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A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number.
| 2 |
Maths
|
At \( 25^{\circ} \mathrm{C} \) the saturated vapour pressure
of water is 3.165 kPa \( (23.75 \mathrm{mm} \mathrm{Hg}) \) Find the saturated vapour pressure of a \( 5 \% \) aqueous solution of urea (carbamide) at the same temperature.
(Molar mass of urea \( =\mathbf{6 0 . 0 5} \) g \( \boldsymbol{m o l}^{-1} \) )
| 1 |
Chemistry
|
Arrange the following as per the
instructions given in the brackets:
\( N a, K, C l, S, S i \) (increasing order of ionization energy)
| 1 |
Chemistry
|
An AP consists of 23 terms. If the sum of the 3 terms in the middle is 141 and the
sum of the last 3 terms is 261 , then the
first term is
A . 6
B. 5
\( c \cdot 4 \)
D. 3
E . 2
| 2 |
Maths
|
Which of the reactant act as oxidant?
\( \boldsymbol{P C l}_{3}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{P C l}_{5} \)
A \( \cdot C l_{2} \)
в. \( P C l_{3} \)
c. Both of these
D. None of these
| 1 |
Chemistry
|
Prove that the area enclosed between
two parabolas \( y^{2}=4 a x \) and \( x^{2}=4 a y \)
is \( \frac{16 a^{2}}{3} \)
| 2 |
Maths
|
A cross between two tall garden pea plants produced all tall plants. The possible genotypes of the parents are
I) \( \pi, \) T
II) TT, Tt
III) \( T t, t \)
IV) \( \mathrm{Tt}, \mathrm{Tt} \)
A . ॥I, IV
B. I, IV
\( c \cdot 1,1 \)
D. II, III
| 0 |
Biology
|
The isotope of hydrogen, \( D_{2} \) forms heavy
water, \( D_{2} O . \) It is qualified as \( D_{2} O \) because it is:
A. a heavy liquid
B. an oxide of heavier isotope of oxygen
c. an oxide of deuterium
D. denser than water
| 1 |
Chemistry
|
Three sides \( A, B \) and \( C \) are moving in a straight line in same direction such that relative velocity of \( A \) wrt \( B \) is \( 2 m / s \) relative velocity of B wrt C is -5m/s. Find relative velocity of \( C \) wrt A. Also write which body is moving in b/w of remaining two bodies.
| 3 |
Physics
|
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \frac{A l \operatorname{co.KOH}}{\Delta} \boldsymbol{B} \stackrel{\boldsymbol{H B r}}{\longrightarrow} \)
\( C \stackrel{N a / \text {ether}}{ } D \) the compound D is
A. ethane
B. propane
c. n-butane
D. n-pentane
| 1 |
Chemistry
|
The excess pressure across a soap bubble of radius \( r \) is \( p=\frac{4 \sigma}{r}, \) where \( \sigma \)
is the surface tension of soap solution.
What is the excess pressure across an
air bubble of the same radius \( r \) formed
inside a container of soap solution?
A \( \cdot \frac{\sigma}{r} \)
в. \( \frac{2 \sigma}{r} \)
c. \( \frac{4 \sigma}{r} \)
D. none of these
| 3 |
Physics
|
Number of revolution per second made by electron in Bohr orbit is called orbital
frequency. If \( \boldsymbol{u}_{n}, \boldsymbol{r}_{n}, \boldsymbol{E}_{n} \) are velocity,
radius and energy level of \( n \) th orbit respectively?
A \( \cdot \frac{u_{n}}{2 \pi r_{n}} \)
B. \( -\frac{2 E_{n}}{n h} \)
c. \( -\frac{2 E_{1}}{n^{3} h} \)
D. either of these
| 1 |
Chemistry
|
An angle is \( 45^{\circ} \) less than two times of
its supplement, then the greater angle is
A \( .75^{\circ} \)
B . \( 100^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 105^{\circ} \)
| 2 |
Maths
|
Write the number of significant digits in \( 6.032 ? \)
A . 4
B. 3
\( c \cdot 2 \)
D. none of the above
| 3 |
Physics
|
The duration of the day form the moment the sun is overhead today to the moment the sun will be overhead
tomorrow is determined by
A. the rotation of the earth's on its axis only
B. the revolution of the earth round the sun only.
c. the rotation of the earth on its axis as well the revolution of the earth around the sun
D. the inclination of the axis of rotation of the earth to its plane of revolution.
| 3 |
Physics
|
Pure \( S e \) at \( 300 K \) has equal electron \( \left(n_{e}\right) \)
and hole \( \left(n_{h}\right) \) concentration of \( 1.5 \times \)
\( 10^{6} m^{-3} . \) Doping by indium increases
\( \boldsymbol{n}_{\boldsymbol{h}}=\mathbf{4 . 5} \times \mathbf{1 0}^{\mathbf{2 2}} \boldsymbol{m}^{-\mathbf{3}} . \) Calculate the
doped silicon.
| 3 |
Physics
|
Which equation has the solution shown
on the number line?
\( \mathbf{A} \cdot x \geq 1 \)
в. \( x \geq-6 \)
c. \( x \neq 1 \)
D. \( x<0 \)
| 2 |
Maths
|
Name the source from which litmus
solution is obtained. What is the use of
this solution?
| 1 |
Chemistry
|
What is the degree of the given monomial \( 7 y ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D.
| 2 |
Maths
|
Colloidal solutions are classified on the
basis of :
A. molecular size
B. orgainc or inorganio
c. surface tension value
D. pH value
| 1 |
Chemistry
|
\( (A g+P b) \) alloy \( \frac{M e l t a n d}{Z i n c i s a d d e d}(A g+P b+ \)
\( Z n) m e l t \stackrel{C o o l}{\longrightarrow} \frac{\text {Layer} X}{\text {Layer} Y} \)
Select the correct statement based on
the above scheme:
A. Layer X contains Zn and Ag
B. Layer Y contains Pb and Ag but amount of silver in this layer is smaller than in layer \( x \)
c. \( x \) and \( Y \) are immiscilbe layer
D. All the correct statements
| 1 |
Chemistry
|
\( \lim _{x \rightarrow 1} 2 x+1 \)
| 2 |
Maths
|
If \( f(x)=x^{2 / 3}, x \geq 0 . \) Then,the area of
the region enclosed by the curve \( y= \) \( f(x) \) and the three lines \( y=x, x=1 \)
and \( x=8 \) is
\( ^{\mathrm{A}} \cdot \frac{63}{2} \)
в. \( \frac{93}{5} \)
\( ^{c} \cdot \frac{105}{7} \)
D. \( \frac{129}{10} \)
| 2 |
Maths
|
What do you observe when water droplets fall on blue cobalt chloride?
| 1 |
Chemistry
|
For the redox reaction \( Z n(S)+C u^{2+}(0.1 M) \rightarrow \)
\( Z n^{2+}(1 M)+C u(s) \) taking place in a cell, \( E_{c e l l}^{0} \) is
1.10 volt. \( E_{\text {cell}} \) for the cell will be:
\( \left(2.303 \frac{R T}{F}=0.0591\right) \)
\( \mathbf{A} \cdot 2 \cdot 14 V \)
B. \( 1.80 V \)
c. \( 1.07 V \)
D. \( 0.82 V \)
| 1 |
Chemistry
|
What is meant by peptide linkage and biocatalysts?
| 1 |
Chemistry
|
The elements of \( (\boldsymbol{A}-\boldsymbol{B}) \) are:
| 2 |
Maths
|
Find differentiation of \( \sec ^{-1} \tan x \)
| 2 |
Maths
|
Express the following as a rational number i.e. in the form \( \frac{a}{b} ; \) where \( a, b \in I \) and \( \boldsymbol{b} \neq \mathbf{0} \)
\( \mathbf{0 . 4 2 5} \)
A \( \cdot \frac{12}{40} \)
в. \( \frac{19}{40} \)
c. \( \frac{41}{40} \)
D. \( \frac{17}{40} \)
| 2 |
Maths
|
If \( a^{2}, b^{2}, c^{2} \) are in A.P., then the following
are also in A.P.
\( \frac{1}{b+c}, \frac{1}{c+a}, \frac{1}{a+b} \)
| 2 |
Maths
|
If the chromosome number in the
somatic cell of gymnosperm is 8. Then the number of chromosomes in the
nucellus of \( C y c a s \) is
A. 08
B. 04
\( c \cdot 16 \)
D. 32
| 0 |
Biology
|
Find the exact position solution of the
equation \( x^{2}+x=30 \)
| 2 |
Maths
|
When a glass rod is rubbed with silk
A. Negative charge is produced on silk but not charge on the glass rod
B. Equal but opposite charge are produced on the both
C. Equal and similar charges are produced on the both
D. Positive charge is produced on the glass rod but no charge on the silk
| 3 |
Physics
|
f \( \sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2} \) then
\( a \) value of \( x \) is:
\( A \)
B. 3
\( c \cdot 4 \)
D. 5
| 2 |
Maths
|
Show that:
\( \int_{-a}^{a} f(x) d x=2 \int_{0}^{a} f(x) d x, \) if \( f(x) \) is an
even function. \( \boldsymbol{I}=\mathbf{0}, \) if \( \boldsymbol{f}(\boldsymbol{x}) \) is an odd
function.
| 2 |
Maths
|
There are 40 students in a chemistry class and 60 students in a physics class. Find the number of students
which are either in physics class or
chemistry class in the following case:
The two classes meet at different hours
and 20 students are enrolled in both the
subjects
| 2 |
Maths
|
An alloy consists of \( 3 \frac{1}{2} g m \) of copper and \( 2 \frac{3}{4} g m \) of tim. Find the ratio of copper so that of tim in the alloy in the simplest form.
| 2 |
Maths
|
Why is \( N_{2} \) less reactive at room
temperature?
| 1 |
Chemistry
|
How many electrons does oxygen have in its outermost shell?
| 1 |
Chemistry
|
The focal length of a convex mirror is 10cm. Its radius of curvature will be:
A . \( 5 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( \mathrm{c} \cdot 20 \mathrm{cm} \)
D. \( 30 c m \)
| 3 |
Physics
|
The term ecosystem was coined by
A. E.P. Odum
B. A.G. Tansley
c. E. Haeckel
D. E. Warming
| 0 |
Biology
|
Prove that \( 2 \sec ^{2} \theta-\sec ^{4} \theta- \)
\( 2 \cos e c^{2} \theta+\cos e c^{4} \theta=\cot ^{4} \theta-\tan ^{4} \theta \)
| 2 |
Maths
|
An outstanding book on the wave nature of light titled "An Introduction to the
Study of Wave Mechanics" was
published in \( 1930 . \) Who was its author?
A. E. Shroedinger
B. A. Sommerfield
c. P.A.M. Dirac
D. Louis de Broglie
| 3 |
Physics
|
The rate law of gaseous reaction:
\( \boldsymbol{A}_{(g)}+\boldsymbol{B}(\boldsymbol{g}) \rightarrow \) product is given by
\( \boldsymbol{K}[\boldsymbol{A}]^{2}[\boldsymbol{B}] . \) If the \( ^{\prime} \mathbf{V}^{\prime} \) of one reaction
vessel is suddenly doubled, which of the following will happen?
A. The rate \( w . r . t^{\prime} A^{\prime} \) will decrease Two times.
B. The rate \( w . r . t^{\prime} A^{\prime} \) will decrease Four times.
c. The rate \( w . r . t^{\prime} B^{\prime} \) will decrease Two times
D. The overall rate will decrease Eight Times of the original Value.
| 1 |
Chemistry
|
The input signal given to a a CE
amplifier having a voltage gain of 150 is \( V_{i}=2 \cos \left(15 t+\frac{\pi}{3}\right) . \) The
corresponding output signal will be
A \( \cdot 300 \cos \left(15 t+\frac{4 \pi}{3}\right) \)
B. \( 300 \cos \left(15 t+\frac{\pi}{3}\right) \)
c.
\( 75 \cos \left(15 t+\frac{2 \pi}{3}\right) \)
D. \( 2 \cos \left(15 t+\frac{5 \pi}{6}\right) \)
| 3 |
Physics
|
The electronic configuration of an atom/ion can be defined by which of the following?
A. Aufbau principle
B. Pauli's exclusion principle
c. Hund's rule of maximum multiplicity
D. All of the above
| 1 |
Chemistry
|
A tube of light emits light of wavelength \( \mathbf{5 2 9 6} \) A. The bulb is rated as 200watt
and \( 20 \% \) of the energy is converted into light. If the whole light emitted is allowed to fall on a metal surface
having work function \( 3.00 \times 10^{-19} J \)
calculate the no. of electrons ejected in
\( \mathbf{1 0} \boldsymbol{s} \)
| 1 |
Chemistry
|
From a point \( Q, \) the length of the
tangent to a circle is \( 24 \mathrm{cm} \) and the
distance of \( Q \) from the centre is \( 25 \mathrm{cm} \) The radius of the circle is
| 2 |
Maths
|
Production of electricity from magnetism is called
A . electric field
B. magnetic field lines
c. electromagnetic induction
D. magnetic induction
| 3 |
Physics
|
The lower edge of a square slab of side \( 50 \mathrm{cm} \) and thickness \( 20 \mathrm{cm} \) is rigidly
fixed to the base of a table. A tangential force of \( 30 \mathrm{N} \) is applied to the slab. If the shear moduli of the material is \( 4 \times \)
\( 10^{10} N / m^{2}, \) then displacement of the
upper edge, in maters is?
A \( .4 \times 10^{-12} \)
В. \( 4 \times 10^{-10} \)
c. \( 6 \times 10^{-10} \)
D. \( 6 \times 10^{-12} \)
E . \( 8 \times 10^{-10} \)
| 3 |
Physics
|
Momentum is a measure of
A. Weight
B. Mass
C . Quantity of motion
D. Velocity
| 3 |
Physics
|
Factorize:
\( (x-y)^{3}-8 x^{3} \)
\( \mathbf{A} \cdot-2(x+y)\left(7 x^{2}-4 x y+y^{2}\right) \)
B . \( -(x-y)\left(x^{2}-4 x y+6 y^{2}\right) \)
\( \mathbf{c} \cdot-(x+2 y)\left(x^{2}-4 x y+y^{2}\right) \)
\( \mathbf{D} \cdot-(x+y)\left(7 x^{2}-4 x y+y^{2}\right) \)
| 2 |
Maths
|
If heads means one and tail means two,
then coefficients of quadratic equation
\( a x^{2}+b x+c=0 \) are chosen by tossing
three fair coins. The probability that roots of the equation are imaginary is
A \( \cdot \frac{5}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{7}{8} \)
D.
| 2 |
Maths
|
What is the probability of getting a king if a card is drawn from a pack of 52
cards?
A \( \cdot \frac{1}{52} \)
в. \( \frac{2}{52} \)
c. \( \frac{3}{52} \)
D. \( \frac{4}{52} \)
| 2 |
Maths
|
The rate of a certain reaction increases
by 2.3 times when the temperature is raised from \( 300 \mathrm{K} \) to \( 310 \mathrm{K} \). If \( \mathrm{k} \) is the
rate constant at \( 300 \mathrm{K} \), then the rate
constant at \( 310 \mathrm{K} \) will be equal to:
\( A \cdot 2 k \)
B.
\( c \cdot 2.3 k \)
\( D \cdot 3 k^{2} \)
| 1 |
Chemistry
|
Order and degree of \( \left(\frac{d y}{d x}\right)^{2}-5 y=3 \cos x \)
are:
A . 2,3
B. 1,2
\( c \cdot 2,2 \)
D. 1,1
| 2 |
Maths
|
Let \( A \) and \( B \) be two symmetric matrices
of order 3
Statement-1:
\( \boldsymbol{A}(\boldsymbol{B} \boldsymbol{A}) \) and \( (\boldsymbol{A B}) \boldsymbol{A} \) are symmetric
matrices.
Statement-2:
\( A B \) is symmetric matrix if matrix
multiplication of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) is
commutative.
A. Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1.
B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement- 1 .
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true.
| 2 |
Maths
|
A spark is produced between two insulated surfaces maintained at a
potential difference of \( 5 \times 10^{6} V . \) If the
energy output is \( 10^{-5} J \), the charge
transferred during the spark is :
A \( \cdot 5 \times 10^{11} C \)
В. \( 5 \times 10^{-11} C \)
C \( \cdot 2 \times 10^{12} C \)
D. \( 2 \times 10^{-12} C \)
| 3 |
Physics
|
The given plane figure is to be coloured.
What will be the expenditure at the rate
of \( \boldsymbol{R} \boldsymbol{s} 15 \) per \( \boldsymbol{m}^{2} ? \)
A . \( R s 450 \)
B. \( R s 480 \)
c. \( R s 570 \)
D. Rs780
| 2 |
Maths
|
Carius method is used for the
quantitative
estimation of
A. \( c \) and
B. Halogens, S, and P
\( c \cdot N \)
D. All
| 1 |
Chemistry
|
Let \( P(n)=n(n+1) \) is an even
number, then which of the following
satisfy \( \boldsymbol{P}(\boldsymbol{n}) \)
A \( . P(3) \)
B. \( P(100) \)
c. \( P(50) \)
D. All of these
| 2 |
Maths
|
Define the following terms:
(i) Glycosidic linkage
(ii) Invert sugar
(iii) Oligo saccharides
| 1 |
Chemistry
|
A bar magnet is dropped along the axis of copper ring held horizontally. The acceleration of fall is
A. equal to g at the place.
B. less than \( g \)
c. more than \( g \)
D. depends upon diameter of the ring and length of the magnet
| 3 |
Physics
|
The pressure \( v / s \) volume graph of an
ideal gas is given in different thermodynamics process which of the
following option in relevant order:
(Isochoric, isobaric, isothermal, adiabatic)
A \( \cdot d, \) a, b,
B. a, d, c,
\( c \cdot a, c, d, b \)
D. a, b, c,
| 1 |
Chemistry
|
If \( \boldsymbol{R} \) is the largest equivalence relation
on a set \( A \) and \( S \) is any relation on \( A \)
then
A \( . R \subset S \)
в. \( S \subset R \)
c. \( R=S \)
D. none of these
| 2 |
Maths
|
What should retarding potential difference be applied between
electrodes of the photocell for the photocurrent to drop to zero?
A. \( 1.5 V \)
в. \( 2.0 V \)
c. \( 1.8 V \)
D. 2.3V
| 3 |
Physics
|
Define standard enthalpy of reaction.
| 1 |
Chemistry
|
The molecular formula of diphenyl
methane is \( C_{13} H_{12} . \) How many structural isomers are possible when one of the hydrogen is replaced by a chlorine atom?
\( A .8 \)
B. 7
\( c .6 \)
\( D \)
| 1 |
Chemistry
|
Consider the following statements regarding gymnosperms and choose the
correct option.
(A) In gymnosperms, the male and female gametophytes have an independent existence.
(B) The multicellular female
gametophyte is retained within the
megasporangium.
(C) The gymnosperms are heterosporous.
\( A \cdot(A) \) and
(B) are true but (C) is false.
B. (A) and
(C) are true but (B) is false.
c. (B) and
(C) are false but (A) is true
D. (A) and
(C) are false but (B) is true.
E. (B) and
(C) are true but (A) is false.
| 0 |
Biology
|
figure bounded by non coplanar triangular planes. So, a tetrahedron has four non-coplanar points as its vertices. Suppose a tetrehedron has points
A,B,C,D as its vertices which have
coordinates \( \left(\boldsymbol{x} \mathbf{1}, \boldsymbol{y} \mathbf{1}, \boldsymbol{z}_{1}\right)\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}, \boldsymbol{z}_{2}\right) \)
\( \left(x_{3}, y_{3}, z_{3}\right) \) and \( \left(x_{4}, y_{4}, z_{4}\right), \) respectively
in a rectangular three dimensional
space. Then, the coordinates of
its centroid are \( \left[\frac{\boldsymbol{x}_{1}+\boldsymbol{x}_{2}+\boldsymbol{x}_{3}+\boldsymbol{x}_{4}}{\boldsymbol{4}}, \frac{\boldsymbol{y}_{1}+\boldsymbol{y}_{2}+\boldsymbol{y}_{3}+\boldsymbol{y}_{4}}{\boldsymbol{4}}\right. \)
Let a tetrahedron have three of its
vertices represented by the points (0,0,0),(6,5,1) and (4,1,3) and
its centroid lies at the point (1,2,5) Now, answer the following question. The coordinate of the fourth vertex of the
tetrahedron is:
A \( \cdot(-6,2,16) \)
B. (1,-2,13)
c. (-2,4,-2)
D. (1,-1,1)
| 2 |
Maths
|
A ware house worker exerts a constant
horizontal force of magnitude \( 85 N \) on a
\( 40 k g \) box that is initally at rest on the floor of the ware house. After moving a
distance of \( 2 m \) the speed of the box is
\( 1 m s^{-1} . \) The coefficent of friction
between the box and the ware house
floor is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-\mathbf{2}}\right) \)
A \( .5 / 16 \)
в. \( 3 / 16 \)
c. \( 19 / 80 \)
D. \( 0.25 / 16 \)
| 3 |
Physics
|
A particle vibrates 10 times in 1 sec. What is the time period of vibration of
the particle
A . \( 10 \mathrm{Sec} \)
B. 1 Sec
c. \( 0.1 \mathrm{sec} \)
D. 0.01 sec
| 3 |
Physics
|
A block of mass \( M \) is hanging over a
smooth and light pulley through a light string. The other end of the string is
pulled by a constant force \( F \). If kinetic energy of the block increases by \( 20 J \) in
1 s. Then:
A. Tension in the string is \( M g \)
B. Tension in the string is \( F \)
c. work done by the tension on the block is \( 20 \mathrm{J} \) in 1 sec
D. Work done by the force of gravity is \( -20 \mathrm{J} \) in 1 sec.
| 3 |
Physics
|
In how many acids among following, the basicity is greater than \( 1 ? \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3} \)
| 1 |
Chemistry
|
Water is poured into a pan and heated over a flame. After some time, the hot water begins rising to the top. Which type of heat transfer is involved in this?
A. conduction
B. convection
c. radiation
D. thermal expansion
E. specific heat
| 3 |
Physics
|
In which of the following animals are bones not present?
A. Earthworm
B. Snail
c. cockroach
D. All of the above
| 0 |
Biology
|
Match the appropriate pairs from Lists
and \( \|: \)
ListList - II
e) Continuous
a) Nitrogen molecule \( \quad \) spectrum
f) Absorption
b) Incandescent solids \( \quad \) spectrum
c) Fraunhofer lines
g) Band spectrum
d) Electric arc between iron
h) Emission rods \( \quad \) spectrum
\( A \cdot a-g, b-e, c-f, d-h \)
B. \( a-f, b-e, c-h, d-g \)
\( \mathbf{C} \cdot a-h, b-e, c-f, d-g \)
D. a-e, b-g, c-h, d-f
| 3 |
Physics
|
Which of the following gives nitrogen on thermal decomposition?
This question has multiple correct options
A. Ammonium nitrite
B. Ammonia
c. Ammonium dichromate
D. Air
| 1 |
Chemistry
|
\( \boldsymbol{x}_{1}=\boldsymbol{A} \sin (\omega \boldsymbol{t}-\mathbf{0 . 1} \boldsymbol{x}) \) and \( \boldsymbol{x}_{2}= \)
\( A \sin \left(\omega t-0.1 x-\frac{\phi}{2}\right) . \) The resultant
amplitude of combined wave is:-
A \( \cdot 2 A \cos \frac{\phi}{4} \)
B. \( A \sqrt{2 \cos \frac{\phi}{2}} \)
\( \mathrm{c} \cdot_{2 A \cos \frac{\phi}{2}} \)
D. \( A \sqrt{2\left(1+\cos \frac{\phi}{4}\right)} \)
| 3 |
Physics
|
An electric dipole is placed near a positive charge. It will experience:
A. a torque only
B. a force only
c. both torque and force
D. it will depend on the orientation of the dipole with respect to the charge
| 3 |
Physics
|
A "moving sidewalk" in a busy airport terminal moves \( 1 m / s \) and is \( 200 m \)
long. A passenger steps onto one end and walks, in the same direction as the
sidewalk is moving, at a rate of \( 2.0 \mathrm{m} / \mathrm{s} \) relative to the moving sidewalk. How much time does it take the passenger
to reach the opposite end of the walkway? (in seconds)
A . 66.7
B. 67.3
c. 63
D. 66
| 3 |
Physics
|
There are 8 types of pant pieces and 9 types of shirt pieces with a man. The number of ways in which a pair (1 pant,
1 shirt) can be stitched by the tailor is
A . 17
B. 56
c. 64
D. 72
| 2 |
Maths
|
If \( \boldsymbol{x}=\frac{\sqrt{\mathbf{3}}+\sqrt{\mathbf{2}}}{\sqrt{\mathbf{3}}-\sqrt{\mathbf{2}}} \) find \( \boldsymbol{x}^{2}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}} \)
| 2 |
Maths
|
A covalent bond is formed when:
A. transfer of electrons take place
B. sharing of electrons take place
C. both sharing and transfer of electrons takes place
D. neither sharing nor transfer of electrons takes place
| 1 |
Chemistry
|
A and \( \mathrm{B} \) are facing the mirror and
standing in such a way that \( A \) can see \( B \)
and \( B \) can see A. Explain this
phenomenon.
| 3 |
Physics
|
Which one of the following statement is false with respect to deep red
colouration produced with \( N H_{4} S C N ? \)
A. The deep red colour is bleached by \( H g(I I) \) jon
B. The deep red colouration is due to the formation of a non-dissociated iron \( (I I I) \) thiocyanate complex.
c. The deep red coloured compound can be extracted by ether or amyl alcoho
D. None of the above
| 1 |
Chemistry
|
Assertion
\( \gamma \) -radiation emission occurs after \( \boldsymbol{\alpha} \) and
\( \beta \) decay.
Reason
Energy levels occur in nucleus.
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.
| 3 |
Physics
|
Sulphur dioxide is a strong reducing agent. However, it can also act as an
oxidizing agent. Which of the following reactions shows its oxidizing nature?
A. Bleaching flower petalss
B. Decolourising of acidfied KMnO \( _{4} \) solution
c. Reaction with \( H_{2} S \) to give sulphur
D. Turning acidified dichromate paper green
| 1 |
Chemistry
|
The surface of the head of a match stick
and sides of a match box are
deliberately made rough to:
A. increase friction
B. decrease friction
c. increase amount of heat
D. decrease amount of heat
| 3 |
Physics
|
The electric potential at a point in free
space due to a charge \( Q \) coulomb is \( Q \times 10^{11} V . \) The electric field at that
point is
A \( \cdot 12 \pi \varepsilon_{0} Q \times 10^{22} V m^{-1} \)
B . \( 4 \pi \varepsilon_{0} Q \times 10^{22} V m^{-1} \)
C \( .12 \pi \varepsilon_{0} Q \times 10^{20} \mathrm{Vm}^{-1} \)
D. \( 4 \pi \varepsilon_{0} Q \times 10^{20} V m^{-1} \)
| 3 |
Physics
|
Solve:
(i) \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{e}^{\boldsymbol{3} \boldsymbol{x}-\boldsymbol{2} \boldsymbol{y}}+\boldsymbol{x}^{2} \boldsymbol{e}^{-\boldsymbol{2} \boldsymbol{y}} \)
| 2 |
Maths
|
What is potentimeter? Write its
principle.
| 3 |
Physics
|
The twisting couple per unit twist for a
solid cylinder of radius \( 4.9 \mathrm{cm} \) is \( 0.1 N / m . \) The twisting couple per unit twist for a hollow cylinder of same material with outer and inner radii of
\( 5 \mathrm{cm} \) and \( 4 \mathrm{cm} \) respectively, will be
A. \( 0.64 N / m \)
В. \( 0.64 \times 10^{-1} N / m \)
c. \( 0.64 \times 10^{-2} N / m \)
D. \( 0.64 \times 10^{-3} N / m \)
| 3 |
Physics
|
If \( D E \| B C \) in \( \triangle A B C, A D= \)
\( 1.5 \mathrm{cm}, B D=3 \mathrm{cm} \) and \( A E=1 \mathrm{cm}, \)
then find \( E C(\text { in } \mathrm{cm}) . \)
| 2 |
Maths
|
\( X \) -rays are produced when a stream of
electrons in an \( X \) -ray tube:
A. hits the glass wall of the tube
B. strikes the metal target
c. passes through a strong magnetic field
D. none of the above
| 1 |
Chemistry
|
toppr
Q Type your question
secondary coil, current through the primary coil and input power are given.
(a) Let the given data be taken as \( \frac{N_{1}}{N_{2}} \)
(turn-ratio), \( i_{1}, \) (input current) and \( P \)
(input power).
(b) Substitute the given values of \( \frac{N_{1}}{N_{2}} \)
and \( i_{1}, \) in the above formula and get the
value of \( i_{2} \)
(c) Write the relation between turn-ratio
and the currents as \( \frac{N_{1}}{N_{2}}=\frac{i_{2}}{i_{1}}, \) where \( i_{2} \) is the current in the secondary coil.
(d) Write the relation between input
power and output power in terms of
\( V_{1}, i_{1}, V_{2}, i_{2} \) i.e. \( V_{1} i_{1}=V_{2} i_{2}=P, \) where
\( V_{1} \) and \( V_{2} \) are the voltage in the primary and secondary coils respectively.
(e) Substitute the values of \( i_{2} \) and \( P \) in
the above relation to get the value of \( V_{2} \)
A \( . \) abdce
B. bcade
c. acbde
D. \( d b c a e \)
| 3 |
Physics
|
A uniform aluminium wire of length \( 3 \mathrm{m} \)
and area of cross-section \( 2 m m^{2} \) is
extended through 12 mm. The energy stored in the wire is
\( \boldsymbol{Y}_{\boldsymbol{A l}}=\boldsymbol{7} \times \mathbf{1 0}^{\mathbf{1 0}} \boldsymbol{N} / \boldsymbol{m}^{2} \mathbf{)} \)
A . \( 336 J \)
B. 33.6 \( J \)
c. \( 3.36 J \)
D. 0.336 J
| 3 |
Physics
|
Starting with an expression for
refraction at a single spherical surface,
obtain an expression for lens maker's formula.
| 3 |
Physics
|
The graph shows position as a function
of time for two trains \( A \) and \( B \) running
on parallel tracks. For time greater than
\( t=0, \) which of the following statement is
true ?
A. Both trains have the same velocity at timet \( _{B} \)
B. Both trains speed up all the time.
c. Both trains may have the same velocity at some time earlier than \( t_{E} \)
D. Graph indicates that both trains have the same acceleration at a given time
| 3 |
Physics
|
Consider the following relations
\( (1) \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{A}-(\boldsymbol{A} \cap \boldsymbol{B}) \)
(2) \( \boldsymbol{A}=\boldsymbol{A}-(\boldsymbol{A} \cap \boldsymbol{B}) \cup(\boldsymbol{A}-\boldsymbol{B}) \)
(3) \( \boldsymbol{A}-(\boldsymbol{A} \cup \boldsymbol{C})=(\boldsymbol{A}-\boldsymbol{B}) \cup(\boldsymbol{A}-\boldsymbol{C}) \)
Which of these is correct
A . 1 and 3
B. 2 only
\( c \cdot 2 \) and 3
D. 1 and 2
| 2 |
Maths
|
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