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\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1} \) and \( \phi(\boldsymbol{x})=\sin ^{2} \boldsymbol{x}+\cos ^{2} \boldsymbol{x} \)
Show that both functions are equal? | 2 | Maths |
Equation of a tangent to the curve \( y= \) \( \cos (x+y), 0 \leq x \leq 2 \pi \) that is parallel
to the line \( x+2 y=0 \) is
A \( \cdot x+2 y=\frac{\pi}{2} \)
в・ \( x+2 y=\frac{\pi}{4} \)
c. \( x+2 y=\pi \)
D. \( x+y=\pi \) | 2 | Maths |
Solve:
\( \mathbf{3}(\boldsymbol{t}-\mathbf{5})-\mathbf{1 6} \boldsymbol{t}=\mathbf{1 2}-\mathbf{2}(\boldsymbol{t}-\mathbf{3}) \) | 2 | Maths |
Energy required to break ethane into its
constituent atoms is \( 2860 K J \). If the
\( C-H \) bond energy is \( 420 \mathrm{KJ}, \) the \( C-C \)
bond energy is: | 1 | Chemistry |
The total number of isotopes of hydrogen and the number of radioactive isotopes among them, respectively, are:
A . 2 and 0
B. 3 and 2
\( c .3 \) and 1
D. 2 and 1 | 1 | Chemistry |
A load of \( 10 \mathrm{kg} \) is suspended by a metal
wire 3 m long and having a cross-
sectional are \( 4 m m^{2} . \) Find (a) the stress
(b) the strain and
(c) the elongation.
Young modulus of the metal is \( 2.0 \times \) \( 10^{11} N m^{-2} \) | 3 | Physics |
During the molecular functioning of genes, which process converts RNA into protein?
A. Trancription
B. Translation
c. Transfection
D. Transfusion | 0 | Biology |
Which of the following is the main cause of late discovery of neutron?
A. Neutron is highly unstable particle
B. Neutron in nucleus moves very fast
c. Neutron is charge-less particle
D. All of the above | 1 | Chemistry |
A biased coin with probability \( P,(0<p< \)
1) of heads is tossed until a head
appear for the first time. If the
probability that the number of tosses
required is even is \( \frac{2}{5} \) then \( P= \)
\( A \cdot \frac{2}{5} \)
B.
\( c \cdot \frac{1}{3} \)
\( D \cdot \frac{3}{5} \) | 2 | Maths |
The wavelength associated with a
photon of energy 3.31 eV is nearly
A. \( 4000 A^{\circ} \)
B. 3750 \( A^{\circ} \)
C \( .5000 A^{\circ} \)
D. 400 A \( ^{\text {о }} \) | 3 | Physics |
Which of the following statements
is/are not true?
This question has multiple correct options
A. All ortho-para directing groups activates the ring
B. All ortho-para directing groups except halogens activate the ring
C. All meta-directing groups have \( \pi \) -bond on the atom directly attached to the ring
D. All meta directing groups are deactivating. | 1 | Chemistry |
Evaluate the given integral. \( \int x \sin 2 x d x \) | 2 | Maths |
When a metal sphere is heated
maximum percentage increase occurs in its :
A. Density
B. Surface area
c. Radius
D. volume | 3 | Physics |
A prism of refractive index \( \sqrt{2} \) has
refracting angle \( 60^{\circ} . \) Answer the
following questions In order that a ray suffers minimum deviation it should be incident at an
angle :
A \( .45^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 30^{\circ} \)
D. none | 3 | Physics |
Assuming the bond direction to the z-
axis, which of the overlapping of atomic orbitals of two atoms \( (A) \) and \( (B) \) will
result in bonding?
(I) \( s \) -orbital of \( A \) and \( p_{x} \) orbital of \( B \)
(II) \( s \) -orbital of \( A \) and \( p_{z} \) orbital of \( B \)
(III) \( p_{y} \) orbital of \( A \) and \( p_{z} \) orbital of \( B \)
(IV) \( s \) -orbital of both \( (A) \) and \( (B) \)
A. I and IV
B. I and II
c. Ill and IV
D. II and IV | 1 | Chemistry |
The end product of fermentation of
sugars by Lactobacillus bacteria is
A . Lactic acid
в. \( C O_{2} \)
C. Methyl alcohol and \( C O_{2} \)
D. Butyl alcohol. | 0 | Biology |
Draw a parallelogram \( A B C D \) in which \( B C=5 \mathrm{cm}, A B=3 \mathrm{cm} \) and \( \angle A B C= \)
\( 60^{0} . \) divide it into triangles \( B C D \) and
\( A B D \) by the diagonal \( B D . \) Construct
the triangle \( B D^{\prime} C^{\prime} \) similar to \( B D C \) with scale factor \( \frac{4}{3} . \) Draw the line
\( \operatorname{segment} D^{\prime} A^{\prime} \) parallel to \( D A, \) where \( A^{\prime} \)
lies on extended side \( B A \). Is \( A^{\prime} B C^{\prime} D^{\prime} \) a
parallelogram?
A. Yes
B. No
c. Data insufficient
D. Ambiguous | 2 | Maths |
An element has 1 st shell fully filled and in
2nd shell has 6 electrons. Explain. | 1 | Chemistry |
\( \int e^{2 x-3}+7^{4-3(x / 2)}+\sin \left(3 x-\frac{1}{2}\right)+ \)
\( \cos \left(\frac{2}{5} x-2\right)+a^{3 x+2} d x \) | 2 | Maths |
Maximum oxidation state of uranium
and plutonium are respectively:
A. 4 and 6
B. 5 and 6
\( c .6 \) and 7
D. 6 and 8 | 1 | Chemistry |
The potential energy for a force field \( \overrightarrow{\boldsymbol{F}} \) is given by \( U(x, y)=\sin (x+y) \)
Magnitude of the force acting on the particle of mass \( m \) at \( \left(0, \frac{\pi}{4}\right) \) is
\( A \)
B. \( \sqrt{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. | 3 | Physics |
A particle of mass \( m \) and momentum \( \vec{p} \) moves on a smooth horizontal table and
collides directly and elastically with a similar particle (of mass \( m \) ) having momentum \( -2 \vec{p} \). The \( \operatorname{loss}(-) \) or gain
\( (+) \) in the kinetic energy of the first particle in the collision is-
A \( \cdot \quad \frac{p^{2}}{2 m} \)
В. \( -\frac{p^{2}}{4 m} \)
c. \( +\frac{3 p^{2}}{2 m} \)
D. zero | 3 | Physics |
pH of any neutral solution is:
A. 0
B. 1
c. 14
D. 7 | 1 | Chemistry |
alkylation reaction?
\( \mathbf{A} \)
B.
\( c \)
D. | 1 | Chemistry |
If the coefficient of variation and
standard deviation of a distribution are
\( 50 \% \) and 20 respectively, then its mean is
A .40
B. 30
c. 20
D. none of these | 2 | Maths |
Evaluate the following:
\( \mathbf{1 0 4}^{\mathbf{3}}+\mathbf{9 6}^{\mathbf{3}} \) | 2 | Maths |
An arrow diagram. | 2 | Maths |
What is the total amount of dividend
paid by the company? | 2 | Maths |
If \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}=(\mathbf{2}, \mathbf{1 0}, \mathbf{1}), \boldsymbol{Q} \) are
collinear points and \( Q_{x}=-1, \) then
\( \boldsymbol{Q}_{z}= \)
A . -3
B. 7
\( c \cdot-14 \)
D. - | 2 | Maths |
By observing the diagram, answer the
following.
a) How does the pressure at A differ
from the pressure at B.?
b) The pressure at \( B \) is greater than the
pressure at D. Is it true?. Justify your
answer.
c) Compare the pressure at \( A \) and \( C \).
d) If the water is replaced with mercury,
how would this affect the pressure at \( A \)
and D? | 3 | Physics |
Maxwell in his famous equations of electromagnetism, introduced the
concept of
A . ac current
B. displacement current
c. impedance
D. reactance | 3 | Physics |
What is the main principle involved in
voltaic cell?
A. Conversion of chemical energy into heat energy
B. Conversion of heat energy into electrical energy
C. Conversion of chemical energy into electrical energy
D. Conversion of electrical energy into chemical energy | 1 | Chemistry |
Which statement correctly completes
the statement?
Except for glycerine, which is achiral, all
the amino acids present in proteins.:
\( \mathbf{A} \)
\( H_{3}^{+} N H C O_{2} H \)
are chiral, but racemic
B. \( H_{2} N C H C O_{2} H \)
have the L configuration at their \( \alpha \) carbon
\( c \)
\( H_{3}^{+} \stackrel{R}{N C}_{H C O_{2}^{-}} \)
have the \( R \) configuration at their \( \alpha \) carbon
D. \( R \)
\( H_{2} N C H C O_{2}^{-} \)
have the S configuration at their \( \alpha \) carbon | 1 | Chemistry |
Stamens attached to petals are
A. Antipetalous
B. Epipetalous
c. Epiphyllous
D. Episepalous | 0 | Biology |
\( \frac{\cos \theta}{\sin \theta} \times \frac{\tan \theta}{\csc \theta} \) | 2 | Maths |
A bulb marked \( 12 V, 24 W \) operates 12
volt battery for 20 minutes. The current flowing through it is :
A \( .2 A \)
в. \( 0.5 A \)
\( c \cdot 1 A \)
D. \( 1.5 A \) | 3 | Physics |
A 2.50 gram sample of which of the following would have the greatest mass of sulfur?
A. \( S r S ; \) molar mass \( =119.69 g / \mathrm{mol} \)
B. \( B e S \); molar mass \( =41.08 g / \mathrm{mol} \)
C . \( K_{2} S \); molar mass \( =110.26 g / \) mol
D. \( N a_{2} S ; \) molar mass \( =78.07 g / m o l \) | 1 | Chemistry |
The general solution of the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{e}^{\boldsymbol{y}+\boldsymbol{x}}+\boldsymbol{e}^{\boldsymbol{y}-\boldsymbol{x}} \) is
A \( \cdot e^{-y}=e^{x}-e^{-x}+c \)
B . \( e^{-y}=e^{-x}-e^{x}+c \)
\( \mathbf{c} \cdot e^{-y}=e^{x}+e^{-x}+c \)
D. \( e^{y}=e^{x}+e^{-x}+c \)
where \( c \) is an arbitrary constant | 2 | Maths |
Three fluids 1,2 and 3 have Bulk Moduli
of \( k 1, k 2 \) and \( k 3 \) respectively. If \( k 1>k 2> \)
k3, which liquid will have the highest compressibility
A . liquid 1
B. liquid 2
c. liquid 3
D. theyll have equal compressibilities | 3 | Physics |
\( z_{1} \) and \( z_{2} \) are two non-zero complex
numbers such that \( z_{1}=2+4 i \)
\( z_{2}=5-6 i, \) then \( z_{2}-z_{1} \) equals
A. \( 3-10 i \)
B. \( 3+10 i \)
c. \( 7-2 i \)
D. \( 10-24 i \) | 2 | Maths |
What are the indications for mineral
deficiency in plants? | 0 | Biology |
Why is sodium extract made acidic
with acetiuc acid before the addition of
lead acetate in the test of sulphur? | 1 | Chemistry |
Predict the position of the elements
which form the largest cation and the
smallest anion in the modern periodic
table. | 1 | Chemistry |
Burning of hydrogen in air is:
A. exothermic reaction
B. endothermic reaction
c. both exothermic and endothermic
D. none of the above | 1 | Chemistry |
The rate of the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+ \)
\( B r_{2}(g) \rightarrow 2 H B r(g) \) is given by:
\( \boldsymbol{r}=\boldsymbol{k}\left[\boldsymbol{H}_{2}\right]\left[\boldsymbol{B} \boldsymbol{r}_{2}\right]^{1 / 2} \)
Which among the following is correct?
A. Order of reaction is 2
B. Molecularity of reaction is 2
c. order of reaction is 1.5
D. Molecularity of reaction is 2.5 | 1 | Chemistry |
The acceleration of a particle which moves along the positive x-axis varies with its position as shown. If the
velocity of the particle is \( 0.8 m / s \) at \( x=0, \) the velocity of the particle at \( x= \)
1.4 is \( (\text { in } m / s) \)
A . 1.6
B. 1.2
c. \( 1 . \)
D. None of these | 3 | Physics |
An ideal gas obeying kinetic gas equation:
A. can be liquefied if its temperature is more than critical temperature
B. can be liquefied at any value of any value T and P
C. can not be liquefied under any value of \( T \) and \( P \)
D. can be liquefied if its pressure is more than critical
pressure | 1 | Chemistry |
A particle of mass \( m \) is moving along
\( x- \) axis with speed \( v \) when it collides
with a particle of mass \( 2 m \) initially at
rest. After the collision, the first particle
has come to rest and the second
particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the
two places? \( (\boldsymbol{\theta}>\mathbf{0}) \)
A. each piece moves with speed \( v \).
B. each piece moves with speed \( v / 2 \)
c. one of the piece moves with speed \( v / 2 \), the other moves with speed greater than \( v / 2 \).
D. each piece moves with speed greater than \( v / 2 \) | 3 | Physics |
short steel rods each of cross-sectional
\( \operatorname{area} 5 c m^{2} . \) The lower ends of \( A \) and \( B \)
are welded to a fixed plate \( C D . \) The
upper end of \( A \) is welded to the \( L- \)
shaped piece \( \boldsymbol{E F G}, \) which can slide
without friction on upper end of \( \boldsymbol{B} . \mathbf{A} \)
horizontal pull of \( 1200 N \) is exerted at
\( G \) as shown. Neglect the weight of \( \boldsymbol{E F G} \)
Longitudinal stress in \( \boldsymbol{A} \) is
A. Tensile in nature and having magnitude \( 180 N / m^{2} \)
B. Tensile in nature and having magnitude \( 240 N / m^{2} \)
c. compressive in nature and having magnitude \( 180 N / c m^{2} \)
D. Compressive in nature and having magnitude \( 240 N / c m^{2} \) | 3 | Physics |
The primary to secondary turns ratio of a transformer is given as \( 2: 3 . \) If the current through the primary coil is \( 3 A \) then the current through load resistance is
\( A \cdot 1 A \)
в. 4.5 А
\( c \cdot 2 A \)
D. 1.5 A | 3 | Physics |
The focal length of a concave mirror is and the distance from the object to the principal focus is p. The ratio of the size of the real image to the size of the object is:
A. \( -\frac{f}{p} \)
в.
\[
\left(\frac{f}{p}\right)^{2}
\]
\( c \)
\[
\left(\frac{f}{p}\right)^{\frac{1}{2}}
\]
D. \( -\frac{p}{f} \)
E . \( -f p \) | 3 | Physics |
Show with the help of a labelled graph how their wavelength \( (\lambda) \) varies with their linear momentum (p). | 3 | Physics |
Arrange the following in order of decreasing acidic strength.pnitrophenol (I), p-cresol (II), m-cresol
(III), phenol (IV):
\( A \cdot|>||>|||>\mid V \)
B. IV>|||> || > |
C. \( |>|||>||>\mid V \)
D. \|\|\( >\|>1>1 v \) | 1 | Chemistry |
How long after the beginning of motion is the displacement of a harmonically oscillating particle equal to one half its
amplitude if the period is \( 24 s \) and
particle starts from rest
A . \( 12 s \)
B . 2 s
\( c \cdot 4 s \)
D. \( 6 s \) | 3 | Physics |
A coil is wound on a transformer of
rectangular cross-section. If all the linear dimensions of the transformer
are increased by a factor 2 and the number of turns per unit length of the coil remains the same, the self
inductance increases by a factor of
A .4
B. 8
c. 12
D. 16 | 3 | Physics |
Construct an equilateral triangle of side
\( \mathbf{5 . 5} \mathrm{cm} \) | 2 | Maths |
\( \boldsymbol{C a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \) in baking powder:
A. Behaves as an acid in moist condition and decomposes \( N a H C O_{3} \) to give \( C O_{2} \)
B. Behave as a base in moist condition and gives \( H_{3} P O_{4} \)
c. Behaves as binder
D. Behaves as a filler | 1 | Chemistry |
For healthy eye least distance of
distinct vision is | 3 | Physics |
Find the derivative of \( \boldsymbol{y}= \) \( \frac{1}{4} \ln \frac{x^{2}-1}{x^{2}+1} \) | 2 | Maths |
Calculate the standard deviation for the
given frequency distribution:
C.I.
\[
\begin{array}{cc}
1-5 & 1 \\
6-10 & 2 \\
11-15 & 3 \\
16-20 & 4 \\
\hline N=10 &
\end{array}
\] | 2 | Maths |
The largest interval lying in \( \left(\frac{-\pi}{2}, \frac{\pi}{2}\right) \) for which the function
\( \left[f(x)=4^{-x^{2}}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (c o\right. \)
is defined, is-
A . \( [0, \pi] \)
в. \( \left(\frac{-\pi}{2}, \frac{\pi}{2}\right) \)
c. \( \left[-\frac{\pi}{4}, \frac{\pi}{2}\right) \)
D. \( \left[0, \frac{\pi}{2}\right) \) | 2 | Maths |
Differentiate the functions with respect
to \( x \)
\( \sec (\tan (\sqrt{x})) \) | 2 | Maths |
In the region of space \( \dot{E} \) and \( \dot{B} \) are parallel. A beam of cathode-rays moving in the same direction as \( \dot{E} \) enters the
space. Which of the following conclusions is correct
A. The cathode rays will travel straight
B. The cathode rays wil lbe deflected towards right
c. The speed of cathode ray particles increases
D. The speed of cathode ray particles decreases | 3 | Physics |
Larger particles scatter light at the end of the spectrum the least.
A. Blue
B. Green
c. violet
D. Red | 3 | Physics |
One molar solution of which substance
will have maximum O.P?
A. Nacı
B. Glucose
c. Fructose
D. starch | 0 | Biology |
Synovial fluid is present in
A. spinal canal
B. Cranial cavity
C. Freely movable joints
D. All of the above | 0 | Biology |
What do you understand by following.
(i) Dissociation constant of an acid
(ii) Solubility product
(iii) Heterogenous equilibrium | 1 | Chemistry |
\( H_{2} \) does not show litmus test. From
this, we can say, that the oxide of
hydrogen is in nature.
A . acidic
B. neutral
c. basic
D. amphoteric | 1 | Chemistry |
In Period 3 of the Periodic Table, element
B is placed to the left of element A. On the basis of this information, choose
the correct word from the brackets of
complete the following statement.
(i) The element B would have(lower/higher) metallic character
than \( A \)
(ii) The element A would probably have(lesser/higher) electron affinity than B.
(iii) The element A would have(greater/smaller) atomic size than
B. | 1 | Chemistry |
Explain two physiological effects of auxia. | 0 | Biology |
Explain the formation of a Rainbow. | 3 | Physics |
length \( L, \) pivoted at its centre and
balanced with a weight \( W \) at a distance
\( x \) from the left end is shown in the
figure. Two positive point charges
q and \( 2 q \) are attached at the left and
right ends of the rod. A distance \( h \)
directly below each of these charges is
a fixed positive charge \( Q \). The distance
\( x^{\prime} \) in terms of \( q, Q, L \) and \( W \) is
(Assume than \( L>>h \) and neglect
masses of the point charges)
A.
\( ^{\mathbf{B}} \cdot \frac{4 q Q L+\varepsilon_{0} h^{2} W L}{8 \pi h^{2} W} \)
\( ^{\mathbf{C}} \cdot \frac{q Q L+4 \pi \varepsilon_{0} h^{2} W L}{8 \pi \varepsilon_{0} h^{2} W} \)
D. \( \frac{q Q L+\varepsilon_{0} h^{2} W L}{h^{2} W} \) | 3 | Physics |
The value of \( a_{1}+a_{2} \) is equal to
A . 30
B. -30
c. 27
D. -27 | 2 | Maths |
The valence electrons are involved in
formation of covalent bonds is/are
called:
A. non-bonding electrons
B. Ione pairs
c. unshared pairs
D. None of these | 1 | Chemistry |
\( f \frac{4 a b^{2}\left(-5 a b^{3}\right)}{10 a^{2} b^{2}}=-K b^{3} \) then value of
\( \boldsymbol{K} \) is | 2 | Maths |
Global warming is caused by
greenhouse effect. Justify. | 0 | Biology |
Assertion
Krebs cycle is amphibolic.
Reason
Krebs cycle produces maximum amount of ATP.
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 | 0 | Biology |
Find total number of subsets of \( \{p: p \) is a letter in the word 'poor'? | 2 | Maths |
Angle which the normal ray makes with
the mirror is equal to:
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( \mathrm{c} \cdot 90^{\circ} \)
D. \( 180^{\circ} \) | 3 | Physics |
Drive an expression for Electric field due to an Electric dipole at a point on the axial line. | 3 | Physics |
Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities
\( K \) and \( 2 K, \) respectively.The equivalent thermal conductivity of the slab is
A \( \cdot 2 / 6 K \)
B. \( \sqrt{2} \) к
\( c .3 K \)
D. \( 4 / 3 K \) | 3 | Physics |
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
The sum of the digits of a two-dlgit number is \( 9 . \) Also, nine times this
number is twice the number obtained
by reversing the order of the digits. Find
the number
A. Number is 18
B. Number is 36
c. Number is 81
D. None of these | 2 | Maths |
Consider a sinusoidal travelling wave
shown in the given figure. The wave
velocity is \( +40 c m / s . \) Find the frequency
of the wave.
A \( .20 H z \)
B. \( 30 H z \)
c. \( 25 H z \)
D. \( 10 H z \) | 3 | Physics |
Addition of \( N a_{2} C O_{3} \) to the solution of
an oxide in water produces \( C O_{2} . \) This experiment indicates that:
A. the oxide is basic
B. the oxide is amphoteric
c. the oxide is that of the a metal
D. the oxide is that of the a non-metal | 1 | Chemistry |
Two trains \( A \) and \( B \) each of length 400 m are moving on two parallel tracks with a uniform speed \( 72 \mathrm{km} h^{-1} \) in the same
direction with \( A \) ahead of \( B \). The driver of
B decides to overtake \( A \) and accelerates
by \( 1 \mathrm{m} s^{-2} \). If after 50 s, the guard of \( B \) just brushes past \( A, \) what was the original distance between them?
A. \( 450 \mathrm{m} \)
B. 1000 \( \mathrm{m} \)
\( c . \) 1250 \( m \)
D. 2250 \( \mathrm{m} \) | 3 | Physics |
Name The reciprocal of frequency
A. Time period
B. Amplitude
c. Intensity
D. None | 3 | Physics |
The weight of coffee (in gms) in 70 packets is given below. Determine the modal weight of coffee in packets
202 \( \quad 203 \)
Packe
A . \( 201 \mathrm{gms} \)
в. \( 201.70 \mathrm{gms} \)
\( c \cdot 202 g m s \)
D. 202.70 gms | 2 | Maths |
A barometric liquid having high density produces a shorter column of liquid.
A. True
B. False | 3 | Physics |
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be given by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( [\boldsymbol{x}]^{2}+[\boldsymbol{x}+\mathbf{1}]-\mathbf{3}, \) where \( [\boldsymbol{x}] \) denotes the
greatest integer less than or equal to \( x \) Then, \( \boldsymbol{f}(\boldsymbol{x}) \) is
A. many-one and onto
B. many-one and into
c. one-one and into
D. one-one and onto | 2 | Maths |
Chromium plating is done on many articles so that they
A. Have shiny appearance
B. Do not corrode
c. Resist Scratches
D. All of these | 3 | Physics |
State the S.I. units of mass and weight.
A. gand kg
B. kg and g
c. \( \mathrm{kg} \) and \( \mathrm{N} \)
D. \( \mathrm{N} \) and \( \mathrm{kg} \) | 3 | Physics |
Potash alum is represented by the formula:
A \( \cdot K_{2} S O_{4} \cdot A l_{2}\left(S O_{4}\right)_{3} \cdot 24 H_{2} O \)
B . \( K \cdot A l\left(S O_{4}\right)_{2} \cdot 12 H_{2} O \)
c. Both (a) and (b)
D. None of these | 1 | Chemistry |
The adiabatic Bulk modulus of a
diatomic gas at atmospheric pressure is
A. \( 0 \mathrm{Nm}^{-2} \)
B. \( 1 \mathrm{Nm}^{-2} \)
c. \( 1.4 \times 10^{4} N m^{-2} \)
D. \( 1.4 \times 10^{5} \mathrm{Nm}^{-2} \) | 3 | Physics |
Atomic number of a few elements are
given below:
10,20,7,14
Identify the period to which these elements belong?
A. 2,4,2,3
B. 3, 2, 3, २.
c. 2,2,3,3
D. 3, 3, 2, 2. | 1 | Chemistry |
When an electron transitions from \( n= \)
2 to \( n=5, \) will it be visible to the naked
eye?
A. Yes, the emission occurs at 434 nm which is the blue range of light
B. Yes, the emission occurs at 434 nm which is the red range of light
c. No, the absorption occurs at the infrared red region of the electromagnetic spectrum
D. No, the absorption occurs in the blue range of light but our eyes are unable to detect absorption | 1 | Chemistry |
The value of the integral \( \int_{0}^{\overline{2}} \sin ^{5} x d x \)
is
A \( \cdot \frac{4}{15} \)
B. \( \frac{8}{5} \)
c. \( \frac{8}{15} \)
D. \( \frac{4}{5} \) | 2 | Maths |
Let \( \vec{u} \) be a vector on rectangular system
with sloping angle \( 60^{\circ} . \) Suppose that \( |\vec{u}-\hat{i}| \) is geometric mean of \( |\vec{u}| \) and \( |\vec{u}-2 \hat{i}|, \) where \( \vec{i} \) is the unit vector along
\( x \) -axis, then \( |\vec{u}| \) has the value equal to \( \sqrt{a}-\sqrt{b}, \) where \( a, b \in N . \) Find the value \( \frac{(\boldsymbol{a}+\boldsymbol{b})^{3}+(\boldsymbol{a}-\boldsymbol{b})^{3}}{\mathbf{7}} \) | 2 | Maths |
If \( A \) is non-singular and \( (A+I)(A- \)
\( \mathbf{3} \boldsymbol{I})=\mathbf{0} \) then \( \mathbf{3} \boldsymbol{A}^{-1}-\boldsymbol{A}+\mathbf{2} \boldsymbol{I} \)
A . \( I \)
B.
c. \( 2 I \)
D. \( 6 I \) | 2 | Maths |
Match column A with column B | 1 | Chemistry |
In Kjeldahl's method, nitrogen present is quantitatively converted to
A. \( N_{2} \)
B . \( \left(N H_{4}\right)_{2} S O_{4} \)
c. \( N O_{2} \)
D. \( N H_{3} \) | 1 | Chemistry |
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