When \( S O_{2} \) is passed through acidified
\( K_{2} C r_{2} O_{7} \) solution :
A. the solution turned blue
B. the solution is decolourised
\( \mathrm{c} \cdot \mathrm{SO}_{2} \) is reduced
D. green \( \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3} \) is formed


Which one of the following is an example of the binomial scientific
name?
A . Green algae
B. Snow leopard
c. Rana tigrina
D. China-rose


The system of classification of angiosperms which is based on a few number of characters is referred to as
A. Artificial system
B. Natural system
c. Phylogenetic system
D. All of the above


Angles opposite to the equal sides of a triangle are equal.ff true enter 1 else 0


In a geometric series, the first term \( =a \)
common ratio \( =r . \) If \( S_{n} \) denotes the
sum of the \( n \) terms and \( U_{n}=\sum_{n=1}^{n} S_{n} \)
then \( r S_{n}+(1-r) U_{n} \) equals to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot n a \)
D. \( n a \)


In the given figure, \( A B=B C \) and
\( A C=C D . \) Prove that: \( \angle B A D \)
\( \angle A D B=3: 1 \)


For \( 2 \geq r \geq n,\left(\begin{array}{c}r \\ n\end{array}\right)+2\left(\begin{array}{c}r-1 \\ n\end{array}\right)+\left(\begin{array}{c}r-2 \\ n\end{array}\right) \)
A \( \cdot\left(\begin{array}{c}r-1 \\ n+1\end{array}\right) \)
B \( \cdot 2\left(\begin{array}{c}r+1 \\ n+1\end{array}\right) \)
\( \mathbf{c} \cdot 2\left(\begin{array}{c}r \\ n+1\end{array}\right) \)
D. \( \left(\begin{array}{c}r \\ n+1\end{array}\right) \)


Formation of a gametophyte (i.e. embryo sac or pollen) on a sporophyte without any reduction division is known
as
A. Apospory
B. Parthenogenesis
c. Apogamy
D. Amphimixis


Derive the distance traveled by an
object in \( n^{t h} \) sec with the help of graph


Q Type your question
a wall. The jeep has to take a sharp
perpendicular turn along the wall. A rocket flying at uniform speed of 100kmh \( ^{-1} \) starts from the wall towards
the jeep which is \( 30 k m \) away. The
rocket reaches the windscreen and
returns to wall. Total distance covered
by the rocket is
A . \( 100 k m \)
\( \mathbf{B} .50 k m \)
\( c .37 k m \)
D. \( 75 k \)


Tension is measured in units of
A. Momentum
B. Force
c. Length
D. None


A functional aspect of an ecosystem is
A. Producers, consumers and abiotic environment
B. Regulation of populations
C. Light, temperature, oxygen and carbon dioxide
D. Both A and C


Write the polynomial in standard form
and also write down their degree. \( 4 z^{3}-3 z^{5}+2 z^{4}+z+1 \)


Short / Long answer type questions.
Give a brief account of complex tissue present in plants.


In a dicot leaf, vascular bundles are
found in the
A. Chloroplast
B. Palisade tissue
c. Lower epidermis
D. Upper epidermis
E. spongy mesophyll


Repeated observations in an experiment gave the values 1.29,1.33,1.34,1.35,1.32,1.36,1.30
and \( 1.33 . \) Calculate the mean value,
absolute error, relative error, and
percentage error


Gases have low
A. density ; compressibility
B. compressibility ; density
C. compressibility ; inter- molecular force
D. compressibility ; volume


If \( \boldsymbol{A}=\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}, \boldsymbol{B}=\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1} \)
then \( \boldsymbol{A}-\mathbf{2} \boldsymbol{B} \)


Rutherford's scattering experiment is related to the size of the:
A. nucleus
B. atom
c. electron
D. neutron


Which nuclear reaction shows the
release of a beta particle?
\( \mathbf{A} \cdot_{92}^{235} U+_{0}^{1} n \rightarrow_{56}^{140} K r+_{56}^{140} B a+3_{0}^{1} n \)
B. \( _{84}^{210} P o \rightarrow_{82}^{206} P b+_{2}^{4} H e \)
\( \mathbf{C} \cdot_{6}^{14} C \rightarrow_{7}^{14} N+_{-1}^{0} e \)
D. \( _{47}^{106} A g+_{-1}^{0} e \rightarrow_{46}^{106} P d \)
\( \mathbf{E} \cdot_{19}^{38} K \rightarrow_{18}^{38} A r+_{+1}^{0} e \)


In the given circle identify and write
The sector


Two wheels \( A \) and \( B \) are mounted on the
same axle. moment of inertia of \( A \) is 6
\( \mathrm{kg} \boldsymbol{m}^{2} \) ans it is rotating at \( 600 \mathrm{rpm} \)
when \( \mathrm{B} \) is at rest. What is moment of inertia of \( \mathrm{B} \), if their combined speed ids
400 rpm?
\( A \cdot 9 \mathrm{kg} m^{2} \)
B. 4 kg \( m^{2} \)
\( \mathrm{c} \cdot 3 \mathrm{kg} \mathrm{m}^{2} \)
\( D \cdot 5 \mathrm{kg} m^{2} \)


Calculate the length of a chord which is at a distance of \( 12 \mathrm{cm} \) from the centre
of a circle of radius \( 13 \mathrm{cm} \)


A particle is moving with a constant speed along a straight line path. A force is not required to:
A. Increase its speedd
B. Decrease its momentum
c. change the direction
D. Keep it moving with uniform velocity


\( f(x)\left\{\begin{array}{cc}x^{4} & x^{2}<1 \\ x & x^{2} \geq 1\end{array} \) Discuss the \right.
existence of limit at \( x=1 \) and \( x=-1 \)
A. Limit exist at both \( x=1 \) and \( x=-1 \)
B. Limit does not exist at both \( x=1 \) and \( x=-1 \)
c. limit exist at \( x=1 \) but not at \( x=-1 \)
D. limit exist at \( x=-1 \) but not at \( x=1 \)


statement
(1): A metallic plate
containing a circular hole is heated
then the size of the hole increases.
statement
(2): The expansion of the solid always takes place readily outwards.
A. statement 1 and statement 2 are correct and statement 2 is correct an explanation for statement 1
B. statement 1 and statement 2 are correct and statement 2 is not the correct explanation for statement
c. statement 1 is true and statement 2 is false
D. statement 1 is wrong and statement 2 is true


\( \left[_{\boldsymbol{A} \mathbf{1}} \boldsymbol{C u}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{3}(\boldsymbol{O} \boldsymbol{H})\right]^{+}+ \)
\( \left[\boldsymbol{A l}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{O} \boldsymbol{H})\right]^{2+} \)
Choose the correct statement:
A \( . A_{1} \) is a base and \( A_{3} \) is an acid
B. \( A_{3} \) is conjugate acid of \( A_{1} \) and \( A_{4} \) is conjugate base of
\( A_{2} \)
C. \( A_{3} \) is conjugate base of \( A_{1} \) and \( A_{4} \) is conjugate acid of \( A_{2} \)
D. Noneofthese


Which of the following elements is a metalloid?
A. Lithium
B. Beryllium
c. Boron
D. Carbon


Assertion
Let \( f: R \rightarrow R \) be defined as \( f(x)= \)
\( a x^{2}+b x+c, \) where \( a, b, c \varepsilon R \) and \( a \neq \)
0
If \( f(x)=0 \) is having non-real roots, then \( \int \frac{d x}{f(x)}=\lambda \tan ^{-1}(g(x))+k \)
where \( \lambda, k \) are constants and \( g(x) \) is
linear function of \( x \)
Reason
\( \tan \left(\tan ^{-1} g(x)\right)=g(x) \forall x \in R \)
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


\( 1 \mathrm{M}= \)
LY
A vehicle travells with speed of 18 kmph than vehicle travells - .........m distance in
one second?

Normal force applied on body of mass \( m^{\prime} \) on slope of 0 is.


Applying mean value theorem on \( \boldsymbol{f}(\boldsymbol{x})=\log \boldsymbol{x} ; \boldsymbol{x} \in[\mathbf{1}, \boldsymbol{e}] \) the value of \( \boldsymbol{c}= \)
\( \mathbf{A} \cdot \log (e-1) \)
в. \( e-1 \)
\( \mathbf{c} \cdot 1-e \)
\( D \)


la, b, c are is G.P and \( a-b, c-a \) and \( b-a \)
are in H.P, then \( a+4 b+c \) is equal to


Brush border is characteristic of
A. Malpighian corpuscle
B. Collecting tube
c. Proximal convoluted tubule
D. All of the above


Vitamin A is present in?
A. fish liver oil
B. milk
c. butter
D. all of these


\( A \) and \( B \) are symmetric matrices of the same order. \( \boldsymbol{X}=\boldsymbol{A B}+\boldsymbol{B A} \) and \( \boldsymbol{Y}= \)
\( \boldsymbol{A B}-\boldsymbol{B A} \)
\( (\boldsymbol{X} \boldsymbol{Y})^{\boldsymbol{T}}= \)
A . \( X Y \)
в. \( Y X \)
\( c \cdot-Y X \)
D. \( X+Y \)


When \( N a C l \) solution is added to
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})_{3} \) sol then:
A \( \cdot\left[F e(O H)_{3}\right] F e^{3+} \) is formed
В \cdot \( \left[\mathrm{Fe}(\mathrm{OH})_{3}\right] \mathrm{Cl}^{-} \) is formed
C \( \cdot \operatorname{Fe}(O H)_{3} \) is coagulated
D・ \( \left[\operatorname{Fe}(O H)_{3}\right] N a^{+} \) is formed


Which one of the following is a
quadratic polynomial?
A \( \cdot x^{2}+3 \)
B. \( x^{3}+x^{2}+4 \)
\( \mathbf{c} \cdot 2 x^{4}+4 x^{3}+3 x^{2}+6 \)
D. None of the above


Which of the following stage of M-phase is considered as tetraploid stage?
A. Anaphase of mitosis
B. Anaphase-I of meiosis
c. Metaphase-II of meiosis
D. More than one option is correct


1.75 g of solid NaOH is added to 0.25 \( d m^{3} \) of \( 0.1 \mathrm{M} N i C l_{2} \) solution.
Calculate pH of final solution. (write your answer to nearest integer)
Given_ \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{N} \boldsymbol{i}(\boldsymbol{O} \boldsymbol{H})_{2}=\mathbf{1 . 6} \times \mathbf{1 0}^{-14} \)


Which is correct about saccharin?
\( A \)
B. It is 600 times sweeter than sugar
c. It is used as sweetening agent
D. All of these


The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown
by Bheeshm on him and with six other
arrows he killed the rath driver of
Bheeshm. With one arrow each, he
knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square
root of arrows he laid Bheeshm
unconscious on an arrow bed. Find the
total number of arrows Arjun had.


The correct order of acidic character in
the above compounds is:
\( A \cdot a>b>c>d \)
\( B \cdot c>a>d>b \)
\( \mathbf{C} \cdot b>c>a>d \)
\( \mathrm{D} \cdot \mathrm{a}>\mathrm{c}>\mathrm{b}>\mathrm{d} \)


The element with least melting point in VIA group is :
A.
B. s
\( c \cdot s e \)
D. Te


Solve the following by using the method of completing square. \( 6 x^{2}-11 x+3=0 \)


Halide containing halogen attached to
\( s p^{3} \) carbon is/are:
This question has multiple correct options
A. allylic halide
B. vinylic halide
c. benzylic halide
D. aryl halide


In a parallel plate capacitor, the capacity increases if :
A. area of the plate is decreased
B. distance between the plates increases
C . area of the plate increases
D. dielectric constant decrease


The number of protons, electrons and neutrons respectively in a molecule of heavy water is:
A. 10,10,10
в. 8,10,11
c. 10,11,10
D. 11,10,10


The number of ATP molecules produced by the electron transport system from Krebs cycle intermediates in a single turn is
A . 11
B. 14.
c. 12
D. 16


A gas, which is produced by the heating potassium chlorate, is:
A. \( H_{2} \)
в. \( S O_{2} \)
c. \( C O \)
D. HCl
E. \( O_{2} \)


Which of the following IUPAC name will be used to name carboxylic acid functional group?
A. -one
B. -oic acid
\( c .-a \)
D. - -ane


In Mendeleev's periodic table, gaps were left for the elements to be discovered
later. Which of the following elements found a place in the periodic table later?
A. Germanium
B. Chlorine
c. oxygen
D. silicon


If \( A, B, C, D \) are four points such that
\( \angle B A C=30^{\circ} \) and \( \angle B D C=60^{\circ} \) then
prove that
D is the centre of the circle through \( A, B \) and \( \mathrm{C} \)


toppr LoGil JOIN NOW
Q Type your question
curve and determine the median.


Which direction will you face if you start facing east and make \( 1 \frac{1}{2} \) of a revolution clockwise?


Prove that \( \left|\begin{array}{ccc}\boldsymbol{a}^{2}+\mathbf{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}^{2}+\mathbf{1} & \boldsymbol{b} \boldsymbol{c} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c b} & \boldsymbol{c}^{2}+1\end{array}\right|= \)
\( \mathbf{1}+\boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2} \)


The highest possible oxidation states of uranium and plutonium, respectively,
are:
A .6 and 4
B. 7 and 6
c. 4 and 6
D. 6 and 7


When will the couple acting on the coil be
(i) maximum
(ii) minimum?
A. (i) When plane of coil is normal to the magnetic field,
(ii) When plane of coil is normal to the magnetic field
B. (i) When plane of coil is parallel to the magnetic field
(ii) When plane of coil is parallel to the magnetic field.
C. (i) When plane of coil is parallel to the magnetic field,
(ii) When plane of coil is normal to the magnetic field
D. None of the above


heated together, the maximum weight
of \( C l_{2} \) gas evolved will be:
A. 2 gm
B. 0.975 gm
c. \( 0.486 \mathrm{gm} \)
D. 0.972 gm


If the function \( f: R \rightarrow R \) be such that
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}], \) where \( [\boldsymbol{x}] \) denotes the
greatest integer less than or equal to \( x \)
then \( \boldsymbol{f}^{-1}(\boldsymbol{x}) \) is
\( ^{\mathrm{A}} \cdot \frac{1}{x-[x]} \)
B \cdot \( [x]-x \)
c. not defined
D. none of these


Which differential equation correctly represents the above process?
A \( \cdot \frac{d N}{d t}+\lambda N=q_{0} t \)
в. \( \frac{d N}{d t}-\lambda N=q_{0} t \)
c. \( \frac{d N}{d t}+q_{0} t=\lambda N \)
D. \( \frac{d N}{d t}+q_{0} t=-\lambda N \)


The Sl unit of gravitational potential is :
A. Joule/kg
B. Joule^ /kg
c. kg/Joule
D. Joule/kg \( ^{2} \)


When \( \alpha \) -particles are sent through a
thin metal foil, most of them go straight through the foil because:
This question has multiple correct options
A. \( \alpha \) - particles are much heavier than electrons
B. \( \alpha \) -particles are positively charged
c. most part of the atom is empty space
D. \( \alpha \) -particles move with high speed


Find the general solution of the differential equation \( \frac{d y}{d x}-y=\cos x \)


In vertebrates, lacteals are found in
A . Ileum
B. Ischium
c. oesophagus
D. Ear


Select the wrongly paired one from the
following.
A. Hepatic caecae - Exretion
B. Crop in grasshopper - Temporary storage of food
C. Blood of grasshopper-Haemolymph
D. Egetion - Removal of undigested food from the body.


The sum of the squares of deviation of
10 observations from their mean 50 is
\( 250, \) then coefficient of varition is
A . 10\%
B. 40\%
c. 50\%
D. None of these


Assertion
Ethane is a gas while ethyl alcohol is a
İiquid.
Reason
Ethyl alcohol has greater molecular
mass than ethane.
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


Find the middle term of the sequence
formed by all three-digit numbers which leave a remainder 5 when divided by 7
Also find the sum of all numbers on
both sides of middle term.


Assertion
The maximum height reached by an object projected vertically up is directly proportional to the initial velocity u.
Reason

The maximum height reached by an object thrown up with an initial velocity
u is given by \( \boldsymbol{h}=\frac{\boldsymbol{u}^{\mathbf{2}}}{\mathbf{2} \boldsymbol{g}} \)
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 area lying in the first quadrant inside the circle \( x^{2}+y^{2}=12 \) and
bounded by the parabolas \( \boldsymbol{y}^{2}= \)
\( 4 x, x^{2}=4 y \) is:
A \( \cdot\left(\frac{\sqrt{2}}{3}+\frac{3}{2} \sin ^{-1} \frac{1}{3}\right) \)
B \( \cdot 4\left(\frac{\sqrt{2}}{3}+\frac{3}{2} \sin ^{-1} \frac{1}{3}\right) \)
\( ^{c} \cdot\left(\frac{\sqrt{2}}{3}+\frac{3}{2} \sin ^{-1} \frac{1}{3}\right) \)
D. none of these


In a half wave rectifier, the output is
taken across a \( 90 \Omega \) load resistor. If the resistance of diode in forward biased
condition is \( 10 \Omega \), the efficiency of rectification of ac power into dc power is
A . \( 40.6 \% \)
B. \( 81.2 \% \)
c. \( 73.08 \% \)
D. \( 36.54 \% \)


Which of the following does NOT
represent a zero polynomial?
\( \mathbf{A} \cdot p(x)=0 \)
B \( \cdot p(x)=0 . x^{0} \)
\( \mathbf{C} \cdot p(x)=x^{0} \)
D \( \cdot p(x)=x^{0}-1 \)


The value of \( \int \frac{\left(a x^{2}-b\right) d x}{x \sqrt{c^{2} x^{2}-\left(a x^{2}+b\right)^{2}}} \) is
equal to
A \( \cdot \frac{1}{c} \sin ^{-1}\left(a x+\frac{b}{x}\right)+k \)
B. \( \operatorname{csin}^{-1}\left(a+\frac{b}{x}\right)+k \)
c. \( \sin ^{-1}\left(\frac{a x+\frac{b}{x}}{c}\right)+k \)
D. none of these


An automobile travelling with speed of
\( 60 k m / h, \) can brake to stop within a distance of 20 m. If the car is going
twice as fast, i.e. \( 120 \mathrm{km} / \mathrm{h} \), the
stopping distance will be:
A . \( 20 m \)
в. 40 т
\( c \cdot 60 m \)
D. \( 80 m \)


Burning \( M g+N O_{2} \) will give:
A \( . N_{2} \)
в. \( N O \)
c. \( N_{2} O \)
D. \( N_{2} O_{5} \)


In the process of electromagnetic induction, the magnitude of the induced emf depends on:
Select the correct options from the following This question has multiple correct options
A. The number of turns of the coil
B. The magnetic flux linked with the coil
c. The rate of change of magnetic flux linked with the coi
D. Area of the coil


Calculate the number of patients in the hospital using step deviation method.
\begin{tabular}{|l|l|l|l|l|}
\hline Rooms & 20 & 30 & 40 & 50 \\
\hline Nübbrof patients & 7 & 14 & 21 & 28 \\
\hline
\end{tabular}
A . 30
в. 40
c. 50
D. 60


Which of the following oxides of nitrogen is solid at or below 273 K?
A \( \cdot N O_{2} \)
B. \( N_{2} O_{3} \)
\( c \cdot N_{2} O \)
D. \( N_{2} O_{5} \)


Let \( \boldsymbol{X}=\{1,2,3,4,5\} . \) fr the relation \( \boldsymbol{g}= \)
\( \{(1,2),(2,3),(3,4),(4,5),(5,1),\} \) on
\( X \) is a function from \( X \) to \( X \).then find
\( \boldsymbol{g}(\boldsymbol{g}(\boldsymbol{g}(\boldsymbol{4}))) \)


Which one of the following orders is
correct regarding the \( -I \) effect of the
substituents?
A. \( -N R_{2}<-O R>-F \)
B . \( -N R_{2}>-O R>-F \)
c. \( -N R_{2}<-O R<-F \)
D. \( -N R_{2}>-O R<-F \)


Find the acute angle the line \( x / 1= \)
\( \boldsymbol{y} / \mathbf{3}=\boldsymbol{z} / \mathbf{0} \) and plane \( \mathbf{2} \boldsymbol{x}+\boldsymbol{y}=\mathbf{5} \)


lonization potential in a period is lowest
for:
A. halogens
B. inert gases
c. alkali metals
D. alkaline earth elements


The velocity of light in a medium is half its velocity in air. If a ray of light emerges from such a medium into air, the angle of incidence, at which it will
be totally internally reflected, is
A . 15
B. \( 30^{\circ} \)
\( c \cdot 45 \)
D. \( 60^{\circ} \)


Define Atomic radii, covelentradii
metallic radii?


A random variable ' \( X \) ' has the following probability distribution:
\[
\begin{array}{lcccc}
x=x & 0 & 1 & 2 & 3 \\
P(X=x) & 0 & k & 2 k & 2 k
\end{array}
\]
Find:
(i) \( k \)
(ii) The Mean and
(iii) \( \boldsymbol{P}(\boldsymbol{0}<\boldsymbol{X}<\mathbf{5}) \)


During lactic acid fermentation,
\( A \cdot O_{2} \) is used, \( C O_{2} \) is not liberated.
B. \( O_{2} \) is not used, \( C O_{2} \) is liberated.
\( \mathrm{C} \cdot \mathrm{O}_{2} \) is used, \( \mathrm{CO}_{2} \) is liberated.
D. Neither \( O_{2} \) is used, nor \( C O_{2} \) is liberated.


Find the mean of the following frequency distribution:
\( \begin{array}{llll}\text { Class } & \text { 0- } & \text { 6- } & \text { 1 } \\ \text { interval: } & \text { 6 } & \text { 12 } & \text { 1 }\end{array} \) \( 12- \)
18
3
24
Frequency: \( \quad 7 \) 10


The area of a circular field is \( 13.86 m^{2} \)
Find the circumference of the field.


In Millinkan's oil drop experiment, a charged oil drop of mass \( 3.2 \times 10^{-14} k g \)
is held stationary between parallel plates \( 6 m m \) apart, by applying a
potential difference of \( 1200 V \) between them. How many electrons does the oil
drop carry? \( \left(\text { Given } g=10 m s^{-2}\right) \)
A. 7
B. 8
\( c \cdot 9 \)
D. 10


Thin layer chromatography can be used
to distinguish between different amino acids. If a particular amino acid has low solubility in the mobile phase used, then the other amino acid :
A. will have a low Rf value
B. must have a high molecular mass.
c. will move at a speed close to that of the solvent
D. will spend more time dissolved in the mobile phase than attached to the stationary phase.


A student is given two samples of nucleotides. One sample contains DNA nucleotides and the other sample contains RNA nucleotides, but the two samples have not been labeled.
What information would assist the
student in identifying which sample contained the DNA nucleotides versus
the RNA nucleotides?
A. The sugar in DNA nucleotides contains six carbon atoms and the sugar in an RNA molecule contains five carbon atoms.
B. The sugar in DNA nucleotides is an aldehyde sugar anc the sugar in RNA nucleotides is a ketone sugar
c. The sugar in DNA nucleotides contains one less oxyger atom than the sugar in RNA nucleotides
D. The sugar in DNA nucleotides is in the alpha configuration and the sugar in RNA nucleotides is in the beta configuration


For a projectile, the physical quantities which remain constant are:
A. vertical component of velocity and kinetic energy
B. potential energy and kinetic energy
c. acceleration and horizontal component of velocity
D. potential energy and acceleration


In the diagram shown below, the input
is across the terminals \( A \) and \( C \) and the
output is across \( B \) and \( D \) Then the
output is
A. Zero
B. Same as input
c. Full wave rectified
D. Half wave rectified


\( \boldsymbol{R}_{4}= \)
\{(1,3),(2,5),(4,7),(5,9),(3,1)\}
Is it a mapping? IF True enter 1 else enter 0


A magnifying glass is also known as
A . a telescope
B. an astronomical telescope
c. a compound microscope
D. a simple microscope


Q Type your question_
sornetıries consider a thingy aldacried
to a horizontal spring and moving horizontally on a frictionless surface,
instead of the hanging thingy that we have been looking at. Suppose that the
two springs and the two thingies are
identical. Think about whether these
two systems are significantly different
in other respects and decide which one
of the following statements is true.
A. The systems have different periods because their motions are aligned differently with the gravitational field.
B. The hanging system has a slightly smaller period because the weight of the spring has to be accounted for.
C. The hanging system has a slightly larger period because the weight of the spring has to be accounted for.
D. The two systems have identical periods, no matter what the weight of the spring is.


The ratio of energies of first two excited states hydrogen atom is?
\( A \cdot 3 / 1 \)
B. \( 1 / 4 \)
\( c \cdot 4 / 9 \)
D. \( 9 / 4 \)


If a chord of a circle \( x^{2}+y^{2}=32 \)
makes equal intercepts of length \( l \) on
the co-ordinate axes, then
\( \mathbf{A} \cdot \ell<8 \)
в. \( \ell<16 \)
\( \mathbf{c} \cdot \ell>8 \)
D. \( \ell>16 \)


When an ebonite rod is rubbed with fur
the charge acquired by the fur is
A. Positive
B. Negative
c. No charge
D. Can't say


By the reduction of carbonyl compounds
the alcohol not obtained is:
A. primary alcohol
B. secondary alcohol
c. tertiary alcohol
D. all the above


What is Poisson's ratio?


Complete the following sentences:
A fuse is a short piece of wire of high and of material of low
A . resistance, melting point
B. meting point, resistance
c. capacitance, melting point.
D. conductance, melting point


A steady current \( I \) flows along an infinitely long hollow cylindrical conductor of radius \( \mathbf{R} . \) This cylinder is placed coaxially inside an infinite solenoid of radius \( 2 \mathrm{R} \). The solenoid has
n turns per unit length and carries a
steady current \( I . \) Consider a point \( \mathbf{P} \) at a
distance r from the common axis. The
correct statement \( (s) \) is (are):
This question has multiple correct options
A. in the region \( 0<\mathrm{r}<\mathrm{R} \), the magnetic field is non-zero
B. in the region \( R<r<2 R \), the magnetic field is along the common axis
c. in the region \( \mathrm{R}<\mathrm{r}<2 \mathrm{R} \), the magnetic field is tangential to the circle of radius r, centered on the axis
D. in the region \( r>2 R \), the magnetic field is non-zero


A spherical shape jar has a radius of 2
cm. What is the volume of the jar?
A. \( 30.493 \mathrm{cm}^{3} \)
В. \( 13.493 \mathrm{cm}^{3} \)
c. \( 23.493 \mathrm{cm}^{3} \)
D. \( 33.493 c m^{3} \)


Assertion
Compounds of \( \boldsymbol{H} \boldsymbol{g}^{2+} \) ions having an ionic radius of 116 pm are more covalent in character than those of
\( C a^{2+} \) ions with almost identical size
\( 114 p m) \) and the same charge.
Reason
For two ions of the same size and
charge, one with an \( (\boldsymbol{n}-\mathbf{1}) \boldsymbol{d}^{10} \boldsymbol{n s}^{\mathbf{0}} \)
electronic configuration will be more
polarizing than a cation with an \( (n- \)
1) \( s^{2}(n-1) p^{6} n s^{0} \) electronic
configuration.
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.


Chemiosmotic theory of ATP synthesis
in mitochondria is based on
A \( \cdot \mathrm{K}^{+} \) gradient
B. H \( ^{+} \) gradient
c. Nat gradientt
D. \( \mathrm{ca}^{2+} \) gradient.


Represent the following mixed infinite decimal periodic fractions as common fractions:
Simplify the following expressions. \( \left(\left(\frac{y}{y-x}\right)^{-2}-\frac{(x+y)^{2}-4 x y}{x^{2}-x y}\right) \frac{x}{x^{2} y^{2}} \)


A long cylindrical pipe of radius \( 20 \mathrm{cm} \) is closed at its upper end and has an airtight piston of negligible mass as
shown. When a \( 50 \mathrm{Kg} \) mass is attached
to the other end of piston, it moves down
by a distance \( \Delta l \) before coming to
equilibrium. Assuming air to be an ideal gas, \( \Delta l / L( \) see figure ) is close to \( \left(g=10 m / s^{2}, \) atmospheric pressure is \right.
\( 10^{5} \) Pascal
A .0 .01
в. 0.02
\( c .0 .04 \)
D. 0.0


The material selected for solar cell
fabrication has
This question has multiple correct options
A. band gap (1.0 to 1.8 eV)
B. high optical absorption \( \left(10^{4} \mathrm{cm}^{-1}\right) \)
c. electrical conductivity
D. band gap (0.4 to 1. eV)


Assertion
\( \boldsymbol{S}_{3} \boldsymbol{O}_{\boldsymbol{6}}^{2-}(\text { trithionate }) \) has \( \boldsymbol{S}-\boldsymbol{S} \) bond
Reason
It is a conjugate base of \( \boldsymbol{H} \boldsymbol{S}_{3} \boldsymbol{O}_{\boldsymbol{6}}^{-} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


A square is rectangle. Give reason


A boat moving perpendicular to the bank with a velocity of \( 7.2 \mathrm{km} / \mathrm{h} \). The
current carries it \( 150 \mathrm{m} \) downstream,
find the velocity of the current.(The
width of the river is \( 0.5 \mathrm{km} \) )
A \( \cdot 0.4 m s^{-1} \)
В. \( 1.2 m s^{-1} \)
c. \( 0.5 m s^{-1} \)
D. \( 0.6 m s^{-1} \)


Two uniform boards, tied together with
the help of a string, are balanced on a surface as shown in Fig. The coefficient
of static friction between boards and
surface is \( 0.5 . \) The minimum value of \( \theta \)
for which this type of arrangement is
possible is :
\( \mathbf{A} \cdot 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 37^{\circ} \)
D. It is not possible to have this type of balanced
arrangementt


Using Bohr's atomic model, derive an equation for radius of orbit of an electron.


Non electrolyte solution is of a chemical compound which :
A. Contain ions
B. conducts electricity
c. Does not conduct electricity
D. None of the above


The velocity of a helium nucleus travelling in a curved path in a magnetic field is \( V \). The velocity of a proton moving in the same curved path in the same magnetic field is :
A. \( V \)
в. \( 4 V \)
\( c \cdot 2 V \)
D. \( V / 2 \)


\( \mathrm{C}_{6}^{14} \) and \( \mathrm{O}_{8}^{16} \) are :
A. isotones
B. isotopes
c. isomers
D. none of the above


ff \( y \) varies directly as \( x \) and \( y=12 \)
when \( x=4, \) then find the linear
equation.


Fig. 16.10 shows the word REST written in two ways in front of a mirror. Show how
the word would appear in the mirror.
The


Red and blue beams of light is incident
on a prism as shown in the figure.
Which of the following statements is
true?
A. The blue light bends more than the red light as the blue light has a longer wavelength.
B. The red light bends more than the blue light as the red light has a longer wavelength.
C. The blue light bends more than the red light as the blue light has a shorter wavelength.
D. The red light bends more than the blue light as the red light has a shorter wavelength.
E. The red and blue lights bend by the same amount as all colors of light refract equally.


A bar magnet of length of \( 0.1 m \) has a
pole strength of 50 Am. Calculate the
magnetic field at a distance of \( 0.2 m \) from its centre on (i) its axial line and
(ii) its equatorial line.


Beryllium and aluminium exhibit many properties which are similar but the two elements differ in
A. forming covalent halides
B. forming polymeric halides
c. exhibiting maximum covalency in compounds
D. exhibiting amphoteric nature in their oxides


Choose the correct answers from the
alternatives given. What is the function of DNA ligase in recombinant technology?
A. Cut DNA into many fragments
B. Carry DNA into a new cell
c. Link together newly joined fragments of DNA
D. Separate fragments of DNA by their length and electrical charges


The melting point of cadmium bromide
is \( 568^{\circ} \mathrm{C} \). Which of the following
equations best describes what occurs when cadmium bromide is heated to
\( 568^{\circ} C ? \)
A \( \cdot \operatorname{CdBr}(s) \rightarrow \operatorname{CdBr}(l) \)
B . \( \operatorname{CdBr}_{2}(s) \rightarrow \operatorname{CdBr}_{2}(l) \)
c. \( \operatorname{CdBr}_{2}(s) \rightarrow C d(s)+B r_{2}(g) \)
D. \( \operatorname{CdBr}_{2}(s) \rightarrow C d^{2+}(a q)+2 B r^{-}(a q) \)


\( \ln \Delta P Q R, \) if \( P R^{2}=P Q^{2}+Q R^{2}, \) prove
that \( \angle Q \) is right angle.


\( C O_{2} \) acts as a greenhouse gas because
A. It is transparent to heat but traps sunlight
B. It is transparent to sunlight but traps heatt
c. It is transparent to both sunlight and heat.
D. It traps both sunlight and heatt


Find the value of \( 703-1+1-400 \)


The relation \( R \) defined on the \( \operatorname{set} A= \)
\{1,2,3,4,5\} by \( R= \)
\( \left\{(x, y):\left|x^{2}-y^{2}\right|<16\right\} \) is given by
A \( \cdot\{(1,1),(2,1),(3,1),(4,1),(2,3)\} \)
B - \{(2,2),(3,2),(4,2),(2,4)\}
C \( \cdot\{(3,3),(4,3),(5,4),(3,4)\} \)
D. None of these


In the quadrilateral (1) given below, \( A B|| D C, E \) and \( F \) are mid point of \( A D \)
and \( B D \) respectively. Prove that \( \boldsymbol{E G}=\frac{1}{2}(\boldsymbol{A B}+\boldsymbol{D C}) \)


Water be boiled by
sending steam into it


Diamond is harder than graphite
because:
A. graphite is planar
B. diamond has free electron
c. graphite has \( s p^{3} \) hybridization
D. none of above


In LEDs, the longer lead is connected to and the shorter lead is connected
to
A. negative terminal; positive terminal
B. positive terminal; negative terminal
c. negative terminal; neutral terminal
D. positive terminal; neutral terminal


\( \int \frac{x^{2}\left(x \sec ^{2} x+\tan x\right)}{(x \tan x+1)^{2}} d x \)
\( \mathbf{A} \cdot x^{2}\left[-\frac{1}{x \tan x+1}\right]+2 \log (x \sin x+\cos x)+C \)
B \( \cdot x^{2}\left[\frac{1}{x \tan x+1}\right]+2 \log (\sin x+x \cos x)+C \)
\( \mathbf{c} \cdot x\left[-\frac{1}{x \tan x+1}\right]+2 \log (\sin x+x \cos x)+C \)
D \( \cdot x\left[\frac{1}{x \tan x+1}\right]+2 \log (x \sin x+\cos x)+C \)


A man of mass \( \mathrm{M} \) stands at one end of a
plank of lenght L which lies at rest on a frictionless surface. The man walk to
the other end of the plank. If the mas of the plank is \( \frac{M}{3}, \) the distance that the man moves relative to the ground is
A. \( \frac{3 L}{4} \)
в. \( \frac{L}{4} \)
c. \( \frac{4 L}{5} \)
D. \( \frac{L}{3} \)


The outer diameter of a spherical shell
is \( 10 \mathrm{cm} \) and the inner diameter is 9
cm.Find the volume of the metal
contained in the shell. Also find its outer
surface area.


A large solenoid of windings of 400
turns per meter carries a current \( 5 \mathrm{A} \)
The magnetic field at the centre of the solenoid is about:
A . \( 1.2 \mathrm{mT} \)
B. zero
c. \( 5.0 \mathrm{mT} \)
D. 2.5 mT


Which one of the following four glands
is correctly matched with the
accompanying description?
A. Thyroid- hyperactivity in young children causes cretinism
B. Thymus- starts undergoing atrophy after puberty
C. Parathyroid- secretes parathormone, which promotes movement of calcium ions from blood into bones during calcification
D. Pancreas- delta cells of the islets of Langerhans secrete a hormone, which stimulates glycolysis in liver


Critical count of Platelete is
A. \( 4 \times 10^{4} / m m^{3} \)
B. 1 lakh/mm^ \( ^{3} \)
c. 2 lakh \( / m m^{3} \)
D. 4 lakh \( / m m^{3} \)


The G.M. between 1 and 25 is


We need fresh air for breathing. Some sources that cause pollution of air are mentioned here. Can you pick the false one?
A. Coal fires
B. Heavy rain
c. volcanoes
D. Forest fires


The relationship between pressure and volume was first noted by while
confirmed their discovery and published the result.
A. Richard Towneley and Henry Power, Robert Boyl
B. Richard Towneley and Henry Power, Robert Hooke
C. Robert Boyle and Robert Hooke, Robert Boyle
D. None of these


Nylon-6, 6 is a:
A. polyester
B. polyamide
C . polyacrylate
D. none of the above


Why is charcoal a better fuel when
compared to wood?
A. Charcoal burns without flames
B. Charcoal has higher heat generation efficiency
c. Both A and B
D. None


Find the 50 th term of the sequence:
\( \frac{1}{n}, \frac{n+1}{n}, \frac{2 n+1}{n} \dots \dots \dots \dots \)


In a bridge rectifier, the number of diodes required is
A . 1
B. 2
\( c .3 \)
\( D \)


Let \( \boldsymbol{f} \) be an increasing function on \( [\boldsymbol{a}, \boldsymbol{b}] \) and \( g \) be a decreasing function on \( [a, b] \)
then on \( [a, b] \)
This question has multiple correct options
A. fog is a decreasing function.
B. gof is an increasing function.
c. \( f o g \) is an increasing function.
D. None of these


Find the value of \( \frac{\mathbf{6} !}{\mathbf{3} !} \)


Why does a blacksmith heat the metal
rim to fix it on a cart wheel?


Which one of the following processes does not occur during formation of
\( \boldsymbol{C H} \boldsymbol{C l}_{3} \) from \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \) and bleaching
powder?
A. Hydrolysis
B. Oxidation
c. Reduction
D. Chlorination


The condition that the line \( \frac{x-\alpha^{\prime}}{l}= \) \( \frac{\boldsymbol{y}-\boldsymbol{\beta}^{\prime}}{\boldsymbol{m}}=\frac{\boldsymbol{z}-\boldsymbol{\gamma}^{\prime}}{\boldsymbol{n}} \) in the plane \( \boldsymbol{A} \boldsymbol{x}+ \)
\( \boldsymbol{B} \boldsymbol{y}+\boldsymbol{C} \boldsymbol{z}+\boldsymbol{D}=\mathbf{0} \) is
\( \mathbf{A} \cdot A \alpha^{\prime}+B \beta^{\prime}+C \gamma^{\prime}+D=0 \) and \( A l+B m+C n \neq 0 \)
B \( \cdot A \alpha^{\prime}+B \beta^{\prime}+C \gamma^{\prime}+D \neq 0 \) and \( A l+B m+C n=0 \)
C \( \cdot A \alpha^{\prime}+B \beta^{\prime}+C \gamma^{\prime}+D=0 \) and \( A l+B m+C n=0 \)
D \( \cdot A \alpha^{\prime}+B \beta^{\prime}+C \gamma^{\prime}=0 \) and \( A l+B m+C n=0 \)


A steady potential difference of 100 V produces heat at a constant rate in a resistor. The alternating voltage which will produce half the heating effect in the same resister will be
\( A \cdot 100 v \)
B. 50
c. 70.7 \( v \)
D. 141.4


Assertion
Rusting of iron is considered an
oxidation reaction
Reason
Rust is another name for iron oxide
which occurs when iron is exposed to
oxygen and moisture for a long period of
time. Overtime the oxygen combines with the metal at atomic level forming a compound called an oxide. Rust forms
when iron undergoes oxidation. The
main catalyst for the rusting process is
water.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The following properties belong to
a. The number of nucleons in the atoms
of different elements remains the same
b. The atomic number for different
elements is different
c. The number of protons and electrons
is always equal
A. Isotopes
B. Isobars
c. Isotones
D. None of the above


The circumference of the base of a
cylindrical vessel is \( 132 \mathrm{cm} \) and its height is 25 cm. How many litres of water can it hold? \( \left(1000 \mathrm{cm}^{3}=1 l\right) \)


The kinetic energy needed to project a body of mass \( m \) from the earth surface
(radius \( R \) ) to infinity is
\( \mathbf{A} \cdot m g R / 2 \)
в. \( 2 m g R \)
\( c . m g R \)
D. \( m g R / 4 \)


Using proposed solution for \( v, \) find the acceleration.
A .
в. \( \frac{g}{2} \)
c. \( \frac{g}{3} \)
D. none of these


Point \( D \) has coordinates as (3,4,5)
Referring to the given figure, find the
coordinates of point \( \boldsymbol{E} \)
\( \mathbf{B} \cdot(0,4,5) \)
C. (0,5,4)
D. (0,3,4)


If a charged particle is projected perpendicular to uniform magnetic
field, then
a) force experienced will be perpendicular to the magnetic field and
initial velocity.
b) force experienced will be perpendicular to the magnetic field and instantaneous velocity
c) the work done by the magnetic field
is zero.
d) the particle experiences both radial and tangential accelerations.
A. a, b, c are correct d is wrong
B. all are correct
c. a, b are correct, c, d are wrong
D. a, b, c are wrong, d is correct


Ten students of class \( X \) took part in
Mathematics quiz. If the number of girls is 4 more than the number of boys.
Represent this situation algebraically.


The non-metal used to treat rubber in
the process of vulcanization is:
A. sulphur
B. phosphorus
c. carbon
D. chloride


Which one of the following leads to third line of Balmer spectrum from red end (For hydrogen atom)?
A \( .2 \rightarrow 5 \)
В . \( 5 \rightarrow 2 \)
\( \mathrm{c} \cdot 3 \rightarrow 2 \)
D. \( 4 \longrightarrow 1 \)


How many maximum atoms of \( I F_{7} \) are
present in the same plane?


Q Type your question.
viscous and incompressible liquids of
\( \boldsymbol{H} \)
densities \( d \) and \( 2 d, \) each of height \( \frac{-}{2} \) as
shown in figure. The lower density liquid is open to the atmosphere having
pressure \( P_{0} . \) A homogeneous solid cylinder of length \( L\left(L<\frac{H}{2}\right) \) cross \( \boldsymbol{A} \)
sectional area \( - \) is immersed such that \( \mathbf{5} \)
it floats with its axis vertical at the
liquid-liquid interface with the length
in the denser liquid. The total pressure at the bottom of the container is given as \( p=p_{o}+\frac{x H+L}{4} . \) Find \( x \)


Which of the following electronic configuration shows that the atom is in excited state?
B . \( 1 s^{2} 2 s^{2} 2 p^{4} \)
\( \mathrm{c} \cdot 1 s^{2} 2 s^{2} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} \)
E \( \cdot 1 s^{2} 2 s^{2} 3 s^{1} \)


Calculate the mean from the following
data:


One mole of a compound AB reacts with one mole of a compound CD according
to the equation \( \boldsymbol{A B}_{(\boldsymbol{g})+} \boldsymbol{C D}_{(g)} \rightleftharpoons \)
\( A D_{(g)}+C B_{(g)} \) When equilibrium had
been established it is was found that
\( 3 / 4 \) mole of reactants \( A B \) and \( C D \) had
been converted to \( A D \) and \( C B \), there is no
change in volume. The equilibrium constant for the reaction is :
A. \( 9 / 16 \)
B . 1/9
\( c \cdot 16 / 9 \)
D. 9


If \( \boldsymbol{A}=\left[\begin{array}{cccc}\mathbf{5} & \mathbf{6} & \mathbf{- 2} & \mathbf{3} \\ \mathbf{1} & \mathbf{0} & \mathbf{4} & \mathbf{2}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{cccc}\mathbf{3} & \mathbf{- 1} & \mathbf{4} & \mathbf{7} \\ \mathbf{2} & \mathbf{8} & \mathbf{2} & \mathbf{3}\end{array}\right], \) then find \( \mathbf{A}+\mathbf{B} \)


If a hyperbola passes through the foci of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \) and its
traverse and conjugate axis coincide
with major and minor axes of the
ellipse, and product of the
eccentricities is 1, then:
This question has multiple correct options
A eqaations of the hyperbola is \( \frac{x^{2}}{9}-\frac{y^{2}}{16}=1 \)
B - Equations of the hyperbola is \( \frac{x^{2}}{9}-\frac{y^{2}}{25}=1 \)
C. Focus of the hyperbola is (5,0)
D. Focus of the hyperbola is \( (5 \sqrt{3}, 0) \)


Inter-molecular hydrogen bond is not
present in:
A. Ammonia
B. water
c. Hydrofluoric acid
D. Salicylaldehyde


The number \( \frac{13}{15} \) is correctly represented
on number line
\( A \)
\( \begin{array}{cccccc}< & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \frac{1}{15} & & & \frac{13}{15} & \frac{15}{15} & \frac{17}{15}\end{array} \)
B. \( \begin{array}{ccccccc}\langle 1 & & 1 & 1 & 1 & 1 & 1 \\ 10 & & \frac{13}{15} & \frac{14}{15} & \frac{15}{15} & \frac{16}{15} & \frac{17}{15}\end{array} \)
\( c \)
\( \begin{array}{lllllllll}\nwarrow_{1} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \frac{2}{15} & \frac{3}{15} & \frac{4}{15} & & \frac{13}{15} & \frac{14}{15} & \frac{15}{15} & \frac{16}{15} & \cdots & .\end{array} \)
D. \begin{tabular}{ccccccccc}
\hline 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
\( \frac{14}{15} \) & \( \frac{15}{15} \) & \( \frac{16}{15} \) & \( \frac{17}{15} \) & \( \frac{18}{15} \) & \( \frac{6}{15} \) & \( \frac{13}{15} \) & \( \cdot \) & \( \cdot \)
\end{tabular}


Angular momentum of an electron in
the \( n \) th orbit of hydrogen atom is given
by:
\( ^{A} \cdot \frac{n h}{2 \pi} \)
в. \( n h \)
c. \( \frac{2 \pi}{n h} \)
D. \( \frac{\pi}{2 n h} \)


Give two examples of each of situation in which you push or pull to change the state of motion of an objects.


Write down any two difference between nucleoside and nucleotide.


How many chiral carbon atoms are there in 1-chloro-2,5-dimethyl cyclohexane?
\( A \cdot 3 \)
B.
\( c \cdot 2 \)
D.


If \( g \) is the acceleration due to gravity on
the surface of the earth, the gain in potential energy of an object of mass \( \boldsymbol{m} \)
raised from the earth's surface to a
height equal to the radius \( R \) of the earth is
\( ^{\mathrm{A}} \cdot \frac{m g R}{4} \)
в. \( \frac{m g R}{2} \)
\( \mathbf{c} \cdot m g R \)
D. \( 2 m g R \)


The glomerulus is a network of parallel capillaries which are approximately in number
A. 5
B. 50
\( c .500 \)
D. 5000


Write chemical formula of washing soda. How is it obtained from baking soda? Name the one industrial use of
washing soda other than washing clothes.


If \( ^{n} C_{12}=^{n} C_{8}, \) find \( ^{n} C_{17},^{22} C_{11} \)


There are_ \( -\ldots-\ldots \) moles of anion in
one mole of sodium sulphate.


If \( \int_{0}^{a} x^{2} d x \) is equal to the 9 , then find the value of \( a \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D. 4


How many oxyanions among the following show disproportionation? \( \boldsymbol{C l O}^{-}, \boldsymbol{C l O}_{2}^{-}, \boldsymbol{C l O}_{3}^{-}, \boldsymbol{C l} \boldsymbol{O}_{4}^{-} \)


The vapour pressure of a pure liquid \( \mathbf{A} \)
is 70 torr at 300 K. It forms an ideal
solution with another liquid B. The mole fraction of \( \mathrm{B} \) in the solution is 0.2 and
total pressure of solution is 84 torr at \( 300 \mathrm{K} . \) The vapour pressure of pure liquid B at 27C is?
A. 0.14 torr
B. 560 torr
c. 140 tor
D. 70 torr


A conducting circular loop of area \( 1 \mathrm{nm} \) is placed compulsary with a long, straight wire at a distance of current
which changes from 10 A to zero in 0.1
s. Find the average emf induced in the
loop in 0.1 s.


In figure the input is across the
terminals \( A \) and \( C \) and the output is
across \( \mathrm{B} \) and \( \mathrm{D} \). Then the output is
A . zero
B. same as input
C. half wave rectifier
D. full wave rectifier


If \( (a, b) \) lies on circle with centre as origin, then its radius will be
A \( . a-b \)
B. \( a+b \)
c. \( \sqrt{a^{2}+b^{2}} \)
D. \( a^{2}+b^{2} \)


Select the correct statements from the
following
A. A simple harmonic motion is necessarily periodic
B. A simple harmonic motion may be oscillatory
C. An oscillatory motion is necessarily periodic
D. A periodic motion is necessarily oscillatory


For each of the given solid, the three
views are given. Identify for each solid
the corresponding top, front and side
views.


Which of the following Mycoplasma strains are harmful to the humans?
A. M.genitaliumm
B. M. Hominis
c. Mycoplasma pneumonia
D. All of the above


All of these are the characters of
angiosperms except they
A. Are most advanced
B. Bear true fruits
c. Bear covered seeds
D. Are cryptogams
E. Show double fertilization


\( A \) and \( B \) are two concentric circular
conductors of centre \( \boldsymbol{O} \) and carrying
currents \( I_{1} \) and \( I_{2} \) as shown in the
adjacent figure. If ratio of their radii is
1 : 2 and ratio of the flux densities at \( O \)
due to \( A \) and \( B \) is \( 1: 3, \) then the value of
\( \boldsymbol{I}_{1} / \boldsymbol{I}_{2} \) is:


The velocity of a particle is given as
\( \boldsymbol{v}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}+\boldsymbol{c} \boldsymbol{t}^{2} \). the velocity is
measured in \( \mathrm{ms}^{-1} \), then units of a and
\( c \) are
\( \mathbf{A} \cdot m s^{-1} \) and \( m s^{-3} \)
B. \( m s^{-2} \) and \( m s \)
\( \mathbf{c} \cdot m^{2} s \) and \( m s^{2} \)
D. \( m s \) and \( m s^{-1} \)


Rhizopus reproduces asexually through
A. Sporangiospores
B. Aplanospores
c. chlamydospores
D. All of the above


Evaluate \( : \int(\tan x-\cot x)^{2} d x \)


This environmental pollutant belongs to a group of dangerous chemicals known as persistent organic pollutants. The
chemical name for this pollutant is
\( \mathbf{2}, \mathbf{3}, \mathbf{7}, \mathbf{8}-\boldsymbol{T} \boldsymbol{C} \boldsymbol{D} \boldsymbol{D} . \) Name it
A. Dibenzofurans
B. Biphenyls
c. Dioxin
D. Aldrin


\( f(x)=\left\{\begin{array}{lr}\frac{2^{x+2}-16}{4^{x}-16}, \text { if } x \neq 2 \\ k, & \text { if } x=2\end{array}\right. \)
continuous at \( x=2, \) find \( k \)


The velocity of a body at any instant is \( 10 \mathrm{m} / \mathrm{s} . \) After \( 5 \mathrm{sec}, \) velocity of the particle is \( 20 \mathrm{m} / \mathrm{s} \). The velocity at 3 seconds before is
(assume uniform accelaration)
A. \( 8 \mathrm{m} / \mathrm{sec} \)
B. 4 m/sec
c. \( 6 \mathrm{m} / \mathrm{sec} \)
D. \( 7 \mathrm{m} / \mathrm{sec} \)


A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :
A \( \cdot \frac{10}{3^{5}} \)
в. \( \frac{17}{3^{5}} \)
c. \( \frac{13}{3^{5}} \)
D. \( \frac{11}{3^{5}} \)


Two particle execute \( S H M \) of same amplitude and frequency along the same straight line, They pass one another going in opposite direction each time their displacement is half of their amplitude. The phase difference between them is
A \( \cdot 0^{\circ} \)
B. \( 120^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 135^{\circ} \)


Consider the reaction,
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{C} \boldsymbol{d} \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}+\boldsymbol{C} \boldsymbol{d}^{2} \)
The standard electrode potentials for
\( A g^{+} \rightarrow A g \) and \( C d^{2+} \rightarrow C d \) couples
are 0.80 volt and -0.40 volt
respectively.
(i) What is the standard potential \( E^{\circ} \) for
this reaction?
(ii) For the electrochemical cell, in
which this reaction takes place which electrode is negative electrode?


The plano-convex lens of focal length 20 \( \mathrm{cm} \) and \( 30 \mathrm{cm} \) are placed together to form a double convex lens, the final
focal length will be :
\( \mathbf{A} \cdot 12 \mathrm{cm} \)
B. \( 60 \mathrm{cm} \)
\( \mathbf{c} \cdot 20 c m \)
D. \( 30 \mathrm{cm} \)


\( N H_{3}+O_{2} \rightarrow \)
Complete the reaction.


Solutions of two electrolytes \( A \) and \( B \) each having concentration of \( 0.2 \mathrm{M} \) have
conductivities \( 2 \times 10^{-2}, 4 \times 10^{-4} \mathrm{S} / \mathrm{cm} \)
respectively. Which will offer greater resistance to the file of current and
why?


Factorize the following
\( 5 y^{2}-29 y+20 \)
A. \( (5 y-4)(y-5) \)
B. \( (5 y+4)(y-5) \)
c. \( (5 y-4)(y+5) \)
D. None of these


If the glancing angle of incidence is \( 50^{\circ} \) then calculate the angle between the
incident ray and the reflected ray:
A \( .50^{\circ} \)
B . \( 100^{\circ} \)
\( \mathrm{c} \cdot 130^{\circ} \)
D. \( 80^{\circ} \)


How much is the work done in pulling up a block of wood weighing \( 2 k N \) for a length of \( 10 m \) on a smooth plane
inclined at an angle of \( 30^{\circ} \) with the
horizontal?
A. \( 1.732 k J \)
\( J \)
в. \( 17.32 k J \)
c. \( 10 k J \)
D. 100kJ


Write Sl unit of angular momentum.


\( f\left(a_{1}, a_{2}, a_{3}, \dots, a_{n-1}, a_{n} \) are in A.P., then \right.
show that \( \frac{1}{a_{1} a_{n}}+\frac{1}{a_{2} a_{n-1}}+\frac{1}{a_{3} a_{n-2}}+ \)
\( \ldots \cdot \frac{1}{a_{n} a_{1}}= \)
\( \frac{2}{\left(a_{1}+a_{n}\right)}\left[\frac{1}{a_{1}}+\frac{1}{a_{2}}+\dots \frac{1}{a_{n}}\right] \)


Figure shows the ray diagram of a
A. Simple microscope
B. Compound microscope
c. simple Telescope
Compound Telescope


Benzene diazonium chloride on reaction
with phenol in weakly basic medium gives:
A. diphenyl ether
B. p-hydroxy azobenzene
c. chlorobenzene
D. benzene


Read the statements and mark the
correct significance of eyelids:
a. It protects the eye from foreign
objects.
b. It shut out the light when not required.
c. It makes the eyes beautiful
A \( . \) a and \( b \)
B. b and c
c. a and \( c \)
D. All are true


The lengths of two sides of a triangle are \( 3 \mathrm{cm} \) and \( 4 \mathrm{cm} . \) Which of the following, can be the length of third side to form a triangle?
A . \( 0.5 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .8 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


Hybridization is the chemist's attempt to explain the observed molecular shape by constructing hybridized atomic orbitals with the appropriate
inter orbital angles. The molecule for
which deviation from a normal bond
angle is observed, \( V S E P R \) theory suggests electron pair repulsive interaction \( (l p-l p>l p-b p>b p) \)
While from hybridization point of view that is a departure from normal hybridization because the angle between any equivalent hybrid orbitals determines the fraction of \( s \) and \( p \)
characters of the hybrid and vice-versa. In which species number of lone pairs on iodine and number of d-orbitals used
in hybridization by iodine are the same?
A \( \cdot I C l_{2}^{+} \)
в. \( I C l_{2} \)
\( \mathrm{c} \cdot I F_{7} \)
D. \( I C l_{4} \)


A compound of aluminium and chlorine is composed of 9.0 g Al for every 35.5 g of chlorine. The empirical formula of the compound is:
A. \( A l C l \)
в. \( A l C l_{3} \)
c. \( A l C l_{2} \)
D. \( A l C l_{4} \)


A particle starts from the origin at \( t=0 \) with an initial velocity of \( 3.0 \hat{i} m / s \) and
moves in the \( x-y \) plane with a constant acceleration \( (\mathbf{6 . 0} \hat{\mathbf{i}}+ \) \( 4.0 \hat{j}) m / s^{2} . \) The \( x- \) coordinates of the
particle at the instant when its \( y- \)
coordinates is \( 32 m \) is \( D \) meters. The
value of \( D \) is:
\( \mathbf{A} .50 \)
B. 60
c. 40
D. 32


Which of the following enzyme digests other enzymes?
A. Dehydrogenases
B. Lipases
c. Peptidases
D. Aldolases


When you visit a hill station, which of the following you should use for shopping?
A. bags made up of cotton
B. bags made up of polyethene
c. bags made up of nylon
D. none of the above


\( \boldsymbol{C a}, \boldsymbol{N a}, \boldsymbol{M} \boldsymbol{g}, \boldsymbol{Z} \boldsymbol{n}, \boldsymbol{F e}, \boldsymbol{H}, \boldsymbol{C u}, \boldsymbol{H} \boldsymbol{g}, \boldsymbol{A} \boldsymbol{g}, \boldsymbol{A} \)
Given elements are in order of
decreasing reactivity according to electrochemical series. Half-reaction
possible for the shown electrochemical
cell at the anode is:
A \( \cdot C u^{2+}+e^{-} \rightarrow C u+ \)
B \( \cdot Z n(s) \rightarrow Z n^{2+}+2 e^{-} \)
c. \( Z n^{2+}+2 e^{-} \rightarrow Z n(s) \)
D. \( C u(s) \rightarrow C u^{2+}+2 e^{-} \)
E \( \cdot C u^{2+}+2 e^{-} \rightarrow C u(s) \)


Solve the equation:
\( \mathbf{5} \boldsymbol{x}+\mathbf{2} \frac{\mathbf{3}}{\mathbf{5}}=\mathbf{9}-\frac{\mathbf{4}}{\mathbf{5}} \boldsymbol{x} \)


Find vector equation of line passing through (1,4,1),(1,2,2)
A \( . \bar{r}=\bar{i}+(4-2 \lambda) \bar{j}+(1+\lambda) \bar{k} \)
B . \( \bar{r}=\bar{i}+(4+2 \lambda) \bar{j}+(1+\lambda) \bar{k} \)
c. \( \bar{r}=\bar{i}-(4-2 \lambda) \bar{j}+(1+\lambda) \bar{k} \)
D. \( \bar{r}=\bar{i}+(4-2 \lambda) \bar{j}+(1-\lambda) \bar{k} \)


An amino acid may be represented by general formula \( \boldsymbol{H}_{2} \boldsymbol{N}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{R}- \)
COOH. If \( \boldsymbol{R}=-\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C}_{6} \boldsymbol{H}_{5} \) then it is
phenylananine (Phe) and if \( \boldsymbol{R}=\boldsymbol{C H}_{3} \)
then it is alanine (Ala). Find the
sequence of reagents from those given below to synthesize Phe-Ala.
\( \mathrm{cH}_{3} \)
(1) \( \mathrm{zNH}_{\mathrm{G}}^{\mathrm{HCO}_{3} \mathrm{H}} \)
\( \mathrm{cH}_{2} \mathrm{G}_{5} \)
(2)
(з) ZNHCнсО \( _{2} \) Н
(4) \( \mathrm{H}_{2} \mathrm{NCH} \mathrm{CO}_{2} \mathrm{CH}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \)
A. 1 and 2
B. 1 and 4
\( c \cdot 2 \) and 3
D. 3 and 4


In case of the electromagnetic waves the angle between the electric and
magnetic field vectors is
A . \( \pi \)
В. \( \pi / 2 \)
c. zero
D. none of these


For what value of " \( c^{\prime \prime} \) will the equations
\( 3 x-4 y=7 \) and \( x+c y=13 \) have no
solution?
A \( \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
\( c .-4 \)
D. \( \frac{-4}{3} \)


IUPAC symbol of atomic number 119
A. \( U u h \)
в. Uun
c. \( U u e \)
D. \( U u b \)


The velocity time graph of a particle moving along a straight line has the
form of a parabola \( t^{2}-6 t+8 \mathrm{m} / \mathrm{s} \). Find
the velocity (in \( \mathrm{m} / \mathrm{s} \) ) when acceleration of particle is zero:
A . -1
B. -2
c. -3
D. -


The value of p for which system has a solution is
A . 1
B. 2
c. 0
D. -


Determine the force acting between two parallel current carrying conductor wires. Write theoretical definition of
ampere on this basis.


Coordinates of the centre of the circle
which bisects the circumferences of the
circles \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{1}: \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{x}- \)
\( \mathbf{3}=\mathbf{0} \) and \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\mathbf{2} \boldsymbol{y}-\mathbf{3}=\mathbf{0} \) is
A \( \cdot(-3,-3) \)
B. (3,3)
c. (2,2)
D. (-2,-2)


For given current distribution, each
infinite length wire produces magnetic
field \( B \) at origin their resultant
magnetic field at origin \( \boldsymbol{O} \) is:
A . \( 4 B \)
В. \( \sqrt{2} B \)
\( c \cdot 2 \sqrt{2} B \)
D. zero


A \( 2.0 c m \) object is placed \( 15 c m \) in front
of a concave mirror of focal length \( 10 \mathrm{cm} \)
What is the size and nature of the
image?
A. \( 4 c m \), real
B. \( 4 \mathrm{cm} \), virtual
c. \( 1.0 \mathrm{cm} \), real
D. None of these


Glycoside linkage is an
A. Amide linkage
B. Ether linkage
c. Ester linkage
D. None of these


Assertion
Ammonia is a base.
Reason
Ammonia when dissolved in water
takes up proton to form ammonium and
furnishes \( \boldsymbol{O H}^{-} \) ions.
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


ABA closes stomata, but which of the
following hormone encourage them to open?
A . Gibberellic acid
B. Auxin
c. cytokinin
D. Ethylene


The value of \( \hat{y} \). \( \hat{z} \) is equal to
A. \( \frac{-1}{4} \)
B. \( \frac{3}{4} \)
c. 0
D. \( \frac{1}{2} \)


Which of the following is not related with photosynthesis in purple sulphur bacteria :-
A. Requirement of hydrogen doner
B. Requirement of light
c. Release of oxygen
D. Use of atmospheric \( C O_{2} \)


Rani requested her teacher to tell the therapeutic uses of recombinant protein, Platelet growth factor.


If a magnetic material is having magnetic susceptibility \( (\chi)=-1, \) then
the relative magnetic permeability \( \left(\mu_{r}\right) \) and type of magnetic material is?
A. \( 0, \) diamagnetic
B. 2, ferromagnetic
c. 1 , paramagnetic
D. -1, diamagnetic


The value of \( \int_{0}^{\pi / 2} \frac{\cos 3 x+1}{2 \cos x-1} d x \) is equal
to
A . 2
B.
c. \( \frac{1}{2} \)
D.


A die is thrown 4 times. The probability of getting atmost two 6 is
\( \mathbf{A} \cdot 0.984 \)
B. 0.802
c. 0.621
D. 0.72


What value of \( x \) makes the lines \( A B \)
and \( \bar{C} D \) parallel to each other?


State whether given statement is True or False
To prevent heat conduction to our hands, handle of cooking vessels are made of bad conductors.
A. True
B. False


In the reaction \( C_{(g)}+C O_{2(g)} \rightleftharpoons 2 C O_{(g)} \)
the equilibrium pressure is 12 atm. IF
\( 50 \% \) of \( C O_{2} \) reacts, \( K_{p} \) for the change
is:
A . 12 atm
B. 32 atm
\( c .64 a t m \)
D. 16 atm


Propeller blades in aeroplane are \( 2 \mathrm{m} \)
long. When propeller is rotating at 1800 rev/min, compute the tangential velocity of tip of the blade.


Find the sum of all four digit numbers that can be formed using the digits \( \mathbf{1}, \mathbf{3}, \mathbf{5}, \mathbf{7}, \mathbf{9} \)


One unit of electric energy is equal to:
A. One kilowatt hour
B. one watt hour
c. 100 Joules
D. none of these


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is a function satisfying
\( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x} \boldsymbol{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and
\( f\left(\frac{3}{4}\right)=\left(\frac{3}{4}\right), \) then \( f\left(\frac{9}{16}\right)= \)
\( A \cdot \frac{3}{4} \)
B. \( \frac{9}{16} \)
c. \( \frac{\sqrt{3}}{2} \)
D.


Find vector equation of line passing through the point whose position vector
is \( \mathbf{3} \hat{\mathbf{i}}-\mathbf{4} \hat{\mathbf{j}}+\hat{\boldsymbol{k}} \) and parallel to the vector
\( 2 \hat{i}+\hat{j}-3 \hat{k} . \) Also write the equation in
Cartesian form.


A dancer is standing on a rotating platform taking two sphere on her hands. If she drops down the sphere on ground then dancer's
A. angular velocity will increase
B. angular momentum and angular velocity both will unchanged
c. angular momentum unchanged and angular velocity will increase
D. both will decrease


An aeroplane is rising vertically with acceleration a. Two stones are dropped
from it at an interval of time t. The
distance between them at time \( t^{\prime} \) after
the second stone is dropped will be
A \( \cdot \frac{1}{2} t\left[g t+2 g t^{\prime}+2 a t^{\prime}\right] \)
B \( \cdot \frac{1}{2}(g+a)\left(t+2 t^{\prime}\right) t \)
c. \( \frac{1}{2}(g+a)\left(t-t^{\prime}\right)^{2} \)
D \( \cdot \frac{1}{2}(g+a)\left(t+t^{\prime}\right)^{2} \)


If radius of the were to shrink by \( 1 \%, \) It's mass remain same the the value of gon
the earth
surface would
A. increase by \( 0.5 \% \)
B. decrease by \( 0.5 \% \)
c. increase by \( 2 \% \)
D. decrease by \( 2 \% \)


write down the general and IUPAC name of the compound.
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \)


The visible region of hydrogen spectrum was first studied by
A. Lyman
B. Balmer
c. Pfund
D. Brackett


The evolutionary most advanced
inflorescence is found in
A . Dahlia
B. Salvia
c. calotropis
D. Yucca


\( 6 x-1=2 x+9 \) value of \( x \)
A \( \cdot 1 \frac{1}{2} \)
в. \( -2 \frac{1}{2} \)
c. \( \frac{4}{10} \)
D. \( _{2} \frac{1}{2} \)


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


Identify the compound that exhibits maximum ionic character among the
following:
A \( . M g C l_{2} \)
в. \( B a C l_{2} \)
c. \( N a C l \)
D. \( C s C l \)


The usual valency of hydrogen is:
A . -2
B. 0
c. +1 or sometimes -1
D. +2


\( \frac{\boldsymbol{x}^{2}-\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}^{3}-\mathbf{8}}=\frac{\boldsymbol{A}}{\boldsymbol{x}-\mathbf{2}}+\frac{\boldsymbol{B} \boldsymbol{x}+\boldsymbol{C}}{\boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}+\mathbf{4}} \Rightarrow \)
\( \boldsymbol{A}+\boldsymbol{B}= \)
\( A \cdot 0 \)
B.
\( c .-1 \)
\( D \)


From a variable point of an ellipse \( \frac{x^{2}}{d^{2}}+ \) \( \frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=1 \) normal is drawn to the ellipse.
Find the maximum distance of the
normal from the centre of the ellipse.
\( \mathbf{A} \cdot a+b \)
B. \( a-b \)
c. \( a^{2}-b^{2} \)
D. \( -a+b \)


is prepared on a large
scale from water gas.
A. Methanol
B. Ethanol
c. Methane
D. Ethane


How do histones acquire positive charge?


Cement is a man-made material used
in building.
A . True
B. False


The term greenhouse effect was given by
A. Fourier
B. Tyndall
c. Arrhenius
D. Linnaeus


The energy of a photons is equal to the
kinetic energy of a proton. If \( \lambda_{1} \) is the de
Broglie wavelength of a proton, \( \lambda_{2} \) the wavelength associated with the photon, and if the energy of the photon is \( \mathrm{E} \), then
\( \left(\lambda_{1} / \lambda_{2}\right) \) is proportional to:
\( \mathbf{A} \cdot E^{4} \)
B. \( E^{1 / 2} \)
c. \( E^{2} \)
D. \( E \)


Divide \( p(x)=x^{3}-3 x^{2}+5 x- \)
\( \mathbf{3} \) by \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2}-\mathbf{2} \)


Which of the following are correct regarding normal distribution curve?
(i) Symmetrical about the line \( \boldsymbol{X}=\boldsymbol{\mu} \) (Mean)
(ii) Mean \( = \) Median \( = \) Mode
(iii) Unimodal
(iv) Points of inflexion are at \( \boldsymbol{X}=\boldsymbol{\mu} \pm \boldsymbol{\sigma} \)
A . (i), (ii)
B. (ii), (iv)
c. (i), (ii), (iii)
D. All of these


Suppose \( F=2 x \) and \( u \) at \( x=1 \) is \( 10 J, \) find \( u \)
at \( x=2 \)


The central dogma of molecular genetics states that genetic information flows from :
A. DNA \( \rightarrow \) RNA \( \rightarrow \) Proteins
B. DNA \( \rightarrow \) RNA \( \rightarrow \) Carbohydrates
c. Amino acids \( \rightarrow \) Proteins \( \rightarrow \) DNA
D. DNA \( \rightarrow \) Carbohydrates \( \rightarrow \) Proteins


The mass of a lift is 2000 kg. When the tension in the supporting cable is \( 28000 \mathrm{N}, \) then its acceleration is
A \( \cdot 30 \mathrm{ms}^{-2} \) downwards
B. \( 4 \mathrm{ms}^{-2} \) upwards
c. \( 4 \mathrm{ms}^{-2} \) downwards
D. \( 14 \mathrm{ms}^{-2} \) upwards


The activity of \( \alpha \) -amylase in the endosperm of barley germinatingseed is induced
by
A. Ethylene
B. Cytokinin
c. IAA
D. Gibberellin


The radius of the sun is \( 7 \times 10^{8} m \) and
its mass is \( 2 \times 10^{30} k g \). What is the
order of magnitude of density of the
sun?
\( \mathbf{A} \cdot 1.4 \times 10^{3} k g / m^{3} \)
В \( \cdot 10^{7} k g / m^{3} \)
c. \( 1.5 \times 10^{3} k g / m^{3} \)
D. \( 10^{3} k g / m^{3} \)


When a flower can be cut in two equal
portion from only one plane it is called?
A. Actinomorphic
B. Zygomorphic
c. symmetrical
D. Bilateral


Major use of petroleum is in
A. Industries
B. Transport on land and air
c. Factories
D. shipping


Why \( A l F_{6}^{3-} \) has an expanded octet?


For a first order reaction \( \boldsymbol{A} \rightarrow \mathbf{2} \boldsymbol{B}+\boldsymbol{C} \)
It was found that at the end of 10
minutes from the start,the total optical
rotation of the system was \( 60^{0} \) and when the reaction is complete.lt was
\( 180^{0} . \) The \( \mathrm{B} \) and \( \mathrm{C} \) are only optically active and initially only A was taken.
i) What is the rate constant of the above
reaction (in hour)?
ii) At what time (in minute) from the
start, total optical rotation will be \( 90^{0} \) Take \( \log 2=0.3, \log 3=0.48, \log 7=0.85, \) in 10
\( =2.3 \)


\( \boldsymbol{C C l}_{4}+\mathbf{2}(\boldsymbol{H}) \stackrel{\boldsymbol{F} e / \text {Steam}}{\longrightarrow} \boldsymbol{A}+\boldsymbol{H C l} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C H}+\boldsymbol{H}_{2} \boldsymbol{O} \frac{40 \% \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{1 \% \boldsymbol{H g S O}_{4} / \boldsymbol{6 0}^{\circ} \boldsymbol{C}} \)
\( \boldsymbol{B} \)
The organic compound formed when \( \boldsymbol{A} \)
and \( B \) reacts together is
and it is used as
A. chloropicrin, insecticide
B. chloretone, wargas
c. chloretone, hypnotic
D. chloropicrin, hypnotic


Explain arrangement of human teeth.


State whether true or false:
A concave lens, if kept at a proper distance from an object, can form its real image.
A. True
B. False


Assertion
STATEMENT \( 1: S O_{2} \) obtained either by
the oxidation of \( H_{2} S \) or decomposition
of sulphate salt contains sulphur and oxygen in the mass ratio 1: 2
Reason
STATEMENTT
\( 2: S_{(s)}+O_{2(g)} \rightarrow S O_{2(g)} \)
A. Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for statement 1.
B. Statement 1 is True, Statement 2 is True; Statement 2 i not a correct explanation for Statement 1
c. Statement 1 is True, Statement 2 is False
D. Statement 1 is False, Statement 2 is True


Assertion
Atoms with completely filled and half filled subshells are stable.
Reason
Completely filled and half-filled subshells have the symmetrical distribution of electrons and have
maximum exchange energy
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


Bats detect the obstacles in their path
by receiving the reflected
A. infrasonic waves
B. ultrasonic waves
c. micro waves
D. radio waves


A particle of mass \( m \) is made to move
with a uniform speed \( v_{0} \) along the perimeter of a regular hexagon. The magnitude of impulse applied at each corner of the hexagon is


Consider the Gaussian surface that
surrounds part of the charge distribution shown in Fig. Then, the contribution to the electric field at point
\( \boldsymbol{P} \) arises from charges.
B. \( q_{3} \) and \( q_{4} \) only
c. \( q_{1}, q_{2}, q_{3} \) and \( q_{4} \)
D. None of the above


What are the components of a transcription unit?


The \( \boldsymbol{K}_{s p} \) for \( \mathrm{AgCl} \) is \( 2.8 \times 10^{-10} \) at \( \mathrm{a} \)
given temperature. The solubility of AgCl in 0.01 molar \( \mathrm{HCl} \) solution at
this temperature will be :
A . \( 2.8 \times 10^{-12} \mathrm{molL}^{-1} \)
В. \( 2.8 \times 10^{-8} \) molL\( ^{-1} \)
c. \( 5.6 \times 10^{-8} \) molL\( ^{-1} \)
D. \( 2.8 \times 10^{-4} \mathrm{molL}^{-1} \)


If the conjugate of \( (x+i y)(1-2 i) \) is
\( (1+i), \) then
A. \( x+i y=1-i \)
в. \( x+i y=\frac{1-i}{1-2 i} \)
c. \( x-i y=\frac{1-i}{1+2 i} \)
D. \( _{x-i y}=\frac{1-i}{1+i} \)


\( M n O_{4}^{2-}(1 \text { mole }) \) in neutral aqueous medium is disproportionate to:
A \( \cdot 2 / 3 \) mole of \( M n O_{4}^{-} \) and \( 1 / 3 \) mole of \( M n O_{2} \)
B . 1/3 mole of \( M n O_{4}^{-} \) and 2/3 mole of \( M n O_{2} \)
c. \( 1 / 3 \) mole of \( M n_{2} O_{7} \) and \( 1 / 3 \) mole of \( M n O_{2} \)
D. 2/3 mole of \( M n_{2} O_{7} \) and \( 1 / 3 \) mole of \( M n O_{2} \)


If \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\}, \boldsymbol{B}=\{\boldsymbol{x}, \boldsymbol{y}\}, \) find
\( \boldsymbol{A} \boldsymbol{X} \boldsymbol{B}, \boldsymbol{B} \boldsymbol{X} \boldsymbol{A}, \boldsymbol{A} \boldsymbol{X} \boldsymbol{A}, \boldsymbol{B} \boldsymbol{X} \boldsymbol{B} \)


Find the distance between
(2,3,-5) and (1,6,3)


Q Type your question
two parts are tield together by a ring made of a metal strip of cross-sectional area \( \mathrm{S} \) and length L. L is slightly less
than \( 2 \pi R \). To fit the ring on the wheel, it
is heated so that its temperature rises
by \( \Delta T \) and it just steps over the wheel
As it cools down to surrounding
temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the
metal is \( \alpha \) and its Young's modulus is
U, the force that one part of the wheel
applies on the other part is?
\( \mathbf{A} \cdot S Y \alpha \Delta T \)
в. \( \pi S Y \alpha \Delta T \)
\( \mathbf{c} \cdot 2 S Y \alpha \Delta T \)


Seventy five ball pens \( \operatorname{cost} R s 637.50 \)
Find the price of 23 ball pens. How many
pens can be bought for \( R s 800 \) and how
much money will be left?


centre Order of shape \( \quad \) of \( \quad \) rotation \( \quad \) rotat rotation
Equilateral Triangle
Rectangle 0
Square \( R \)
Find \( P, Q, R \) and \( S \) respectively.
A. Intersection point of medians, 2 , intersection point of diagonals, \( 90^{\circ} \)
B. Intersection point of medians, 2 , intersection point of
diagonals, \( 180^{\circ} \)
C. Intersection point of altitudes, \( 4, \) intersection point of
diagonals, \( 25^{\circ} \)
D. Intersection point of sides, \( 4, \) intersection point of diagonals, \( 45^{\circ} \)


The roadway bridge over a canal is in the form of an arc of a circle of radius
\( 20 m . \) What is the maximum speed with
which a car can cross the bridge without leaving the ground at the highest point.
A \( \cdot 10 \mathrm{ms}^{-1} \)
B. \( 12 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 14 \mathrm{ms}^{-1} \)
D. \( 16 \mathrm{ms}^{-1} \)


Weight' of a body may have the following attributes. It is the gravitational force acting on a body at the earth's surface
II. It is independent of the mass of the
body
III. The body is weightless during free fall
IV. It is different at different places on
earth's surface.
A . I, Il and III only
B . I, III and IV only
c. I and III only
D. I, II, III and IV


A particle moves in a line with velocity given by \( \frac{d s}{d t}=s+1 . \) The time taken by the particle to cover a distance of 9 meter is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \log 10 \)
\( c \cdot 2 \log , 10 \)
D. 10


A container is filled with 20 moles of an
ideal diatomic gas at absolute
temperature \( T . \) When heat is supplied
to gas, temperature remains constant but 8 moles dissociate into atoms. Heat
energy given to gas is
A \( .4 R T \)
в. \( 6 R T \)
\( c .3 R T \)
D. \( 5 R T \)


Solve the equation:
\( 4 x^{2}-4 p x+\left(p^{2}-q^{2}\right)=0 \)


The \( _{--}-_{-}-_{-}-_{-} \) of an atom is very hard
and dense.


Find the equation of the line having an
inclination \( 30^{\circ} \) with the positive direction of \( X \) axis and cut off an
intercept of 6 on the positive side of \( Y \)
axis.


The area of rhombus whose diagonals
are \( 16 \mathrm{cm}, 24 \mathrm{cm} \)


Which is the correct statement?
This question has multiple correct options
A. Starch is a polymer of \( \alpha \) -glucose.
B. Amylose is a component of cellulose.
C. Proteins are composed of only one type of amino acids.
D. In cyclic structure of furanose, there are four carbon atoms and one oxygen atom.


Circle O has diameters AB and CD
perpendicular to each other. AM is any
chord intersecting \( \mathrm{CD} \) at \( \mathrm{P.} \) Then \( A P . \overline{A M} \) is equal to:
A. \( \overline{A O} . \overline{O B} \)
в. \( \overline{A O} . \overline{A B} \)
\( c \cdot \overline{C P} \cdot \overline{C D} \)
D. \( \overline{C P} . \overline{P D} \)
ह. \( \overline{c O} . \overline{O P} \)


Match the following.


A force which produces an acceleration in a body equal to acceleration due to
gravity on earth, when the body has a unit mass is called
A. Gravitational unit of force
B. Gravity force
\( c . \) Both
D. None


A light ray makes an angle of incidence
\( 60^{\circ}, \) when it falls on a plane reflecting
sheet
The angle of deviation will be:
A \( .20^{\circ} \)
B . \( 40^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 80^{\circ} \)


In the Lassaigne's test for the detection of nitrogen in an organic compound, the appearance of blue colored compound is due to:
A. ferric ferricyantde
B. ferrous ferricyanide
c. ferric ferrocyanide
D. ferrous ferrocyanide


When an ideal diatomic gas is heated at constant pressure then what fraction of heat given is used to increase internal energy of gas?
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{3}{7} \)
D.


The hydration energy of \( M g^{2+} \) is greater than that of :
A \( . A l^{3} \)
В. \( N a^{+} \)
\( c \cdot B e^{2} \)
D. \( M g^{3+} \)


An experiment's diary reads as follows; "a charged particle is projected in a magnetic field of \( (7.0 \hat{i}-3.0 \hat{j}) \times \)
\( 10^{-3} T . \) The acceleration of the particles
is found to be \( (x \hat{i}+7.0 \hat{j}) \times 10^{-6} m / s^{2} \)
Find the value of \( x \)


Find the Odd one among : 517,661,814 922,1066,1256
A. 66
B. 814
\( c . \) 1256
D. 922


Which molecule/ion out of the following does not contain unpaired electrons?
A \( \cdot N_{2}^{+} \)
в. \( O_{2} \)
\( c \cdot O_{2}^{2} \)
D. \( B_{2} \)


Fill in the blanks.
The - - - - consists of natural numbers,
zero and negative of natural numbers. Zero is called the \( -\dots-\dots \) called the
multiplicative identity
A. Integers, additive identity, 1
B. Integers, additive inverse, 1
c. Whole numbers, additive identity,
D. Rational numbers, additive inverse,


An ant is at a corner of a cubical room of
side a. The ant can move with a
constant speed u. The minimum time
taken to reach the farthest corner of the
cube is?
A \( \cdot \frac{3 a}{u} \)
B. \( \frac{\sqrt{3} a}{u} \)
c. \( \frac{\sqrt{5} a}{u} \)
D. \( \frac{(\sqrt{2}+1) a}{u} \)


If \( \boldsymbol{I}_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x \)
then \( \frac{1}{I_{2}+I_{4}}, \frac{1}{I_{3}+I_{5}}, \frac{1}{I_{4}+I_{6}} \) are in?
A . \( A . P \)
в. \( H . P \)
c. \( G . P \)
D. None of these


If a satellite is revolving very close to the surface of earth, then its orbital
velocity does not depend upon
A. mass of satellite
B. mass of earth
c. radius of earth
D. orbital radius


For a heater rated at \( 4.4 \mathrm{kW} ; 220 \mathrm{V} \) Calculate the energy consumed by the heater in 4 hours?
A. \( 12 \mathrm{kWh} \)
B. 17.6 kWh
\( c \cdot \) okwh
D. \( 4.4 \mathrm{kWh} \)


Assertion
An astronaut experience weightlessness in a space satellite
Reason

When a body falls freely it does not experience gravity.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The potential at a point due to a charge
of \( 5 \times 10^{-7} \) C located \( 10 \mathrm{cm} \) away is:
A. \( 3.5 \times 10^{5} \mathrm{V} \)
B. 3.5 \( \times 10^{4} \mathrm{v} \)
c. \( 4.5 \times 10^{4} v \)
D. \( 4.5 \times 10^{5} \mathrm{v} \)


Identify the compound which gives
carbon with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)


The value of \( 3^{7} C_{0}+4^{7} C_{1}+5^{7} C_{2}+ \)
\( -----------10^{7} C_{7} \) is
A \( \cdot 10(2)^{6} \)
B . \( 13(2)^{7} \)
c. \( 14(2)^{6} \)
D. \( 13(2)^{6} \)


In the adjoining figure, \( A B C D \) is a
trapezium in which \( A B \)

DC and \( A D=B C . \) If \( P, Q, R, S \) be
respectively the midpoints of \( B A, B D \) and \( C D, C A \) then show that
PQRS is a rhombus.


There is flag-staff at the top of 10 metres high tower. If the flag-staff
makes an angle \( \tan ^{-1}(1 / 8) \) at a point
24 metres away from the tower, then the
height of the flag staff in metres is
A \( .26 / 7 \)
B. 27/8
c. \( 27 / 6 \)
D. 26 /3


Statement 1: Trimethyl amine is more basic than trisilyl amine.

Statement 2: Silicon in trisilyl amine is more electronegative than carbon of trimethyl amine.
A. Statement 1 is True, statement 2 is True, statement 2 is a correct explanation of statement 1
B. Statement 1 is True, statement 2 is True, statement 2 is not a correct explanation of statement
c. Statement 1 is true, Statement 2 is False
D. Statement 1 is False, Statement 2 is True


Which metal pairs when coupled will get maximum emf for a voltaic cell?
\( A \cdot F e \) and \( C u \)
B. Pb and Cu
c. Cu and Au
D. ca and cu


Write the relations as sets of ordered
pairs
\( \{(x, y): y=3 x, x \in\{1,2,3\}, y \in\{3,6 \)


If the triangle \( A B C \) in the question 7 above is revolved 7 above is resolved the side \( 5 \mathrm{cm}, \) then find the volume of the solid so obtained Find also ratio of the
volumes of the two solids obtained in
Questions 7 and 8


Which of the following is not true for a galvanic cell when written in an abbreviated form?
A. Right hand electrode is a positive terminal.
B. Right hand electrode acts as cathode
c. Electrons are given out in the external circuit from anode
D. Electrons are given out in the external circuit from cathode


Oxidation of \( H C l \) with oxygen releases:
A \( . H_{2} \)
в. \( C l_{2} \)
\( c \cdot O_{2} \)
D. \( H_{2} S_{S} \)


There will be no force between two wires
carrying currents if currents are
A. parallel to each other
B. antiparallel to each other
C. perpendicular to each other
D. none of these.


A point charge \( q \) is brought form infinity
and is placed at the centre of a
conducting neutral spherical shell of
inner radius \( a \) and outer radius \( b, \) then
work done by external agent is:
\( A \)
B. \( \frac{k q^{2}}{2 b} \)
c. \( \frac{k q^{2}}{2 b}-\frac{k q^{2}}{2 a} \)
D. \( \frac{k q^{2}}{2 a}-\frac{k q^{2}}{2 b} \)


After an aeroplane completes a voyage,
its muzzle feels warmer than the
middle and back portion of the main body. This is because:
A. the muzzle tears apart the air layers and suffers more air friction
B. the muzzle suffers less air friction
c. the muzzle suffers zero air friction
D. none of these


A convex lens of focal length \( 1.5 \mathrm{m} \) is
placed in a system of coordinate axis
such that its optical centre is at origin and principal axis coinciding with the x-axis. An object and a plane mirror are arranged on the principal axis as shown n fig. Find value of \( d \) (in \( m \) ) so that \( y \) coordinate of image (after refraction and reflection) is \( 0.3 \mathrm{m} . \) (Take \( \tan \theta= \)
\( \mathbf{0 . 3}) \)


The value of \( \int e^{x}\left[\frac{1+\sin x}{1+\cos x}\right] d x \) is
A \( \cdot \frac{1}{2} e^{x} \sec \frac{x}{2}+C \)
B \( \cdot e^{x} \sec \frac{x}{2}+C \)
c. \( \frac{1}{2} e^{x} \tan \frac{x}{2}+C \)
D. \( e^{x} \tan \frac{x}{2}+C \)


In the extraction of aluminium metal,
one of the process is summarised as
follows:
Which of the following entries correctly
summarises reagents, electrodes and
products of the process?
A. \( \begin{array}{ccccc}A & B & C & D & E \\ N a O H & A l^{3+} & H F & N a_{3} A l F_{6} & \text {Cathode}\end{array} \)
B. \( \begin{array}{ccc}A & B & C \\ _{N a} O H & N a A l O_{2} & C O_{2}\end{array} \)
\( D \)
\( E \) NaF Anode
\( c \)
\( \begin{array}{cc}A & B \\ H_{2} S O_{4} & A l_{2}\left(S O_{4}\right)_{3}\end{array} \)
\( C \)
Cathode \( N H_{3} \) \( N a_{3} A l F_{6} \)
D. \( \begin{array}{cc}A & B \\ N a O H & N a A l O_{2}\end{array} \) \( C \) \( D \)
\( a_{2} A l \) \( E \)
Cathode \( \mathcal{P}_{2} \quad N a_{3} A l F_{6} \)


\begin{tabular}{l|l|l}
& \( \mathbf{X} \) & \( \mathbf{Y} \) \\
& & \\
Normal & 2,8,7 & \\
Electronic Configuration Nature of oxide & 2, 8, 2 Dissolves in water and turns blue litmus red & Very low solubility in water. Dissolves in hydrochloric acid \\
Tendency for oxidising and reducing reactions Electrical and Thermal conductivity & Tends to oxidise elements and compounds Very poor electrical conductor Poor thermal conductivity & Tends to act as a reducing agent Good Electrical conductor Good Thermal conductor \\
Tendency to form alloys and amalgums & to form alloys & Forms alloys \\
\hline
\end{tabular} Using the information above, complete
the following
Metals tend to electrons and
\( \operatorname{act} a s \)
agents in their
reactions with elements and
compounds.


A certain hydrate has a formula
\( M g S O_{4} \times H_{2} O . A \) quantity of \( 54.2 \mathrm{gm} \)
of the compound is heated on an oven to
drive off the water. If the steam
generated exerts a pressure of 24.80
\( \operatorname{atmin} a 20 L \) container at \( 120^{\circ} \mathrm{C} \)
Calculate \( x \)
\( A \cdot 2 \)
B. 5
\( c \cdot 6 \)
D. 7


Column - I What is and İ
\( x \)
Magnetic A. \( A g_{2} S \) separation "
\( Y \)
Forth Flotation
B.
\[
\mathrm{FeCr}_{2} \mathrm{O}_{4}
\]
\( z \)
Gravity c. separation \( A l_{2}\left(S i O_{3}\right)_{3} \)
Match the method of concentration of
the ore in column I with the ore in
column II and select the correct
alternate:
A \( . X-A, Y-B, Z-C \)
B. \( X-B, Y-A, Z-C \)
c. \( X-C, Y-A, Z-B \)
D. \( X-B, Y-C, Z-A \)


A pendulum bob of mass \( m=80 m g \)
carrying a charge of \( \boldsymbol{q}=\boldsymbol{2} \times \mathbf{1 0}^{-8} \boldsymbol{C} \), is
at rest a horizontal uniform electric
field of \( \boldsymbol{E}=\mathbf{2 0}, \mathbf{0 0 0} \boldsymbol{V} / \boldsymbol{m} . \) The tension \( \boldsymbol{T} \)
in the thread of the pendulum and the angle \( \alpha \) it makes with vertical is (take
\( \boldsymbol{g}=\mathbf{9} . \boldsymbol{8} \boldsymbol{m} / \boldsymbol{s}^{2} \boldsymbol{)} \)
This question has multiple correct options
A \( \cdot \alpha \approx 27^{\circ} \)
в. \( T \approx 880 \mu N \)
c. \( T=8.8 \mu N \)
D. \( \alpha \approx 356 o \)


Which of the following is/ are correct
statement(s)?
This question has multiple correct options
A. Cement is an important material in electronic industry
B. Sheets, blocks, pillars and pipes are made from concrete produced from cement.
C . Cement is a wet white powder with coarse particles.
D. Cement is made from silica (sand), alumina, lime, iron oxide and magnesia.


Which among the following statements is/are correct?
This question has multiple correct options
A. \( \Psi^{2} \) represents the atomic orbitals
B. The number of peaks in radial distribution is \( (n-1) \)
C . Radial probability density \( \rho_{n l}(r)=4 \pi r^{2} R_{n l}^{2}(r) \)
D. A node is a point in space where the wave function has zero amplitude


Assertion
The mass of a body cannot be
considered to be concentrated at the
centre of mass of the body for the
purpose of computing its moment of inertia.
Reason
Then the moment of inertia of every
body about an axis passing through its centre of mass would be zero.
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


Let \( a=m i n\left[x^{2}+2 x\right], x \in R \) and \( b= \)
\( \lim _{x \rightarrow 0} \frac{\sin x \cdot \cos x}{e^{x}+e^{-x}} . \) Then value of \( a+b \) is
A . -1
B . 2
\( c .1 \)
D.


Negative terminal of a dry cell is formed
by:
A. zinc container
B. carbon rodd
c. graphite rod
D. both A and B


Which of the following statements
differentiates between terrestrial and
aquatic ecosystems?
A. Organisms in terrestrial ecosystems are dependent on oxygen, while those in aquatic ecosystems are not.
B. Nutrients are a limiting factor for populations in aquatic ecosystems but not for terrestrial populations
C. Producers make up the greatest amount of biomass in terrestrial ecosystems, while in aquatic ecosystems they do not.
D. Sunlight is a limiting factor for populations in terrestrial ecosystems but not for populations in aquatic ecosystems.
E. Energy in aquatic ecosystem is transferred from lower to higher trophic levels, but it moves in the opposite direction in aquatic ecosystems


Find the total surface area of cubes
having the following sides.
\( \mathbf{5 . 5} \boldsymbol{m} \)


\( \boldsymbol{p} \vee \boldsymbol{q} \) is true, when
A. either \( p \) of \( q \) are true
B. \( p \) is true and \( q \) is false
\( \mathbf{c} \cdot p \) is false and \( q \) is true
D. All of these


Which of the following is correct with respect to adolescence?
A. Starts at the puberty and ends with cessation of growth
B. Starts at the end of puberty and ends at the beginning of adulthood
c. Post puberty period when external sex characters appear
D. None of these


The dorsal portion of skeleton found on
the abdomen of cockroach is
A. Pleuron
B. Sternum
c. Tergum
D. Vertex


Oxalosuccinic acid, a transient
intermediary compound of Krebs cycle
is
A. 4-carbon compound
B. 5-carbon compound
c. 6-carbon compound
D. 3-carbon compound


\( \ln \operatorname{an} S_{N} 1 \) reaction of alkyl halide on
chiral centres there is:
A. \( 100 \% \) recemization
B. inversion more than retention leading to partial racemization
c. \( 100 \% \) retention
D. \( 100 \% \) inversion


Which statement is true about 2nd law of
Thermodynamics?
A. Heat can be converted to into work without changes in system or surroundings
B. It is possible to construct a perpetual motion machine of second kind
C. All spontaneous process are thermodynamically irreversible
D. All spontaneous process are thermodynamically reversible


Which of the following elements exhibit maximum outermost electrons?
A . Na a
в. Мв
\( c \cdot s i \)
\( D \)


If the momentum of an electron is
changed by \( P, \) then the de-Broglie wavelength associated with it changes by \( 0.5 \% \). The initial momentum of
electron will be :
\( \mathbf{A} \cdot 400 P \)
в. \( \frac{P}{200} \)
\( c \cdot 100 P \)
D. 200P


Strength of an acid solution or a basic solution can be determined by knowing the hydrogen ion concentrations in
them, using a pH scale.
(i) Neutral solution has pH 7.
(ii) Acidic solution has pH less than 7 .
(iii) Basic solution has pH more than 7 .
The pH of a solution is inversely proportional to hydrogen(H+) ion concentration in it.
Teacher told three students Renuka,
Bhawna and Seema to test their saliva
with pH paper before and after having their lunch. Identify the correct observation from the following.
A. Bhawna observed that pH paper turned red and recorded pH value of \( 2.3-2.5 \) after having lunch
B. Seema observed that pH paper turned yellow and recorded pH value of \( 5.6-5.8 \) before having lunch
c. Renuka observed that pH paper turned green and recorded pH value of 7.4-7.9 before having lunch
D. observations made by both Renuka and Seema were correct


Which of the following technique uses high temperature to convert ore into raw metals?
A. Pyrometallurgy
B. Hydrometallurgy
c. Both a and
D. None of above


Karan and shashank borrowed 6000
each at the rate of \( 12 \% \) per annum for a
period of 2 years and 3 years respectively.Find the difference of interest paid by them.


Match the names of the special cells
with the names of the organs / parts in which they occur. Choose the answer,
which gives the correct combinations of the alphabets of the two columns.
Cells
A. Cellsof Von \( \quad \) p. Small intestine Kupffer
q. Proximal convolutec
в. \( \beta \) cells \( \quad \) tubules
Brush border cells
D. Paneth cells
t. Islets of Langerhans
A. \( A-r, B-p, C-t, D-q \)
в. \( A-r, B-t, C-p, D-q \)
c. \( A-r, B-s, C-q, D-p \)
D. \( A-r, B-t, C-q, D-p \)


Write the differential equation representing the family of curves \( y= \)
\( m x, \) where \( m \) is an arbitrary constant.


Let \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \in \)
\( \boldsymbol{R}, \boldsymbol{f}(\mathbf{5})=\mathbf{2}, \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{3}, \) then \( \boldsymbol{f}^{\prime}(\mathbf{5}) \)
equals:
A .4
B.
\( c \cdot \frac{1}{2} \)
\( D \)


The value of \( x \) in the equation \( 3 x^{x+1} \)
\( C_{2}=2 \times^{x+2} C_{2}, x \in N \) is
\( \mathbf{A} \cdot x=4 \)
B. \( x=5 \)
c. \( x=6 \)
D. \( x=7 \)


Assertion
Force on a body \( A \) by body \( B \) is equal and opposite to the force on the body B by A.
Reason

Force in nature always occur between
pairs of bodies
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


4.0 grams of caustic soda contains:
B. 4 g atoms of \( N a \)
c. \( 6.02 \times 10^{22} \) atoms of \( N a \)
D. 4 moles of NaOH


Which of the following is false for heat?
\( A \). It is a form of energy.
B. It cannot be seen but only can be felt.
C. If a body's temperature is increased, it gains heat energy
D. It is always produced from chemical energy


Compound 'X' is bubbled through
bromine dissolved in \( C C l_{4} \& \) the
product formed is
\( C H_{2} B r-C H_{2} B r . \) Draw the structural
formula of 'X' and state what type of reaction 'X' has undergone


The intensity of magnetic field is \( \mathrm{H} \) and moment of magnet is M. The maximum
potential energy is
A. мн
B. 2 МН
\( c \cdot 3 \) МН
D. 4 MH


The electrostatic potential due to the
charge configuration ot point \( P \) as
shown in figure for \( b<<a \) is
\( A \)
\[
\frac{2 q}{4 \pi \varepsilon_{0} a}
\]
B.
\[
\frac{2 q b^{2}}{4 \pi \varepsilon_{0} a^{3}}
\]
\( c \)
\[
\frac{q b^{2}}{4 \pi \varepsilon_{0} a^{3}}
\]
D. zero


Solve \( \int \frac{e^{x}(x-1)}{(x+1)^{3}} d x \)
A \( \cdot \frac{-e^{x}}{(x+1)^{2}}+c \)
в. \( \frac{e^{x}}{(x+1)^{2}}+c \)
c. \( \frac{e^{x}}{(x+1)^{3}}+c \)
D. \( \frac{-e^{x}}{(x+1)^{3}}+c \)


A liquid of specific heat 0.3 at \( 90^{\circ} \mathrm{C} \) is mixed with another liquid of specific
heat 0.5 at \( 15^{\circ} \mathrm{C} \). If final temperature of
the mixture is \( 60^{\circ} \mathrm{C} \), then find the ratio of masses of the two liquids mixed.


Which of the following is not a redox reaction?
A. \( M g+N_{2} \rightarrow M g_{3} N_{2} \)
B . \( M n O_{4}^{-}+C_{2} O_{4}^{2-} \rightarrow M n^{2+}+C O_{2} \)
c. \( C u S O_{4}+K I \rightarrow 2 C u I+I_{2}+K_{2} S O_{4} \)
D. \( A g C l+N H_{3} \rightarrow\left[A g\left(N H_{3}\right)_{2}\right] C l \)


The process of zone refining is used in the purification of :
A . \( A l \)
в. \( G e \)
c. \( C u \)
D. \( A g \)


Oxidative decarboxylation of pyruvic acid results in the formation of
I. Acetyl CoA
Il. \( C O_{2} \)
III. ATPIV. NADH \( +\boldsymbol{H}^{+} \)
A. I only
B. I and II only
c. I, Il and III only
D. I, II and IV only
E. III and IV only


If two waves of same frequency and same amplitude, on superposition, produce a resultant disturbance of the
same amplitude, the wave differ in phase by
\( A \)
в. \( 2 \pi / 3 \)
c. zero
D. \( \pi / 3 \)


A wave represented by the equation \( \boldsymbol{Y}=\boldsymbol{A} \cos (\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}) \) is superimposed
with another wave to form a stations
wave such that the point \( x=0 \) is a node. The equation of the other wave is
A \( .-A \sin (k x+\omega t) \)
B. \( -A \cos (k x+\omega t) \)
c. \( A \sin (k x+\omega t) \)
D. \( A \cos (k x+\omega t) \)


What should we do if dust particles go
into our eyes while playing in the ground?
A. Wash your eyes with chlorine water
B. Wash your eyes with clean water
c. Wash your eyes with salt water
D. Wash your eyes with dettol


Explain the Hatch-Slack pathway.


What is the value of \( \sin ^{2} 25^{0}+\sin ^{2} 65^{0} ? \)


Current in a coil is increased at a
constant rate. The current in the second
coil is also increased at the same rate.
At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced
voltage and the energy stored in the
first coil are \( I_{1}, V_{1}, \) and \( W_{1} \) respectively. Corresponding values for
the second coil at the same instant are
\( I_{2}, V_{2} \) and \( W_{2} \) respectively. Then
A. \( \frac{W_{2}}{W_{1}}=8 \)
в. \( \frac{W_{2}}{W_{1}}=\frac{1}{8} \)
c. \( \frac{W_{2}}{W_{1}}=4 \)
D. \( \frac{W_{2}}{W_{1}}=\frac{1}{4} \)


When the tension in a metal wire is \( T_{1} \)
its length is \( l_{1} \). When the tension is \( T_{2} \)
its length is \( l_{2} \). The natural length of
wire is
\( ^{\mathbf{A}} \cdot \frac{T_{2}}{T_{1}}\left(l_{1}+l_{2}\right) \)
в. \( T_{1} l_{1}+i_{2} l_{2} \)
c. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
D. \( \frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}} \)


An \( L-C-R \) series circuit with \( L= \)
\( 0.120 H, R=240 \Omega, \) and \( C=7.30 \mu F \)
carries an rms current of \( 0.450 A \) with a
frequency of \( 400 H z . \) What is the average rate at which electrical energy is dissipated (converted to other forms) in the inductor?


Is the following sequence an \( A P ? \) If
true, find the common difference \( d \) and
write three more terms.
\( \mathbf{0},-\mathbf{4},-\mathbf{8},-\mathbf{1 2} \)


The probable direct ancestor of modern
man is
A. Java man
B. Peking mann
c. Cromangnon man
D. Neanderthal man


A sum of Rs. 46,875 was lent out as simple interest and at the end of 1 year
8 months the total amount was Rs.
\( \mathbf{5 0}, \mathbf{0 0 0} . \) Find the rate of interest per
cent per annum.
A . \( 3.5 \% \)
в. \( 4.5 \% \)
c. \( 5 \% \)
D. \( 4 \% \)


Which of the following numbers has least number of significant figures?
A. 0.80760
00 0066600
B. 0.80200
\( c .0 .08076 \)
D. 80.267


Assertion
Sodium bicarbonate is an acidic salt.
Reason
It gives basic solution in water.
A. If both assertion and reason are correct and reason is the correct explaination of the assertion
B. If both assertion and reason are correct, but reason is
not the correct explanation of the assertion
C. If assertion is correct, but reason is incorrect
D. If assertion is incorrect, but reason is correct


Estimation of halogens in organic compounds is done by:
A. Carius method
B. Kjeldahl's method
c. Duma's method
D. Messenger's method


Distilled water though pure, is not preferred to drink due to its flat insipid
taste.
A. True
B. False


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \) and \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{x}|, \) then \( \boldsymbol{f}(\boldsymbol{x})+ \)
\( g(x) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B . \( 2 x \)
\( \mathbf{c} \cdot 2 x \) if \( x \geq 0 \)
D. \( 2 x \) if \( x \leq 0 \)


Bond energy of a molecule is:
A . always positive
B. either positive or negative
c. always negative
D. dependent on the physical state of the system


Two identical spheres of gold are in
contact with each other. The
gravitational attraction between them
is
A. Directly proportional to the square of the radius
B. Directly proportional to the cube of the radius
C. Directly proportional to the fourth power of the radius
D. Inversely proportional to the square of the radius


Chromosome number is halved in
meiosis during
A. Metaphase I
B. Anaphase I
c. Metaphase II
D. Telophase I


Oxygen in our blood is transported by a Protein, named:
A. Keratin
B. Collagen
c. Haemoglobin
D. Myoglobin


\( \frac{\frac{\pi}{4}}{\frac{\pi}{4}} \)


Name the nitrogenous base present in sphingolipids.


State True or False.
A gas differs from a liquid in that, except during collisions, the molecules of gas are widely separated from each other and move in paths that are largely unaffected by intermolecular force.
A. True
B. False


Define photo-oxidation and photorespiration.


According to Lewis, the ligands are:
A. acidic in nature
B. basic in nature
c. neither acidic nor basic
D. some are acidic and others are basic


Parallax angles
\( 0.01 / \)arcsec are very difficult to
measure from Earth
\( A . \) more than
B. less than
c. equal to
D. greater than or equal to


Given two independent events \( A \) and \( B \) such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 6 .} \)
Find \( \boldsymbol{P}\left(\boldsymbol{A}^{\prime} \cap \boldsymbol{B}^{\prime}\right) \)


The sum of the deviations of the
variates from the arithmetic mean is
always.
\( A \cdot+1 \)
B. 0
\( c \cdot-1 \)
D. Real number


Two spheres of equal mass \( A \) and \( B \) are
given \( +q \) and \( -q \) charge respectively then:
A. Mass of A increases.
B. Mass of B increases.
C. Mass of A remains constant.
D. Mass of B decreases.


The given alcohol is (primary/ secondary) alcohol. (If your answer is primary type 1 else 2)
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{OH}
\]


When molecules are in a condensed
physical state (liquid or solid), they exert attractive intermolecular forces
(IMF), on one another. One example of this type of attractive force is hydrogen bonding.

Which of the labelled arrows \( (\leftarrow \text { and } \leftrightarrow) \) in the diagram BEST illustrated
hydrogen bonding for ammonia, \( N H_{3} ? \)
A. Hydrogen Bond
в.
c.
D. None of the above


If \( A \) is an event of a random experiment, then \( A^{C} \) or \( A^{-} \) or \( A^{\prime} \) is called the
compliment of the event.
If true then enter 1 and if false then
enter 0
A. 0
B. Can't determine
\( c \)
D. None of these


ff \( \left[\begin{array}{cc}\mathbf{4} & -\mathbf{3} \\ \mathbf{2} & \mathbf{1 6}\end{array}\right]=\left[\begin{array}{cc}\mathbf{4} & -\mathbf{3} \\ \mathbf{2} & \mathbf{2}^{t}\end{array}\right], \) then \( \mathbf{t}= \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)


A metallic element has a cubic lattice.
Each edge of the unit cell is \( 2 \AA \). The
density of the metal is \( 2.5 \mathrm{cm}^{-3} \) The unit
cells in 200 g of metal are :
A \( .1 \times 10^{2} \)
В. \( 1 \times 10^{26} \)
\( c \cdot 1 \times 10^{2} \)
2
D. \( 1 \times 10^{25} \)


The enthalpy of \( S-S \) bond from the
following data is:
\( (\text { i }) C_{2} H_{5}-S-C_{2} H_{5}(g) ; \Delta_{f} H^{o}= \)
\( -147.2 \mathrm{kJ} / \mathrm{mol} \)
\( (\text { ii }) C_{2} H_{5}-S-S- \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{f} \boldsymbol{H}^{o}=-\mathbf{2 0 1 . 9} \mathrm{kJ} / \mathrm{mol} \)
\( (\text { iii }) S(g) ; \Delta_{f} H^{o}=-222.8 \mathrm{kJ} / \mathrm{mol} \)
A. \( 124.5 \mathrm{kJ} / \mathrm{mol} \)
B. 887.5 kJ / mol
c. 967.5 kJ / mol
D. 277.5 kJ / mol


The wave length of a radio wave is \( 1.0 \mathrm{m} \) Find its frequency.


If earth's radius were to hypothetically shrink by \( 1 \% \), the value of \( G \) would
A. shrink by \( 1 \% \)
B. expand by \( 1 \% \)
c. remain the same
D. shrink by \( 0.01 \% \)


\( \boldsymbol{R}-\boldsymbol{C O O H}+\boldsymbol{R}-\boldsymbol{C O O N a} \rightarrow ? \)


Resistance of a platinum resistance thermom-eter is 2 ohm at \( 20^{\circ} \mathrm{C}, 4 \) ohm
at \( 100^{\circ} C \) and 2.2 ohm at some
temperature. this temperature-is
A \( \cdot 20^{\circ} \mathrm{C} \)
B. 30
\( \mathbf{c} \cdot 40^{\circ} \mathrm{C} \)
D. \( 28^{\circ} \mathrm{C} \)