Find the equation of the plane through the line
\( \boldsymbol{P}=\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c} \boldsymbol{z}+\boldsymbol{d}=\mathbf{0} \)
\( \boldsymbol{Q}=\boldsymbol{a}^{\prime} \boldsymbol{x}+\boldsymbol{b}^{\prime} \boldsymbol{y}+\boldsymbol{c}^{\prime} \boldsymbol{z}+\boldsymbol{d}^{\prime}=\mathbf{0} \)
and parallel to the line \( \frac{x}{l}=\frac{y}{m}=\frac{z}{n} \)
A \( \cdot P\left(a^{\prime} l+b^{\prime} m+c^{\prime} n\right)+Q(a l+b m+c n)=0 \)
B - \( P\left(a^{\prime} l+b^{\prime} m+c^{\prime} n\right)-Q(a l+b m+c n)=0 \)
c. \( Q\left(a^{\prime} l+b^{\prime} m+c^{\prime} n\right)-P(a l+b m+c n)=0 \)
D. \( Q\left(a^{\prime} l+b^{\prime} m+c^{\prime} n\right)+P(a l+b m+c n)=0 \)


The pairs of species of oxygen and their magnetic behaviours are noted below. Which of the following presents the correct description?
A \( \cdot O, O_{2}^{2-} \) - Both paramagnetic
B. \( O_{2}^{-}, O_{2}^{2-} \) - Both diamagnetic
C. \( O^{+}, O_{2}^{2-} \) - Both paramagnetic
D. \( O_{2}^{+}, O_{2} \) - Both paramagnetic


In R-L-C series circuit, the potential differences across each element is \( 20 V \)
Now the value of the resistance alone is
doubled, then P.D. across \( \mathrm{R} \), L and \( \mathrm{C} \)
respectively.
A. \( 20 V, 10 V, 10 V \)
В. \( 20 V, 20 V, 20 V \)
c. \( 20 V, 40 V, 40 V \)
D. \( 10 V, 20 V, 20 V \)


The \( X \) and \( Y \) components of a
displacement vector are (15,7)\( m \). Find the magnitude and direction of \( \vec{A} \)


Storage roots found in clusters at base
of stem are
A. Nodulose roots
B. Annulated roots
c. Tuberous roots
D. Fasciculated roots
E. Moniliform roots


If \( x^{2}+y^{2}+10=(2 \sqrt{2 x}+4 \sqrt{2} y) \) then
the value of \( (x+y) \) is
A \( .4 \sqrt{2} \)
B. \( 3 \sqrt{2} \)
\( c \cdot 6 \sqrt{2} \)
D. \( 9 \sqrt{2} \)


Marshall's acid is:
\( \mathbf{A} \cdot H_{2} S O_{5} \)
\( \mathbf{B} \cdot H_{2} S_{2} O_{7} \)
\( \mathbf{c} \cdot H_{2} S_{2} O_{3} \)
D. \( H_{2} S_{2} O_{8} \)


The coordinates of the point \( P(x, y) \) which divides the line segment joining the points \( \boldsymbol{A}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right) \) and \( \boldsymbol{B}\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}\right) \)
internally in the ratio \( m_{1}: m_{2} \) are
\( \left(\frac{m_{1} x_{2}-m_{2} x_{1}}{m_{1}+m_{2} 1}, \frac{m_{1} y_{2}-m_{2} y_{1}}{m_{1}+m_{2}}\right) \)
A . True
B. False
c. Ambiguous
D. Data insufficient


Which group belong to the same distinct class?
A. Sterols, Waxes, Amino acids, Starch
B. Lipids, RNA, Glycine, Cellulose
c. DNA, RNA, Nucleosides, Nucleotides
D. Ribose, sucrose, Glucose, Maltose


Which of the following is not an equivalence relation on \( Z \) ?
A \( . a R b \Leftrightarrow a+b \) is an even integer
B. \( a R b \Leftrightarrow a-b \) is an even integer
\( c \cdot a R b \Leftrightarrow a<b \)
D. \( a R b \Leftrightarrow a=b \)


Suppose 2 kg of sugar contains 9106
crystals. How many sugar crystals are there in (i) 5 kg of sugar?
(ii) \( 1.2 \mathrm{kg} \) of
sugar?


\( \tan \theta=-2, \theta \epsilon(0, \pi) \) then which of the
following is correct
This question has multiple correct options
A \( \cdot \sin \theta=\frac{-2}{\sqrt{5}} \)
B. \( \sin \theta=\frac{2}{\sqrt{5}} \)
\( ^{\mathrm{C}} \cdot \cos \theta=\frac{-1}{\sqrt{5}} \)
D. \( \cos \theta=\frac{1}{\sqrt{5}} \)


A hemispherical glass body of radius 10 \( c m \) and refractive index 1.5 is silvered
on its curved surface. A small air bubble
is \( 6 \mathrm{cm} \) below the flat surface inside it
along the axis. The position of the
image of the air bubble made by the mirror is seen:
A. \( 14 \mathrm{cm} \) below flat surface
B. 20 \( c m \) below flat surface
c. \( 16 \mathrm{cm} \) below flat surface
D. \( 30 \mathrm{cm} \) below flat surface


The graph above shows the number of
units sold in 2015 for five different
video games console. The price of
consoles \( A, B, C, D, \) and \( E \) are \( \$ 100, \) \( \$ 150, \$ 200, \$ 250, \) and \( \$ 300 \)
respectively. Which of the five consoles generated the most total revenue?
A . \( A \)
в. \( B \)
\( c . D \)
\( D \)


If \( S_{1}, S_{2} \) and \( S_{3} \) are the sum of first
\( \boldsymbol{n}, \mathbf{2 n} \) and \( \mathbf{3 n} \) terms of a geometric series respectively, then prove that \( \boldsymbol{S}_{1}\left(\boldsymbol{S}_{3}-\boldsymbol{S}_{2}\right)=\left(\boldsymbol{S}_{2}-\boldsymbol{S}_{1}\right)^{2} \)


Calculate the volume of a cylinder
where the area of a base is \( 40 \mathrm{mm}^{2} \) and
height is \( 4.5 \mathrm{mm} \)
A \( \cdot 180 \mathrm{cm}^{3} \)
В. \( 181 \mathrm{mm}^{3} \)
\( \mathbf{c} \cdot 180 m m^{3} \)
D. \( 180.4 \mathrm{mm}^{3} \)


The blocks are connected as shown in
figure on a horizontal frictionless table.
if \( \boldsymbol{m}_{1}=\mathbf{1} \mathbf{k g} \boldsymbol{m}_{2}=\mathbf{8} \mathbf{k g} \boldsymbol{m}_{3}=\mathbf{2 7 k g} \) and
\( \boldsymbol{T}_{3}=\boldsymbol{6} \boldsymbol{4} \boldsymbol{N}, \boldsymbol{T}_{2} \)
\( A \cdot 18 N \)
в. 9 N
c. 3. 375 N
D. 1.75 N


The vapours of which of the following compound burns with green coloured flame?
A. \( C H C l_{3} \)
в. \( C H_{3} C O C H_{3} \)
c \( \cdot C_{2} H_{5} O H \)
D. \( C H_{3} C H O \)


Select the correct option:
Identify \( A, B \) and \( C \) in the given reaction of lactic acid fermentation and select
the correct option. Pyruvic acid \( + \) Lactate deh
\( \boldsymbol{A}_{\boldsymbol{F} \boldsymbol{M} \boldsymbol{N}, \boldsymbol{Z} \boldsymbol{n}^{2+}}^{\text {and }} \boldsymbol{B}+\boldsymbol{C} \)
A \( \cdot \) A-NADH ; B- Lactic acid \( +C O_{2} ; \) C- \( N A D^{+} \)
B. A-NADH; B-Lactic acid ; C- \( N A D^{+} \)
c. \( A-N A D^{+} ; \) B- Lactic acid \( ; \) C- NADH
D. A-NAD'; B-Lactic acid + \( C O_{2} ; \) C-NADH


If \( \tan \theta=\frac{3}{4} \) Find \( 3 \cos A+4 \sin A \)


a) An organic compound (A) of
molecular formula \( C_{7} H_{6} O \) is not reduced by fehling's solution but will undergo cannizaro reaction. Compound
(A) reacts with aniline to give compound (B)
compound
(A) also reacts with \( C l_{2} \) in
the absence of catalyst to give compound
(C). Identify \( A, B \) and \( C \) and explain the reactions.
b) The \( K_{a} \) of propanoic acid is \( 1.34 \times \)
\( 10^{-5} . \) What is the \( p H \) of a solution
containing 0.5M propanoic acid and 0.5M sodium propanoate?


Radius of the circular garden is
9.1 metre. What is the \( \operatorname{cost}(\text { in } R s) \) of
preparing lawn in it at the rate of Rs.100 per 1 sq metre? \( \left(\pi=\frac{22}{7}\right) \)


A sinusoidal voltage \( V=200 \sin 314 t \) is
applied to a \( 10 \Omega \) resistor. Find the frequency of the supply.
\( \mathbf{A} \cdot 40 H z \)
B. \( 50 \mathrm{Hz} \)
\( \mathbf{c} \cdot 60 H z \)
D. \( 80 H z \)


The ratio of turns in the transformer is
given as \( 2: 3 . \) If the current passing through the primary coil is 3 A. Find the current through the load resistance:
A. \( 4.5 \mathrm{A} \)
B. 1.5 A
\( c \cdot 2 A \)
D. 1 A


The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal:
\( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}(\boldsymbol{s})+\boldsymbol{3} \boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{F} \boldsymbol{e}(\boldsymbol{l})+ \)
\( \mathbf{3} C O_{2}(\boldsymbol{g}) \)
Using Le Chatelier's principle, predict which one of the following will not disturb the equilibrium?
A. Removal of \( C O_{2} \)
B. Removal of \( C O \)
\( c . \) Addition of \( C O_{2} \)
D. Addition of \( F e_{2} O_{3} \)


The balloon like outgrowths of parenchyma in the lumen of a vessel are known as
A. Histogen
B. Tyloses
c. Phellogen
D. Tunica


Assertion
Let \( \boldsymbol{f}:(\boldsymbol{e}, \infty) \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \log (\log (\log x)) \) is invertible.
Reason
\( f \) is both one-one and onto.
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


An electron, \( \alpha \) - particle and a proton
have the same kinetic energy. A comparison of their de Broglie wavelengths yields:
A \( \cdot \lambda_{p}>\lambda_{a}<\lambda_{c} \)
B . \( \lambda_{e}>\lambda_{a}<\lambda_{p} \)
c. \( \lambda_{a}<\lambda_{p}<\lambda_{e} \)
D. \( \lambda_{p}<\lambda_{e}<\lambda_{a} \)


The belt of an electrostatic generator is \( 50 \mathrm{cm} \) wide and travels at \( 30 \mathrm{cm} / \mathrm{sec} \)
The belt carries into the sphere at a rate
corresponding to \( 10^{-4} \) ampere. What is the surface density of charge on the belt.
A \( \cdot 6.7 \times 10^{-5} \mathrm{Am}^{-2} \)
В. \( 6.7 \times 10^{-4} \mathrm{Am}^{-2} \)
c. \( 6.7 \times 10^{-7} \mathrm{Am}^{-2} \)
D. \( 6.7 \times 10^{-8} \mathrm{Am}^{-2} \)


In a meter bridge experiment, the null point is obtained at \( 20 \mathrm{cm} \) from one end of the wire when resistance \( \boldsymbol{X} \) is
balanced against another resistance \( Y \)
If \( X<Y \), then where will the new position of the null point be from the
same end, if one decides to balance a
resistance of \( 4 X \) against \( Y ? \)
\( \mathbf{A} \cdot 40 \mathrm{cm} \)
в. \( 80 \mathrm{cm} \)
\( c .50 \mathrm{cm} \)
D. \( 70 \mathrm{cm} \)


Which of the following salt will form a basic solution upon hydrolysis?
A. \( N a C_{2} H_{3} O_{2} \)
в. \( H C_{2} H_{3} O_{2} \)
c. \( K C l \)
D. \( N H_{3} \)
E . \( H C l \)


If \( F \) is force and \( r \) is radius, then torque
is :
\( \mathbf{A} \cdot \vec{r} \times \vec{F} \)
В. \( \vec{r} \vec{F} \)
c. \( |r||F| \)
D. r/F


In pyrophosphoric acid, \( \boldsymbol{H}_{\mathbf{4}} \boldsymbol{P}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{7}} \)
number of \( \sigma- \) and \( d \pi-p \pi \) bonds
respectively are
A. 8 and 2
B. 6 and 2
c. 12 and zero
D. 12 and 2


A particle goes from \( A \) to \( B \) with a speed of \( 40 \mathrm{km} / \mathrm{h} \) and \( \mathrm{B} \) to \( \mathrm{C} \) with a speed of 60 \( \mathrm{km} / \mathrm{h} \). If \( \mathrm{AB}=6 \mathrm{BC} \), the average speed in km/h between \( A \) and \( C \) is
A. \( 42 \mathrm{km} / \mathrm{h} \)
B. 50km/h
c. \( 60 \mathrm{km} / \mathrm{h} \)
D. \( 40 \mathrm{km} / \mathrm{h} \)


\( 1 \mathrm{kg} \) of iron (specific heat \( 120 \mathrm{Cal} \mathrm{kg}^{-1} \mathrm{C} \)
-1 ) is heated by \( 1000^{\circ} \mathrm{C} \). The increase in
its mass is :
A. zero
B . \( 5.6 \times 10^{-8} \mathrm{kg} \)
\( \mathbf{c} \cdot 5.6 \times 10^{-16} \mathrm{Kg} \)
D. \( 5.6 \times 10^{-12} \mathrm{g} \)


Which is the most ductile metal known?
A. Silver
B. Platinum
c. Gold
D. copper


The resistance of the platinum wire of a platinum resistance thermometer at the ice point is \( 5 \Omega \) and at steam point
is \( 5.39 \Omega . \) When the thermometer is
inserted in a hot bath, the resistance of
the platinum wire is \( 5.795 \Omega . \) Calculate the temperature of the bath.


Most readily hydrolised halide is:
\( \mathbf{A} \cdot C_{6} H_{5} C l \)
В \( \cdot\left(C_{6} H_{5}\right)_{2} C H C l \)
c. \( C_{6} H_{5} C H_{2} C l \)
D \( \cdot\left(C_{6} H_{5}\right)_{3} C C l \)


Consider the following statements:
\( S_{1}: \lim _{x \rightarrow 0^{-}} \frac{[x]}{x} \) is an indeterminate from
(where [] denotes greatest integer function).
\( \boldsymbol{S}_{2}: \lim _{x \rightarrow \infty} \frac{\sin \left(3^{x}\right)}{3^{x}}=0 \)
\( S_{3}: \lim _{x \rightarrow \infty} \sqrt{\frac{x-\sin x}{x+\cos ^{2} x}} \) does not exist.
\( \boldsymbol{S}_{4} \)
\( \lim _{n \rightarrow \infty} \frac{(n+2) !+(n+1) !}{(n+3) !}(n \in N)=0 \)
Which of the statements \( S_{1}, S_{2}, S_{3}, S_{4} \)
are true or false:
A. \( F T F T \)
в. \( F T T T \)
c. \( F T F F \)
D. \( T T F T \)


The gravitational potential difference between the surface of a planet and a point \( 20 m \) above it is \( 16 J / k g . \) Then the
work done in moving a 2 kg mass by
\( 8 m \) on a slope 60 degree from the
horizontal, is:
A . \( 11.1 \mathrm{J} \)
B. \( 5.5 J \)
\( c .16 J \)
D. 27.7 J


The lightest radioactive isotope in periodic table is:
A. tritium
B. deuterium
c. protium
D. none of these


Select suitable name for the process
\( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+2 \mathrm{ADP}+\mathrm{Pi} 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+\mathrm{CO}_{2}+ \)
2ATP
A. Photorespiration.
B. Lactate fermentation
c. Aerobic respiration
D. Alcoholic fermentation


The cathode rays tube experiments
carried out by J.J. Thomson
demonstrated that:
A. ratio of charge to-mass for the particles of the cathode rays varies as different gases are placed in the tube
B. the mass of an atom is essentially all contained in its very small nucleus.
C. cathode rays are streams of negatively charged ions.
D. the charge-to-mass ratio for an electron is same for all gases.


Charge \( q \) is uniformly spread on a thin
ring of radius \( R \). The ring rotates about its axis with a uniform frequency \( \boldsymbol{f} \boldsymbol{H} \boldsymbol{z} \) The magnitude of magnetic induction at the centre of the ring is
A \( \cdot \frac{\mu_{0} q f}{2 R} \)
в. \( \frac{\mu_{0} q}{2 f R} \)
c. \( \frac{\mu_{0} q}{2 \pi f R} \)
D. \( \frac{\mu_{0} q f}{2 \pi R} \)


If \( A D, B E \) and \( C F \) are the medians of \( \angle \)
ABC, then which one of the following
statements is
correct?
\( \mathbf{A} \cdot(A D+B E+C F)=(A B+B C+C D) \)
B \( \cdot(A D+B E+C D)>\frac{3}{4}(A B+B C+C A) \)
\( \mathbf{c} \cdot(A D+B E+C F)>\frac{3}{4}(A B+B C+C A) \)
D. \( (A D+B E+C F)=\frac{1}{2}(A B+B C+C A) \)


If each element of a second order
determinant is either zero or one, what
is the probability that the value of the determinant is positive? (Assume that the individual entries of the
determinant are chosen independently,
each value being assumed with probability \( \left.\frac{1}{2}\right) \)


The are of cross-section of steel wire is
\( 0.1 \mathrm{cm}^{2} \) and Young's modulus of steel is
\( 2 \times 10^{11} N \quad m^{-2} . \) The force required to
stretch by \( 0.1 \% \) of tis length is then
A . \( 1000 N \)
в. 2000N
c. \( 4000 N \)
D. \( 5000 N \)


A gold leaf electroscope is given a positive charge so that its leaves diverge. How is the divergence of leaves affected, when a glass rod rubbed with
silk is rolled on the disc of
electroscope?
A. divergence increases
B. divergence decreases
c. divergence remains same
D. can't say


The diode used in the circuit shown
below has a constant voltage drop of
\( 0.6 V \) at all currents and a maximum
power rating of 300 milli watt. What
should be the value of the resistance \( \boldsymbol{R} \)
if maximum current passes through the diode?
A . \( 4 \Omega \)
B . \( 2 \Omega \)
\( c .1 \Omega \)
D. \( 32 \Omega \)


Which of the following facts about the complex \( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \) is wrong?
A. The complex involves \( d^{2} s p^{3} \) hybridisation and is octahedral in shape
B. The complex is paramagnetic
c. The complex is an outer orbital complex.
D. The complex gives white precipitate with silver nitrate solution.


A man tries to remain in equilibrium,
This question has multiple correct options
A. he must exert equal forces on the two walls
B. the forces of friction at the two walls must be equal.
C. friction must be present on both walls
D. the coefficients of friction must be the same between
both walls and the man


Q Type your question.
surrounded by an incompressible liquid in a cylindrical container. A massless
piston of area \( A \) floats on the surface of
the liquid. The magnitude of fractional change in the radius of the sphere \( \left(\frac{d R}{R}\right) \) when a mass \( M \) is placed slowly on the
piston to compress the liquid is:
\( ^{\mathrm{A}} \cdot \frac{M g}{3 A B} \)
в. \( \frac{M g}{A B} \)
c. \( \frac{3 M g}{A B} \)
D. none of thes


A car moving with speed of \( 40 \mathrm{km} / \mathrm{hr} \) can be stopped by applying brakes after at least \( 2 m \). If the same car is moving
with a speed of \( 80 \mathrm{km} / \mathrm{hr} \) what is the minimum stopping distance?
A \( .2 m \)
в. \( 4 m \)
\( c .6 m \)
D. \( 8 m \)


Evaluate: \( \lim _{x \rightarrow 1} \frac{x^{\frac{-2}{3}}-1}{x^{\frac{-3}{4}}-1} \)
A \( \cdot \frac{5}{9} \)
B. \( \frac{9}{5} \)
\( c \cdot \frac{8}{9} \)
\( D \)


Assertion
Vibrational energy of diatomic molecule corresponding to each degree of
freedom is \( k_{B} T \)
Reason
For every molecule, vibrational degree of freedom is 2
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which one of the following is a nonpathogenic bacteria of human intestines?
A. Mycobacterium sp.
B. Escherichia coli
c. Entamoeba coli
D. Balantidium coli


Assertion: Chloroform vapours burn
with a green flame. Reason: Chloroform is green coloured liquid.
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Convert into fraction :-
\( 52 \% \)


Lymph differs from blood in having
\( A \). No WBCs
B. No proteins
c. No RBCs
D. None of the above


Which of the following statements is
wrong?
A. Sound travels in straight line
B. Sound travels as waves
C. Sound is a form of energy
D. Sound travels faster in vacuum than in air


f current through the conductor Y is reversed in direction, will neutral point lie between \( X \) and \( Y \), to the left of \( X \) or to
the right of Y?


Mark the wrong statement about
denaturation of proteins.
A. The primary structure of the protein does not change
B. Globular proteins are converted into fibrous proteins
C. Fibrous proteins are converted into globular proteins
D. The biological activity of the protein is destroyed


Calculate \( K_{a} \) for a dibasic acid if its
concentration is \( 0.05 N \) and hydrogen
ion concentration is \( 1 \times 10^{-3} \) mol \( L^{-1} \)


Klinostat is employed in the study of
A. Osmosis
B. Growth movements
c. Photosynthesis
D. Respiration


A rubber balloons of negligible mass is filled with \( 500 g \) of water. Its weight in water will be:
A \( .250 g \)
в. \( 500 g \)
c. zero
D. \( 100 g \)


The coefficient of linear expansion of stee and brass are \( 11 \times 10^{-6} /^{\circ} \mathrm{C} \) and \( 19 \times \)
\( 10^{-6} /^{\circ} \mathrm{C} \) respectively. If their difference in
lengths at all temperatures has to kept constant at \( 30 \mathrm{cm} \), their lengths at \( 0 \mathrm{C} \)
should be:
A. \( 71.25 \mathrm{cm} \) and \( 41.25 \mathrm{cm} \)
B. 82 cm and 52 cm
c. \( 92 \mathrm{cm} \) and \( 62 \mathrm{cm} \)
D. 62.25 cm and 32.25 cm


Which of the following set of species have same hybridisation state but different shapes?
A \( \cdot N O_{2}^{+}, N O_{2}, N O_{2} \)
в. \( C l O_{4}, S F_{4}, X e F_{4} \)
c. \( N H_{4}^{+}, H_{3} O^{+}, O F_{2} \)
D. \( S O_{4}^{2-}, P O_{4}^{3-}, C l O_{4} \)


The altitude of a parallelopiped whose three coterminous edges are the vectors, \( \overline{\boldsymbol{A}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} ; \overline{\boldsymbol{B}}=\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)
\( \& \bar{C}=\bar{i}+\bar{j}+3 \hat{k} \) with \( \bar{A} \) and \( \bar{B} \) as the
sides of the base of the parallelopiped is
A. \( 2 / \sqrt{19} \)
в. \( 4 / \sqrt{19} \)
c. \( 2 \sqrt{38} / 19 \)
\( D . \) none


Solve the inequality and show the graph
of the solution on number line:
\( \frac{x}{2} \geq \frac{(5 x-2)}{3}-\frac{(7 x-3)}{5} \)


The captain of a plane wishes to proceed due west. The cruising speed of the plane is \( 245 m / s \) relative to the air.
A weather report indicates that a
\( 38 m / s \) wind is blowing from the south to the north. In what direction, measured to due west, should the pilot
head the plane relative to the air? (in
degrees)
\( A \cdot 8 \)
B. 9
\( c .6 \)
D. 5


Fill in the blank:
A \( _{-} \) image is one which can be
obtained on a screen.
A . virtual
B. real
c. imaginary
D. None


Following table gives frequency distribution of amount of bonus paid to
the workers in a certain factory.
Bonus Below Below Below paid \( 500 \quad 600 \)
\[
700
\]
(in Rs.)
No. of 12
24
workers
Find median amount of bonus paid to
the workers.
A. 801.27 Rs.
B. 812.27 Rs.
c. 846.27 Rs.
D. 735.29 Rs.


Multiple Answer Question Which of the following position of elements have same number of valence
electrons as that of element of atomic
number 6?
This question has multiple correct options
A. Group 14 and period 3
B. Group 14 and period 4
C. Group 6 and period 4
D. Group 14 and period 6


Gases do not liquefy above the critical temperature because above critical
temperature:
A. The gaseous become ideal
B. The intermolecular attraction vanishes
C. The kinetic energy of molecules become so large that the attractive forces become unable to hold the
molecules together
D. The repulsive forces dominates in the molecules


What is the percent profit earned by the
shopkeeper on selling the articles in his
shop?
I. Labeled price of the article sold was
\( 130 \% \) of the cost price.
II. cost price of each article was \( \boldsymbol{R} \boldsymbol{s} . \mathbf{5 5 0} \).
III. A discount of \( 10 \% \) on labeled price
was offered.
A. Only I
B. Only II
c. I and III
D. All the three are required
E. Question cannot be answer even with information in all the three statements


Which one of the following is not a limiting factor for photosynthesis?
A. Oxygen
B. Carbon dioxide
c. chlorophyll
D. Light


The Cartesian equation of the plane \( \overrightarrow{\boldsymbol{r}}=(1+\boldsymbol{\lambda}-\boldsymbol{\mu}) \hat{\boldsymbol{i}}+(\boldsymbol{2}-\boldsymbol{\lambda}) \hat{\boldsymbol{j}}+(\boldsymbol{3}- \)
\( 2 \lambda+2 \mu) \hat{k} \) is-
\( \mathbf{A} \cdot 2 x+y=5 \)
В . \( 2 x-y=5 \)
c. \( 2 x+z=5 \)
D. \( 2 x-z=5 \)


Prove \( \operatorname{cosec}^{6} \boldsymbol{A}-\cos ^{6} \boldsymbol{A}= \)
\( \mathbf{3} \cot ^{2} \boldsymbol{A} \operatorname{cosec}^{2} \boldsymbol{A}+\mathbf{1} \)


Evaluate:
\( \sin ^{-1}\left(\sin \frac{5 \pi}{6}\right) \)


a conducting sphere \( A \) of radius a, with
charge \( Q, \) is placed concentrically
inside a conducting shell \( B \) of radius \( b \)
B is earthed. \( C \) is the common centre of
A and B:
This question has multiple correct options
A \( \cdot \) The field at a distance r from \( \mathrm{C} \), where \( a \leq r \leq b \), is \( k \frac{Q}{r^{2}} \)
B. The potential at a distance r from C, where \( a \leq r \leq b \), is
\( k \frac{Q}{r} \)
C. The potential difference between A and B is, \( k Q\left(\frac{1}{a}-\frac{1}{b}\right) \)
D. The potential difference between r and C, where \( a \leq \) \( r \leq b, \) is \( k Q\left(\frac{1}{a}-\frac{1}{b}\right) \)


State whether the given statement is true or false :
Friction is a necessary evil.
A. True
B. False


Name the part of the internal ear that
is concerned with the maintenance of
balance.


Nitrogen can combine directly at higher temperature to give nitrides with:
This question has multiple correct options
A. Mgg
в. А।
\( c \cdot z n \)
D. Fe


Find the \( n^{t h} \) term of the Geometric
Progression.
\( \mathbf{1 0 0},-\mathbf{1 1 0}, \mathbf{1 2 1}, \dots \)


Select the intramolecular redox
reaction(s) among the following.
This question has multiple correct options
A \( .2 K C l O_{3} \rightarrow 2 K C l+3 O_{2} \)
B. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \rightarrow N_{2}+C r_{2} O_{3}+4 H_{2} O \)
\( c \cdot C l_{2} \rightarrow C l^{-}+C l O_{3} \)
D. \( N H_{4} N O_{2} \rightarrow N_{2}+2 H_{2} O \)


Hydrogen bond is a covalent
bond.
A. stronger than
B. weaker than
c. equal in strength to
D. cannot be predicted


For a particle executing SHM having amplitude 'a' the speed of the particle is one half of its maximum speed when its displacement from the mean position is
\( A \cdot a / 2 \)
в.
c. \( a \frac{\sqrt{3}}{2} \)
D. 2a


\( 100 \% \) copper is obtained from crude
copper by :
A. zone refining method
B. electrorefining
c. liquation
D. poling


Bulk modulus of water is \( 2 \times 10^{9} N / m^{2} \)
The change in pressure required to increase the density of water by \( 0.1 \% \) is
A. \( \$ \$ 21 \) times \( 10^{\wedge}\{9\} N /\left\{m^{\wedge}\{2\} \$ \$\right. \)
B. \$\$21times 10^283N/ \{m\wedge(2) \$\$
c. \( \$ \$ 21 \) times \( 10^{\wedge}\{6\} N /\left\{m^{\wedge}(2) \$ \$\right. \)
D. \$\$21times 10^{223N/ } \{ m ^ { \wedge } ( 2 ) \$ \$


Elements can be diagonsed by
A. Emission spectroscopy
B. NMR spectroscopy
C. Infra-red spectroscopy
D. Absorption spectroscopy


If \( \vec{a} \) and \( \vec{b} \) are two vectors then the value of \( (\vec{a}+\vec{b}) \times(\vec{a}-\vec{b}) \) is:
A \( \cdot 2(\vec{b} \times \vec{a}) \)
B. \( -2(\vec{b} \times \vec{a}) \)
c. \( \vec{b} \times \vec{a} \)
D. \( \vec{a} \times \vec{b} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for \( \boldsymbol{y}=\boldsymbol{x}^{10}+\mathbf{1 0}^{\boldsymbol{x}}+\mathbf{1 0} \boldsymbol{x}+\mathbf{1 0} \)


A magnifying glass forms:
A. a real and diminished image
B. a real and magnified image
C . a virtual and magnified image
D. a virtual and diminished image.


Which of the following pairs of vectors
are parallel?
A \( . \vec{A}=\hat{i}-2 \hat{j} ; \vec{B}=\hat{i}-5 \hat{j} \)
B . \( \vec{A}=\hat{i}-10 \hat{j} ; \vec{B}=2 \hat{i}-5 \hat{j} \)
c. \( \vec{A}=\hat{i}-5 \hat{j} ; \vec{B}=\hat{i}-10 \hat{j} \)
D. \( \vec{A}=\hat{i}-5 \hat{j} ; \vec{B}=2 \hat{i}-10 \hat{j} \)


Then the displacement of the centre of mass \( \mathrm{m} \) at time \( \mathrm{t} \) is :
A \( \frac{F t^{2}}{2 m} \)
B. \( \frac{F t^{2}}{3 m} \)
c. \( \frac{F t^{2}}{4 m} \)
D. \( \frac{F t^{2}}{m} \)


\( \left(x^{2}+3 x+1\right)=(x-2)^{2} \) is an
equation of degree
A. three
B. one
c. four
D. two


When white light is passed through two consecutive prisms, the resultant will
be:
\( A \). rainbow colors
B. white beam
c. no light
D. yellow light


Draw neat labelled diagrams of lateral view of human brain.


The value of \( \lim _{x \rightarrow \infty} \frac{x+\cos x}{x+\sin x} \) is
A . -1
B. 0
c.
D. None of these


Find the output order for the following
matrix multiplication \( \boldsymbol{A}_{\mathbf{4} \times \mathbf{2}} \times \boldsymbol{B}_{\mathbf{2} \times \mathbf{4}} \) ?
\( A \cdot 2 \times 4 \)
B. \( 4 \times 4 \)
\( c \cdot 4 \times 2 \)
D. Multiplication not possible


A colonial hydrozoan is
A . Aurelia
B. Hydra
c. Metridium
D. obelia


Which of the following statements is incorrect?
A \( \cdot K_{4}\left[N i(C N)_{4}\right] \) and \( K_{2}\left[N i(C N)_{4}\right] \) both have same
magnetic moment
B. \( K_{4}\left[N i(C N)_{4}\right] \) is a diamagnetic while \( K_{4}\left[N i\left(C l l_{4}\right] \) is \right.
paramagnetic
\( \mathbf{c} \cdot_{K_{4}}\left[N i(C N)_{4}\right] \) is diamagnetic while \( K_{2}\left[N i(C N)_{4}\right] \) is
tetrahedral
D. \( K_{4}\left[N i(C l)_{4}\right] \) and \( K_{4}\left[N i(C N)_{4}\right] \) both have same
geometrical shapes


An antacid tablet is taken when a
person suffers from acidity. Explain why?


A body moving towards a finite body at
rest collides with it. It is possible that:
This question has multiple correct options
A. both the bodies come to rest
B. both the bodies moves after collision
C. the moving body comes to rest and the stationary body starts moving
D. the stationary body remains stationary, the moving body changes its velocity


A mixture contains 1 mole of volatile
liquid \( A\left(P_{A}^{\circ}=100 m m H g\right) \) and 3
moles of volatile liquid \( \boldsymbol{B}\left(\boldsymbol{P}_{\boldsymbol{B}}^{\circ}=\right. \)
\( 80 m m H g) . \) If solution behaves ideally
the total vapour pressure of the distillate is :
A. \( 85 \mathrm{mm} \) Hg
B. \( 85.88 \mathrm{mm} \) Н
\( \mathbf{c} .90 \mathrm{mm} \mathrm{Hg} \)
D. \( 92 \mathrm{mm} \) Hg


Ethyl chloride is not useful in preparing
A. PVC
B. TEL (Tetraethyllead)
c. Grignard reagent
D. Diethyl ether


Check the commutativity and associativity of the following binary operation:
\( *^{\prime} \) on \( Q \) defined by \( a * b=(a-b)^{2} \) for
all \( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{Q} \)


Let \( \boldsymbol{A}=\{\boldsymbol{x} \epsilon \boldsymbol{Z}: \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1 2}\} . \) Show that
\( \mathrm{R}=\{(a, b): a, b \epsilon A,|a-b| \) is divisible
by \( 4\} \) is an equivalence relation. Find
the set of all elements related to \( 1 . \) Also
write the equivalence class [2]


An equimolar quantities of ethanol and
propanol is heated with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
The product formed is /are?
A. \( C_{2} H_{5} O C_{2} H_{5} \)
в. \( C_{3} H_{7} O C_{3} H_{7} \)
c. \( C_{2} H_{5} O C_{3} H_{7} \)
D. all of these


Consider the following four statements
(i)- (iv) and select the correct option
stating which ones are true (T) and which ones are false (F)
(i) In male cockroach, genital pouch or chamber lies at the hind end of
abdomen bounded dorsally by 9 th and 10th terga and ventrally by the 9 th sternum.
(ii) In cockroach, the haemolymph is composed of colourless plasma and haemocytes
(ii) In female cockroach each ovary is formed of a group of ten ovarian tubules or ovarioles, containing a chain developing ova
(iv) In cockroach the nymph grows by moulting about 13 times to reach the adult form.
A \( \cdot\left(\text { i) }-F_{i} \text { (ii) }-\text { T; (iii) }-F_{i} \text { (iv) }-T\right. \)
B. (i)- F; (ii)- F; (iii) - T; (iiv)- T
\( c \cdot(i)-T_{i}(\text { ii })-T ;\left(\text { (iii) }-F_{i}(\text { iv } \gamma)-T\right. \)
D. (i)- T; (ii)- F; (iii) - T; (iv) - f


Although Rutherford's planetary mode of the atom was a major step forward in understanding the structure of the atom, which of the following was a major problem for this model-one that Bohr's model attempted to fix?
A. Electrons cannot orbit in elliptical paths
B. Cometary electrons would interfere with the normal orbits of electrons
C. Gravity is too strong to allow stable electron orbits
D. orbiting electrons would emit electromagnetic energy and spiral into the nucleus
E. orbiting electrons are all the same size, unlike the planets


What is rectification? Explain the working of bridge rectifier. Draw the input and output signals.


The high temperature \( (\approx 1200 K) \)
decomposition of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}(\boldsymbol{g}) \)
occurs as follows, as per simultaneous 1
stercactions. \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \stackrel{\boldsymbol{K}_{1}}{\longrightarrow} \boldsymbol{C} \boldsymbol{H}_{4}+\boldsymbol{C O}_{2} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \stackrel{\boldsymbol{K}_{2}}{\longrightarrow} \boldsymbol{C H}_{2} \boldsymbol{C O}+\boldsymbol{H}_{2} \boldsymbol{O} \)
What would be the \( \% \) of \( \mathrm{CH}_{4} \) by mole in the product mixture (excluding
\( \left.\boldsymbol{C H}_{3} \boldsymbol{C O O H}\right) ? \)
A \( \cdot \frac{50 k_{1}}{\left(k_{1}+k_{2}\right)} \)
В. \( \frac{100 k_{1}}{\left(k_{1}+k_{2}\right)} \)
c. \( \frac{200 k_{1}}{\left(k_{1}+k_{2}\right)} \)
D. It depends on time


gas is lighter than air.
A. Oxygen
B. Carbon dioxide
c. Hydrogen
D. None of these


What are the average distance and the most probable distance of an electron from the nucleus in the 1 s orbital of a
hydrogen atom? \( \left(a_{0}= \) the radius of the \right. first Bohr orbit)
A \( .1 .5 a_{0} \) and \( a_{0} \)
B. \( a_{0} \) and \( 5 a_{0} \)
c. \( 1.5 a_{0} \) and \( 0.5 a_{0} \)
\( \mathbf{D} \cdot a_{0} \) and \( 0.5 a_{0} \)


What is the nucleon number of an
atom?
A. The number of neutrons
B. The number of protons
c. The total number of protons and neutrons
D. The total number of protons and electrons


Which of the following statement can be related to catabolism?
A. It is an exergonic reaction
B. It is an endergonic reaction
c. It helps to break complex molecules to simple ones.
D. Both A and C


Self inductance of a long solenoid is directly proportional to(Where \( L \) is the length of solenoid)
A. \( L \)
B . \( L^{2} \)
c. \( 1 / L \)
D. \( 1 / L^{2} \)


What is a Quadratic Equation?


For the estimation of sulphur by Carius method, the organic compound is heated in Carius tube with:
A \( . B a C l_{2} / H C l \)
в. \( B a C l_{2} / H_{2} S O_{4} \)
c. \( A g C l / H C l \)
D. \( \operatorname{CaCl}_{2} / \mathrm{HCl} \)


What are weedicides? Give their effect
on the ecology of a place.


The engine of a car produces an acceleration of \( 6 m / s^{2} \) in the car. If this
car pulls a block of the same mass, then the acceleration would be:
\( \mathbf{A} \cdot 6 m / s^{2} \)
B . \( 12 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 3 m / s^{2} \)
D. \( 1.5 \mathrm{m} / \mathrm{s}^{2} \)


The area common to the cardioids \( r= \)
\( \boldsymbol{a}(\mathbf{1}+\cos \boldsymbol{\theta}) \) and \( \boldsymbol{r}=\boldsymbol{a}(\mathbf{1}-\cos \boldsymbol{\theta}) \) is:
\( ^{A} \cdot\left(\frac{3 \pi}{2}+4\right) a^{2} \)
в. \( \left(\frac{3 \pi}{2}-4\right) a^{2} \)
c. \( \left(\frac{\pi}{2}+4\right) a^{2} \)
D \( \cdot\left(\frac{\pi}{2}-4\right) a^{2} \)


If the vertices of a triangle are (-1,6,-4),(2,1,1) and (5,-1,0) then
the centroid of the triangle is
В. (2,2,-1)
\( ^{\mathbf{c}} \cdot\left(3,3,-\frac{3}{2}\right) \)
D. none of these


If \( I_{n}=\int_{0}^{\pi / 4} \tan ^{n} x d x, \) then
\( \frac{1}{I_{2}+I_{4}}, \frac{1}{I_{3}+I_{5}}, \frac{1}{I_{4}+I_{6}}, \dots \) are in
A. A.P
B. G.P.
c. н.P
D. none


Write down and simplify:
The 25 th term of \( (5 x+8 y)^{30} \)


Three horses \( \boldsymbol{H}_{1}, \boldsymbol{H}_{2}, \boldsymbol{H}_{3} \) entered a field which has seven portions marked
\( P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6} \) and \( P_{7} \). If no two
horses are allowed to enter the same
portion of the field, in how many ways can the horses graze the grass of the field?


In
A.P. the first term is -4, the last term
is 29 and the sum of all its terms is
150. Find its common difference.


What is the total resistance and current
in the circuit?
A. \( 2.5 \Omega, 0.4 A \)
B. \( 2 \Omega, 1.6 A \)
c. \( 2.5 \Omega, 1.6 A \)
D. \( 6 \Omega, 1.6 A \)


The angle between two vectors \( \vec{A}= \) (4,-2,5) and \( \vec{B}=(3,1,-2) \) is:
A \( \cdot 60^{\circ} \)
в. \( 30^{\circ} \)
\( c \cdot 90^{0} \)
D. \( 45^{\circ} \)


Let \( \mathrm{ABC} \) be a triangle and let \( \mathrm{S} \) be its circumcentre and \( \mathrm{O} \) be its orthocentre.
The \( \overline{\mathbf{S A}}+\overline{\mathbf{S B}}+\overline{\mathbf{S C}}= \)
A. 450
в. 3ज्ठ
c. 2 So
D. So


Prove:
\( \left(x+\frac{1}{x}\right)^{2}=x^{2}+\frac{1}{x^{2}}+2 \)


In a school, \( 14 \% \) of students take computer classes and \( 67 \% \) take drama classes.What is the probability that a
student neither takes computer class nor takes drama class?
A \( \frac{8}{100} \)
в. \( \frac{29}{100} \)
c. \( \frac{53}{100} \)
D. \( \frac{19}{100} \)


Correct the mistakes, if any in the
following statement.
¡) Second period is a short period. It contains only two elements.
ii) Group 18 elements are called Halogen family.


The maximum number of hydrogen
bonds in which water molecule can
participate is:
A . 1
B . 2
\( c .3 \)
D. 4


At present the Dipnoans are distributed
over
A. Europe and North America
B. Latin America and Australia
c. Europe and Latin America
D. North America and Australia


The boundary of a black hole is called
A. event horizon
B. Schwartzchild radius
c. chandra Sekhar limit
D. Einstein's space time


A disc of mass \( \mathrm{m} \) and radius \( \mathrm{R} \) has a
concentric hole of a radius r. Its
moment of inertia about an axis
through its centre and perpendicular to its plane is :
A \( \cdot \frac{1}{2} m\left(R^{2}+r^{2}\right) \)
B . \( \frac{1}{2} m\left(R-r^{2}\right) \)
C \( \cdot \frac{1}{2} m\left(R^{2}-r^{2}\right) \)
D \( \cdot \frac{1}{2} m\left(R+r^{2}\right) \)


Use geometric series to express \( 0.555 \ldots=0 . \overline{5} \) as a rational number
A \( \cdot \frac{1}{5} \)
в. \( \frac{5}{9} \)
c. \( \frac{5}{99} \)
D. None of these


Write any five salient features of ICBN


If ABCD is a parallelogram in which and \( Q \) are the centroids of \( \Delta A B D \) and
\( \Delta B C D, \) then, PQ equals:
\( A \cdot A Q \)
B. AP
c. ВР
D. DQ


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


If the points (2,5),(4,6) and \( (a, a) \) are
collinear, then find the value of \( a \)
A . 4
B. -4
\( c .-8 \)
D.


Ethers containing up to how many carbon atoms are soluble in water, due
to their hydrogen bond formation with water molecules?
\( A \cdot 3 \)
B. 4
\( c .5 \)
D.


Let \( a=2 i-j+k, b=i+2 j-k \) and
\( c=i+j-2 k \) be three vectors. A vector
in the plane of \( b \) and \( c \) whose projection on \( a \) is of magnitude \( \sqrt{\frac{2}{3}} \) is This question has multiple correct options
A. \( 2 i+3 j-3 k \)
B. \( 2 i+3 j+3 k \)
c. \( 2 i-j+5 k \)
\( \mathbf{D} \cdot 2 i+j+5 k \)


Dipole-induced dipole interactions are present in which of the following pairs:
A. HCl and He atoms
B. \( S i F_{4} \) and He atoms
c. \( H_{2} \) O and alcohol
D. \( C l_{2} \) and \( C C l_{4} \)


If a charge on the body is 1 nC, then how many electrons are present on the body?
A \( \cdot 1.6 \times 10^{19} \)
B . \( 6.25 \times 10^{9} \)
c. \( 6.25 \times 10^{27} \)
D. \( 6.25 \times 10^{28} \)


Two complex numbers are represented
by ordered pairs \( z_{1}:(6,4) \& z_{2}:(4,-5) \)
which of the following is real part of
\( z_{1}+z_{2} ? \)
A . -1
B. 10
\( c \cdot 6 \)
D. None of these


Find the accurate statement for the
significance of Avogadro's number?
A. It is the conversion factor between grams and atomic mass units
B. It is a universal physical constant just as the speed of light.
C. It is the number of particles that is required to fill a \( 1- \) liter container.
D. It is the inverse diameter of an H atom.
E. It is the number of electrons in the universe.


Butane can be converted into 2
methyl propane, if heated with:
A. \( A l_{2} C l_{6} \)
в. \( C r_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)
D. \( N i \)


Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial
(i) \( t^{2}-3,2 t^{4}+3 t^{3}-2 t^{2}-9 t-12 \)
(ii) \( x^{2}+3 x+1,3 x^{4}+5 x^{3}-7 x^{2}+ \)
\( 2 x+2 \)
(iii) \( x^{3}-3 x+1, x^{5}-4 x^{3}+x^{2}+3 x+ \)
\( \mathbf{1} \)


Which one of the following explains light both as a stream of particles and
as wave motion?
A . Diffraction
в. \( \lambda=h / p \)
c. Interference
D. Photoelectric effect


On squared paper, copy the triangle in the following figure. In this case, draw the line (s) of symmetry if any identify the type of the triangle.


Out of 500 first year students, 260
passed in the first semester and 210 passed in the second semester. If 170
did not pass in either semester, how many passed in both semesters?
A . 30
B. 40
c. 70
D. 140


If the distance between the points \( \boldsymbol{A}(\mathbf{4}, \boldsymbol{p}) \) and \( \boldsymbol{B}(\mathbf{1}, \mathbf{0}) \) is 5 units, then the
value(s) of \( p \) is are
A. 4 only
B. - 4 only y
\( c .\pm 4 \) only
D. 0


In a row of girls, Mridula is \( 18^{t h} \) from the
right and Sanjana is \( 18^{t h} \) from the left. If both of them interchange their position, Sanjana becomes \( 25^{t h} \) from the left,
how many girls are there in the row?
A . 40
B. 41
c. 42
D. 35 5


A true species consists of a population which is?
A. Sharing the same niche
B. Interbreeding
c. Feeding over the same food
D. Geographically isolated


Short Answer Type Question. Give an account of atmosphere.


A parallel plate capacitor consists of circular plates with radius \( 10 \mathrm{cm} \)
separated by a distance of \( 0.5 m m . \) The capacitor is charged by an external source such that the electric field
between the plates changes at a rate \( 5 \times 10^{13} V m-1 s-1 . \) The displacement
current through the capacitor is
A \( .1 .4 m A \)
в. \( 14 m A \)
\( c .14 A \)
D. \( 1.4 A \)


Explain Wurtz-Fitting reaction.


For Gas \( \rightleftharpoons \) Solid equilibrium; which one
is not correct?
A. \( \Delta G=0 \)
B. \( \Delta H=T \Delta S \)
c. \( \Delta H=-v e \)
\( \mathbf{D} \cdot \Delta S=+v e \)


An electric dipole \( \pm 4 \mu C \) is kept at coordinate points (1,0,4) are kept at \( (2,-1,5), \) the electric field is given by \( \vec{E}=20 \hat{i} N C^{-1} . \) Calculate the torque on
the dipole.


In the Young's double slit experiment two light beams of wavelengths \( \lambda= \)
\( 6000 A^{\circ} \) and \( \lambda=4800 A^{\circ} \) are used. The
distance between two slits is \( 2.5 m m \)
The distance between slits and the
screen is \( 1.5 m . \) The distance between
the central maxima obtained with two
beams will be
A . zero
B. \( 1.872 m m \)
c. \( 2.872 m m \)
D. \( 2.652 m m \)


Which one of the following generally acts as an antagonist to gibberellins?
A. NAA
B. ABA
\( c \cdot \) ।АА
D. Zeatin


Following questions may have more
than one correct options. The given graphs/data I, II, III and IV
represent general trends observed for
different physisorption and chemisorption processes under mild
conditions of temperature and
pressure
Which of the following choice(s) about I,
II, III and IV is/are correct?
This question has multiple correct options
A. I is physisorption and II is chemisorption
B. I is physisorption and III is chemisorption
C. IV is chemisorption and II is chemisorption
D. IV is chemisorption and III is chemisorption


forms hydrogen bonds.
A \( \cdot C H_{4} \)
в. \( \mathrm{CO}_{2} \)
c. \( N H_{3} \)
D. \( N_{2} \)
\( E \cdot O_{2} \)


Consider the reaction \( C_{2} H_{5} O^{\ominus}+ \)
Dimethyl sulphate
\( (M e-O-\underbrace{S}_{V}^{O}-O-M e) \rightarrow \)
The leaving group is:
A. \( M e O S O_{2} O^{\circ} \)
в. \( M e O^{\circ} \)
\( \mathrm{c} \cdot \mathrm{Me}^{\circ} \)
D. \( \operatorname{Me} \mathrm{O} \mathrm{SO}_{2}^{\text {o }} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{1})^{2}-\mathbf{1},(\boldsymbol{x} \geq-\mathbf{1}) . \) Then
the \( \operatorname{set} S=\left\{x: f(x)=f^{-1}(x)\right\} \) is


1000 small water drops each of radius
\( r^{\prime} \) and charge \( ^{\prime} q^{\prime} \) coalesce together to one spherical drop. The potential of the big drop is larger than that of the smaller drops by a factor of:
A. 1000
в. 100
c. 10
D.


The interest is supposed compound
unless the contrary is state.

A person borrows 672 pounds to be repaid in 5 years by annual instalments
of 120 pounds; find the rate of interest, reckoning simple interest.


\( A \) and \( B \) are two objects with mass \( 6 k g \)
and \( 34 k g \) respectively. Then
A. \( A \) has more inertia than \( B \)
B. \( B \) has more inertia than \( A \)
c. \( A \) and \( B \) both have same inertia
D. None of the above is true


White light is incident normally on a glass slab. Inside the glass slab,
A. Red light travels faster than other colours
B. Violet light travels faster than other colours
c. Yellow light travels faster than other colours
D. All colours travel with the same speed


Which of the following alcohol has the highest boiling point?
A. Butan \( -2-o l \)
B. \( 2- \) Methylpropan \( -2- \) ol
c. Propan \( -2- \) ol
D. Butan \( -1-o l \)


A particle A has charge +q and a particle B has a charge +9q with each of them having the same mass m.If both the particles are allowed to all from rest through the same potential difference, then the ratio of their speed is
A .1: 2
B. \( 1: \sqrt{3} \)
c. \( 1: 2 \sqrt{2} \)
D. none of these


(A) The sporophyte in liverworts is more elaborate than that in mosses.
(B) Salvinia is heterosporous.
(C) In Pinus, male and female cones are
borne on different trees.
(D) The life-cycle in all seed bearing plants is diplontic. The two wrongly matched statements
together are
A. Statement B and C
B. Statement A and B
c. Statement A and C
D. Statement A and D


Numerator in the fraction \( \frac{4}{7} \) is
A . 4
B. 7
\( c \cdot \frac{4}{7} \)
D.


State True or False:
Ds is the latest IUPAC approved name of the element of atomic number 110
A . True
B. False


Find the value of the following:
(i) \( 15^{3} \) (ii) \( (-4)^{3} \)
(iii) \( (1.2)^{3}(\text { iv })\left(\frac{-3}{4}\right)^{3} \)


Contact forces
A. Are action at a distance forces
B. Ex-gravitational forces
C. Act when the bodies are in physical contact with other
D. All


For the process:
\( \boldsymbol{H}_{2} \boldsymbol{O}[\boldsymbol{l}, \boldsymbol{T}(\boldsymbol{K}), \boldsymbol{P}(\boldsymbol{b} \boldsymbol{a} \boldsymbol{r})] \rightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}[\boldsymbol{g}, \boldsymbol{T}(\boldsymbol{K}), \boldsymbol{P}(\boldsymbol{b} \boldsymbol{a} \boldsymbol{r})] . \) Mark correct
statements.
This question has multiple correct options
A \( \cdot \Delta G=0, \) if \( P= \) vapour pressure of \( H_{2} O(l) \) at \( T K \)
B . \( \Delta G=+v e \), if \( P \) = vapour pressure of \( H_{2} O(l) \) at a temperature above TK
C . \( \Delta G=+v e, \) if \( P> \) vapour pressure of \( H_{2} O(l) \) at \( T K \)
D. \( \Delta G=-v e \), if \( P< \) vapour pressure of \( H_{2} O(l) \) at \( T K \)


Fora reaction, \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\boldsymbol{C}, \) it was found
that at the end of 10 minutes from the
start, the total optical rotation of the
system was \( 50^{\circ} \) and when the reaction
is complete, it was \( 100^{\circ} \mathrm{C} \) Assuming
that only \( B \) and \( C \) are optically active and dextro rotatory, the rate constant of this first order reaction would be?
A \( \cdot 0.069 \min ^{-1} \)
B. 0.69 min \( ^{-1} \)
c. 6.9 min \( ^{-1} \)
D. \( 6.9 \times 10^{-2} \) min \( ^{-1} \)


Assertion
Equilibrium Constant of a reaction increases if temperature is increased.
Reason

The forward reaction becomes faster
with increase of temperature.
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


ff \( \boldsymbol{y}=\frac{a}{2}\left(e^{\frac{x}{a}}+e^{\frac{-x}{a}}\right) \) and \( \frac{d^{2} y}{d x^{2}}=y, \) then a
equals
A .
в.
\( c \cdot \frac{1}{3} \)
D. \( \frac{1}{\sqrt{2}} \)


Find the remainder when \( x^{4}+x^{3}- \)
\( 2 x^{2}+x+1 \) is divided by \( x-1 \)
\( A \cdot 2 \)
B. -
\( c \cdot-2 \)
D.


Define excretion.


\( \boldsymbol{H}_{2} \boldsymbol{O}^{18}+\boldsymbol{N} \boldsymbol{a} \rightarrow \underset{(b a s e)}{(\boldsymbol{A})}+(\boldsymbol{B}) \)
\( o \)
\( \boldsymbol{C H}-\mathbf{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{3}+ \)
\( (A) \rightarrow(C)+(D) \) alcohol
Product \( (C) \) of the reaction is:
\( ^{\mathbf{A}} \cdot_{C H_{3}-C-_{18}^{\|}}^{0}-H \)
в. \( \quad \stackrel{o^{\prime 8}}{N}-O-H \)
\[
C H_{3}-C-O-H
\]
D.
\[
C H_{3}-C-O^{\ominus} N_{a}^{\oplus}
\]


\( \mathbf{1}+\mathbf{3}+\mathbf{6}+\mathbf{1 0}+\ldots+\frac{(\boldsymbol{n}-\mathbf{1}) \boldsymbol{n}}{\mathbf{2}}+ \)
\( \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})}{\mathbf{2}}= \)
A. \( \frac{n(n+1)(n+2)}{3} \)
B. \( \frac{(n+1)(n+2)}{6} \)
c. \( \frac{n(n+1)(n+2)}{6} \)
D. \( \frac{(n+2)(n+1)^{2}}{3} \)


Magnetic field at the center (at nucleus) of the hydrogen-like atoms (atomic number \( =Z \) ) due to the motion
of electron in \( n^{t h} \) orbit is proportional to
A \( \cdot \frac{n^{3}}{z^{5}} \)
B. \( \frac{n^{4}}{z} \)
c. \( \frac{z^{2}}{n^{3}} \)
D. \( \frac{z^{3}}{n^{5}} \)


\( A B C D \) is a rhombus and \( P, Q, R \) and \( S \)
are the mid-points of the sides \( A B, B C, C D \) and \( D A \) respectively.
Show that the quadrilateral \( P Q R S \) is a
rectangle


Find the quadratic equation in \( x, \) whose
solutions are 3 and 2
A \( \cdot x^{3}-5 x+6=0 \)
B. \( x^{2}-5 x+6=0 \)
c. \( x^{2}-3 x+6=0 \)
D. \( x^{2}-5 x+7=0 \)


Q Type your question
z. Here z is the vertical distance inside
the slab, measured from the top. The slab is placed between two media with
uniform refractive indices \( n_{1} \) and \( n_{2} \)
\( \left(>n_{1}\right), \) as shown in the figure. A ray of
light incident with angle \( \boldsymbol{\theta}_{\boldsymbol{i}} \) from
medium 1 and emerges in medium 2
with refraction angle \( \theta_{f} \) with lateral
displacement \( l \) Which of the following statement(s) is (are) true?
This question has multiple correct options
A. \( l \) is dependent on \( n(z) \)
B \( \cdot n_{1} \sin \theta_{1}=\left(n_{2}-n_{1}\right) \sin \theta_{f} \)
\( \mathbf{c} \cdot n_{1} \sin \theta_{i}=n_{2} \sin \theta_{f} \)
dependent of \( n \)


What is 'dispersion of white light'? State
its cause. Draw a ray diagram to show the dispersion of white light by a glass prism.


The value of \( \lim _{n \rightarrow \infty} \frac{3^{n}+2^{n}}{3^{n}-2^{n}} \) is
A . -1
B.
\( c \cdot 0 \)
D.


Phosphorus is estimated by Carius method as magnesium pyrophosphate.
A. True
B. False


If diagonal of a rectangle is \( 26 \mathrm{cm} \) and one side is \( 24 \mathrm{cm} \).Find the other side?


If the ionization energy of hydrogen
atom is \( 13.6 e V \) then the wavelength of the radiation required to excite the
electron in \( L i^{++} \) from first to third Bohr
orbit is approximately
A . \( 1140 A \)
В. \( 914 A \)
c. \( 11.4 A \)
D. \( 134 A \)


The attached figure shows the
characteristics of:
A. Zener diode
B. Avalanche diode
C. Photodiode
D. LED


An ac generator consists of a coil of 200 turns, \( 100 \mathrm{cm} \) in diameter. If the coil
rotates at 500 rpm in a magnetic field of \( 0.25 \mathrm{T} \), then the maximum induced
emf
A . 20.6 \( v \)
B. 51.7
c. 4.1
D. None of the above


Two short dipoles moment P are placed
at two corners of a square as shown in the figure. What is the ratio of magnitudes of electric field at two
points 0 and \( A ? \)
\( A \cdot 2 \)
B. \( 2 \sqrt{2} \)
\( c \)
D. \( \sqrt{2} \)


\( p-\frac{1}{v} \) graph for a gas under constant
temperature is
A. Straight line
B. Circle
c. hyperbola
D. parabola


Which of the following have zero average value in a plane electromagnetic wave?
(i) Magnetic field
(ii) Electric field
(iii) Electric energy
(iv) Magnetic energy.
\( A \cdot \) (i) and (ii)
B. (i) and (iv)
c. (ii) and (iii)
D. (iii) and (iv)


Match the following. SET A SET B
Name of hormone Functional
group in hormones
1) Testosterone
a) double
bond
2) Estradiol
b) Ketone
3) Progesterone
c) Alcohols
4) Ethylene
d) Alcohol and ketone
A \( \cdot 1-d ; 2-c ; 3-b ; 4-a \)
B. \( 1-a ; 2-b ; 3-c ; 4-d \)
\( c \cdot 1-c ; 2-d ; 3-a ; 4-b \)
D. \( 1-b ; 2-c: 3-d: 4-c \)


Why are lightning conductors pointed in shape?
A. To reduce mass
B. It attracts more electric charge due to very small radius and hence surface area
c. It allows more current
D. It repels the incident lightning discharge


The length of a curved surface is
measured by using
A. metre scale only
B. thread only
c. both metre scale and thread
D. none of these


Atomicity of white or yellow phosphorus
is 4 and it is represented as \( P_{4} \) molecule,calculate the value of
expression \( \frac{x \cdot y}{z} \) regarding this
molecule.
Where \( x: \) Total number of vertex angles
in \( P_{4} \) molecule
y: Total number of lone pairs in \( P_{4} \) molecule
z: Total number of P- - -P bonds in
\( P_{4} \) molecule


f \( x=\{a, b, c, d\} \) and \( y=\{b, d, g, f\} \)
find \( \boldsymbol{x}-\boldsymbol{y} \) and \( \boldsymbol{y}-\boldsymbol{x} \)
Draw the appropriate venn diagram for
\( \boldsymbol{A}^{\prime} \cap \boldsymbol{B}^{\prime} \)


For the reaction given below the values of standard Gibbs free energy of formation at \( 298 \mathrm{K} \) are given. What is the nature of the reaction?
\( \boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{S} \rightarrow \mathbf{2} \boldsymbol{H} \boldsymbol{I}+\boldsymbol{S} \)
\( \boldsymbol{\Delta} \boldsymbol{G}_{f}^{0}(\boldsymbol{H} \boldsymbol{I})=\mathbf{1 . 8} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \Delta G_{f}^{0}\left(H_{2} S\right)=33.8 k J m o l^{-1} \)
A. Non-spontaneous in forward direction
B. Spontaneous in forward direction
c. Spontaneous in backward direction
D. Non-spontaneous in both forward and backwardd directions


Show that the equation of the line passing through the origin and making an angle \( \theta \) with the line \( y=m x+c \) is
\( \frac{\boldsymbol{y}}{\boldsymbol{x}}=\frac{\boldsymbol{m} \pm \tan \boldsymbol{\theta}}{1 \mp \boldsymbol{m} \tan \boldsymbol{\theta}} \)


toppr
\( Q \) туре
A large number of atoms/molecules (approximately \( 6.023 \times 10^{23} \) ) are
present in few grams of any chemical compound varying with their atomic/molecular masses. To handle
such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry, and radiochemistry. the following example illustrates a typical case, involving chemical/electrochemical reaction,
which requires a clear understanding of the mole concept.

A 4.0 molar aqueous solution of NaCl is prepared and \( 500 \mathrm{mL} \) of this solution is electrolyzed. This leads to the evolution of chlorine gas at one of the electrodes (atomic mass: \( \mathrm{Na}=23, \mathrm{Hg}=200 ; 1 \)
faraday =96500 coulombs) The total charge (coulombs) required for complete electrolysis is:
A . 24125
B. 48250
c. 96500
D. 193000


\( 100 m l \) of \( 0.2 M H_{2} S O_{4} \) is reacted with
\( 100 m l \) of \( 0.5 M N a O H \) solution. what
is the normality of the solution
A . 0.3N
B. 0.8N
c. \( 0.1 \mathrm{N} \)
D. 1N


In the pressure-volume diagram given below, the isochoric, isothermal
isobaric and isoentropic parts
respectively are:
A. \( B A, A D, D C, C B \)
B. \( D C, C B, B A, A D D D, D D, C B, B A, A D, D \)
c. \( A B, B C, C D, D A \)
D. \( C D, D A, A B, B C \)


Convert the statement into an equation Adding 14 to 9 times \( y \) is 89
A \( .14 y+9=89 \)
B. \( 14+9 y=89 \)
c. \( 14-9 y=-89 \)
D. \( 14+y=89 \)


The area included between the curve
\( x^{2}+y^{2}=a^{2} \) and \( \sqrt{|x|}+\sqrt{|y|}= \)
\( \sqrt{\boldsymbol{a}}(\boldsymbol{a}>\mathbf{0}) \) is:
A \( \cdot\left(\pi+\frac{2}{3}\right) a^{2} \)
B \( \cdot\left(\pi-\frac{2}{3}\right) a^{2} \)
\( c \cdot \frac{2}{3} a^{2} \)
D. \( \frac{2 \pi}{3} a^{2} \)


Noble gases form compounds very
easily with?
A. Sulphur
B. Nitrogen
c. oxygen
D. Fluorine


Explain the physical phenomena
involved in the formation of a rainbow
with a diagram


If a band is played on the moon the
sound will


Write the IUPAC name of the complex
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right]^{+} . \) What type of
isomerism does it exhibit?


As the planet revolves from point \( \mathrm{P} \) to
point \( Q, \) the velocity of the planet.
A. Increases
B. Decreases
c. Remains same
D. Equal is magnitude and opposite in direction


\( f\left[\begin{array}{ll}\mathbf{4} & \mathbf{3} \\ \boldsymbol{x} & \mathbf{5}\end{array}\right]=\left[\begin{array}{ll}\boldsymbol{y} & \boldsymbol{z} \\ \mathbf{1} & \mathbf{5}\end{array}\right] \) then find the value
of \( x, y \) and \( z \)


White light reflected at normal incidence from a soap film has minima
at \( 6500 A \) and maxima at \( 7500 A \) in the
visible region with not minima in between. If \( \mu \) is \( \frac{5}{3} \) for the thin film, the thickness of film is :
A \( \cdot 7.40 \times 10^{-7} \mathrm{cm} \)
B. \( 9.75 \times 10^{-5} \mathrm{mm} \)
c. \( 9.70 \times 10^{-7} \mathrm{cm} \)
D. \( 9.75 \times 10^{-4} \mathrm{mm} \)


At \( 100^{\circ} \mathrm{C} \) and 1 atm, if the density of the
liquid water is \( 1.0 g c m^{-3} \) and that of
water vapour is \( 0.0006 g \mathrm{cm}^{-3}, \) then the volume occupied by water molecules in
1 L of steam at this temperature is:
\( \mathbf{A} \cdot 6 \mathrm{cm}^{3} \)
B. \( 60 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 0.6 \mathrm{cm}^{3} \)
D. \( 0.06 \mathrm{cm}^{3} \)


Center of gravity of an object depends on its which of the following? This question has multiple correct options
A . Mass
c. shape
D. weight


Solve the following equation:
\( \cos x=\sqrt{3} \)


Weight of diamonds are measured in
A. grams
B. carats
\( c \cdot k g \)
D. pounds


the study of the
structure, properties, and preparation of chemical compounds that consist primarily of carbon and hydrogen.
A. organic chemistry
B. Inorganic chemistry
c. Physical chemistry
D. Analytical chhemitry


Solve the equation \( \mathbf{5}^{x^{2}+3 x+2}=\mathbf{1} \)
find the difference between the roots of
the equation.


compounds are soluble
in polar solvent.


The bacteria live in the large intestine of
human are
A. Bifidobacterium
B. Methanogens
c. Lactobacillus
D. All of the above


What is shortest wavelength line in the
Paschen series of \( L i^{2+} \) ion?


Quantum numbers \( l=2 \) and \( m=0 \)
represent which orbital?
A \( \cdot d_{x y} \)
B. \( d_{x^{2}-y^{2}} \)
\( c \cdot d_{z} \)
D. \( d_{x x} \)


Among the following compounds, which
will produce \( \boldsymbol{P O C l}_{3} \) with \( \boldsymbol{P C l}_{5} \) ?
\( A \cdot \) only \( O_{2} \)
B. \( O_{2} \) and \( C O_{2} \)
c. \( C O_{2}, O_{2} \) and \( P_{4} O_{10} \)
D. \( S O_{2}, H_{2} O, H_{2} S O_{4} \) and \( P_{4} O_{10} \)


\( \lim _{n \rightarrow \infty}\left[\frac{1}{n^{2}} \sec ^{2} \frac{1}{n^{2}}+\frac{2}{n^{2}} \sec ^{2} \frac{4}{n^{2}}+\ldots+\frac{1}{n}\right. \)
equals
A \( \cdot \frac{1}{2} \operatorname{cosec} 1 \)
B \( \cdot \frac{1}{2} \sec 1 \)
c. \( \frac{1}{2} \tan 1 \)
D. tan 1


Municipality officials use chlorine in water purification because:
A. chlorine cleans water
B. chlorine helps water to cool easily
c. chlorine coagulates mud particles
D. chlorine kills harmful bacteria


When an object is placed at a distance of \( 60 \mathrm{cm} \) rom a convex spherical mirror, the magnification produced is \( \frac{1}{2} . \) Where should the object be placed to get a magnification of \( 1 / 3 \)


A smooth inclined plane having angle of
inclination \( 30^{\circ} \) with horizontal has a
mass 2.5 kg held by a sprang which is fixed at the upper end as shown in figure. If the mass is taken \( 2.5 \mathrm{cm} \) up along the surface of the inclined plane,
the tension in the spring reduces to zero
If the mass is then released, the angular frequency of oscillation in radian per second is:
A. 0.707
В. 7.07
c. 1.414
D. 14.14


Identify a matrix
В. \( A=\{1,2\} \)
\( \mathbf{c} \cdot A=\left[\begin{array}{ll}1 & 2\end{array}\right] \)
D. None of these


Agriculture can cause soil
contamination due to:
A. accumulation of animal manures
B. illicit dumping of tainted crops on land
C. improper sanitation system
D. both \( A \) and \( B \)


Most oxidsing agent is:
\( \mathbf{A} \cdot\left[W O_{4}\right]^{2-} \)
B. \( \left[\mathrm{CrO}_{4}\right]^{2-} \)
c. \( \left[\mathrm{Ce} \mathrm{O}_{4}\right]^{2} \)
D. \( \left[M n O_{4}\right]^{2-} \)


An ideal solution contains two volatile
liquids \( \boldsymbol{A}(\boldsymbol{p}=\mathbf{1 0 0} \text { tor } \boldsymbol{r}) \) and
\( B(p=200 \text { tor } r) . \) If mixture contain 1
mole of \( A \) and 4 mole of \( B \) then total
vapour pressure of the distillate is:
A . 150
в. 180
c. 188.88
D . 198.88


The volume of 0.5 moles of a gas at 273
\( \mathrm{K} \) and \( 380 \mathrm{mm} \) pressure is:
A . 11.2 lit
B. 22.4 litt
c. 2.24 lit
D. 1.12 litt


Red rot of sugarcane' and 'white rust of radish' are respectively caused by
A. Albugo candida and Cerospora
B. Colletotrichum and Fusarium
c. Phythium and Phytophthora
D. Albugo candida and Puccinia graminis
E. Colletotrichum and Albugo candida


Which of the following physical quantities has no unit?
A. Relative density
c. Pressure
D. Thrust


\( \lim _{x \rightarrow 0} \frac{\sqrt{1-\cos x}}{x} \) is equal to
A. \( -\frac{1}{\sqrt{2}} \)
B. \( \frac{1}{\sqrt{2}} \)
c. 0
D. Does not exist


List I
¡. Cyanide process
A. Ultrapure Ge
ii. Floating process
B. Pine oil
creduction
C. Extraction of \( A l \)
iii. Electrolytic
iv. Zone refining
D. Extraction of \( A u \)
Match List-I with List-II and select the
correct answer using the codes given
below the lists:
\( \mathbf{A} \cdot \mid-\mathrm{C},\|-\mathrm{A},\| \mathrm{I}-\mathrm{D}, \mathrm{IV}-\mathrm{B} \)
B. \( \mid-D,\|-B,\| I-C, I V-A \)
C \( . \mid-C,\|-B,\| I-D, I V-A \)
D. \( \mid-D,\|-A,\| I-C, I V-B \)


Identify the triangle as equiangular, acute, obtuse or right.
Answer: Obtuse
Mark answer as 1 if true else 0 if false


Factors of \( a^{2}+4 a+4 \) are:
A \( \cdot(a+2)^{2} \)
в. \( (a+1)^{2} \)
c. \( (a-2)^{2} \)
D. \( (a-1)^{2} \)


An unbiased normal coin is tossed \( n \)
times. Let \( E_{1}: \) event that both heads and
tails are present in \( n \) tosses. \( E_{2} \) :event that the coin shows up heads at most
once. The value of \( n \) for which \( E_{1} \) and \( E_{2} \)
are independent is
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Given a uniform electric field \( \boldsymbol{E}=\mathbf{5} \times \) \( 10^{3} \hat{i} N / C . \) What would be the flux
through the same square if the plane
makes an angle of \( 30^{\circ} \) with the \( x \) -axis?
A. \( 5 N m^{2} / C \)
B. \( 25 N m^{2} / C \)
\( \mathbf{c} \cdot 50 N m^{2} / C \)
D. \( 500 \mathrm{Nm}^{2} / \mathrm{C} \)


\( \left(a m_{1}^{2}, 2 a m_{1}\right),\left(a m_{2}^{2}, 2 a m_{2}\right) \) and
\( \left(a m_{3}^{2}, 2 a m_{3}\right) \)


Number of positive continuous functions \( f(x) \) defined in [0,1] for which \( \int_{0}^{1} f(x) d x=1, \int_{0}^{1} x f(x) d x=2 \)
\( \int_{0}^{1} x^{2} f(x) d x=4 \)
\( A \)
B. 4
c. Infinite
D. None of these


'I.U.P.A.C.', stands for?
A. lodine Under Packing
B. International Union of Pure and Applied Chemistry
C. International Units of Protein and Carbohydrates
D. International Understanding on Physical Aspects of Chemistry


Figure shows a cross-section of a long
ribbon of width \( \omega \) that is carrying a
uniformly distributed total current \( i \) into the page. Calculate the magnitude and direction of the magnetic field \( \vec{B} \) at a point \( P \) in the plane of the ribbon at a distance d from its edge.
\[
\begin{array}{ll}
P & x \times x \cdot x \times x \times x \times x \\
& d
\end{array}
\]


Increased level of carbon dioxide in the
atmosphere traps the heat rays reflected by the earth causing an increase in the temperature on the
earth. This is
A. Local warming
B. House warming
c. Global warming
D. Country warming


Why are cold storages constructed with
double walls?


Evaluate the following limits:
\( \lim _{x \rightarrow 0} x \operatorname{cosec} x \)


The tension, length, diameter and density of a string \( \mathrm{B} \) are double than that of another string A. Which of the following overtones of B is same as the fundamental frequency of A?
A . \( 1 s \)
B. 2nd
\( c .3 r d \)
D. 4 th


Match the following components of
Column 'A' with the components of
Column'B'.
Column Column 'B' 'A'
(1)
(A) A trap which looks and smells like Venus fly \( \quad \) a flower to catch the insects trap
(2)
(B) Flower opens in the morning Balsam
(3)
(C) Fruit bursts open to Drosera
(4)
(D) Tentacles on leaves which can trap Lotus \( \quad \) insects
\( A \cdot(1)-(A),(2)-(C),(3)-(D),(4)-(B) \)
B. \( (1)-(A),(2)-(C),(3)-(B),(4)-(D) \)
C \( \cdot(1)-(D),(2)-(C),(3)-(A),(4)-(B) \)
D. \( (1)-(D),(2)-(B),(3)-(A),(4)-(C) \)


A wire bent as shown in Fig is oriented
along yz plane. Find the magnetic field
at \( P \) and \( P_{1} \)
A \( \cdot \frac{\mu_{0} I}{4 a}, \frac{\mu_{0} I}{2 \pi x_{x}} \)
B. \( \frac{\mu I}{4 a}, \frac{\mu I}{2 \pi\left(x^{2}+a^{2}\right)} \)
C. \( \frac{\mu_{0} I}{4 a}, \frac{\mu_{0} I}{2 \pi a\left(x^{2}+a^{2}\right)} \)
D. none of thes


Heat energy of \( 2100 \mathrm{J} \) is given to a gas at a constant pressure of \( 10^{5} \) Pa. The increase in internal energy, if the change in volume is \( 5 \times 10^{-3} m^{3}, \) is:
A . 1500
B. 1400 J
c. 1600 J
D. 800 J


What is the effective capacitance
between points \( X \) and \( Y ? \)
A \( .24 \mu F \)
\( \mathbf{B} \cdot 18 \mu F \)
c. \( 12 \mu F \)
D. \( 6 \mu F \)


When pollutants in the air mix up in a chemical reaction, they form an even more dangerous chemical.these pollutants are called
A. primary air pollutant
B. secondary air pollutant
c. tertiary air pollutant
D. none of above


Sewage is a complex mixture
containing suspended:
A. solids organic and inorganic nutrients
B. organic impurities only
C. inorganic impurities only
D. all of the above


The function of enzymes in the living
system is to:
A. Transport oxygen
B. Provide immunity
c. Catalyse biochemical reaction
D. Provide energy


A body is dropped from a certain height from the ground. When it is halfway down, it possess,
A. Only K.E.
B. Both K.E. and P.E.
c. only P.E.
D. zero energy


Current of \( \frac{50}{\pi} H z \) frequency is passing through an A.C circuit having series combination of resistance \( \boldsymbol{R}=\mathbf{1 0 0} \mathbf{\Omega} \)
and inductor \( L=1 H, \) then phase
difference between voltage and current
is
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


SA node is found in
A. Lungs
B. Brain
c. spleen
D. Heart


Stability and center of gravity of an object whose stability can be increased
by
A. lowering center of gravity and increasing area of base
B. lowering center of gravity and decreasing area of base
c. moving center of gravity higher and increasing areas of base
D. moving center of gravity higher and decreasing area of base


A motorbike travels \( 425 \mathrm{km} \) in 5
hours.How much distance will be
covered by it in 3.2 hours?


Evaluate: \( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\left(1-\tan \frac{x}{2}\right)(1-\sin x)}{\left(1+\tan \frac{x}{2}\right)(\pi-2 x)^{3}} \)
A \( \cdot \frac{1}{16} \)
\( B \cdot \frac{1}{8} \)
\( c \cdot 0 \)
D. \( \frac{1}{32} \)


Which of the following measurements has 4 significant figures?
A. 500. grams
B. 50000 grams
c. 500.0 grams
D. 500.00 grams


The measure of the third angle of the
triangle. ( in degrees )
\( 110^{\circ}, 23^{\circ},--- \)


Fermentation is represented by the
equation
A \( \cdot C_{6} H_{12} O_{6}+6 O_{2} \stackrel{\text {light}}{\rightarrow} 6 C O_{2}+H_{2} O+673 k c a l \)
B . \( C_{6} H_{12} O_{6}+\rightarrow 2 C_{2} H_{5} O H+2 C O_{2}+18 k c a l \)
c. \( 6 C O_{2}+12 H_{2} O \stackrel{\text { Chlorophyll }}{\longrightarrow} C_{6} H_{12} O_{6}+6 H_{2} O+6 O_{2} \)
D. \( 6 C O_{2}+6 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 O_{2} \)


Describe the structure, biosynthesis and metabolism of auxins.


\( \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2}=\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \frac{C l_{2}}{\boldsymbol{H}_{2} \boldsymbol{O}} \boldsymbol{A} \stackrel{\boldsymbol{O H}^{-}}{\boldsymbol{\beta}} \boldsymbol{B} \)
The compound \( B \) is:
\( A \)
в. \( \left(C H_{3}\right)_{2} C-C\left(C H_{3}\right) \)
он \( C l \)
\( \mathrm{c} \cdot\left(C H_{3}\right)_{2} C-C\left(C H_{3}\right)_{2} \)
\( _{O H O H} \)
D. none of the above


Fill in the blank and complete the
analogy by choosing the correct alternative from the options given. Helium : Duplet state : : Argon :
A. Duplet state
B. Triplet state
c. Octet state
D. None of the above


As shown in the figure, charges \( +q \) and \( q \) are placed at the vertices \( B \) and \( C \) of
an isosceles triangle. The potential at
the vertex \( A \) is
\( A \)
в. \( \frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{\sqrt{a^{2}+b^{2}}} \)
\( c \)
D. zero


An electron and a proton each travel
with equal speeds around circular
orbits in the same uniform magnetic field as indicated (not to scale) in fig.
The field is into the page on the
diagram. The electron travels .... around
the \( \ldots . \) circle and the proton travels... around the \( \ldots . \) circle
A. clockwise, smaller, counterclockwise, larger
B. counterclockwise, larger, counterclockwise, smaller
c. clockwise, larger, counterclockwise, smaller
D. counterclockwise, larger, clockwise, smaller


Teminism is same as
A. Transcription
B. Translation
C. Reverse transcription
D. DNA synthesis


When \( C H_{3} M g I \) is made to react with
acetone and the addition product is hydrolysed, we get a/an:
A. primary alcohol
B. secondary alcohol
c. tertiary alcohol
D. aldehyde


In the above figure, tube A contains
copper fillings and tube B contains aluminum fillings. If a strong magnet is
brought close to the two tubes as shown
in the figure, then
(A) Centre of gravity of the tube A move
towards the right
(B) Centre of gravity of tube B move
towards the right
A. Only A is true
B. Only B is true
c. Both \( A \) and \( B \) are true
D. Neither A nor B is true


The wave produced in a resonance tube
is
A . Longitudinal
B. Transverse
c. Transverse stationary
D. Longitudinal stationary


Which one of the following characteristics is not correct for
physical adsorption?
A. Adsorption increases with increase in temperature
B. Adsorption is spontaneous
C. Both enthalpy and entropy of adsorption are negative
D. Adsorption on solids is reversible


Why \( B e O \) and \( A l_{2} O_{3} \) are amphoteric?


General electronic configuration of representative elements is :
A \( \cdot n s^{1}-n s^{2} n p^{5} \)
В. \( n s^{2} n p^{6} \)
C \( \cdot n s^{1}-n s^{2} n p^{6} \)
D. none of these


An ordinary pack of 52 cards is well shuffled. The top card is then turned
over. What is the probability that the top
card is a red card.


Concentrated \( H N O_{3} \) reacts with iodine
to give:
A . \( H I \)
в. \( H I O_{3} \)
\( \mathrm{c} \cdot \mathrm{NO}_{2} \)
D. None of these


One point on the plank is at rest
immediately after the collision, Where
is it?


A big truck moving along a straight line at a speed of \( 54 \mathrm{km} / \mathrm{hr} \) stop in \( 5 \mathrm{s} \) after the breaks are applied. Find the acceleration.


A solid sphere, a hollow sphere and a disc, all having the same mass and
radeius, are placed at the top of an incline and released. The friction
coefficients between the objects and
the incline are same and not sufficient
to allow pure rolling. The least time will be taken in reaching the bottom by
A. the solid sphere
B. the hollow sphere
c. the disc
D. all will take the same time


Assertion
The magnetic moment of \( M g \) -atom is
more than \( K \) -atom as the former has
two electrons in outermost shell.
Reason
The magnetic moment of \( N \) -atom is
more than magnetic moment of \( O \) -atom
and former has more number of
unpaired electrons.
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 the correct explanation for Assertion.
D. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.


The ease of formation of which of
following chlorides is maximum?
A . \( N a C l \)
в. \( K C l \)
c \( . R b C l \)
D. \( C s C l \)


The magnitude of a frictional force
depends on:
This question has multiple correct options
A. the surface area of contact
B. the weight of the object
C. the nature of the surface in contact
D. none


Make the correct pairs from below
mentioned \( X \) and \( Y \)
\[
\boldsymbol{X}
\]
a) Dehydrating agent
1) Sulphur dioxide gas
b) In preparation of fire
2) Concentrated crackers \( \quad \) sulphur acid
c) Weak bleaching agent
3 ) Dihydrogen gas
d) Lightest gas
4) Sulphur
\( \mathbf{A} \cdot(a-2),(b-4),(c-1),(d-3) \)
B \( \cdot(a-3),(b-2),(c-4),(d-1) \)
C \( .(a-4),(b-3),(c-1),(d-2) \)
D. \( (a-3),(b-1),(c-2),(d-4) \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{5} \boldsymbol{s} \boldsymbol{i} \boldsymbol{n}^{2} \boldsymbol{x} \) be
an increasing function on the set \( R \) Then, a and b satisfy
A \( \cdot a^{2}-3 b-15>0 \)
B . \( a^{2}-3 b+15>0 \)
c. \( a^{2}-3 b+15<0 \)
D. \( a>0 \) and \( b>0 \)


Excess of \( K I \) and \( d i l . H_{2} S O_{4} \) were
\( \operatorname{mixed} \operatorname{in} 50 m L H_{2} O_{2} . \) The liberated \( I_{2} \)
required \( 20 m L \) of \( 0.1 N N a_{2} S_{2} O_{3} \)
Find out the strength of \( H_{2} O_{2} \) in
\( \boldsymbol{g} \) per litre.


Radial symmetry is often exhibited by animals having
A. One opening of alimentary canal
B. Ciliary mode of feeding
c. Benthos or sedentary nature
D. None of the above


Which of the following expressions are applicable to the moving coil galvanometer?
A \( \cdot \overrightarrow{F_{m}}=q(\vec{V} \times \vec{B}) \)
в. \( B=B_{0} \tan \theta \)
c. \( \vec{\tau}=\vec{M} \times \vec{B} \)
D. none of these


Number of irrational terms in the binomial expansion of \( \left(3^{1 / 5}+7^{1 / 3}\right)^{100} \)
is
A . 94
B. 88
c. 93
D. 95


Assertion
Angle of repose is equal to angle of
limiting friction.
Reason
When the body is just about to move, the force of friction in this stage is called as limiting friction.
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 length of the cork cylinder inside
the water in equilibrium is:
\( A \cdot 6 c m \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 8 c m \)
D. 3 cm


Which of the following RNA's picks up specific amino acid from amino acid pool in the cytoplasm to ribosome during protein synthesis?
\( \mathbf{A} \cdot \) tRNA
B. mRNA
c. rRNA
D. All of the above


The presence of nitrogen in the organic compound is tested as:
A. \( N_{2} \)
в. \( N H_{3} \)
c. \( N O \)
D. \( C N \)


Use the bond energies to estimate \( \Delta \boldsymbol{H} \)
for this reaction:
\[
\boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{g})
\]
Bond
\[
H-H
\]
\( 436 k J_{m o l}-1 \)
\( \mathbf{A} \cdot-127 k J \)
B . \( -209 k J \)
c. \( -484 k J \)
D. \( -841 k J \)


Find the equation of the circle with
centre (-1,-2) and radius 5


Light of wavelength \( 6000 A^{\circ} \) from a distant source falls on a slit 0.5 mm
wide. The distance between two dark
bands on each side of the central
bright band of the diffraction pattern observed on a screen placed at a distance \( 2 m \) from the slit is:
A . 1.2 nm
B. 2.4 nm
\( c .3 .6 n m \)
D. \( 4.8 \mathrm{mm} \)


The coordinates of any point, which lies
on \( x \) axis are
A \( .(0, x, 0) \)
в. \( (x, 0,0) \)
c. \( (x, x, 0) \)
D. \( (x, x, x) \)


Factorise: \( 49 x^{2}-\frac{16}{25} \)


Which one of the following is a sesamoid bone?
A . Pelvis
B. Patella
c. Pterygoid
D. Pectoral girdle


Find the equation of the circle concentric with \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{4} \boldsymbol{x}-\boldsymbol{6} \boldsymbol{y}- \)
\( 3=0 \) and which touches the \( y- \) axis.


\( \int_{0}^{\pi / 2} \sin x \cos x d x \) is equal to:


If temperature scale is changed from \( C \)
to \( F, \) numerical value of specific heat
will
\( A \). increase
B. decrease
c. remain same
D. nothing can be decided


What are trophic levels? Give an
example of a food chain and state the different trophic levels in it.


n balls each of mass m impinge elastically each second on a surface with velocity u. The average force experienced by the surface will be
A . mnu
B. \( 2 m n u \)
c. \( 4 m n u \)
D. \( m n u / 2 \)


There are 37 terms in an \( A . P ., \) the sum
of three terms placed exactly at the
middle is 225 and the sum of last three
terms is \( 429 . \) Write the \( A . P \)


If \( a \sin ^{3} x+b \cos ^{3} x=\sin x \cos x \) and
\( a \sin x=b \cos x \) then \( a^{2}+b^{2}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


What happens when anisole is treated
with \( C H_{3} C l / \) anhydrous \( A l C l_{3} ? \) Write
chemical equation in support of your
answer


When a body is projected vertically up from the ground its velocity is reduced to \( \frac{1}{4} \) th of its velocity at ground at height
h. Then the maximum height reached
by the body is
A \( \cdot \frac{15}{32} h \)
в. \( \frac{15}{16} h \)
c. \( \frac{15}{8} h \)
D. \( \frac{5}{4} h \)


A wire of length L and 3 identical cells of negligible internal resistances are
connected in series. Due to the current,
the temperature of the wire is raised by
\( \Delta T \) in a time t. A number \( N \) of similar
cells is now connected in series with a
wire of the same material and cross-
section but the length 2 L. The temperature of the wire is raised by
the same amount \( \Delta T \) in the same t. The
value of \( \mathrm{N} \) is
\( A \cdot 3 \)
B. 2
\( c \cdot 6 \)
D. 4


If one were to apply Bohr model to a
particle of mass ' \( m^{\prime} \) and charge \( ^{\prime} q^{\prime} \) moving in a plane under the influence of
a magnetic field \( B \), the energy of the
charged particle in the \( n^{t h} \) level will be:
\( ^{A} \cdot n\left(\frac{h q B}{8 \pi m}\right) \)
в. \( n\left(\frac{h q B}{4 \pi m}\right) \)
c. \( n\left(\frac{h q B}{2 \pi m}\right) \)
D. \( n\left(\frac{h q B}{\pi m}\right) \)


The total energy of in the electron in the hydrogen atom in the ground state is \( -13.6 e V . \) Which of the following is its
kinetic energy in the first exited state?
A. 13.6 eV
B. 6.8 eV
c. \( 3.4 e V \)
D. 1.825 eV


From a lot of 6 items containing 2
defective items, a sample of 4 items are
drawn at random. Let the random
variable X denote the number of
defective items in the sample. If the sample is drawn without replacement, find the probability distribution of \( X \)


The ratio of the area of two similar
triangles is \( 9: 16, \) then the ratio of their
corresponding sides will be


The features which help to distinguish the male from the female are called as
A. sex chromosomes
B. Primary sexual characters
c. Secondary sexual characters
D. All of the above


A smooth block loosely fits in a circular tube placed on a horizontal surface. The
block moves in a uniform circular
motion along the tube. Which wall (inner or outer) will exert a non-zero
normal contact force on the block?


Property of carbon gives rise to the structural isomerism of organic compounds is:
A. catenation
B. multiple bond formation
c. functional group
D. Both A and B


The tire pictured below is rolling to the
left at a constant speed without
slipping on a horizontal roadway.
What is the direction of the acceleration
of the part of the tire that is in contact
with the road?
A. Left
B. Right
c. up
D. Down
E. The acceleration of this part of the tire is zero


Find the unknown angles in the given
figures :
\( (i i) \)


Divide:-
\( \boldsymbol{X}^{2}+\mathbf{5} \boldsymbol{X}+\mathbf{6} \boldsymbol{b} \boldsymbol{y} \boldsymbol{X}+\mathbf{2} \)


Let \( R \) be the equivalence relation on the
\( \operatorname{set} Z \) of integers given by \( \boldsymbol{R}= \)
\( \{(a, b): 2 \text { divides } a-b\} . \) Write the
equivalence class \( [\mathbf{0}] \)


Two radioactive materials \( A \) and \( B \) have
decay constants 5 \lambda and \( \lambda \) respectively. Initially both \( A \) and \( B \) have the same number of nuclei. The ratio of the
number of nuclei of \( A \) to that of \( B \) will be
\( \frac{1}{e} \) after a time
A \( \cdot \frac{1}{5 \lambda} \)
в. \( \frac{1}{4 \lambda} \)
\( c \cdot \frac{5}{4 \lambda} \)
D. \( \frac{4}{5 \lambda} \)


by two statements, Statement 1 and
Statement \( 2 . \) Of the given four
alternatives after the statements,
choose the one that best describes
the statements.
A thin air film is formed by putting the
convex surface of a plane convex lens
over a plane glass plate. With monochromatic light, this film gives an
interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

Statement 1: When light reflects from the air-glass plate interface, the reflected wave suffers a phase change
of \( \pi \)
Statement 2: The center of the
interference pattern is dark.
A. Statement 1 is True, Statement 2 is False
B. Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1
c. Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1.
D. Statement 1 is False, Statement 2 is True.


\( \ln 1900, \) the forest cover of the world comprised
A. 2500 million ha
B. 7000 million ha
c. 5500 million ha
D. 1700 million ha


How many optical isomer will the tartaric acid show?
A . 3
B. 4
c. 0
\( D \)


How is \( n- \) propoxypropane
synthesized from propan \( -1- \) ol?
Write the mechanism of this reaction.


Enter 1 if true else 0 . If \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=4 \hat{i}-2 \hat{j}+3 \hat{k} \) and
\( \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}-\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
then \( 2 \hat{i}-4 \hat{j}+4 \hat{k} \) a vector of
magnitude 6 units which is parallel to the vector \( 2 \vec{a}-\vec{b}+3 \vec{c} \)


Pressure can be measured by using Mercuric as well as Aneroid barometer.
A. True
B. False


The rating of a fuse depends upon the
A. thickness of the fuse wire
B. length of the wire
\( c \cdot \) both
D. none


What is eutrophication?
A. Increased concentrations of chemical nutrients
B. Increased level of water
C. Oxygen depletion
D. None of the above


Which of the following is not a general
method of preparation of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. By action of heat on nitric acid and sulphur
B. By passage of chlorine through an aqueous solutions of sulphur dioxide
c. By dissolution of sulphur trioxide in water
D. None of the above


Of the following the commonly used as a laboratory desiccator is :
A. \( N a_{2} C O_{3} \)
в. \( C a C l_{2} \)
c. Nacı
D. None of the above


How many grams of \( N a O H \) should be
added to water to prepare \( 250 \mathrm{ml} \) solution of 2 M NaOH ?
A \( \cdot 9.6 \times 10^{3} \)
В. \( 2.4 \times 10^{3} \)
c. 20
D . 24


You know that \( \frac{1}{7}=0.142857 . \) Find the decimal expansions of \( \frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7} \) are
without actually doing the long division?


Two number are selected at random
(without replacement ) from the first six positive integers. Let \( X \) denote the larger of the numbers obtained. Find \( E \)
\( (x) \)


An electric kettle is rated \( 2.5 k W, 250 V \)
What is the cost of running the kettle
for two hours at Rs. 5.40 per unit?
A. \( R s .17 .00 \)
B. \( R s .27 .00 \)
c. \( R s .26 .00 \)
D. \( R s .16 .20 \)


A codon is made up of
A. single nucleotide
B. Two nucleotides
C. Three nucleotides
D. Four nucleotides


A cork floating in a calm lake is executing \( S H M \) of frequency \( f \). When a boat passes close to the cork then the
A. Frequency becomes greater than \( f \)
B. Frequency becomes less than \( f \)
c. Frequency remains constant
D. None of these


Right ventricular wall is thinner than the left ventricular wall. Why?


How will you show that air supports burning?


How many mL of \( 0.3 \mathrm{M} K_{2} C r_{2} O_{7}(\text { acidic }) \)
is required for complete oxidation of 5
\( \mathrm{mL} \) of \( 0.2 \mathrm{M} \) Sn \( C_{2} \mathrm{O}_{4} \) solution.
(Round off to 1 decimal place)


The angle made by the line \( \sqrt{\mathbf{3}} \boldsymbol{x}-\boldsymbol{y}+ \)
\( \mathbf{3}=\mathbf{0} \) with the positive direction of \( \mathbf{X} \)
axis is
\( A \cdot 30 \)
B . 45
\( c \cdot 60 \)
D. \( 90^{\circ} \)


\( \boldsymbol{R} \boldsymbol{X}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a}+\boldsymbol{X} \boldsymbol{R} \rightarrow \boldsymbol{R}-\boldsymbol{R}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{X} \)
Role of Na and name of the reaction
mentioned above is:
A. Reducing agent and Kolbe's reaction
B. Oxidising agent and Wurtz reaction
c. Reducing agent and Wurtz reaction
D. Oxidising agent and Kolbe's reaction


What is the acidity order of the
following compounds?
\( \mathbf{A} \cdot I>I I>I I I>I V>V \)
\( \mathbf{B} \cdot I I>I I I>I V>V>I \)
\( \mathbf{c} \cdot V>I I I>I>I I>I V \)
D. \( V>I I I>I I>I>I V \)


Which of the following statements is wrong about symmetry, while the other
three are correct?
A. Any plane that passes through the centre does not divide the body into equal halves in most sponges
B. The body of an arthropod can be divided into identical halves in two planes
c. Any plane passing through the central axis of the body divides Hydra into two identical halves
D. The body of an annelid can be divided into identical halves in only one plane.


Five hundred milliliters of solution of 0.1
M Na Br has how many milligrams of bromine?
A. 200 \( \mathrm{mg} \)
B. 400 mg
c. \( 2,000 \mathrm{mg} \)
D. \( 4,000 \mathrm{mg} \)
E. 20,000 \( \mathrm{mg} \)


A plane is in a level flight at a constant speed and each of its two wings has an
area of \( 25 m^{2} . \) If the speed of air is
\( 180 \mathrm{kmh}^{-1} \) over the lower wing and
\( 234 k m h^{-1} \) over the upper wing surface, the plane's mass is : (Take density of air \( =1 k g m^{-3} . \) )
A. \( 4.400 g m \)
в. \( 4400 g \) т
c. \( 44.0 k g \)
D. \( 4400 k g \)


Suppose evolution on earth has
occurred in such a way that there are 96 amino acids instead of 20 DNA has 12
different types of bases and DNA synthesis occur in the same way as today.The minimum number of bases per DNA condon would be
A \( \cdot 12 \)
B. 8
\( c \cdot 2 \)
D. 3


Identify the electron donor for the electron transport chain in photosynthesis.
A. Oxygen
B. NADPH \( _{2} \)
c. NADP
D. water


Glomerulus occurs in ...................... capsule.
A. Bowman's
B. Kreb's
C. Pacinian
D. None of the above


The linear momentum of a ball of mass
\( 50 g \) is \( 0.5 k g m s^{-1} . \) Find its velocity.
\( \mathbf{A} \cdot 0.01 \mathrm{ms}^{-1} \)
B. \( 1 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 5 \mathrm{ms}^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)


Which of the following molecule doesn't have \( d \pi-p \pi \) bonding?
\( A \cdot S O_{2} \)
В. \( P_{4} O_{10} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{4} \)
D. \( B_{3} N_{3} H_{6} \)


On approximately what percent of the
days was the 2 p.m temperature above
\( 40^{\circ} F \) but less than \( 70^{\circ} F ? \)
a
A. Approx. \( 50 \% \)
B. Approx. \( 70 \% \)
c. Approx. \( 60 \% \)
D. None of these


Find the principle value of: \( \cos ^{-1}\left(-\frac{1}{2}\right) \)


If \( g \) on the surface of the Earth is
\( 9.8 m s^{-2}, \) its value at a height of
\( 6400 k m \) is: (Radius of the Earth \( = \)
\( 6400 k m) \)
A. \( 4.9 \mathrm{ms}^{-2} \)
В. \( 9.8 \mathrm{ms}^{-2} \)
c. \( 2.45 \mathrm{ms}^{-2} \)
D. \( 19.6 \mathrm{ms}^{-2} \)


Write down next three numbers to
continue the pattern.
1,76,\( 300 ; 1,76,400 \)


A body is projected vertically upward
with a velocity of \( 10 m s^{-1} \). It reaches maximum height \( h \) at time \( t . \) In time \( \frac{t}{2} \) the height covered is
A \( \cdot \frac{h}{2} \)
в. \( \frac{2}{5} h \)
\( c \cdot \frac{3}{4} h \)
D. \( \frac{5}{8} h \)


Column I contains physical quantity/process while column I contains formula/principle. Match
column I and II such that the
formula/principle is correct corresponding to the quantity in column I.


Which of the following pairs of solutions are expected to be isotonic, temperature being the same?
A \( \cdot 0.1 \mathrm{M} \) glucose and \( 0.1 \mathrm{M} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{N}^{+} \mathrm{H}_{3} \mathrm{Cl} \)
B. \( 0.1 \mathrm{M} \) NaCl and \( 0.05 \mathrm{M} \) BaCl ,
c. \( 0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} \) and \( 0.1 \mathrm{M} \mathrm{KNO} \)
D. \( 0.1 \mathrm{M} \) BaCl\( _{2} \) and \( 0.075 \mathrm{M} \) FeCl\( _{3} \),


The sum of \( n \) terms of \( 1^{2}+\left(1^{2}+\right. \)
\( \left.2^{2}\right)+\left(1^{2}+2^{2}+3^{2}\right)+\dots . \)
A \( \cdot \frac{n(n+a)(2 n+1)}{6} \)
в. \( \frac{n(n+1)(2 n-1)}{6} \)
c. \( \frac{1}{12} n(n+1)^{2}(n+2) \)
D. \( \frac{1}{12} n^{2}(n+1)^{2} \)


The domain of \( \frac{1}{\sqrt{x-x^{2}}}+ \) \( \sqrt{3 x-1-2 x^{2}} \) is
\( ^{\mathbf{A}} \cdot\left(\frac{1}{2}, 11\right) \)
в. \( \left(\frac{1}{2}, 31\right) \)
c. \( \left(\frac{1}{2}, 17\right) \)
D \( \cdot\left(\frac{1}{2}, 41\right) \)


Conjugate base of a weak acid has \( \boldsymbol{K}_{b}=\mathbf{1 0}^{-9} . \) The equilibrium constant
for the reaction of acid with strong base is:
\( \mathbf{A} \cdot 10^{-19} \)
B . \( 10^{-3} \)
\( c \cdot 10^{9} \)
D. \( 10^{5} \)


Compare the energies of two radiations
\( \boldsymbol{E}_{1} \) with wavelength \( 800 \mathrm{nm} \) and \( \boldsymbol{E}_{2} \)
with wavelength \( 400 \mathrm{nm} \)
A. \( E_{1}=2 E_{2} \)
в. \( E_{1}=E_{2} \)
\( \mathbf{c} \cdot E_{2}=2 E_{1} \)
D \( \cdot E_{2}=-\frac{1}{2} E_{1} \)


If \( \bar{E} \) and \( \bar{F} \) are complementary events of E and F respectively and if \( 0< \)
\( \boldsymbol{P}(\boldsymbol{F})<1, \) then
This question has multiple correct options
A \( \cdot P(E / F)+P(\bar{E} / F)=1 \)
B . \( P(E / F)+P(E \bar{F})=1 \)
c. \( P(\bar{E} / F)+P(E \bar{F})=1 \)
D . \( P(E \bar{F})+P(\bar{E} \bar{F})=1 \)


An unpolarized beam of light is incidents on a group of four polarizing sheets, which are arranged in such a way, that of the characteristic direction
of each polarizing sheet makes an
angle of \( 30^{0} \) with that of the preceding
sheet. The percentage of incident light transmitted by the first polarizered will be :
\( \mathbf{A} \cdot 100 \% \)
B. \( 50 \% \)
c. \( 25 \% \)
D. \( 12.5 \% \)


IUPAC name for \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{2+} \) is:
A. hexammoniacobaltate(II) ion
B. hexaamminecobaltate(II) ion
c. hexammoniacobalt(II) ion
D. hexaamminecobalt(II) ion


Which of the following side chain reaction/s can be used to reduce the
activity groups such as \( (O H) \) or
\( \left(-N H_{2}\right) ? \)
This question has multiple correct options
A. Benzoylation
B. Acetylation
c. Tosylation
D. sulphonation


A cracker is thrown into air with a
velocity of \( 10 \mathrm{m} / \mathrm{s} \) at an angle of \( 45^{\circ} \) with
the vertical. When it is at a height of 0.5 \( \mathrm{m} \) from the ground, it explodes into a number of pieces which follow different parabolic paths. What is the velocity of centre of mass, when it is at a height of \( 1 \mathrm{m} \) from the ground? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A \( .4 \sqrt{5} \mathrm{m} / \mathrm{s} \)
B . \( 2 \sqrt{5} \mathrm{m} / \mathrm{s} \)
c. \( 4 \sqrt{4} m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


Critical temperature of \( N_{2}, C O \) and
\( C H_{4} \) are 126,134 and \( 190 \mathrm{K} \)
respectively. Arrange them in increasing order of adsorption on the surface of activated charcoal?


Consider following statements.
\( (I) \) The size of the lanthanide ions
\( \left(M^{3+}\right) \) decreases as the atomic
number of \( M \) increases.
\( (I I) \) Electronic spectra of lanthanides show very broad bands.
\( (I I I) \) As with transition metals, coordination number six is very
common in lanthanide complexes.
Which of the statements given above
is/are correct?
A. \( I \) only
B. \( I \) and \( I I \)
c. \( I \) and \( I I I \)
D. III only


The number of solutions of the system
of equations \( \operatorname{Re}\left(z^{2}\right)=0 ;|z|=2 \) is
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


Sundew is also known as
A. Dionaea
B. Nepenthes
c. Drosera
D. Striga


A cell can be balanced against \( 110 \mathrm{cm} \)
and \( 100 \mathrm{cm} \) of potentiometer wire respectively, with and without being short-circuited through a resistance of
10\Omega. Its internal resistance is :
A . \( 1.0 \Omega \)
B. \( 0.5 \Omega \)
c. \( 2.0 \Omega \)
D. zero


Describe in short the hereditary and acquired characters.


Match the column:
a. optic nerve
i. coloured part of the eye
ii. refracts light and focuses a
b. ciliary muscle real image on the back of eye
iii. it can increase or decrease
c. lens \( \quad \) the thickness of lens
¡v. carries information to the
d.iris \( \quad \) brain about light that strikes the retina
\( A \cdot a-i, b-i i i, c-i v, d-i i \)
B. a-ii,b-i,c-iv,d-iii
C \( . a-i \) ii, b-iv,c-i,d-ii
D. a-iv,b-iii,c-ii,d-i


Write two similarities between
chemistry of lanthanoids and actinoids.


If \( I_{n}=\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{2} n x}{\sin ^{2} x} d x, \) then \( I_{1}, I_{2}, I_{2}, \cdots \)
are in
A. A.P
в. G.
c. н.P.
D. none


The mean deviation from the data
\( \mathbf{3}, \mathbf{1 0}, \mathbf{1 0}, \mathbf{4}, \mathbf{7}, \mathbf{1 0}, \mathbf{5} \)
\( \mathbf{A} \cdot \mathbf{3} \)
B . 2
c. 3.75
D. 2.57
E. None of these


In the arrangement shown in the figure,
if the surface is smooth, the
acceleration of the hanging block \( \boldsymbol{m}_{2} \)
will be \( \left(m_{1} \text { is on the table }\right) \)
A \( \cdot \frac{m_{2} g}{4 m_{1}+m_{2}} \)
В. \( \frac{2 m_{2} g}{4 m_{1}+m_{2}} \)
c. \( \frac{2 m_{2} g}{m_{1}+4 m_{2}} \)
D. \( \frac{2 m_{1} g}{m_{1}+m_{2}} \)


If the vectors \( 3 \bar{p}+\bar{q} ; 5 \bar{p}-3 \bar{q} \) and \( 2 \bar{p}+ \)
\( \bar{q} ; 4 \bar{p}-2 \bar{q} \) are pairs of mutually
perpendicular vectors then \( \sin (\theta) \) is \( (\theta \) is the angle between \( \overline{\boldsymbol{p}} \) and \( \overline{\boldsymbol{q}} \)
A \( \cdot \sqrt{55} / 4 \)
B . \( \sqrt{55} / 8 \)
c. \( 3 / 16 \)
D. \( \sqrt{247} / 16 \)


When \( 1^{0} \) amine reacts with \( C H C l_{3} \)
in ethanolic \( K O H, \) the product
formed is:
A. an isocyanide
B. an aldehyde
c. a cyanide
D. an alcohol


Explain the internal structure of kidney?


toppr
Q Type your question
is given by \( y=f(x-150 t) \) where \( x \) is in
meters and t is in seconds.

The pulse (y) is plotted as a function of
\( x \) for \( t=0 . \) Draw the pulse (in the panels
given)
(i) as a function of \( x \) for \( t=0.04 s \)
(ii) as a function of \( t \) for \( x=0 \)
A \( \cdot V=150 \mathrm{m} / \mathrm{s} ; \quad x=v t ; \quad x=150 \times \frac{4}{100}=6 \mathrm{cm} \)
B. \( V=120 \mathrm{m} / \mathrm{s} ; \quad x=v t ; \quad x=150 \times \frac{4}{100}=6 \mathrm{cm} \)
\( \mathrm{C} \cdot \mathrm{V}=150 \mathrm{m} / \mathrm{s} ; \quad x=v t ; x=120 \times \frac{4}{100}=6 \mathrm{cm} \)
\( V=150 m / s ; \quad x=v t ; x=150 \times \frac{4}{100}=5 \mathrm{cm} \)


A solution containing a mixture of \( 0.05 M N a C I \) and \( 0.05 \mathrm{M} \) Nal is taken.
\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}=\mathbf{1 0}^{-10} \) and \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I}= \)
\( 4 \times 10^{-16} \) ). When \( A g N O_{3} \) is added to
such a solution
A. \( A g C I \) and \( A g I \) will be precipitate together
B. First \( A g C l \) will be precipitated
C. First \( A g I \) will be precipitated
D. neither \( A g I \) nor \( A g C l \) precipitate


The enzyme converting Angiotensin-I to Angiotensin-II is secreted by?
A. Kidneys
B. GI tract
c. Lungs
D. Heart


Atomic number of platinum is?
A . 68
B. 78
c. 74
D. 64


\( \ln a \Delta A B C, D, E, F \) are respectively
the mid- points of \( B C, C A, \) and \( A B . \) If
the lengths of side \( A B, B C \) and \( C A \) are \( \mathbf{7} c \boldsymbol{m}, \mathbf{8} \boldsymbol{c m}, \mathbf{9} \boldsymbol{c m}, \) respectively, find the
perimeter of \( \Delta \) DEF.
A . \( 12 \mathrm{cm} \)
B. \( 21 \mathrm{cm} \)
c. \( 24 \mathrm{cm} \)
D. \( 16 \mathrm{cm} \)


Solve \( :\left[\left(4 x^{4}-3 x^{3}-2 x^{2}+4 x-3\right)\right. \)
divide by \( (x-1) \)


What mass of sodium chloride would be decomposed by \( 9.8 \mathrm{g} \) of sulphuric acid if \( 12 \mathrm{g} \) of sodium bisulphate and \( 2.75 \mathrm{g} \) of hydrogen chloride were produced in a
reaction?
\( A \cdot 14.75 \mathrm{g} \)
в. 3.8 g
c. \( 4.95 \mathrm{g} \)
D. 2.2 g


The B-H curve (i) and (ii) shown in the
given figure is associated with
A . (i) diamagnetic and (ii) paramagnetic substance
B. (i) paramagnetic and (ii) ferromagnetic substance
\( c . \) (i) soft iron (ii) stee
D. (i) steel and (ii) soft iron


Given below are the names of few
elements based on their position in the periodic table. Identify the element which is not correctly placed.
A. An element which tends to lose three electrons Aluminium
B. An element which tends to gain two electrons - lodine
c. An element with valency four - silicon
D. A transuranium element- Plutonium


Derive an expression for electric field due to an electric dipole at a point on its axial line.


ff \( D=\left|\begin{array}{ccc}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right| \) and \( D_{0}= \)
\( \left|\begin{array}{ccc}\boldsymbol{k} \boldsymbol{a}_{1} & \boldsymbol{k} \boldsymbol{b}_{1} & \boldsymbol{k} \boldsymbol{c}_{1} \\ \boldsymbol{k} \boldsymbol{a}_{2} & \boldsymbol{k} \boldsymbol{b}_{2} & \boldsymbol{k} \boldsymbol{c}_{2} \\ \boldsymbol{k} \boldsymbol{a}_{3} & \boldsymbol{k} \boldsymbol{b}_{3} & \boldsymbol{k} \boldsymbol{c}_{3}\end{array}\right| \) then show that
\( \boldsymbol{D}_{0}=\boldsymbol{k}^{3} \boldsymbol{D} \)


The plot of \( \log \) K against \( \frac{1}{T} \) is a straight line with a positive slope (K being the equilibrium constant of a reaction), which of the following is then correct?
A. The reaction is endothermic in nature
B. The reaction will be exothermic in nature
c. The reaction goes to further extent on raising the temperature
D. None of these


Very high number of alveoli present in a lung is meant for
A. More space for increasing volume of inspired air
B. More area for diffusion
c. Making the organ spongy
D. Increasing nerve supply


Indicate the wrong statement on the
basis of the periodic table.
A. The most electronegative element in the periodic table is fluorine.
B. Scandium is the first transition element and belongs to fourth period.
C. There are three transition series in the periodic table each containing 10 elements.
D. Along a period halogens have maximum negative electron gain enthalpy.


Two equal chords of a circle intersect
within the circle Then the
corresponding segments of the chords
are
A . not always equal
B. not equal
c. not related anyway
D. equal


The direction of river in the following
contour pattern is.
\( A \cdot D \) to \( B \)
B. B to C
\( c \), Ato
cto


Instrument used to measure the
temperature is
A. protractor
B. stethoscope
c. thermometer
D. none of these


toppr
Q Type your question.
uniform magnetic field \( B \) with constant velocity \( \boldsymbol{v} \) at \( t=0 . \) The longest side of the frame is perpendicular to the direction of velocity If i is the instantaneous current through the frame then choose the alternative
showing the correct variation of i with time
\( A \)
\( (\mathrm{A}) \)
в.
\( (\mathrm{B}) \)
\( c \)
\( (\mathrm{C}) \)
\( D \)
\( (\mathrm{D}) \)