}, 68^{\text {? }} \)


A potential difference of \( V \) volts is
applied on an \( \alpha \) -particle at rest in order
to get sufficient velocity so that when it is projected from infinity towards \( \boldsymbol{A} \boldsymbol{u} \)
foil, it can reach closest upto \( x \) meters
from \( A u \) nucleus. If instead of an \( \alpha \)
particle, a proton is used in the above experiment and is accelerated from rest by the same potential difference, then
the closest distance from the \( \boldsymbol{A} \boldsymbol{u} \)
nucleus upto which it can reach is \( y \)
meters. The ratio \( x: y \) is
A . 2: 1
B. 3:2
\( c \cdot 1: 1 \)
D. 2:3


If a letter is selected at random from the
letters of the word LOGARITHMS, then
what is the probability that it will be a consonant?


In which of the following polymers,
ethylene glycol is one of the monomer
units?
\( A \)
B \( \cdot\left(-C H_{2}-C H_{2}\right)_{n} \)
\( c \)


What are the properties of acids?
This question has multiple correct options
A. It produces the hydroxyl ion \( \left(O H^{-}\right) \)
B. It produces the hydronium ion \( \left(H_{3} O^{+}\right) \) in aqueous solution
C. They are proton donors
D. They have low pH


At time \( t=0, \) two bodies \( A \) and \( B \) are at
the same point. A moves with constant
velocity \( V \) and \( B \) starts from rest and moves with constant acceleration. Relative velocity of B with respect to A when the bodies meet each other is:
A \( \cdot \frac{V}{2} \)
в. \( \frac{V}{3} \)
c. \( V \)
D. \( 2 V \)


Write a \( 2 \times 2 \) matrix which is both
symmetric and skew symmetric.


Alligator occurs in
A. India
B. America and China
C. Africa
D. Australia


A body is acted upon by two forces each of magnitude \( F, \) but in opposite directions. State the effect of the forces
if both forces act at the same point of
the body. Which of the following is/are
true?
A. Resultant force \( =0 \)
B. Moment of forces \( =0 \)
c. No motion
D. All of the above


A nucleus with atomic number \( z \) and
neutron number N undergoes two decay processes. The result is a nucleus with atomic number Z-3 and neutron
number N-1. Which decay processes took place?
A . Two \( \beta^{-} \) decays
B. Two \( \beta^{+} \) decays
C. \( A n \alpha-d e c a y \) and \( a \beta^{-} \) decay
D. An \( \alpha- \) decay and a \( \beta^{+} \) decay


Multiple Answers Type Objective Questions:
Which of the following act as negative catalysts?
A. Ethanol in oxidation of chloroform
B. Tetra ethyl lead used as antiknocking agent
C. Glycerol in the decomposition of \( H_{2} O_{2} \)
D. all are currect


The equilibrium constant for the
reaction \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \)
\( C O_{2}(g)+H_{2}(g) \) is 3 at \( 500 K . \ln a 2 \)
litre vessel \( 60 \mathrm{gm} \) of water gas
[equimolar mixture of \( \left.\mathrm{CO}(\mathrm{g}) \text { and } \boldsymbol{H}_{2}(\boldsymbol{g})\right] \)
and \( 90 \mathrm{gm} \) of steam is initially taken.
What is the equilibrium concentration of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) at equilibrium (mole/L)?
A . 1.75
в. 3.5
\( c \cdot 1.5 \)
D. 0.75


Alcohols can be converted to various
types of gasoline(period) by shapeselective catalyst.
A. Maltase
B. ZSM- 5
c. Lindlar's catalyst
D. ziegler Natta catalyst


Which of the following has the largest de Broglie wavelength, provided all have equal velocity?
A. Carbon dioxide molecule
B. Ammonia molecule
c. oxygen molecule
D. Nitrogen molecule


Prove that
\( \cos \frac{\pi}{15} \cos \frac{2 \pi}{15} \cos \frac{3 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{5 \pi}{15} \cos \frac{6}{1} \)
1
\( 2^{7} \)


An arithmetic sequence starts as \( \mathbf{5}, \mathbf{9}, \mathbf{1 3}, \dots \dots \dots, . \) What is the next term?
Is 2012 a term of this sequence? Why?


Assertion
STATEMENT \( 1: \sim(p \leftrightarrow \sim q) \) is equivalent
to \( (\boldsymbol{p} \vee \sim \boldsymbol{q}) \wedge(\sim \boldsymbol{p} \vee \boldsymbol{q}) \)
Reason
STATEMENT \( 2: \sim(p \leftrightarrow q) \) is equivalent
to \( (\boldsymbol{p} \wedge \sim \boldsymbol{q}) \vee(\sim \boldsymbol{p} \wedge \boldsymbol{q}) \)
A. Statement 1 is True, Statement 2 is True; Statement 2 i a correct explanation for Statement 1
B. Statement 1 is True, Statement 2 is True ; Statement 2 is NOT a correct explanation for Statement 1
c. statement 1 is True, Statement 2 is False
D. Statement 1 is False, Statement 2 is True


Compute \( \operatorname{Lim} \frac{3^{x}-2^{x}}{x} \)


Carbon dioxide is the major component
of greenhouse gases.
A. True
B. False


The chemical formula of starch is
A \( \cdot\left(C_{6} H_{10} O_{5}\right)_{n} \)
в. \( \left(C_{6} H_{12} O_{6}\right)_{n} \)
c. \( C_{12} H_{22} O_{11} \)
D. \( C H_{3} \) СООН


Halogenated hydrocarbons have many
uses.

What have halogenated hydrocarbons
been used for?
solvents
2 refrigerants
3 monomers in polymer manufacture
\( A \cdot 1,2 \) and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct


The torque of force \( \overrightarrow{\boldsymbol{F}}=(2 \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}}) \)
N acting at the point \( \vec{r}= \) \( (3 \hat{i}+2 \hat{j}+3 \hat{k}) m \) about origin is (in \( \mathrm{N}- \)
\( \mathrm{m}) \)
A . \( 6 \hat{i}-6 \hat{j}+12 \hat{k} \)
B . \( 17 \hat{i}-6 \hat{j}-13 \hat{k} \)
c. \( -6 \hat{i}+6 \hat{j}-12 \hat{k} \)
D. \( -17 \hat{i}+6 \hat{j}+13 \hat{k} \)


A carnot cycle is having maximum
efficiency because
A. it comprises of two adiabatic process which requires no heat in its execution.
B. it comprises of two isothermal process.
C. its every process is reversible
D. none of the above


Which of the following is not a true
statement about detergents?
A. Anionic detergents are sodium salts of sulphonated long chain alcohols or hydrocarbons.
B. Cationic detergents are quarternary ammonium salts of amines with acetates, chlorides or bromides as
ions.
C. Non-ionic detergents do not contain any ion in their constitution.
D. Detergents containing branched hydrocarbon chains are biodegradable.


\( \mathbf{5 0} \boldsymbol{m} \boldsymbol{L} \) of \( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \) is added to
\( 75 m L \) of \( 0.1 M N H_{4} C l \) to make a
basic buffer. If \( p K_{a} \) of \( N H_{4}^{+} \) is 9.26
calculate \( \boldsymbol{p} \boldsymbol{H} \)
A .4 .44
B. 7.89
c. 9.56
D. 10.76


\( n \)
Fig. 1.8
1.8
A. retardation is uniform
B. velocity is decreasing with time
c. beyond M, the body has negative velocity
D. all the above are correct


Which one of the following is oxidised
by \( \mathrm{MnO}_{2} ? \)
A \( \cdot \mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CH}_{2}-\mathrm{OH} \)
B. \( \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3} \)
c. \( \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{3} \)
D. \( \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{OH} \)


What is the action of the following reagents on ammonia:
(a) Nessler's reagent
(b) Sodium metal


\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}\frac{\tan [x]-[x] \tan 1}{x} & ; \boldsymbol{x} \neq 0 \\ \boldsymbol{0} & ; \boldsymbol{x}=0\end{array}, \) then \right.
\( \boldsymbol{f}^{\prime}\left(\mathbf{0}^{-}\right) \) is [where \( [\boldsymbol{x}] \) denotes integer part
of \( \boldsymbol{x} \)
A . 0
B.
\( c \cdot-1 \)
D. Does not exist


A card sheet divided into squares each
of size \( 1 \mathrm{mm}^{2} \) is being viewed at a distance of \( 9 \mathrm{cm} \) through a magnifying glass (a converging lens of focal length \( 9 \mathrm{cm} \) ) held close to the eye.(a) What is the magnification produced by the lens? How much is the area of each
square in the virtual image?(b) What is the angular magnification (magnifying power) of the lens?(c) Is the magnification in
(a) equal to the magnifying power in (b)? Explain


Can the speed of a body be negative?


In an isosceles triangle, the base angles
are equal. The vertex angle is \( 40^{\circ} . \) What
are the base angles of the triangle? (Remember, the sum of three angles of
a triangle is \( 180^{\circ} \) ).


A number of methods are used for the
manufacture of the alkali metal
compounds. Accordingly match the processes listed in column-I with the compound(s) listed in column-II.


The moving air from the hair dryer removes the molecules of liquids as soon as they escape from the surface of
your hair.
Which factor of evaporation is responsible for the above example?
A. Temperature
B. Motion of air
c. Nature of liquid
D. Humidity of surrounding


How many steps are required for the following conversion?


A thin circular ring of mass \( M \) and
radius \( r \) is rotating about its axis with constant angular velocity \( \omega . \) Two objects each of mass \( \mathrm{m} \) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by
A \( \cdot \frac{(M+2 m) \omega}{2 m} \)
в. \( \frac{2 M \omega}{M+2 m} \)
c. \( \frac{(M+2 m) \omega}{M} \)
D. \( \frac{M \omega}{M+2 m} \)


In a transformer, in which the losses
may be neglected, the ratio of the primary voltage to secondary voltage is found to be \( 4: 1 . \) The ratio of the
primary to secondary turns and the ratio of the primary current to secondary current are respectively in
the ratio of :
\( A \cdot 4: 1 \& 1: 4 \)
B. \( 1: 4 \& 4: 1 \)
c. \( 4: 1 \& 4: 1 \)
D. \( 1: 4 \& 1: 4 \)


What is the distance in space between (1,0,5) and (-3,6,3)\( ? \)
A . 4
B. 6
c. \( 2 \sqrt{11} \)
D. \( 2 \sqrt{14} \)
E . 12


Which one of the following represents a d-block element?
\( \mathbf{A} \cdot[R n] 6 d^{10} 7 s^{2} 7 p^{2} \)
B \( \cdot[X e] 4 f^{1} 5 d^{1} 6 s^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{14} 5 d^{1} 6 s^{2} \)
D \( \cdot[X e] 5 d^{1} 6 s^{2} \)


Which of the following has auxin like
property?
A. \( \alpha \) -Naphthalene acetic acid
B. \( \beta \) -Naphthalene acetic acid
c. Both (A) and (B)
D. None of the above


Hybrid orbital having maximum p character is:
\( A \cdot s p^{3} d \)
В \( \cdot s p^{3} \)
c. \( s p \)
D. \( s p^{3} d^{2} \)


Lightning is a phenomenon
A. Electromagnetic
B. Current electricity
c. Electrochemical
D. Electrostatic


The differential equation of the family of
curve \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{a}(\boldsymbol{x}+\boldsymbol{a}) \) is
A \( \cdot y^{2}=4 \frac{d y}{d x}\left(x+\frac{d y}{d x}\right) \)
B. \( \quad y^{2}\left(\frac{d y}{d x}\right)^{2}+2 x y \frac{d y}{d x}-y^{2}=0 \)
c. \( y^{2} \frac{d y}{d x}+4=0 \)
D. \( 2 y \frac{d y}{d x}+4 a=0 \)


State the two laws of reflection of light.


If someone grew lots of trees close to each other, would this become a forest?


When hydrogen burns in oxygen, is produced.
A. water
B. hydrogen peroxide
c. acid
D. base


Which of the following isomeric pairs
shows ionization isomerism?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]\left[\operatorname{Cr}(C N)_{6}\right] \) and \( \left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]\left[\operatorname{Co}(C N)_{6}\right] \)
\( \mathbf{B} \cdot\left[C r\left(H_{2} O\right)_{6}\right] C l_{3} \) and \( \left[C r\left(H_{2} O\right)_{5} C l\right] C l_{2} H_{2} O \)
\( \mathbf{C} \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \) and \( \left[P t\left(N H_{3}\right)_{4}\right]\left[P t C l_{4}\right] \)
\( \mathbf{D} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} B r\right] S O_{4} \) and \( \left[C o\left(N H_{3}\right)_{5} S O_{4}\right] B r \)


Matter is composed of:
A. atoms
B. molecules
C . tiny particles
D. all of the above


A coin tossed vertically by a passenger
sitting in a train that is moving with a
uniform velocity, still returns to his
palm. This demonstrates the principle
of.
A. Inertia(Newton's First Law of Motion)
B. Conservation of angular momentum
c. Addition of velocities of the train and the coin
D. Addition of forces due to gravity and the toss of the coin


Two coins are tossed 1000 times and
the outcomes are recorded as below:
\( \mathbf{2} \) No of heads \( \mathbf{0} \)
250 Frequency \( 200 \quad 550 \)
Based on this information, the probability for at most one head is \( \frac{a}{b} \)
Where \( (a, b)=1, \) then
A \( \cdot \frac{1}{5} \)
в.
\( c \cdot \frac{4}{5} \)
D.


Two cells, having emfs of \( 10 V \) and \( 8 V \)
respectively, are connected in series
with a resistance of \( 24 \Omega \) in the external
circuit. If the internal resistances of
each of these cells in ohm are \( 200 \% \) of
the value of their emf's respectively,
find the terminal potential difference
\( \operatorname{across} 8 V \) battery.
A \( .0 .3 A, 3.2 V \)
B. \( 0.5 A, 3.2 V \)
c. \( 0.3 A, 1.2 V \)
D. \( 0.5 A, 2.2 V \)


Total numbers of hybrid orbitals present
\( \operatorname{in} C H_{3}-C \equiv C H \) are:
\( \mathbf{A} \cdot \mathbf{8} \)
B. 6
\( c \cdot 4 \)
D.


If \( f(x)=\operatorname{sgn}\left(x^{5}\right) \) then which of the
following is/are false (where sgn denotes signum function) This question has multiple correct options
\( \mathbf{A} \cdot f^{\prime}\left(0^{+}\right)=1 \)
B. \( f^{\prime}\left(0^{-}\right)=1 \)
C. \( f \) is continuous but not differentiable at \( x=0 \)
D. fis discontinuous at \( x=0 \)


The capacitive reactance at \( 1600 H z \) is
81 \Omega. When the frequency is doubled then capacitive reactance will be
A . \( 40.5 \Omega \)
в. \( 81 \Omega \)
\( c \cdot 162 \Omega \)
D. Zero


Which of the following vessel in rabbit starts with capillaries and ends in
capillaries?
A. Pulmonary artery
B. Renal vein
c. Hepatic portal vein
D. Renal artery


Find the value of \( f(x)=x^{3}-3 x+5 \) at
\( \boldsymbol{x}=\mathbf{1 . 9 9} \)


Find the direction cosine \( l, \boldsymbol{m}, \boldsymbol{n} \) of line
which are connected by the relations \( \boldsymbol{l}+\boldsymbol{m}+\boldsymbol{n}=\mathbf{0} . \boldsymbol{2 m} \boldsymbol{n}+\boldsymbol{2} \boldsymbol{m} \boldsymbol{l}-\boldsymbol{n l}=\mathbf{0} \)


If \( u \) denotes 1 atomic mass unit. One
atom of an element has mass exactly equal to \( A u, \) where \( A \) is mass number
of element.
\( \mathbf{A} \cdot A=1 \)
B. \( A=12 \)
c. \( A=16 \)
D. \( A \) can take up any integral value from 1 to 110


The probability that \( A \) hit a target is
\( 1 / 4 \) and the probability that \( B \) hits the target is \( 1 / 3 . \) If each of them fired once, what is the probability that the target will be hit atleast once?


Write the structures of \( \left(\mathbf{C H}_{3}\right)_{3} \mathbf{N} \) and
\( \left(M e_{3} S i\right)_{3} N . \) Are they isostructural?
Justify your answer.


If the projection of point \( \boldsymbol{P}(\overrightarrow{\boldsymbol{p}}) \) on the
plane \( \vec{r} \cdot \vec{n}=q \) is the point \( S(\vec{s}), \) then?
A \( \cdot \vec{s}=\frac{(q-\vec{p} \cdot \vec{n}) \vec{n}}{|\vec{n}|^{2}} \)
В \( \cdot \vec{s}=\vec{p}+\frac{(\vec{p} \cdot \vec{n}-q)}{|\vec{n}|^{2}} \vec{n} \)
C・ \( _{\vec{s}}=\vec{p}-\frac{(\vec{p} \cdot \vec{n}) \vec{n}}{|\vec{n}|^{2}} \)
D \( \vec{s}=\vec{p}-\frac{(q-\vec{p} \cdot \vec{n}) \vec{n}}{|\vec{n}|^{2}} \)


are the non-living
components of the cell.
A. Lysosomes
B. Vacuoles
c. Nuclei
D. Golgi bodies


Which of the following are chemical changes?
(i) Melting of iron metal
(ii) Rusting of iron
(iii) Bending of an iron rod
(iv) Drawing a wire of iron metal
A. only (ii)
B. (ii) and (iii)
c. (iii) and (iv)
D. (i) and (iv)


What is the change in the temperature on Fahrenheit scale and on Kelvin scale,
if a iron piece is heated from \( 30^{\circ} \) to
\( 90^{\circ} \mathrm{C} ? \)
A \( \cdot 108^{\circ} F, 60 K \)
в. \( 100^{\circ} F, 55 K \)
c. \( 100^{\circ} F, 65 K \)
D. \( 60^{\circ} F, 108 K \)


\( \boldsymbol{p} \boldsymbol{H} \) of \( \boldsymbol{B a}(\boldsymbol{O H})_{2} \) solution is 12. Its
solubility product is :
A \( .5 .0 \times 10^{-7} \)
B. \( 0.6 \times 10^{-12} \)
c. \( 4.0 \times 10^{-8} \)
D. \( 5.0 \times 10^{-9} \)


Solve \( \& \) graph the solution set of \( -2< \)
\( 2 x-4 \) and \( -2 x+5 \geq 13, x \epsilon R \)


If \( n \) is the orbit number of the electron
in a hydrogen atom, the correct statement among the following is
A. Electron energy increases as \( n \) increases
B. Hydrogen emits infrared rays for the electron transition from \( n=\infty \) to \( n=1 \)
C. Electron energy is zero for \( n=1 \)
D. Electron energy varies as \( n^{2} \)


The functional groups present in the following compound is:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O H} \)
A. ketone
B. alcohol
c. aldehyde
D. carboxylate


Although chlorine is an electron withdrawing group yet it is ortho, para directing in nature. Why?


The type of teeth used to tear a
sugarcane is
A. Incisors
B. Canines
c. Premolars
D. Molars


1 Hz is:
A. 1 vibration per minute.
B. 360 vibration per minute.
C . 10 vibration per minute.
D. 60 vibration per minute.


\( \mu=\sqrt{15} \) is true for the pair:
A \( \cdot C o^{+2}, C r^{+3} \)
B. \( F e^{+2}, C r^{+3} \)
c. \( F e^{+3}, C r^{+2} \)
D. \( M n^{+2}, F e^{+2} \)


Of the following complex ions, one is a Bronsted-lowry acid. That one is:
\( \mathbf{A} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+} \)
B. \( \left[F e C l_{4}\right]^{-} \)
c. \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \)
D. \( _{\left[Z n(O H)_{4}\right]^{2-}} \)


Two cats Billy and Kitty together catch 60 mice. If Billy catches three mice for every two caught by Kitty, the number of mice caught by Kitty is
A .24
B. 30
\( c . \) 36
D. 40


If \( \frac{a+3 i}{2+i b}=1-i, \) show that \( (5 a- \) \( 7 b)=0 \)


The spontaneous change in specific rotation of an opacity active compound is called ?
A. Mutarotation
B. Rearrangements
c. Inversion
D. Retention


The name of the compound is cyclohexylidene methanone.
A . True
B. False


Evaluate \( 1.6+2.9+3.12+\ldots+ \)
\( \mathbf{n}(\mathbf{3 n}+\mathbf{3})= \)
A \( \cdot n(n+1)(n+2) \)
B. \( (n+1)(n+2)(n+3) \)
c. \( (n+2)(n+3)(n+4) \)
D. \( (n-1) n(n+1) \)


Differentiate between.
Inspiratory capacity and expiratory capacity


If the expression \( \frac{x-p}{x^{2}-3 x+2} \) takes all
real values for \( x \in R \) then find the
limits for 'p'.


\( x^{2}-2 x+1 ; 2 x \) multiply this
polynomial


What should be subtracted from \( 2 a^{2}- \)
\( b^{2}+3 a^{2} b \) to get \( a^{2}+b^{2}+3 a b^{2}-6 ? \)


Intra-abdominal testes are found in
A. Bat
B. Elephant
c. whale
D. All of the above


A mass is suspended from the end of a
spring. When the system is oscillating the amplitude of oscillation is \( 4 \mathrm{cm} \) and the maximum kinetic energy of
oscillation of the system is 1 joule.
Then the force constant of the spring is:
A. \( 2500 \mathrm{N} / \mathrm{m} \)
в. \( 1250 \mathrm{N} / \mathrm{m} \)
c. \( 500 \mathrm{N} / \mathrm{m} \)
D. \( 250 \mathrm{N} / \mathrm{m} \)


If the sum of adjacent angles of a
quadrilateral is equal to \( 180^{\circ}, \) then
quadrilateral is
A . a parallelogram
B. connex
c. concave
D. none of the above


Suggest a reason as to why \( C O \) is
poisonous.


Newton's law of motion cannot be
applicable to the particle moving at a speed comparable to the speed of
A. Light
B. Sound
c. Rocket
D. Bullettrain


Glycolate metabolism occurs in
A. Lysosome
B. Ribosomes
c. Glyoxysomes
D. Peroxisome


\( (x-2) \) is a factor of the expression \( x^{3}+ \)
\( a x^{2}+b x+6 . \) when this expression is
divided by \( (x-3), \) it leaves the remainder \( 3 . \) find the values of a and \( b \)


What is the average power dissipation in an ideal capacitor in AC circuit?
\( \mathbf{A} \cdot 2 C V^{2} \)
в. \( \frac{1}{2} C V^{2} \)
c. \( Z \) ero
D. \( C V^{2} \)


Which of the following factors are responsible for the increase in the rate
of a surface catalysed reaction?
I. A catalyst provides proper orientation for the reactant molecules to react
II. Heat of adsorption of reactants on a catalyst helps reactant molecules to.overcome activation energy
III. The catalyst increases the activation energy of the reaction
IV. Adsorption increases the local concentration of reactant molecules on
the surface of the catalyst Select the correct answer using the codes given below:
A . I and II
B. I and III
c. ।, ॥ land IV
D. I, II and III


Hygroscopic roots occur in
A. Vanda
B. Rhizophora
C . Bryophyllum
D. All the above


If \( \vec{a} \) and \( \vec{b} \) are non-collinear vectors and
\( \boldsymbol{A}=(\boldsymbol{p}+\mathbf{4} \boldsymbol{q}) \boldsymbol{a}+(\boldsymbol{2} \boldsymbol{p}+\boldsymbol{q}+\mathbf{1}) \boldsymbol{b} \)
\( \boldsymbol{B}=(-\mathbf{2} \boldsymbol{p}+\boldsymbol{q}+\mathbf{2}) \boldsymbol{a}+(\mathbf{2} \boldsymbol{p}-\boldsymbol{3} \boldsymbol{q}-\mathbf{1}) \boldsymbol{b} \)
then determine \( p \) and \( q, \) so that \( 3 A= \)
\( 2 B \)
A. \( p=1 \) and \( q=-0.3 \)
B. \( p=-1 \) and \( q=1.1 \)
C. \( p=2 \) and \( q=-1 \)
D. \( p=-2 \) and \( q=1.8 \)


The formulae of chloride of metal \( M \) is
\( M C l_{2} . \) The metal \( M \) belongs to
group.


The last element in period 2 is lithium
A. True
B. False


Name one metal that reacts slowly with
dil. sulphuric acid :
A. Iron
B. Ferrous sulphate
c. Hydrogen
D. All of these


The structure given below represents:
\[
\mathrm{CH}_{3}-\underbrace{\mathrm{CH}_{3}}_{\mathrm{CH}_{3}}-\mathrm{NH}_{2}
\]
A. quarternary ammonium Salt
B. primary amine.
c. secondary amine.
D. tertiary amine.


A converging lens (focal length \( ^{\prime} f^{\prime} \) ) is broken in two equal pieces and placed at \( 60 \mathrm{cm} \) as shown along with the
object. It is found that real images are formed at the same place and ratio of
image heights is \( 9: 1, \) if the value of \( ^{\prime} f^{\prime} \) is \( \left(22+\frac{1}{x}\right) \mathrm{cm} \) then value of \( ^{\prime} x^{\prime} \) is :


A flat, square surface with sides of length L is described by the equations. \( \boldsymbol{x}=\boldsymbol{L}, \mathbf{0} \leq \boldsymbol{y} \leq \boldsymbol{L}, \mathbf{0} \leq \boldsymbol{z} \leq \boldsymbol{L} \)
The electric flux through the square due to a positive point charge q located at the origin( \( x=0, y=0, z=0 \) ) is
A. \( \frac{q}{4 \varepsilon_{o}} \)
в. \( \frac{q}{6 \varepsilon_{o}} \)
c. \( \frac{q}{24 \varepsilon_{o}} \)
D. \( \frac{q}{48 \varepsilon_{o}} \)


The most abundant element in the
universe is:
A. helium
B. oxygen
c. silicon
D. hydrogen


Two balls of masses \( 2 g \) and \( 6 g \) moving with \( K E \) in the ratio of \( 3: 1, \) What is the
ratio of their linear momenta?
A . 1: 1
B . 2: 1
\( c \cdot 1: 2 \)
D. None of these


From the top of a tower, a particle is thrown vertically downwards with a velocity of \( 10 \mathrm{m} / \mathrm{s} \). The ratio of the
distances, covered by it in the \( 3^{r d} \) and
\( 2^{n d} \) seconds of the motion is (Take \( g= \)
\( \left.\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A . 5: 7
B. 7: 5
\( c \cdot 3: 6 \)
D. 6: 3


What is the value of \( \sqrt{441} ? \)
A . 20
в. 2
\( c \cdot 22 \)
D. None of these


At lower temperature, most gases show:
A. negative deviation
B. positive deviarion
c. positive and negative decviation
D. none of the above


Denitrification is caused by
A. Pseudomonas
B. Nitrobacter
c. Nitrosomonas
D. Azotobacter


Convert the given fractional numbers to
per cents. \( \frac{1}{8} \)
\( \frac{5}{4} \)
\( \frac{3}{40} \)
\( \frac{2}{7} \)


Find if polynomial \( x^{4}-3 x^{3}+7 x^{2}- \)
\( 8 x+12 \) is exactly divisible by \( x^{2}- \)
\( 2 x+2 \)


Let \( A B C D \) be a square of side length 1
and \( \Gamma \) a circle passing through \( B \) and \( C \) and touching \( A D . \) The radius of \( \Gamma \) is
A
в.
c. \( \frac{1}{\sqrt{2}} \)
D.


If \( \mathrm{N} \) is the number of turns in a coil, the
value of self-inductance varies are
\( \mathbf{A} \cdot \mathbf{N}^{\mathbf{0}} \)
B.
c. \( N^{2} \)
\( D \cdot N^{-2} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{4}}{\mathbf{3}} \boldsymbol{x}^{3}-\mathbf{4} \boldsymbol{x}, \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{2} . \) Then
the global minimum value of the function is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( -8 / 3 \)
c. -4
D. none of these


Two point charges \( +q \) and \( +q \) are fixed at \( (a, 0,0) \) and \( (-a, 0,0) . \) A third point charge \( -q \) is at origin. State whether its equilibrium is stable, unstable or neutral if it is slightly displaced along
\( \boldsymbol{x}- \) axis.
A . Stable
B. Unstable
c. Neutral
D. Data insufficient


When a certain metal was irradiated
with a light of \( 8.1 \times 10^{16} \) Hz frequency,
the photoelectron emitted had 1.5 times the kinetic energy as did the photoelectrons emitted when the same metal was irradiated with light \( 5.8 \times \)
\( 10^{16} \mathrm{Hz} \) frequency. If the same metal is
irradiated with light of 3.846 nm
wavelength,what will be the energy of the photoelectron emitted?
A \( .1 .8 \times 10^{2} e V \)
В. \( 3.65 \times 10^{-17} J \)
c. \( 2.28 \times 10^{2} e V \)
D. \( 4.37 \times 10^{-17} J \)


The smallest rationalizing factor of \( \sqrt[3]{63} \) is
A \( \cdot \sqrt[3]{37} \)
в. \( \sqrt[3]{62} \)
\( c \cdot \sqrt[3]{147} \)
D. \( \sqrt[3]{243} \)


Assertion (A): The basic nature of VA
group hy-drides decreases from ammonia to bismuthine.
Reason (R): Availability of lone pair on the cen-tral atom in hydrides decreases
down the group.
A. Both (A) and (R) are true and
(R) is the correct
explanation of (A)
B. Both (A) and (R) are true and (R) is not the
correct explanation of (A)
\( c . \) (A) is true and
(R) is false
D. (A) is false but (R) is true


Which of the following has highest second ionization energy?
A . \( N i \)
в. \( V \)
\( c \cdot C r \)
D. \( M n \)


Write Gauss's theorem of electrostatics.
Obtain an expression for the intensity of electric field near a uniformly charged
straight wire of infinite length with its help.


If the radius of earth decreases by \( 10 \% \) the mass remaining unchanged, what will happen to the acceleration due to gravity?
A. Decreases by \( 19 \% \)
B. Increases by \( 19 \% \)
c. Decreases by more than \( 19 \% \)
D. Increases by more than \( 19 \% \)


Which of the following metal(s) form(s) polynuclear carbonyl?
A . Na a
в. Мв
\( c . \) мп
\( D \cdot A \)


Which of the following has the largest heart?
A . Giraffe
B. Lion
c. crocodile
D. None of the above


Identify the salt(s) of an oxyacid formed
from univalent metal \( (M) \)
This question has multiple correct options
A \( . M_{2} S O_{4} \)
B. \( M\left(N O_{3}\right)_{2} \)
\( \mathbf{c} \cdot M_{3} C l O_{3} \)
D. \( M H C O_{3} \)


A black and a red dice are rolled.
(a) Find the conditional probability of
obtaining a sum greater than \( 9, \) given that the black die resulted in a 5 .
(b) Find the conditional probability of
obtaining the sum 8 , given that the red die resulted in a number less than 4
A. 0.33,0.11
B. 0.51,0.76
c. 0.56,0.43
D. 0.11,0.65


State whether the following statement
is True or False.
The current in the circuit with
inductance \( L \) and resistance \( R \) and
voltage \( \boldsymbol{E} \sin \omega \boldsymbol{t} \) is given by \( \boldsymbol{L} \frac{\boldsymbol{d} \boldsymbol{i}}{\boldsymbol{d} \boldsymbol{t}}+\boldsymbol{R} \boldsymbol{i}= \)
Esinwt.if \( i=0 \) at \( t=0 \) then,current is
given by \( i=\frac{E}{\sqrt{E^{2}+L^{2} \omega^{2}}}[\sin (\omega t- \)
\( \left.\phi)+e^{-R t / L} \sin \phi\right] \) where \( \phi= \)
\( \tan ^{-1}\left(\frac{L \omega}{R}\right) \)
A. True
B. False


charge particles are pictured in the
same magnetic field which points into the screen (represented by blue \( X^{\prime} \) s) The particles are moving at the same speeds but in different directions, as
indicated by the red arrows. How do the particles rank, in terms of
the force they experience due to their
movements in the magnetic field, greatest first?
A. 1,2,3
B. 1 and 2 tie, 3
c. 3,1 and 2 tie
D. 3,2,1
E. All tie


Three numbers are chosen at random
without replacement from \( 1,2,3, \dots . ., 10 \) The probability that the minimum of
the chosen numbers is 3 or their
maximum is 7 is
A \( \cdot 1 / 2 \)
в. \( 1 / 3 \)
c. \( 1 / 4 \)
D. \( 11 / 40 \)


Give two different examples of pair of
(i)
similar figures


Identify the plant, if veins are appearing parallel on leaves.
A. The plant is a dicot
B. The plant is a monocot
c. The plant is a gymnosperm
D. The plant is an angiosperm
E. The plant is a bryophyte


What would be the best method to bring about the following conversion? \( C H_{3} \)
\( C H_{3}-C_{1}^{\prime}-C H=C H_{2} \longrightarrow C H_{3}- \)
\( \boldsymbol{C H}_{3} \)
\( \dot{C}-C H C H_{3} \)
\( C H_{3} \quad O H \)
\( \mathbf{A} \cdot B H_{3}, T H F ; \) then \( H_{2} O_{2}, O H^{-} \)
B. \( H B r ; \) then \( N a O H / H_{2} O \)
c. conc. \( H_{2} S O_{4}, \) then \( H_{2} O \), heat
D. \( H g(O A c)_{2} / T H F-H_{2} O \), then \( N a B H_{4}, O H^{-} \)


A force of \( \left(4 x^{2}+3 x\right) N \) acts on a
particle which displaces it from \( \boldsymbol{x}= \)
\( 2 m \) to \( x=3 m . \) Te work done by the force
is:
A . \( 32.8 \mathrm{J} \)
B. \( 3.281 J \)
c. \( 0.328 J \)
D. zero


For a first-order reaction; \( \mathbf{A} \rightarrow \mathbf{B} \), the
reaction rate at a reactant
concentration of \( 0.01 \mathrm{M} \) is found to be
\( 2.0 \times 10^{-5} \) mole \( L^{-1} s^{-1} . \) The half-life
period of the reaction is:
A . 300 s
в. \( 30 s \)
\( c .220 s \)
D. 347


If a wire is bent into the shape of a
square, then the area of the square is \( 81 \mathrm{cm}^{2} . \) When the same wire is bent
into a semi-circular shape, then the
area of the semi circle will be
\( \mathbf{A} \cdot 22 \mathrm{cm}^{2} \)
B. \( 44 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 77 \mathrm{cm}^{2} \)
D. \( 154 \mathrm{cm}^{2} \)


A particle moves in a straight line with constant acceleration a. The
displacements of particle from origin in
times \( t_{1}, t_{2} \) and \( t_{3} \) are \( s_{1}, s_{2} \) and \( s_{3} \) respectively. If time are in AP with
common difference d and
displacements are in GP, then prove that \( a=\frac{(\sqrt{s_{1}-\sqrt{s_{3}}})^{2}}{d^{2}} \)


State True or False:
Saturation current depends on
temperature.
A. True
B. False


In man expired air contains oxygen about
A . \( 4 \% \)
B . 10\%
c. \( 16 \% \)
D. 20\%


Write the reactions of (i) aromatic and
(ii) aliphatic primary amines with nitrous acid.


Name the connecting link between glycolysis and TCA cycle and explain it.


The following table gives the daily wages of workers in a factory. Compute the standard deviation and the
coefficient of variation of the wages of
the workers.
\( \begin{array}{lllll}\begin{array}{l}\text { Wages } \\ \text { (Rs) }\end{array} & \begin{array}{l}\text { 125- } \\ \text { 175 }\end{array} & \begin{array}{l}\text { 175- } \\ \text { 225 }\end{array} & \begin{array}{l}\text { 225- } \\ \text { 275 }\end{array} & \begin{array}{l}\text { 275- } \\ \text { 325 }\end{array}\end{array} \)
of
workers
?


Some physical quantities are given in list 1. The related units are given in list
2. Match the correct pairs
List 1 List 2
a) Magnetic Field Intensity \( W b m^{-1} \)
e)
) Magnetic Flux f) \( W b m^{-2} \)
b)
c Potential Magnetic \( W b \)
c) g)
h) \( A m^{-1} \)
d) Magnetic Induction
A. \( a-e, b-f, c-g, d-h \)
B. a-h, b-g, c-e, d-f
c. a-h, b-e, c-g, d-f
D. a-f, b-g, c-e, d-h


A student performs an experiment for determination of \( \boldsymbol{g}=\left[\frac{\mathbf{4} \boldsymbol{\pi}^{2} \boldsymbol{L}}{\boldsymbol{T}^{2}}\right], \boldsymbol{L}=\mathbf{1} \boldsymbol{m} \)
and he commits an error of \( \triangle L \). For The
takes the time of n oscillations with the
stopwatch of least count \( \triangle T . \) For which
of the following data, the measurement of \( g \) will be most accurate?
A. \( \triangle L=0.5, \Delta T=0.1, n=20 \)
B. \( \triangle L=0.5, \Delta T=0.1, n=50 \)
c. \( \triangle L=0.5, \Delta T=0.01, n=30 \)
D. \( \triangle L=0.5, \Delta T=0.05, n=50 \)


Let \( P(x, y) \) be a moving point in the \( x- \) \( \boldsymbol{y} \) plane such that \( [\boldsymbol{x}] .[\boldsymbol{y}]=2, \) where \( [.] \)
denotes the greatest integer function, then area of the region containing the points \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) is equal to:
A. 1 sq. units
B. 2 sq. units
c. 4 sq. units
D. None of these


Match the following and choose the
correct combination from the options
given.
\( \begin{array}{llll} & \text { Column-I } & & \text { Column-II } \\ \text { A. } & \begin{array}{l}\text { Walter } \\ \text { Sutton }\end{array} & \text { 1. } & \begin{array}{l}\text { Discovered } \\ \text { penicillin }\end{array} \\ \text { B. } & \begin{array}{l}\text { Thomas } \\ \text { Hunt }\end{array} & \text { 2. } & \begin{array}{l}\text { Discovered the } \\ \text { chromosomal } \\ \text { basis of heredity }\end{array} \\ \text { D. } & \begin{array}{l}\text { James } \\ \text { Watson }\end{array} & \text { 3. } & \begin{array}{l}\text { Described the } \\ \text { phenomenon of } \\ \text { linkage and } \\ \text { crossing over }\end{array} \\ & \text { Morgan } & & \begin{array}{l}\text { Discovered the } \\ \text { double helical } \\ \text { structure of DNA }\end{array}\end{array} \)
A. A-1, B-4, C- 2, D-3
B. A- 2, B-3, C-1, D-4
C. \( A-3, B-2, C-1, D-4 \)
D. A- 2, B-3, C-4,D-1
E. A- 4, B-1, C-2,
\( D \)


If \( A \) is an event of a random experiment such that \( P(A): P(\bar{A})=5: 11 \), then
find \( P(A) \) and \( P(\bar{A}) \)


For the velocity time graph shown in the
figure, the distance covered by the body in the last two seconds of its motion is
what fraction of the total distance
travelled by it in all the seven seconds?
\( A \)
B. 4
\( c \)
D.


A wave has velocity v in medium P and velocity \( 2 v \) in medium \( Q \). If the wave is incident in medium \( \mathrm{P} \) at an angle of 30 then the angle of refraction will be
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


A wax candle burns with yellow flame.
Give reason.


Explain why some of the leaves may get detached from a tree if we vigorously shake it branch.


Draw a labelled diagram of a candle flame and explain what happens in
each zone.


The increasing \( d \) -character in
hybridisation of \( X e \) in
\( X e F_{2}, X e F_{4}, X e F_{6} \) is :
A. \( \mathrm{XeF}_{2}<\mathrm{XeF}_{4}<\mathrm{XeF}_{6} \)
B. \( \mathrm{XeF}_{4}<\mathrm{XeF}_{2}<\mathrm{XeF}_{6} \)
\( \mathbf{c} \cdot \mathbf{X}_{\mathbf{e}} F_{6}<\mathbf{X} \mathbf{e} F_{4}<\mathbf{X}_{\mathbf{e}} F_{2} \)
D. \( \mathrm{XeF}_{2}<\mathrm{XeF}_{6}<\mathrm{XeF}_{4} \)


Electric heaters used for cooking have the filament or the heating coil on a plate made up of clay because
A. Clay is a bad conductor of heat
B. Clay is a bad conductor of electricity
c. Both \( A \& B \)
D. None of these


Find the volume of a cube of edge \( 6 \mathrm{cm} \)
\( \mathbf{A} \cdot 64 \mathrm{cm}^{3} \)
В. \( 125 \mathrm{cm}^{3} \)
\( c \cdot 216 c m^{3} \)
D. \( 343 \mathrm{cm}^{3} \)


Polysomes lack
A. Proteins
B. mRNA
c. DNA
D. tRNA and rRNA


Rainbow is formed in which direction
with respect to the sun?
A. Same direction
B. Opposite direction
c. Depends on the time of the day
D. North direction


toppr
Q Type your question
objects moving at constant speed in circular paths are shown. The objects speeds, circular path radii, and masses
are given in each diagram.
In which situation does the pictured object have the greatest amount of acceleration due to its circular motion?
\( A \)
B.
\( c \)
\( D \)
E. None of the object in this question is accelerating, since they all are moving at a constant speed


It is given that \( \angle X Y Z=64^{\circ} \) and \( X Y \) is
produced to point P.Draw a figure from the given information If ray y objects \( \angle Z Y P, \) find \( \angle X Y Q \)


How many nodal plane is/are present in
\( \sigma_{s-s}^{*} \) anti-bonding molecular orbital?


Match Column-I with Column-II.
ColumnColumn-II
(a)
(i) Symbiotic association of fungi Saprophyte with plant roots
(ii) Decomposition of dead organic
(b) Parasite materials
(iii) Living on living plants or
(c) Lichens animals
(d)
(iv) Symbiotic association of algae Mycorrhiza and fungi
Choose the correct answer from the
option given.
B. (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
C. (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
D. (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)


Which one of the following shows maximum paramagnetic character?
\( \mathbf{A} \cdot\left[F e(C N)_{6}\right]^{3-} \)
в. \( \left[F e(C N)_{6}\right]^{4-} \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{6}\right]^{3+} \)
D \( \cdot\left[C u\left(H_{2} O\right)_{6}\right]^{2+} \)


Root pressure in maximum, when
A. Transpiration is high and absorption is very low.
B. Transpiration is very low and absorption is high.
C. Absorption is very high and transpiration is also very high.
D. Absorption is very low and transpiration is also low.


The given quadratic equations have real
roots and the roots are equal and it is 1:
\( x^{2}-2 x+1=0 \)
A. True
B. False


About \( 97 \% \) of \( O_{2} \) is transported by RBC.
The remaining \( 3 \% \) is
A. Dissolved in plasma and transported
B. Remains in lungs
c. Attached to cell membranes
D. Inside the mitochondria
E. In peroxisomes


Write any two characteristics of
Chemisorption.


Select the output \( Y \) of the combination
of gates shown in figure for inputs \( \boldsymbol{A}= \)
\( \mathbf{1}, \boldsymbol{B}=\mathbf{0} ; \boldsymbol{A}=\mathbf{1}, \boldsymbol{B}=\mathbf{1} \) and \( \boldsymbol{A}=\mathbf{0}, \boldsymbol{B}= \)
respectively.
A \( .(0,1,1) \)
в. (1,0,1)
c. (1,1,1)
D. (1,0,0)


The reading of poteniometer if \( 4 V \)
battery is used instead of \( e \), is
A \( .88 .3 \mathrm{cm} \)
в. \( 47.3 \mathrm{cm} \)
\( \mathrm{c} .95 \mathrm{cm} \)
D. cannot be calculated


Simplify: \( \left(-3 p q^{2}+4 p q\right)- \)
\( \left(7 p q-9 p q^{2}\right) \)
\( \mathbf{A} \cdot 6 p q^{2}+3 p q \)
B. \( 6 p q^{2}-3 p q \)
c. \( -12 p q^{2}+3 p q \)
D. \( -12 p q^{2}-3 p q \)


Which of the following is/are ionization?
1. \( \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O} \longrightarrow \boldsymbol{H}^{+}+\boldsymbol{O} \boldsymbol{H}^{-} \)
2. \( \boldsymbol{H C l} \longrightarrow \boldsymbol{H}^{+}+\boldsymbol{C l}^{-} \)
A . Only 1
B. Only 2
c. Both 1 and 2
D. None of these


Parkinsonia and Australian Acacia
contains
A. Phylloclade
B. Winged fruitt
c. Parachute mechanism
D. Phyllode


What is the centripetal acceleration of the ball if its mass is doubled?
\( A \cdot a / 4 \)
B. a/2
\( c \)
D. 2a
E. \( 4 a \)


The size of a colloidal particle is:
\( A \cdot>0.1 \mu \)
в. \( 1 m \mu \) to \( 0.1 \mu \)
\( \mathbf{c} .<0.1 m \mu \)
D. More than \( 3000 m \) \mu


The introduction of contaminants into
the natural environment that cause
adverse change is called
A. Pollution
B. Emission
c. Greenhouse effect
D. None of above


Find the value of
\( (1+i)^{6}+(1-i)^{6} \)


Ramji sold an article at a loss of 8
percent. Had she bought it at \( 10 \% \) less
and sold for Rs. 72 more; she would have
gained \( 20 \% \). Find the cost price of the article.
A. 400
в. 450
c. 500
D. 550


How many grams of gas are present in a \( 2.2 L \) sample of gas if the gas has a density of \( 1.8 g / L ? \)
A. \( 1.22 g \)
в. \( 4.00 g \)
\( \mathbf{c} .3 .96 g \)
D. \( 0.02 g \)


Which can act as buffer?
A \( . N H_{4} C l+H C l \)
в. \( C H_{3} C O O H+H_{2} C O_{3} \)
c. \( 40 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{NaCN}+20 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{HCN} \)
D. \( N a C l+N a O H \)


Walking fern name is due to
A. Dispersal by animals
B. Reproduction by spores
c. vegetative reproduction
D. Power of locomotion


Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the
drawn card is more than 3 , what is the
probability that it is an even number?


\( \lim _{x \rightarrow \infty}(\sqrt{x^{2}+8 x+3}- \)
\( \sqrt{x^{2}+4 x+3})= \)
A . 0
B. \( \infty \)
\( c \cdot 2 \)
D. \( \frac{1}{2} \)


Factorise the following expressions:
\( \boldsymbol{p}^{2}+\boldsymbol{6} \boldsymbol{p}+\boldsymbol{8} \)
A \( \cdot(p-2)(p+4) \)
в. \( (p+2)(p+4) \)
c. \( (p+2)(p-4) \)
D. \( (p-2)(p-4) \)


Find points on the curve \( \frac{x^{2}}{9}+\frac{y^{2}}{16}=1 \)
at which the tangents are

Parallel to \( x \) -axis are \( (a, \pm b) \).Find \( a+b \)


The property under multiplication used in each of the following.
\( \frac{-4}{5} \times 1=1 \times \frac{-4}{5}=-\frac{4}{5} \)
This question has multiple correct options
A. Commutative Property
B. Associative Property
c. Distributive Property
D. Identity Property


In the given figure, ABCD is a
parallelogram in which \( \angle D A B=75^{\circ} \)
and \( \angle \mathrm{DBC}=60^{\circ} \) then the measure of \( \angle \)
BDC is equal to?
\( A \cdot 75^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. 55


A stone is dropped from a height equal to \( n R(R \) is the radius of the Earth)
from the surface of the Earth. The
velocity of the stone on reaching the surface of the Earth is :
A \( \cdot \sqrt{\frac{2 g(n+1) R}{n}} \)
в. \( \sqrt{\frac{2 g R}{n+1}} \)
c. \( \sqrt{\frac{2 g n R}{n+1}} \)
D. \( \sqrt{2 g n R} \)


The molecule having a non-zero dipole
moment is :
A. \( H_{2} O_{2} \)
в. \( C H_{4} \)
\( \mathbf{c} \cdot C_{2} H_{6} \)
D. \( B F_{4}^{-} \)


Disease aggravated by pollution is
A. Scurvy
B. Rheumatism
c. Haemophilia
D. Bronchitis


Which of the following is outer orbital complex?
\( \mathbf{A} \cdot\left[C o F_{6}\right]^{-3} \)
B. \( \left[C u\left(H_{2} O\right)_{6}\right]^{+2} \)
C. \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{+2} \)
D. All


Assertion
HClO\( _{4} \) is stronger acid than \( \boldsymbol{H} \boldsymbol{C l O}_{3} \)
Reason
Oxidation state of Cl in \( \boldsymbol{H} \boldsymbol{C l O}_{\mathbf{4}} \) is \( +\mathbf{V} \| \)
and in \( \boldsymbol{H} \boldsymbol{C l O}_{3} ; \) it is \( +\mathbf{V} \)
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


Give the decreasing order of reactivity of the following compounds with \( H B r \)
\( (\mathrm{I}) \)
\( \left.(\mathrm{II}) \mathrm{H}_{3} \mathrm{C}-\bigotimes\right\rangle \)
\( (\mathrm{III}) \mathrm{M}_{\mathrm{e}} \mathrm{O}-\langle\bigcirc\rangle \widehat{\mathrm{O}_{\mathrm{H}}} \)
\( (\mathbf{I V}) \)


Two particles of mass \( 1 \mathrm{kg} \) and \( 2 \mathrm{kg} \) are located at \( x=0 \) and \( x=3 \) m. Find the position of their center of mass.
\( A \cdot 4 m \)
B. 2 \( m \)
\( c \cdot 6 m \)
D. 8 m


The EMFs of the following cells are
\( \boldsymbol{C u}\left|\boldsymbol{C u}^{2+}(\mathbf{1} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{1} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{g}, \boldsymbol{E}^{o}= \)
\( 0.46 V \)
\( Z n\left|Z n^{2+}(1 M) \| C u^{2+}(1 M)\right| C u, E^{o}= \)
\( 1.10 V \)
The EMF of the cell
\( Z n\left|Z n^{2+}\right|\left|A g^{+}(1 M)\right| A g \) will be:
A . \( 1.56 V \)
B . \( -1.56 V \)
c. \( 0.64 V \)
D. \( 2.02 V \)


A ray of light is normally incident on one face of an equilateral glass prism. What will be the angle of incidence at the second face of the prism?
A \( \cdot 0^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Write the truth table for a NAND gate
connected as given in Figure.


The \( K_{a} \) value for the acid \( H A \) is \( 1.0 \times \)
\( 10^{-6} . \) What is the value of \( K \) for the
following reaction? \( \boldsymbol{A}^{+}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \rightleftharpoons \boldsymbol{H} \boldsymbol{A}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot 1.0 \times 10^{-8} \)
В. \( 1.0 \times 10^{8} \)
C \( .1 .0 \times 10^{-3} \)
D \( .1 .0 \times 10^{6} \)


If \( a, b, c \) be in \( A P, \) and \( a^{2}, b^{2}, c^{2} \) are in \( H \)
\( P ., \) then
\( \mathbf{A} \cdot a+b=c \)
B. \( b+c=a \)
c. \( c+a=b \)
\( \mathbf{D} \cdot a b+b c+c a=0 \)


The sound of the human voice is
produced due to
A. movement of tongue
B. vibration in the pharynx
c. vibration in the vocal cord
D. vibration below tongue


A particle moves along the x-axis obeying the equation \( \boldsymbol{x}=\boldsymbol{t}(\boldsymbol{t}-\mathbf{1})(\boldsymbol{t}- \)
2), where \( x \) is in meter and \( t \) is in
second. Find the initial velocity of the particle \( (\boldsymbol{m} / \boldsymbol{s}) \)


Which of the following is the standard for atomic mass?
A \( \cdot \frac{1}{1} H \)
B . \( _{6}^{12} \mathrm{C} \)
\( \mathbf{c} \cdot \frac{i 4}{6} C \)
D. \( _{8}^{6} C \)


If \( n \geq 2 \) then the number of surjections
that can be defined from \( \{1,2,3, \dots n\} \) onto \{1,2\} is
A \( \cdot n^{2}-n \)
B \( \cdot n^{2} \)
\( c \cdot 2^{n} \)
D. \( 2^{n}-2 \)


A bullet fired into a block looses half of
its velocity after penetrating through a distance of \( 0.6 \mathrm{m} . \) Before coming to rest, the total distance traveled would be:
A . \( 0.8 \mathrm{m} \)
B. 1.2 \( m \)
\( c \cdot 1.6 m \)
D. 0.2 \( m \)


For the given circuit of \( \boldsymbol{p}-\boldsymbol{n} \) junction,
the potential barrier is :
A. Raised
B. Lowered
c. Remains same
D. Data insufficient


Find the additive inverse of the number \( \frac{2}{8} \)


Cell cycle was divided into four stages
i.e. \( G_{1}, S, G_{2}, M \) by
A. W. Flemming
B. Strass burger
c. Howard and Pelc
D. Farmer


Calculate the position of the centre of mass of a system consisting of two
particles of masses \( m_{1} \) and \( m_{2} \) separated by a distance L apart.


Nitrolium is used as fertiliser. Explain.


The area of quadrilateral ABCD given below is 269.2 sq.units
f true then enter 1 and if false then
enter \( \mathbf{0} \)


n given figure, express \( x \) in terms of \( a, b \)
and \( c \)


STATEMENT-1: Silver extraction is done
by dissolving its ore into cyanide solution.
STATEMENT-2: In cyanide process, the silver is precipitated from soluble
complex of silver of zinc-dust.
A. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


An object of radius 'R' and mas 'M' is rolling horizontally without slipping with speed 'V'. It the rolls up the hill to a
maximum height \( \boldsymbol{h}=\mathbf{3} \boldsymbol{v}^{2} / \mathbf{4} \boldsymbol{g} \). The
moment of inertia of the object is:
(ge eceleration due to gravity)
\( ^{\mathbf{A}} \cdot \frac{2}{5} M R^{2} \)
в. \( \frac{M R^{2}}{2} \)
c. \( M R^{2} \)
D. \( \frac{3}{2} M R^{2} \)


What is tricarboxylic acid cycle? Describe its different steps.


Select the correct schematic
representation of blood circulation in
human from the followings
\( A \)
\( B \)
\( c \)
\( D \)


Few pairs of molecule are given below. Which bond of the molecule of the pair
is more polar?
(i) \( \quad H_{3} C-H, H_{3} C-B r \)
(ii) \( \quad H_{3} C-N H_{2}, H_{3} C-O H \)
(iii) \( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{O} \boldsymbol{H}, \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{S} \boldsymbol{H} \)
(iv) \( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C l}, \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{B r} \)
A. \( C-B r, C-N, C-O, C-B r \)
в. \( C-B r, C-O, C-O, C-C l \)
c. \( C-B r, C-N, C-S, C-C l \)
D. \( C-B r, C-O, C-S, C-B r \)


Initially the spheres \( A \) and \( B \) are at
potential \( V_{A} \) and \( V_{B} \) respectively. Now
sphere \( \mathrm{B} \) is earthed by closing the
switch. The potential of \( A \) will now
become:
\( A \)
B. \( V_{A} \)
\( \mathbf{c} \cdot V_{A}-V_{B} \)
D. \( V_{B} \)


If a particle moves according to the law, \( s=6 t^{2}-\frac{t^{3}}{2}, \) then the time at which it
is momentarily at rest
A. \( t=0 \) only
B. \( t=8 \) only
c. \( t=0,8 \)
D. none of these


The potential at \( P \) due to induced
charge is
\( ^{\text {A }} \cdot_{K q}\left(\frac{1}{r_{1}}-\frac{1}{r_{2}}\right) \)
в. \( _{K q}\left(\frac{1}{r_{1}}+\frac{1}{r_{2}}\right) \)
\( ^{\text {c. }} K q\left(-\frac{1}{r_{1}}+\frac{1}{r_{2}}\right) \)
D. \( \frac{K q}{r_{1}} \)


Variation of equilibrium constant K for the reaction \( ; 2 A(s)+B(g) \rightleftharpoons \)
\( C(g)+2 D(g) \) is plotted against
absolute \( \mathrm{T} \) in figure as- \( \ln \boldsymbol{K} \boldsymbol{V} \boldsymbol{s}(\mathbf{1} / \boldsymbol{T}) \)
This question has multiple correct options
A. the forward reaction is exothermic
B. the forward reaction is endothermic
c. the slope of line is proportional to \( \Delta H \)
D. adding 'A' 'favours forward reaction
E. removing C favours forward reaction


Calculate the mass and volume at NTP
of hydrogen and chlorine that will be formed by passing 10,000 coulomb of charge through an aqueous solution of potassium chloride. The cell reaction is:
\( 2 K C l+2 H O H \rightarrow 2 K O H+C l_{2}+ \)
\( \boldsymbol{H}_{2} \)


The freezing point depression constant
for water is \( -1.86^{0} \mathrm{Cm}^{-1} . \) If \( 5.00 \mathrm{g} \)
\( N a_{2} S O_{4} \) is dissolved in 45.0 g \( H_{2} O, \) the
freezing point is changed by \( 3.82^{0} C \)
Calculate the vant Hoff factor for
\( N a_{2} S O_{4} \)
A . 2.05
B . 2.63
c. 3.11
D. 0.381


Amphoteric oxides are:
\( \mathbf{A} \cdot S n O, S n O_{2} \)
\( \mathbf{B} \cdot G e O, G e O_{2} \)
C. both (a) and (b)
D. None of these


If the angle between the pass axis of the polarizer and the analyzer is 45 the ratio of the intensities of original
light and the transmitted light after passing through the analyzer is
A \( \cdot \frac{I}{2} \)
B. \( \frac{1}{3} \)
\( c \)
D. \( \frac{I}{4} \)


Convex lens
A. Shrinks the image
B. Magnifies the image
C. sharpens the image
D. Increase the contrast of the image


Which of the following statements
about histones is not true?
A. Histones are very similar between species
B. Histones have many basic amino acids
C. Histones are rich in lysine and arginine
D. Each histone has one single gene that codes for it


Which of the following is the main factor of water pollution?
A. Smoke
B. Industrial waste
c. Detergent
D. Ammonia


Which of the following statements is/are correct ?
a) The magnitude of the vector \( \hat{\mathbf{i}}+4 \hat{\mathbf{j}} \) is
5
b) Force \( (3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}) \mathrm{N} \) acting on a particle causes a displacement 6jิm. The work done by the force is 30
c) If \( \vec{A} \) and \( \vec{B} \) represent two adjacent sides of a parallelogram, then \( |\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}| \) gives the perimeter of that parallelogram
d) A force has magnitude 20N. Its component in a direction making an angle \( 60^{0} \) with the force is \( 10 \sqrt{3} \mathrm{N} \)
A . a \& b are correct
B. a \& c are correct
c. a \( \& \mathrm{d} \) are correct
D. all are wrong


All conventional modern thermonuclear
warheads are also called as
A. fission-fusion-fission
B. Neutron bombs
c. cobalt bombs
D. three stage bomb


Example for an improper fraction is
A \( \cdot \frac{25}{26} \)
в. \( \frac{12}{13} \)
c. \( \frac{15}{14} \)
D. \( \frac{19}{20} \)


One gram mol of helium at \( 27^{0} \mathrm{C} \) is
mixed with three gram mols of oxygen
at \( 127^{0} \mathrm{C} \) at constant pressure. If there is
no exchange of heat with the atmosphere then the final temperature will be
\( A \cdot 375 K \)
в. 175k
c. \( 475 \mathrm{k} \)
D. 575K


Check whether \( 6 x^{3}+x^{2}=2 \) is
a quadratic equations


Which of the following statement is
correct?
A. Liquids obey partially the Ohm's law
B. Liquids fully obeys the Ohm's law
C. Liquid do not obeys the Ohm's law
D. None of the above


A student focused the image of a
distant object using a device 'X' on a white screen 'S' as shown in the figure. If the distance of the screen from the
device is \( 40 \mathrm{cm}, \) select the correct statement about the device.
A. The device X is a convex lens of focal length 20 cm
B. The device X is a concave mirror of focal length \( 40 \mathrm{cm} \)
c. The device \( x \) is a concave mirror of radius of curvature
\( 40 \mathrm{cm} \)
D. The device X is a convex lens of focal length \( 40 \mathrm{cm} \)


Plot the following point in the rectangular coordinate system \( \boldsymbol{C}(-\mathbf{2},-\mathbf{3}) \)


The compound which is formed after sharing of a pair of electrons is called
A. ionic compound
B. atomic compound
c. covalent compound
D. None of these


The two equilibrium \( \boldsymbol{A B} \leftrightharpoons \boldsymbol{A}^{+}+\boldsymbol{B}^{-} \)
and \( A B+B^{-} \leftrightharpoons A B_{2}^{-} \) are
simultaneously maintained in a
solution with equilibrium constant \( \boldsymbol{K}_{\mathbf{1}} \)
and \( K_{2} \) respectively. The ratio of \( \left[A^{+}\right] \) to
\( \left[A B_{2}^{-}\right] \) in the solution is:
A. directly proportional to the concentration of \( B \)
B . inversely proportional to the concentration of \( B \)
c. directly proportional to the square of the concentration of \( B \)
D. inversely proportional to the square of the concentration of \( B \)


After attaining puberty, the boys develop a voice.
A. Heavy
B. Light
c. Thinner
D. High pitched


At a given temperature, total vapour pressure (in torr) of a mixture of volatile
components \( A \) and \( B \) is given by \( P_{T o t a l}=120-75 X_{B} \) hence, the vapour
pressure of pure \( A \) and \( B \) respectively (in Torr) are:
A .120,75
в. 120,195
c. 120,45
D. 75,45


Figure shows a fixed wedge on which two blocks of masses 2 kg and 3 kg are placed on its smooth inclined surfaces.
When the two blocks are released from
rest, find the acceleration of centre of
mass of the two blocks


Which one exception, each of the following units can be used to express mass. What is the exception?
A. Newton
B. Gram
c. kilogram
D. \( N s^{2} / m \)


Bacteria and fungi are best classified
as
A. Scavengers
B. Primary consumers
c. secondary consumers
D. Decomposers


Due to refraction, when seen from
outside, a coin placed under water in a
bowl, appears to
A. go down
B. come up
c. stay where it is
D. move toward left


Which of the following is regarded as a unit of nervous tissue?
A. Axons
B. Dendrites
c. Neurons
D. Myelin sheath


f \( n(A \cup B)=8, n(A)=6, n(B)=4 \)
\( \operatorname{then} n(A \cap B)= \)
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
\( D \)


When a sound wave of wavelength \( \lambda \) is propagating in a medium the maximum velocity of the particle is equal to wave velocity. The amplitude of the wave is
\( A \cdot \lambda \)
B. \( \frac{\lambda}{2} \)
\( c \cdot \frac{\lambda}{2 \pi} \)
D. \( \frac{\lambda}{4 \pi} \)


The process of separation of an organic
compound from its aqueous solution
by shaking with a suitable solvent is termed solvent extraction or differential
extraction.
The organic compound present in
aqueous layer moves to the organic
solvent because:
A. the organic substance is more soluble in the organic solvent
B. organic compound being lighter moves in the upper layer
c. organic solvent is insoluble in water hence organic compound moves up
D. from the supersaturated aqueous solution the solute starts diffusing


Which of the following depicts Mendel's dihybrid ratio?
\( A \cdot 3: \)
B. 9: 3: 3: 1
c. 9: 7
D. 15:


Classify the following function as injection, surjection or bijection:
\( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N} \) given by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2} \)


Energy in the sun is due to
A. Fossil fuels
B. Radioactivity
c. Fission
D. Fusion


What are the chief pollutants of the atmosphere, which are most likely to deplete the ozone layer?
A. Sulphur dioxide
B. Nitrogen oxide and Fluorocarbons
c. Carbon dioxide
D. Carbon monoxide


Reactivity order for SN1
(i) \( C H_{3}-\underset{C l}{C} H-C H_{2}-C H_{3} \)
(ii) \( \boldsymbol{P h}-\boldsymbol{C H}_{3}-\underset{C l}{\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}_{3}} \)
(iii) \( C H_{3}-\quad \begin{array}{c}C l \\ \ \\ 0 \\ 0 C H_{3}\end{array}-C H_{3} \)
(iv) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \)
A. \( i>i i>i i i>i v \)
в. \( i i>i> \) ii \( i>i v \)
c. \( i i>i i>i>i v \)
D . \( i v>i i i>i i>i \)


Complete the table given below
\( \begin{array}{ll}\text { No. of } & \text { No. of } \\ \text { Protons } & \text { Electr }\end{array} \) No. of Electrons Neutror
\( _{13}^{35} C l \)
\[
_{17}^{37} C l
\]


Solve: \( \int \frac{x^{2}-1}{x^{3} \sqrt{2 x^{4}-2 x^{2}+1}} d x \) is equal
to
A \( \cdot \frac{\sqrt{2 x^{4}-2 x^{2}+1}}{x^{2}}+C \)
B. \( \frac{\sqrt{2 x^{4}-2 x^{2}+1}}{x^{3}}+C \)
c. \( \frac{\sqrt{2 x^{4}-2 x^{2}+1}}{x}+C \)
D. \( \frac{\sqrt{2 x^{4}-2 x^{2}+1}}{2 x^{2}}+C \)


Among the methods for extracting metals from their ores, i.e., 1. roasting a metal sulphide, 2. chemical reduction of a metal oxide, and 3. electrolysis, the
preferred method depends on \( E^{\circ} \) value for the reducing half-reaction:
\( \boldsymbol{M}^{n+}(\boldsymbol{a q})+\boldsymbol{n} \boldsymbol{e}^{-} \rightarrow \boldsymbol{M}(\boldsymbol{s}) \)
What are the criteria of selection of a
good reducing agent for extraction of
metals?


Which of the following is not an element?
A. 22 caratgold
B. Graphite
c. Diamond
D. Rhombic sulphur


Assertion
Bohr had to postulate that the electrons in stationary orbits around the nucleus
do not radiate.
Reason
According to classical physics all moving electrons radiate.
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


The ratio of height of a mercury column in a barometer at a place to the height of the liquid column at the same place
are \( 1: 4 . \) Find the density of the liquid


Two identical uniform solid spherical
balls \( A \) and \( B \) of mass \( m \) each are placed
on a the fixed wedge as shown in figure.
Ball B is kept at rest and it is released just before two balls collides. Ball A rolls
down without slipping on inclined plane and collide elastically with ball B. The kinetic energy of ball Ajust after the collision with ball B is:
A \( \cdot \frac{m g h}{7} \)
в. \( \frac{m g h}{2} \)
c. \( \frac{2 m g h}{5} \)
D. \( \frac{7 m g h}{5} \)


In general, metals have very low:
A. Boiling Point
B. Freezing Point
c. Melting Point
D. Specific Heat Capacity


the intrinsic semiconductor at room
temperature is


In \( \triangle A B C, X Y \| B C \) and \( X Y \) divides the triangle into two parts of equal areas. Find \( \left(\frac{B X}{A B}\right) \)


Given below are two reaction of water
with sodium and carbon dioxide, what is the nature of water in these reaction?
\( (\mathrm{i}) 2 N a+2 H_{2} O \rightarrow 2 N a O H+H_{2} \)
\( (\mathrm{ii}) 6 \mathrm{CO}_{2}+12 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{6} \mathrm{H}_{1} 2_{6}+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}+\mathbf{6} \boldsymbol{O}_{2} \)
A . In (ii) water acts as an oxidising agent and in (i) it acts as a reducing agent
B. In (i) water acts as an oxidising agent and in (ii) it acts as a reducing agent
c. In both (i) and
(ii) hydrogen acts as a reducing agent
D. In both (i) and (ii) hydrogen acts as an oxidizing agent


The technique of protecting a metal from
corrosion by connecting it to a second metal (that is more easily oxidized) is
called:
A. galvanization
B. anodic protection
C . cathodic protection
D. sacrificial protection


Which of the following is a disaccharide?
A. sucrose
B. Maltose
c. Lactose
D. All of the above


Calculate the magnification of an
object if it is kept at a distance of \( 3 c m \) from a concave mirror of focal length
\( 4 c m: \)
A . 3
B. 6
c. 9
\( D \)


Find the odd one out for the example of natural air pollutant.
A. pollen, spores
B. Insecticides
c. volcanic gases
D. agricultural burning


Find the area of parallelogram whose
base is \( 48 \mathrm{cm} \) and height is \( 25 \mathrm{cm} \)


\( \frac{1}{8} \)


Which among the following statement is true about the work done in bringing
a unit positive charge from point \( P \) to \( Q \)
in an electrostatic field?
A. Minimum work is done in case of path II
B. Maximum work is done in case of path1
c. Work done is same in all the three paths
D. Work done is zero in case of path


Find a unit vector perpendicular to each of the vectors \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b} \) where \( \vec{a}=3 \hat{i}+2 \hat{j}+2 \hat{k} \) and \( \vec{b}=\hat{i}+2 \hat{j}-2 \hat{k} \)


The pH of solution containing \( 0.10 M \)
sodium acetate and \( 0.03 M \) acetic acid
is: \( \left(p K_{a} \text { for } C H_{3} C O O H=4.57\right) \)
A . 4.09
B. 6.09
c. 5.09
D. 7.09


The magnetic susceptibility of an ideal diamagnetic substance is
A . -
B.
\( c \cdot+1 \)
\( D \cdot \alpha \)


Compound with a molecular formula
\( C_{7} H_{16} \) will have:
A. single covalent bond only
B. at least one double bond
c. at least one triple bond
D. single bond as well as double bond both


How anisole reacts with bromine in
ethanoic acid? Write the chemical
equation for the reaction.


Assertion
Reduciton potential value of \( \left(\boldsymbol{E}^{\circ}\right) \) of \( \mathbf{0} \)
benzoquine (I) is greater than pbezoquinone (II)
Reason
Two adjacent (C=0) groups in (I)
destablise (I) relative to (II).
o-benzoquinone p-benzoquinone
\( (\mathrm{I}) \)
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


One mole of an ideal monoatomic gas is
heated at a constant pressure from 0 to
100. Then the change in the internal energy of the gas is:
\( \left(\text { Given }, \boldsymbol{R}=\mathbf{8 . 3 2} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
A \( \cdot 0.83 \times 10^{3} J \)
в. \( 4.6 \times 10^{3} J \)
c. \( 2.08 \times 10^{3} J \)
D. \( 1.25 \times 10^{3} J \)


A harmonically moving transverse wave on a string has a maximum particle velocity and acceleration of \( 3 \mathrm{m} / \mathrm{s} \) and
\( 90 \mathrm{m} / \mathrm{s}^{2} \) respectively. Velocity of the wave is \( 20 \mathrm{m} / \mathrm{s} \). Find the waveform.
A \( \cdot y=(10 \mathrm{cm}) \sin \left(30 t \pm \frac{3}{2} x+\phi\right) \)
B. \( y=(20 c m) \sin \left(30 t \pm \frac{3}{2} x+\phi\right) \)
c. \( y=(10 \mathrm{cm}) \sin \left(60 t \pm \frac{3}{2} x+\phi\right) \)
D. \( y=(20 \mathrm{cm}) \sin \left(60 t \pm \frac{3}{2} x+\phi\right) \)


Which of the following process helps in the absorption of nutrients in amoeba?
A. Assimilation
B. Engulfment
c. Digestion
D. Excretion


Choose the correct answers from the
alternatives given :
In a eukaryotic cell, most of the
enzymes of the Krebs cycle are located
in the
A. intermembrane space
B. mitochondrial matrix
c. inner mitochondrial membrane
D. plasma membrane


The normal systolic and diastolic
pressure in human beings is
A. \( 80 / 120 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. 130/90 mm of Hg
c. \( 120 / 80 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. 140/80 mm of Hg


In acid buffer solution \( (\mathrm{pH}=4.4), \) the ratio of concentrations of acid to salt
is \( 2: 1 . \) The value of dissociation
constant of weak acid may be:
A \( \cdot 1.8 \times 10^{-4} \)
В. \( 2 \times 10^{-7} \)
c \( .4 \times 10^{-5} \)
D. \( 2 \times 10^{-5} \)


Why \( Z n^{2+} \) is diamagnetic whereas
\( C r^{3+} \) is paramagnetic?


List changes in the body that take place
at puberty.


A woman dancing in high-heeled shoes accidentally steps on her partner's foot with the heel of her shoe. Even though her partner outweighs her by \( 400 \mathrm{N} \) and can easily lift her off the floor, he feels pain because:
A. her weight is concentrated into a small area
B. her small foot has a large momentum
c. her foot has a large inertia
D. his foot has no inertia


Stenohaline fishes are represented by
A. Fresh water fishes only
B. Marine fishes only
C. Those which can tolerate a narrow range of salinity in water only
D. Those which can tolerate a wide range of salinity in water


\( \frac{x^{2}+1}{\left(x^{2}+2\right)\left(2 x^{2}+1\right)}= \)
\( k\left[\frac{1}{x^{2}+2}+\frac{1}{2 x^{2}+1}\right] \Rightarrow k= \)
\( A \cdot \frac{1}{4} \)
B. 3
\( c \cdot \frac{1}{5} \)
D.


If \( \overline{\boldsymbol{p}}=\hat{\boldsymbol{i}}-\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overline{\boldsymbol{q}}=\hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}-\boldsymbol{2} \hat{\boldsymbol{k}} \)
are position vectors of points \( \boldsymbol{P} \) and \( \boldsymbol{Q} \)
find the position vector of the point \( \boldsymbol{R} \) which divides segment \( P Q \) internally in
the ratio 2: 1


Determine the electric dipole moment
of the system of three charges,placed on the vertices of an equilateral triangle as shown in the figure:
A \( \cdot(q l) \frac{\hat{i}+\hat{j}}{\sqrt{2}} \)
В \( \cdot \sqrt{3} q l \frac{\hat{j}-\hat{i}}{\sqrt{2}} \)
\( \mathbf{c} .-\sqrt{3} q l \hat{j} \)
D. \( 2 q l \hat{j} \)


Which of the following complex compounds will exhibit highest paramagnetic behaviour? \( (A t . N o . T i=22, C r=24, C o= \)
\( \mathbf{2 7}, \boldsymbol{Z} \boldsymbol{n}=\mathbf{3 0}) \)
\( \mathbf{A} \cdot\left[Z n\left(N H_{3}\right)_{6}\right]^{2+} \)
в. \( \left[T i\left(N H_{3}\right)_{6}\right]^{3+} \)
c. \( \left[C r\left(N H_{3}\right)_{6}\right]^{3} \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+} \)


Without knowing the electronic configurations of the atoms of elements Mendeleev still could arrange the elements nearly close to the arrangements in the Modern periodic table. How can you appreciate this?


Four students \( A, B, C, \) and \( D \) noted the
initial colour of the solution in beakers
I, II, Ill and IV. After inserting zinc rods in
each solution and leaving it
undisturbed for two hours, noted the
colour of each solution again. The recorded observations in the form of
the table given below:
Which student noted the colour change
in all the four beakers correctly.
\( A \cdot(A) \)
B. (B)
\( c \cdot(c) \)
\( D, \quad O \)


The radioactivity of a sample is \( R_{1} \) at a
time \( T_{1} \) and \( R_{2} \) at a time \( T_{2} . \) If the half-
life of the specimen is \( T, \) the number of atoms that have disintegrated in the
time \( T_{2}-T_{1} \) is proportional to
A \( \cdot T_{2}-T_{1} \alpha\left(R_{1}-R_{2}\right) T \)
В \( \cdot\left(R_{1}-R_{2}\right) \)
c. \( \left(R_{1}-R_{2}\right) / T \)
D \( \cdot\left(R_{1}-R_{2}\right) T \)


Equation of the circle which touches the line \( \mathbf{x}+\mathbf{y}-\mathbf{8}=\mathbf{0} \) and centre \( (\mathbf{3}, \mathbf{3}) \) is
A \( \cdot x^{2}+y^{2}-6 x-6 y=0 \)
B \cdot \( x^{2}+y^{2}-6 x-6 y+4=0 \)
C \( \cdot x^{2}+y^{2}-6 x-6 y+36=0 \)
D. \( x^{2}+y^{2}-6 x-6 y+16=0 \)


Use of the Data Booklet is relevant to
this question.
\( 2.40 g \) of \( p r o p a n-2-o l \) were mixed
with excess acidified potassium dichromate(VI). The reaction
mixture was then boiled under reflux for
twenty minutes. The organic product
was then collected
by distillation. The yield of product was \( 75.0 \% \)
What mass of product was collected?
A \( .1 .74 g \)
B. \( 1.80 g \)
c. \( 2.22 g \)
D. \( 2.32 g \)


State True or False.
Free hydrogen is found naturally on
earth.
A. True
B. False


An operon unit consist of
A. Regulator, operator and recessive gene
B. Regulator, structural and operator gene
C. Regulator, structural, operator and promoter gene
D. Regulator, structural and promoter gene


The teeth used for biting and cutting
food are called as
A. Molars
B. Premolars
c. canines
D. Incisors


Which of the following statements for a
rigid object undergoing pure
translational motion are false?
This question has multiple correct options
A. If an object receives an impulse its kinetic energy must change.
B. An object's kinetic energy can change without the object changing momentum.
C. An object can receive a net impulse without any work being done on it
D. A force may do work on an object without delivering any change in momentum.


In Gymnosperms pollination occurs exclusively by
A. Anemophily
B. Hydrophily
c. zoophily
D. Malacophily


Two sounds of same loudness and same
pitch produced by two different instruments differ their:
A. Amplitudes
B. frequencies
c. wave forms
D. All the above


Sodium has
compared to potassium.
A. less electronegativity
B. more ionization potential
c. larger atomic radius
D. lower melting point


Two identical loops \( P \) and \( Q \) each of
radius \( 5 \mathrm{cm} \) are lying in perpendicular
planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of
the two coils, if they carry currents
equal to \( 3 A \) and \( 4 A \) respectively.


n a right angled \( \triangle A B D, \angle B= \)
\( \mathbf{6 0}^{\circ}, \angle \boldsymbol{A}=\mathbf{3 0}^{\circ} \)
Then \( \sin 30^{\circ} \) is equal to
\( A \)
\( 3 \frac{1}{2} \)
\( c \)
\( D \cdot 1 \)


The areal velocity and the angular momentum of the planet are related by which of the following relations?
(where \( m_{p} \) is the mass of the planet)
A \( \cdot \frac{\Delta \bar{A}}{\Delta t}=\frac{\bar{L}}{2 m_{p}} \)
B \( \cdot \frac{\Delta \bar{A}}{\Delta t}=\frac{\bar{L}}{m_{p}} \)
\( \mathbf{C} \cdot \underset{\Delta t}{\frac{\Delta \bar{A}}{\Delta t}}=\frac{2 \bar{L}}{m_{p}} \)
D. \( \frac{\Delta \bar{A}}{\Delta t}=\frac{\bar{L}}{\sqrt{2 m_{p}}} \)


A force can be applied only when it is in contact with an object. Which of the following is the category of this type of force?
A. Magnetic force
B. contact force
c. Non-contact force
D. Muscular force


The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})= \)
\( x^{2}, \forall x \in R \) is
A. Injection but not surjection
B. Surjection but not injection
c. Injection as well as surjection
D. Neither injection nor surjection


Azeotropic mixtures are:
A. mixture of two solids
B. those which boil at different temperatures
C. those which can be fractionally distilled
D. constant boiling mixtures


1.575 gm of an organic acid was dissolved in \( 250 \mathrm{ml} \) of water. Further, 20 \( \mathrm{ml} \) of this solution required \( 16 \mathrm{ml} \) of \( \frac{N}{8} \) alkali solution for complete neutralisation. If the basicity of the acid
is \( 2, \) find its molecular mass.


Addition to an alkyne is a:
A. three stage process
B. two stage process
C . single stage process
D. none of above


If \( 3^{x+y}=81 \) and \( 81^{x-y}=3^{8}, \) then find
the values ofx and y respectively.
\( A \cdot 3,1 \)
B. 1,3
\( c \cdot-1,3 \)
D. -1,-3


Solve: \( x-3(2+x)>2(3 x-1) \)


Decrease in the pressure for the
following equilibrium: \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(l) \) result in the:
A . formation of more \( H_{2} O(s) \)
B. formation of more \( H_{2} O(l) \)
C . increase in melting point of \( H_{2} O(s) \)
D. decrease in melting point of \( H_{2} O(s) \)


If \( t \) is a parameter,then \( \boldsymbol{x}=\boldsymbol{a}\left(\boldsymbol{t}+\frac{\mathbf{1}}{\boldsymbol{t}}\right) \)
and \( y=b\left(t-\frac{1}{t}\right) \) represent
A. An ellipse
B. A circle
c. A pair of straight lines
D. A hyperbola


In Lassigne's test for nitrogen in an organic compound, the blue colouration is due to the formation of:
A. ferro ferricyanide
B. ferric ferrocyanide
c. ferric cyanide
D. ferrocyanide


Nodal planes of \( \pi \) -bonds \( (\mathrm{s}) \) in \( \boldsymbol{C} \boldsymbol{H}_{2}= \)
\( C=C=C H_{2} \) are located in:
A. all are in molecular plane
B. perpendicular plane which contains \( C-C \sigma \) -bond
c. one in molecular plane and two in a plane perpendicular to molecular plane which contains \( C \) \( C \sigma \) -bonds
D. two in molecular plane and one in a plane perpendicular to molecular plane which bisects \( C-C \) \( \sigma \) -bonds at right angle


Assertion
Electron affinity value of \( C l^{-} \) has negative value.
Reason
Electron affinity values of all uninegative ions are negative.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A mixture of iodine and sand are
separated by method of


Fill in the blank:
If the system has infinite number of solutions, then the equations are said
to be
A. Consistent
B. Inconsistent
c. Dependent
D. Independent


Solve:
\( \boldsymbol{x}^{e}+\boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{e}^{\boldsymbol{e}} \)


Figure shows a meter bridge (which is nothing but a practical Wheatstone bridge), consisting of two resistors \( X \)
and Y together in parallel with a meter long constantan wire of uniform cross
section. Which the help of a movable
contact \( \mathrm{D} \), one can change the ratio of resistance of the two segments of the
wire until a sensitive galvanometer \( G \)
connected across B and D shows no
deflection. The null point is found to be a distance of \( 33.7 \mathrm{cm} . \) The resistor Y is
shunted by a resistance of \( 12 \omega, \) and the null point is found to shift by a distance of \( 18.2 \mathrm{cm} . \) Determine the approximate resistance of \( X \) and \( Y \) in ohm.


The paramagnetic lanthanoid ion among the following is:
A \( \cdot C e^{4} \)
в. \( Y b^{2} \)
c. \( L u^{3} \)
D. \( S m^{2+} \)


Which of the following is true regarding the function \( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{x}^{4} \sin \frac{\boldsymbol{x}}{\boldsymbol{y}} ? \)
A. Not homogenous
B. Homogenous with degree 2
c. Homogenous with degree 3
D. None of the above


Probability cannot be expressed in
A. fraction form
B. ratio form
c. negative form
D. percentage form


Which is not characteristic of \( \pi \) -bond?
A. \( \pi \) - bond is formed when a sigma bond already formed
B. \( \pi \) - bond are formed from hybrid orbitals
C \( . \pi \) - bond may be formed by the overlapping of \( p \) orbitals
D. \( \pi \) - bond results from lateral overlap of atomic orbitals


Which transition in hydrogen spectrum
would have same wavelength as that in
\( H e^{+} \) ion for \( n=4 \) to \( n=2 \) transition?


David is observing his image in a plane mirror. The distance between the mirror
and his image is \( 4 \mathrm{m} \). If he moves \( 1 \mathrm{m} \) towards the mirror, then the distance between David and his image will be:
\( A \cdot 3 m \)
B. \( 5 \mathrm{m} \)
\( c \cdot 6 m \)
D. 8 m


If \( A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right], \) then \( \operatorname{det}\left(A+A^{2}+\right. \)
\( \left.\boldsymbol{A}^{3}+\boldsymbol{A}^{4}+\boldsymbol{A}^{5}\right) \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 32
c. 25
D. 30


Statement-1: In the fermentation
process of molasses, along with yeast,
\( \left(N H_{4}\right)_{2} S O_{4} \) and \( \left(N H_{4}\right)_{3} P O_{4} \) are
added.
Statement-2: Both \( \left(N H_{4}\right)_{3} P O_{4} \) and
\( \left(N H_{4}\right)_{2} S O_{4} \) act as food and help in the
growth of yeast.
A. Statement-1 is True, statement-2 is True; statementis a correct explanation for statement-
B. Statement-1 is True, statement-2 is True; statementis NOT a correct explanation for statement-
c. Statement- - is True, statement-2 is False
D. Statement- 1 is False, statement- 2 is True


A drop of water detaches itself from the
exit of a tap when \( (\sigma= \) surface tension
of water. \( \rho= \) density of water, \( \boldsymbol{R}= \)
radius of the tap exit, \( r= \) radius of the
drop)
\( r>\left(\frac{2 R \sigma}{3 \rho g}\right)^{1 / 3} \)
В. \( \quad r>\frac{2}{3} \frac{\sigma}{\rho g} \)
\( ^{\mathrm{C}} \cdot \frac{2 \sigma}{r}> \) atmospheric pressure
\( r>\left(\frac{2 R \sigma}{3 \rho g}\right)^{2 / 3} \)
E. None of the above


The nucleus finally formed in fusion of
the proton in a proton cycle is that of:
A. Helium
B. Deuterium
c. carbon
D. Hydrogen


Compounds which contain oxides of carbon or carbonate hydrogencarbonate ions are called:
A. Hydrocarbons
B. Organic compounds
c. Inorganic compounds
D. Carbohydrogens


Consider the following reaction, Ethanol \( \stackrel{P B r_{3}}{\longrightarrow} X \stackrel{\text {alc. } K O H}{\longrightarrow} \)
\( \boldsymbol{Y} \frac{(i) \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \text { room temperature }}{(i i) \boldsymbol{H}_{2} \boldsymbol{O}, \text { heat }} \boldsymbol{Z} \)
Product \( Z \) is:
\( \mathbf{A} \cdot C H_{2}=C H_{2} \)
в. \( C H_{3} C H_{2}-O-C H_{2}-C H_{3} \)
c. \( C H_{3} C H_{2}-O-S O_{3} H \)
D. \( C H_{3} C H_{2} \) О \( H \)


Which of the following statement(s) is/are true?
i. Adding a solute raises the
vapor pressure \& boiling point.
ii. The change in boiling \& freezing point depends on molality.
iii. The number of solute particles in
a solvent is an important factor
in determining the boiling point
elevation.
A. i only
B. ii only
c. i and ii
D. ii and iii
E. i, ii and iii


Calculate change in internal energy if \( \triangle H=-92.2 k J, P=40 a t m \) and
\( \triangle V=-1 L \)
A . -42 kJ
B. -88kJ
\( c \cdot+88 k J \)
D. +42 kJ


On the set of all integers defined as \( \boldsymbol{f} \)
\( Z \rightarrow Z \) such that \( f(x)=[x], \) then it is:
\( A \cdot \) not a function
B. a many-to-one function
c. an into function
D. an identity function


What is 'Rain Water Harvesting'? Write its main objectives.(Any two)


If a planet were suddenly stopped in its orbit supposed to be circular, show that it would fall into the sun in a time \( \boldsymbol{T} \times \) \( \left(\frac{\sqrt{2}}{8}\right), \) where \( T \) is the time period of revolution.


The oxidation state of Chlorine in
Bleaching Powder:
\( A \cdot-2 \)
B . - -
\( c \cdot+1 \)
D. -1 and +1


Explain : When \( M n(O H)_{2} \) is made by adding an alkali to a solution
containing \( M n^{2+} \) ions, the ppt quickly darkens, and eventually goes black
A. The black colour is due to the manganese (VI) oxide \( M n_{2} O_{3} \)
B. The black colour is due to the manganese (VI) oxide \( M n O_{2} \)
C. The black colour is due to the manganese (VI) oxide \( M n_{2} O_{5} \)
D. None of these


\( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C} ; \boldsymbol{\Delta} \boldsymbol{H}=+\boldsymbol{6} \boldsymbol{0} \boldsymbol{K} \boldsymbol{J} / \boldsymbol{m o l} \)
\( \boldsymbol{E}_{\boldsymbol{a} t} \) is \( 150 \mathrm{kj} . \) What is the activation energy for the backward reation?
A . 210 k.
B. 105kJ
c. 90 k
D. 145kJ


A universal indicator is made by
dissolving methyl orange, bromothymol blue and phenolphthalein in alcohol. Which of the following processes could best be used to separate the methyl orange component from the universal
indicator solution?
A. Chromatography
B. Filtration
c. Distillation
D. Decantation


A solid disk is rolling without slipping on a level surface at a constant speed of
\( 2.00 m / s . \) How far can it roll up a \( 30^{\circ} \)
ramp before it stops? (Take \( \boldsymbol{g}= \)
\( \left.9.8 m / s^{2}\right) \)


The following table draws the income of finance of a grape season find the mean of their income.
ıncome \( \begin{array}{lll}\mathbf{2 0}- & \mathbf{3 0}- & \mathbf{4 0}- \\ \mathbf{3 0} & \mathbf{4 0} & \mathbf{5 0}\end{array} \) \( - \) (thousand
Rs)
Farmer 10


Aluminium foils are used for:
A. wrapping chocolates and food stuff
B. to prepare hydrogen
\( c \cdot \operatorname{both} A \) and \( B \)
D. none of these


When the free ends of a tester are
dipped into a solution, the magnetic needle shows deflection. Can you
explain the reason?


A horizontal uniform glass tube of \( 100 \mathrm{cm} \) length is sealed at both ends contains 10 \( \mathrm{cm} \) mercury column in the middle the
temperature and pressure of air on either side of mercury column are respectively \( 31^{0} \mathrm{C} \) and \( 76 \mathrm{cm} \) of mercury if the air
column at one end is kept at \( 0^{0} \mathrm{C} \) and the other end at \( 273^{0} \mathrm{C} \) the pressure of
air which is at \( 0^{0} \mathrm{C} \) is (in \( \mathrm{cm} \) of \( \mathrm{Hg} \) )
A. 76
B. 88.2
c. 102.4
D. 122


The rate of chemisorption:
A. decreases with increase of pressure
B. increases with increase of pressure
C. is independent of pressure
D. is independent of temperature


Find \( \frac{\boldsymbol{x}+\boldsymbol{u}+\boldsymbol{y}+\boldsymbol{z}}{\mathbf{5 0}} \)


\( A \) and \( B \) have 460 coins altogether. If \( \frac{3}{4} \) of \( A^{\prime} \) s number of coins is equal to \( \frac{2}{5} \) of
B's number of coins, find how many
coins must \( B \) give to \( A, \) so that they
both have equal number of coins.
A . 50
B. 70
c. 20
D. 90


If \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x}) \) for \( \boldsymbol{a} \leq \boldsymbol{x} \leq \boldsymbol{b}, \) then
\( \int_{a}^{b} f(x) g(x) d x \) equals to:
A. \( f(2)-f(1) \)
В. \( g(2)-g(1) \)
c. \( \frac{[f(b)]^{2}-[f(a)]^{2}}{2} \)
D. \( \frac{[g(b)]^{2}-[g(a)]^{2}}{2} \)


Describe the digestive system of
cockroach.


The electron in a hydrogen atom makes
a transition \( n_{1} \rightarrow n_{2}, \) where \( n_{1} \) and \( n_{2} \)
are the principal quantum numbers of the two states. Assume the Bohr model
as valid in this case. The frequency of the orbital motion of the electron in the
initial state is \( 1 / 27 \) of that in the final
state. The possible values of \( n_{1} \) and \( n_{2} \)
are
A \( \cdot n_{1}=6, n_{2}=3 \)
в. \( n_{1}=4, n_{2}=2 \)
c. \( n_{1}=8, n_{2}=1 \)
D. \( n_{1}=3, n_{2}=1 \)


Solve :
\( \int_{1}^{2} \frac{x}{(x+1)(x+2)} d x \)


Hydrogen gas will reduce:
A. hot cupric oxide
B. hot ferric oxide
c. hot stanic oxide
D. hot aluminium oxide


Derive relation between Kinetic Energy and Momentum


The total number of compounds having at least one bridging oxo group among the molecules given below is:
\( N_{2} O_{3}, N_{2} O_{5}, P_{4} O_{6}, P_{4} O_{7}, H_{4} P_{2} O_{5}, H_{5} P \)


In an entrance test is graded on the basis of two examinations, the
probability of a randomly chosen
student passing the first examination
is 0.8 and the probability of passing the second examination is 0.7 . The
probability of passing at least of them is \( 0.95 . \) What is the probability of passing both?


\( P, Q \) and \( R \) are three sets and \( \xi=P \cup \)
\( Q \cup R \) Given that \( n(\xi)=60, n(P \cap \)
\( Q)=5, n(Q \cap R)=10, n(P)=20 \) and
\( \boldsymbol{n}(\boldsymbol{Q})=23, \) find \( \boldsymbol{n}(\boldsymbol{P} \cup \boldsymbol{R}) \)
A . 37
B . 38
c. 45
D. 52


The middle term in the expansion of \( \left(1-3 x+3 x^{2}-x^{3}\right)^{2 n} \) is
\( \mathbf{A} \cdot 6 n_{C_{3 n}}(-x)^{3 n} \)
B . \( 6 n_{C_{2 \text { n }}}(-x)^{2 n+1} \)
\( \mathbf{c} \cdot 4 n_{C_{S n}}(-x)^{3 n} \)
D. \( 6 n_{C_{3 n}}(-x)^{3 n-1} \)


One gram of charcoal adsorbs \( 400 \mathrm{mL} \) of
\( 0.5 M \) acetic acid to form a monolayer,
and the molarity of acetic acid reduces
to \( 0.49 M . \) Calculate the surface area of
charcoal adsorbed by each molecule of acetic acid, where the surface area of
charcoal is \( 3.01 \times 10^{2} \mathrm{m}^{2} \mathrm{g}^{-1} \)
A. \( 1 \times 10^{-19} \mathrm{m}^{2} \)
В. \( 1.2 \times 10^{-19} \mathrm{m}^{2} \)
D. None of these


The volume of \( 1 m^{3} \) of gas is doubled at
atmospheric pressure. The work done at
constant pressure will be
\( A \cdot 0 \)
B . \( 10^{5} \) call
\( \mathbf{c} \cdot 10^{5} J \)
D. \( 10^{5} \) erg


What is the role of following chemicals in food?
¡) Saccharin
ii) Sodium benzoate


The differential equation of all conics
whose axes coincide with the co-
ordinate axes, is
A \( . x y y_{2}+x y_{1}^{2}-y y_{1}=0 \)
B . \( y y_{2}+y_{1}^{2}-y y_{1}=0 \)
c. \( x y y_{2}+(x-y) y_{1}=0 \)
D. \( \left(y y_{1}\right)^{2}-x y_{1}-y x=0 \)


The blocks are attached by an in extensible light string and pulled vertically upward by force \( 100 \mathrm{N} \) as shown. Find the common acceleration
and tension the string.


When there is a decrease in the
concentration of oxygen in the blood,
the rate of breathing
A. Does not change
B. Increases
c. Decreases
D. Increases or decreases depending on the density of blood


All floral leaves are placed on the
of flower.
A. Thalamus
B. Petal
c. Sepal
D. Ovule


If the EMF of a cell :
\( \boldsymbol{M}\left|\boldsymbol{M}^{2+}(\mathbf{0 . 0 2} \boldsymbol{M}) \| \boldsymbol{H}^{+}(\mathbf{0 . 1} \boldsymbol{M})\right| \boldsymbol{H}_{2} \)
\( a t m) \)
at \( 25^{\circ} \mathrm{C} \) is \( 0.81 \mathrm{V} \). Find the standard
reduction potential of \( M \)
(Write a value to the nearest integer. If an answer is negative then write its
magnitude)


Choose the correct option which describe the simple harmonic motion.
I. The acceleration is constant.
II. The restoring force is proportional to the displacement
III. The frequency is independent of the
amplitude.
A. Il only
B. I and II only
c. I and III only
D. Il and III only
E. I, II and III


The preparation of sodium benzenesulphonate during the preparation of benzene sulphonic acid
involves:
A. dehydration
B. hydrolysis
c. hydration
D. sulfonation


The angle of incidence is given by the
angle :
A. PON
B. QOB
c. NOQ
D. AOP


Water formed is tested by :
A. Copper nitrate test
B. Anhydrous copper sulphate test
c. Aqueous copper sulphate test
D. copper