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Evaluate \( \lim _{x \rightarrow 0} \frac{\tan x}{x} \)
| 2 |
Maths
|
Lianas are
A. Weak stemmed trailers
B. Woody stemmed climbers and twiners
C . Trees with twisted stems
D. Plants with woody stems and medium height
| 0 |
Biology
|
The internal centre of similitude of two
circles \( (x-3)^{2}+(y-2)^{2}= \)
\( \mathbf{9},(\boldsymbol{x}+\mathbf{5})^{2}+(\boldsymbol{y}+\mathbf{6})^{2}=\mathbf{9} \) is
A \( \cdot(-1,-2) \)
B. (-2,-1)
c. (3,2)
(年. (3,2)
D. (-5,-6)
| 2 |
Maths
|
Let 'f' be a function defined from
\( \boldsymbol{R}^{+} \longrightarrow \boldsymbol{R}^{+} \cdot \boldsymbol{I} \boldsymbol{f}(\boldsymbol{f}(\boldsymbol{x} \boldsymbol{y}))=\boldsymbol{x}(\boldsymbol{f}(\boldsymbol{y}))^{2} \) for
all positive numbers \( x \) and \( y . I f f(2)= \) \( \operatorname{find} f(50)= \)
A . 20
B. 30
\( c .3 \)
D. 40
| 2 |
Maths
|
A cart of mass \( 20 \mathrm{kg} \) at rest is to be
dragged at a speed of \( 18 \mathrm{km} \mathrm{h}^{-1} \). If the co-efficient of friction between the cart
and the ground is \( 0.1, \) what is the minimum force required to drag the cart to a distance of \( 10 \mathrm{m} \) ? (Take \( g= \)
\( \left.10 m s^{-2}\right) \)
| 3 |
Physics
|
Why does the total amount of \( C O_{2} \) in the atmosphere remains constant even
though respiration liberates \( C O_{2} ? \)
\( A \cdot C O_{2} \) acts as a buffer
B. \( C O_{2} \) is converted to carbohydrates in photosynthesis
\( \mathrm{c} \cdot \mathrm{CO}_{2} \) forms carbonic acid
D. \( C O_{2} \) undergoes cleavage during photosynthesis
| 0 |
Biology
|
\( 28 g \) of \( N_{2} \) and \( 6 g \) of \( H_{2} \) were kept at
\( 400^{\circ} \mathrm{C} \) in 1 litre vessel, the equilibrium
mixture contained \( 27.54 g \) of \( N H_{3} . \) The
appropriate value of \( \boldsymbol{K}_{c} \) for the above reaction can be (in mole\( ^{-2} \) litre\( ^{2} \) )
\( \mathbf{A} \cdot 75 \)
B. 50
c. 25
D. 100
| 1 |
Chemistry
|
Common name of calcium oxychloride
is
(washing/bleaching) powder
| 1 |
Chemistry
|
The sum of \( n \) terms of three
arithmetical progression are \( S_{1}, S_{2} \) and
\( S_{3} . \) The first term of each is unity and
the common differences are 1,2 and 3
respectively. Prove that \( \left(\boldsymbol{S}_{1}+\boldsymbol{S}_{3}=\boldsymbol{2} \boldsymbol{S}_{2}\right) \)
| 2 |
Maths
|
Sulphuric acid reacts with sodium hydroxide as follows
\( H_{2} S O_{4}+2 N a O H \rightarrow N a_{2} S O_{4}+2 H_{2} O \)
When 1 L of 0.1 M sulphuric acid solution is allowed to react with 1 L of \( 0.1 \mathrm{M} \)
sodium hydroxide solution, the amount of sodium sulphate formed and its molarity in the solution obtained is ?
A. \( 0.1 \mathrm{molL}^{-1} \)
B. \( 7.10 g \)
c. 0.025 mol \( L^{-1} \)
D. \( 3.55 g \)
| 1 |
Chemistry
|
Which of the following forms a virtual and erect image for all positions of the object?
A. Convex lens
B. Plane mirror
c. Convex mirror
D. Concave mirror
| 3 |
Physics
|
A small candle, \( 2.5 \mathrm{cm} \) in size is placed
at \( 27 \mathrm{cm} \) in front of a concave mirror of
radius of curvature \( 36 \mathrm{cm} . \) At what
distance from the mirror should a
screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the
screen have to be moved?
| 3 |
Physics
|
An electric bulb works on the principle
of
A. Archimedes
B. heating effect of current
c. magnetic effect of current
D. none of these
| 3 |
Physics
|
Sapwood is
A. Outer functional part of secondary xylem
B. Inner non functional part of secondary xylem
C. Outer as well as inner part of secondary xylem
D. None of the above
| 0 |
Biology
|
The probability of student \( A \) passing an examination is \( \frac{2}{9} \) and of students, \( B \) passing is \( \frac{5}{9} . \) Assuming the two events:
\( A \) passes'. \( B \) passes' as independent, find the probability of both passing the examination.
| 2 |
Maths
|
What happened when a rubber band is
stretched?
| 3 |
Physics
|
Q Type your question.
projected towards the pulley'P' with an
initial velocity \( u_{0} \) then select incorrect option
A the string would become tight at \( t=\frac{2 u_{0}}{g} \)
3. the distance travelled by 'A' before the string is taut is \( \frac{u_{0}^{2}}{g} \)
c. the distance travelled by 'B' before string is taut is \( \frac{2 u_{0}^{2}}{g} \)
D. the common speed of the blocks just after the string i aut is \( \left[\frac{n+2}{n+1}\right] u_{0} \)
| 3 |
Physics
|
Identify the wrong pair of statements.
I) The number of stamens in 5 flowers of
Allium is equal to those in 5 flowers of Solanum.
Il) The microsporangia of Hibiscus and Asparagus are having 80 pollen grains each. Then the ratio of the number of
pollen grains produced from each stamen of these two plants is 1: 1
III) The ratio of the number of stamens
in the flowers of Pisum and Datura is 2: 1
IV) The number of carpels in a flower of Smilax is equal to the number of carpels in a cyathium inflorescence.
A. ॥I, IV
B . ।, ॥
\( c \cdot 1,1 \)
D. II, III
| 0 |
Biology
|
Find the following in \( 24 \% \) (w/v) of the
solution if the density of the solution is \( 1.06 g m l^{-1} \)
(a) Weight of solute
(b) Weight of solvent
| 1 |
Chemistry
|
A man rows upstream a distance of
\( 9 k m \) or downstream a distance of
\( 18 k m \) taking 3 hours each time. The
speed of the boat in still water is
A \( \cdot 7 \frac{1}{2} k m / h \)
В \( \cdot 6 \frac{1}{2} k m / h \)
c. \( _{5} \frac{1}{2} k m / h \)
D. \( 4 \frac{1}{2} k m / h \)
| 3 |
Physics
|
On the basis of following features identify the correct option:
I. It is stored in air-tight bags.
II. It is used in surgical bandages for setting fractured bones.
A. Plaster of paris
B. Gypsum
c. Dead burnt plaster
D. Both A and B
| 1 |
Chemistry
|
Kumaran went to a shop near his house on a bicycle. The bicycle made a lot of noise when he pedalled it. After coming home, he applied some oil on some parts of the bicycle. Then there was no noise, why?
| 3 |
Physics
|
Which one of the following roles is not charcteristic of an essential element?
A. Being a component of biomolecules
B. Changing the chemistry of soil
c. Being a structural component of energy related chemical compounds.
D. Activation or inhibition of enzymes.
| 0 |
Biology
|
Two blocks of steel A and B, A being two
times heavier than \( \mathrm{B} \), are at \( 40^{\circ} \mathrm{C} \). The
ratio of heat content of \( A \) to \( B \) is:
\( A \cdot 1 \)
B. 4
\( c \cdot 2 \)
D.
| 3 |
Physics
|
Which of the following statements are
correct?
This question has multiple correct options
A. Electron density in \( X Y \) plane of \( 3 d_{x^{2}-y^{2}} \) orbital is zero.
B. Electron density in \( X Y \) plane of \( 3 d_{z^{2}} \) orbital is zero.
C. \( 2 s \) orbital has only one spherical node.
D. For \( 2 p_{z} \) orbital \( Y Z \) is the nodal plane.
| 1 |
Chemistry
|
If
\( \boldsymbol{\theta} \) and \( \phi \) are angles in the 1 st quadrant such that \( \tan \theta=\frac{1}{7} \) and \( \sin \phi=\frac{1}{\sqrt{10}} \)
\( \mathbf{A} \cdot \theta+2 \phi=90^{\circ} \)
B . \( \theta+2 \phi=60^{\circ} \)
c. \( \theta+2 \phi=30^{\circ} \)
D. \( \theta+2 \phi=45^{\circ} \)
| 2 |
Maths
|
A solenoid is
A . an electromagnet
B. a temporary magnet
C. a permanent magnet
D. Both 1 and 2
| 3 |
Physics
|
Super glue or crazy glue is:
A . polymethyl methacrylate
B. polyethyl acrylate
C . polymethyl \( \alpha \) -cyanoacrylate
D. polyethyl methacrylate
| 1 |
Chemistry
|
Define vital capacity. What is its
significance?
| 0 |
Biology
|
\( \mathbf{1 f} \mathbf{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{5} & \mathbf{- 6} \\ \mathbf{- 8} & \mathbf{0} & \mathbf{4} \\ \mathbf{3} & \mathbf{- 7} & \mathbf{2}\end{array}\right] \) then the
cofactors of the elements 3,-7,2 are
p,q,r respectively their ascending order
is
\( \mathbf{A} \cdot \mathbf{p}, \mathbf{r}, \mathbf{q} \)
B. \( \mathrm{q}, \mathrm{r}, \mathrm{p} \)
\( c \cdot p, q, r \)
\( D \cdot r, p, q \)
| 2 |
Maths
|
Mary says "The number I am thinking is divisible by 2 or it is divisible by \( 3 " \). This statement is false if the number Mary is
thinking of is
\( A \cdot 6 \)
B. 8
\( c \cdot 11 \)
D. 15
| 2 |
Maths
|
A man throws a ball weighing \( 500 g \)
vertically upwards with a speed of \( 10 m / s \)
(i) what will be its initial momentum?
(ii) What would be its momentum at the
highest point of its flight?
| 3 |
Physics
|
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 the final
temperature of the mixture is \( 60^{\circ} \mathrm{C} \)
then find the ratio of masses of the two
liquids mixed.
| 3 |
Physics
|
Find the equation of the circle drawn on the intercept made by the line \( 2 x+ \) \( 3 y=6 \) between the coordinate axes as
diameter.
| 2 |
Maths
|
The correct molecular shape for the
molecule \( X e O F_{4} \)
A . tetrahedral
B. trigonal pyramidal
c. trigonal bipyramidal
D. square pyramidal
E. flat
| 1 |
Chemistry
|
If \( x^{2}-2 x^{2} y^{2}+5 x+y-5=0 \) and
\( \boldsymbol{y}(1)=1, \) then
This question has multiple correct options
A \( \cdot y^{\prime}(1)=1 \)
в. \( y^{\prime \prime}(1)=-\frac{4}{3} \)
c. \( \quad y^{\prime \prime}(1)=-\frac{22}{3} \)
D. \( y^{\prime}(1)=\frac{2}{3} \)
| 2 |
Maths
|
Find how the normal acceleration of the
balloon varies as a function of the
height of ascent.
\( \mathbf{A} \cdot \omega_{n}=\frac{a v_{0}}{\sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
B. \( \omega_{n}=\frac{2 a v_{0}}{\sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
\( ^{\mathbf{C}} \cdot_{\omega_{n}}=\frac{3 a v_{0}}{2 \sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
D \( \cdot \omega_{n}=\frac{a v_{0}}{2 \sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
| 3 |
Physics
|
The radius of a circle with centre 0 is 5
\( \mathrm{cm} \) (given figure). Two radii OA and \( \mathrm{OB} \)
are drawn at right angles to each other.
Find the areas of the segment made by the chord \( A B \text { (Take } \pi=3.14) \)
| 2 |
Maths
|
If \( A \) is a skew symmetric matrix of order
3, then the value of \( |\boldsymbol{A}| \) is
A . 3
B. 0
\( c .9 \)
D. 27
| 2 |
Maths
|
The electric field in a region is radially outwards and has a magnitude \( \boldsymbol{E}=\boldsymbol{K} \boldsymbol{r} \)
The charge contained in a sphere of radius \( a \) is :
A. \( K 4 \pi \varepsilon_{0} a^{2} \)
В \( \cdot \quad K \frac{4}{3} \pi \varepsilon_{0} a^{3} \)
c. \( K 4 \pi \varepsilon_{0} a^{3} \)
D. none of these
| 3 |
Physics
|
Insulin contains \( 3.4 \% \) sulphur. The
minimum molecular mass of insulin is
A. 940
в. 350
\( c .470 \)
D. 560
| 1 |
Chemistry
|
Explain with the help of an activity the nature of metallic oxides or hydroxide and non metallic oxide by using metal as sodium and non metal as sulphur.
| 1 |
Chemistry
|
\( \lim _{x \rightarrow \frac{\pi}{3}} \frac{\sqrt{3} \cos x-\sin x}{1-2 \cos x} \)
| 2 |
Maths
|
The co-efficient of \( x^{53} \) in the expression \( \sum_{m=0}^{100} 100 c_{m}(x-3)^{100-m} 2^{m} \) is
B. \( 98_{c_{53}} \)
\( \mathbf{c} .^{65} \sigma_{53} \)
D. \( 100 c_{65} \)
| 2 |
Maths
|
Choose the correct answer from the
alternatives given The lac operon is transcribed when
A. lactose is needed by the cell
B. lactose is available to the cell
c. lactose is unavailable to the cell
D. lactic acid is available to the cell
| 0 |
Biology
|
A particle of mass \( \mathrm{m} \) is tied to a string of length L. The free end of the string is fixed and the particle is whirled in a circular path. The speed of the particle increases from \( 5 \mathrm{m} / \mathrm{s} \) to \( 10 \mathrm{m} / \mathrm{s} \) for 5
secs. The motion is
A. Uniform circular motion
B. Non-uniform circular motion
c. Non uniformly accelerated motion
D. Non of these
| 3 |
Physics
|
A mixture of \( L i_{2} C O_{3} \) and \( K_{2} C O_{3} \) on
strong heating gave 0.25 mole of \( C O_{2} \)
The mole \( \% \) of \( L i_{2} C O_{3} \) and \( C O_{2} \) in the
mixture is :
\( \begin{array}{lll}\text { A } \cdot L i_{2} C O_{3}: 25 \% & K_{2} C O_{3}: 75 \%\end{array} \)
B . \( L i_{2} C O_{3}: 75 \% \quad K_{2} C O_{3}: 25 \% \)
\( \mathrm{c} \cdot L i_{2} C O_{3}: 60 \% \quad K_{2} C O_{3}: 40 \% \)
D. \( L i_{2} C O_{3}: 40 \% \quad K_{2} C O_{3}: 60 \% \)
| 1 |
Chemistry
|
The portion of a line intercepted between the coordinate axes is divided by the point (2,-1) in the ration \( 3: 2 . \) The
equation of the line is :
A. \( 5 x-2 y-20=0 \)
В. \( 2 x-y+7=0 \)
c. \( x-3 y-5=0 \)
D. \( 2 x y+y-4=0 \)
| 2 |
Maths
|
The equation \( y=A \sin ^{2}(k x-\omega t) \)
represents a wave with
A. amplitude A frequency \( \omega / 2 \pi \)
B. amplitude A /2 frequency \( \omega / \pi \)
c. amplitude 2A frequency \( \omega / 4 \pi \)
D. It does not represent a wave motion
| 3 |
Physics
|
ff \( 2\left[\begin{array}{ll}3 & 4 \\ 5 & x\end{array}\right]+\left[\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right] \)
matrices. Find the value of \( x \& y \)
| 2 |
Maths
|
Two cells of emf \( 1.5 v \) and \( 2.0 v \) have
internal resistances \( 0.2 \Omega \) and \( 0.3 \Omega \)
respectively are connected in parallel. Calculate the emf and internal
resistance of the equivalent cell?
| 3 |
Physics
|
Which of the following exhibit minimum number of oxidation states:
A. Mn
B. Np
c. Th
D. cr
| 1 |
Chemistry
|
A wire is stretched through 1 mm by certain load. The extension produced in the wire of same material with double
the length and radius will be
\( \mathbf{A} \cdot 4 m m \)
B. \( 3 m m \)
\( \mathbf{c} \cdot 1 m m \)
D. \( 0.5 m m \)
| 3 |
Physics
|
A disc of radius \( 0.2 m \) is rolling with
slipping on a flat horizontal surface, as shown in figure. The instantaneous
centre of rotation is: (the lowest contact
point is 0 and centre of disc is \( C \) )
A . zero
B. \( 0.1 m \) above 0 on line 0 C
c. \( 0.2 m \) below o on line oc
D. \( 0.2 m \) above 0 on line 0 c
| 3 |
Physics
|
Can you think of two particles which do
not exert gravitational force on each
other?
| 3 |
Physics
|
The image formed by convex lens in a simple microscope is ...... erect and
A. Virtual, magnified
B. Real, magnified
c. Virtual, diminished
D. Real, diminished
| 3 |
Physics
|
\( N_{2} \) can be obtained by heating
\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)
| 1 |
Chemistry
|
An elastic spring is given a force of 1000
N over an area of \( 0.2 m^{2} \)
A. \( 3000 N m^{-2} \)
B. \( 5000 \mathrm{Nm}^{-2} \)
c. \( 500 N m^{-2} \)
D. \( 2500 N m^{-2} \)
| 3 |
Physics
|
The degree and order of the differential equation \( \left[1+\left(\frac{d y}{d x}\right)^{3}\right]^{7 / 3}=7\left(\frac{d^{2} y}{d x^{2}}\right) \)
respectively are:
A. 3 and 7
B. 3 and 2
\( c .7 \) and 3
D. 2 and 3
| 2 |
Maths
|
Simplify \( 2 \frac{2}{7} \div 1 \frac{4}{11} \times 2 \frac{4}{9} \)
| 2 |
Maths
|
Explain the reason which ray of light wil
be transmitted through the face \( A B \) the
refractive index of the prism for red,
green, blue are \( 1.39,1.42,1.47 ? \sin \)
\( \mathbf{7 1}=\mathbf{4 6}^{\circ}, \sin . \mathbf{7 0}=\mathbf{4 4}^{\circ}, \operatorname{sin.67}=\mathbf{4 2}^{\circ} \)
| 3 |
Physics
|
\( \mathbf{2} N \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{S} \boldsymbol{O}_{2} \rightarrow ? \)
A \( \cdot N a_{2} O+H_{2}+S O_{2} \)
в. \( N a_{2} S O_{3}+H_{2} O \)
c. \( N a_{2} S O_{3}+H_{2} \)
D. \( N a_{2} O+H_{2}+O_{2} \)
| 1 |
Chemistry
|
\( \left|\begin{array}{ccc}\mathbf{2}^{3} & \mathbf{3}^{3} & \mathbf{3 . 2}^{\mathbf{2}}+\mathbf{3 . 2}+\mathbf{1} \\ \mathbf{3}^{\mathbf{3}} & \mathbf{4}^{\mathbf{3}} & \mathbf{3 . 3}^{\mathbf{2}}+\mathbf{3 . 3}+\mathbf{1} \\ \mathbf{4}^{\mathbf{3}} & \mathbf{5}^{\mathbf{3}} & \mathbf{3 . 4}^{\mathbf{2}}+\mathbf{3 . 4}+\mathbf{1}\end{array}\right| \) is equal to
\( A \)
B.
\( c \cdot 2 \)
D. 3
| 2 |
Maths
|
Consider the reaction of trans-2-butene
with \( B r_{2} \) in \( C H_{2} C l_{2} . \) Which statement
concerning this reaction is correct?
A. The product is optically active because it possesses two chirality centers.
B. The product is optically inactive because it is a racemic mixture of enantiomers.
C. The product is optically inactive because it is meso.
D. The product is optically inactive because it does not possess any chirality centers.
| 1 |
Chemistry
|
A thin layer of water is transparent but a very thick layer of water is
A. Translucent
в. ०раяче
c. Most transparent
D. None of these
| 3 |
Physics
|
Compare the solubility and thermal stability of alkali metals carbonates with those of the alkaline earth metals
nitrates.
| 1 |
Chemistry
|
Two hailstones with radii in the ratio of
: 2 fall from a great height through the atmosphere. Then the ratio of their
momentum after they have attained terminal velocity is
A . 1:
B. 1: 4
\( c \cdot 1: 16 \)
D. 1: 32
| 3 |
Physics
|
If \( \vec{r}=3 \vec{i}+2 \vec{j}-5 \vec{k}, \vec{a}=2 \vec{i}-\vec{j}+\vec{k} \)
\( \vec{b}=\vec{i}+3 \vec{j}-2 \vec{k} \) and \( \vec{c}=-2 \vec{i}+\vec{j}-3 \vec{k} \)
such that \( \vec{r}=\lambda \vec{a}+\mu \vec{b}+\nu \vec{c} \) then
A \( \cdot \mu, \frac{\lambda}{2}, \nu \) are in \( A P \)
B. \( \lambda, \mu, \nu \) are in \( A P \)
c. \( \lambda, \mu, \nu \) are in \( H P \)
D. \( \mu, \lambda, \nu \) are in \( G P \)
| 2 |
Maths
|
Define the current sensitivity of a
galvanometer. Write S.I unit
Figure shows two circuits each having a
galvanometer and a battery of \( 3 \mathrm{V} \)
When the galvanometer in each
arrangement do not show any deflection
obtain the ratio \( \boldsymbol{R}_{1} / \boldsymbol{R}_{2} \)
| 3 |
Physics
|
Which group of periodic table contains no metal?
A. IA
в. IIIA
c. VIIA
D. vıl
| 1 |
Chemistry
|
Number should be added top \( \frac{-5}{7} \) to get \( \frac{-2}{3} \) is \( \frac{1}{x} . \) Find 'x?
| 2 |
Maths
|
\( \mathbf{f} A=\left[\begin{array}{cc}\frac{-\mathbf{1}+i \sqrt{\mathbf{3}}}{\mathbf{2} i} & \frac{-\mathbf{1}-i \sqrt{\mathbf{3}}}{\mathbf{2} i} \\ \frac{\mathbf{1}+i \sqrt{\mathbf{3}}}{\mathbf{2} i} & \frac{\mathbf{1}-i \sqrt{\mathbf{3}}}{\mathbf{2} i}\end{array}\right], i= \)
\( \sqrt{-i} \) and \( f(x)=x^{2}+2, \) then \( f(A) \) is
equal to
\( ^{A} \cdot\left(\frac{5-i \sqrt{3}}{2}\right)\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
\( ^{\text {В }} \cdot\left(\frac{3-i \sqrt{3}}{2}\right)\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
c. \( \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
D. \( (2+i \sqrt{3})\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
| 2 |
Maths
|
Assertion
Charge on all the condensers connected in series is the same.
Reason
Charge present on a capacitor is directly proportional to its capacitance
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
| 3 |
Physics
|
If \( f:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow(-\infty, \infty) \) is defined
by \( f(x)=\tan x, \) then \( f^{-1}(2+\sqrt{3})= \)
\( A \cdot \frac{\pi}{12} \)
в.
c. \( \frac{5 \pi}{12} \)
D.
| 2 |
Maths
|
A object of mass \( 1 \mathrm{kg} \) and radius \( 1 \mathrm{m} \) is falling vertically downward inside liquid in a gravity free space. At t=0 velocity of
the sphere is \( 2 m s^{-1} . \) If the of viscosity
of the liquid is \( \frac{1}{18 \pi} \) Pas, the velocity of
the ball will become \( 0.5 \mathrm{ma}^{-1} \) after a
time (in second)
\( A \cdot \ln 4 \)
B. \( 2 \ln 4 \)
\( c \cdot 3 \ln 4 \)
D. \( 3 \ln 2 \)
| 3 |
Physics
|
Assertion
An AND gate is a universal gate.
Reason
The boolean expression for AND gate is
\( A \cdot B=C \)
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
| 3 |
Physics
|
State true or false:
In \( \triangle A B C, A D \) is the median and \( D E \)
is parallel to \( B A \), where \( E \) is a point in \( A C \) and Hence \( B E \) is Parallel to BC
A. True
B. False
| 2 |
Maths
|
The concept of displacement current
introduced by Maxwell removes
asymmetry between
A. Gauss's law in electrostatics and Gauss's law in magnetism
B. Faraday's law and Ampere' law
C. Gauss's law and Ampere's law
D. Gauss's law and Faraday's law
| 3 |
Physics
|
Find the greatest value assumed by the function \( \boldsymbol{w}=\left|\boldsymbol{z}-\frac{\boldsymbol{4}}{\boldsymbol{z}}\right|=\mathbf{2} \) where \( \mathbf{z} \) is
a complex variable.
| 2 |
Maths
|
The range of values of p for which the
equation \( \sin \cos ^{-1}\left(\cos \left(\tan ^{-1} x\right)\right)=p \)
has a solution is
\( A \cdot\left(-\frac{1}{\sqrt{2}}, \frac{2}{\sqrt{2}}\right) \)
в. [0,1)
c. \( \left(\frac{1}{\sqrt{21}}\right) \)
D. (-1,1)
| 2 |
Maths
|
Find the largest value of \( x \) for which
\( 2(x-1) \leq 9-x \) and \( x \in W \)
| 2 |
Maths
|
Multiply \( (5-2 x) \) and \( (3+x) \)
A. \( 15-x+2 x^{2} \)
B . \( 15-x-x^{2} \)
c. \( 15-x-2 x^{2} \)
D. \( 15-x+x^{2} \)
| 2 |
Maths
|
A sphere with diameter \( 50 \mathrm{cm} \)
intersects a plane \( 14 \mathrm{cm} \) from the center of the sphere. What is the
number of square centimeters in the area of the circle formed?
A . \( 49 \pi \)
в. \( 196 \pi \)
c. \( 429 \pi \)
D. \( 576 \pi \)
E . \( 2304 \pi \)
| 2 |
Maths
|
In a series circuit, \( \boldsymbol{R}=\mathbf{3 0 0 \Omega}, \boldsymbol{L}= \)
\( \mathbf{0 . 9 H}, \boldsymbol{C}=\mathbf{2 . 0 \mu} \boldsymbol{F} \) and \( \boldsymbol{\omega}=\mathbf{1 0 0 0 r a d} / \boldsymbol{s} \)
The impedance of the circuit is
A . \( 1300 \Omega \)
в. \( 900 \Omega \)
\( \mathbf{c} .500 \Omega \)
D. \( 400 \Omega \)
| 3 |
Physics
|
Choose the incorrect statement related
to the image formed by a plane mirror:
This question has multiple correct options
A. a plane mirror always forms a virtual image
B. the image formed by a plane mirror may be magnified or diminished
C. the image formed by a plane mirror is always unmagnified and laterally inverted
D. the image formed by a plane mirror is always unmagnified and erect
| 3 |
Physics
|
Solve the following equations. \( \sin \frac{x}{2} \cos 2 x+\sin ^{2} x \cos \frac{x}{2}= \)
\( \cos ^{2} x \cos \frac{x}{2} \)
| 2 |
Maths
|
Answer the following questions briefly. Name the different layers of atmosphere.
| 0 |
Biology
|
Which of the following when stretched, break into pieces?
A. Calcium
B. Phosphorus
c. Iron
D. Radium
| 1 |
Chemistry
|
Bacterial infection on eye surface is
protected by the enzyme:
A . urease
B. carbonic anhydrase
c. lysozyme
D. xymase
| 1 |
Chemistry
|
How many of the following letters have rotational symmetry of order more than
1?
\( \mathrm{R}, \mathrm{B}, \mathrm{F}, \mathrm{H}, \mathrm{O}, \mathrm{P}, \mathrm{S}, \mathrm{W}, \mathrm{X}, \mathrm{Z}, \mathrm{N} \)
A .4
B. 9
\( c .5 \)
\( D \)
| 2 |
Maths
|
An element A has atomic number 7. It
will have properties similar to the element with the atomic number:
A. 85
B. 57
\( c \cdot 26 \)
D. 51
| 1 |
Chemistry
|
Solve the differential equation: \( \boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{\boldsymbol{x}}{\boldsymbol{e}^{\boldsymbol{y}}} \)
| 2 |
Maths
|
Two rain drops reach the earth with
different terminal velocities having
ratio \( 9: 4 . \) Then the ratio of their volume
is:
A .3: 2
B . 4: 9
c. 9: 4
D. 27: 8
| 3 |
Physics
|
Which of the following planets takes
minimum time to take one revolution
around the Sun?
A. Mercury
B. Jupiter
c. saturn
D. Pluto
| 3 |
Physics
|
The variable which takes some specific values is called
A. discrete random variable
B. continuous random variable
c. both A and B
D. none
| 2 |
Maths
|
toppr I
Q Type your question
a. \( \boldsymbol{C H}_{\mathbf{3}}-\boldsymbol{S}-\boldsymbol{C H}_{\mathbf{3}} \)
b. \( \boldsymbol{C H}_{\mathbf{3}}-\boldsymbol{C N} \)
c. \( \boldsymbol{C H}_{\mathbf{3}}-\boldsymbol{C u} \)
\( \mathbf{A} \cdot \) a. \( C H_{3}-\tilde{S}-C H_{3} \rightarrow \stackrel{\oplus}{C} H_{3}+\stackrel{\ominus}{S} C H_{3} \)
b. \( C H_{3}-\tilde{C} N \rightarrow C H_{3}+\stackrel{\ominus}{C} N \)
c. \( C \hat{H}_{3}-C u \rightarrow \stackrel{\ominus}{C} H_{3}+C u \)
\( (C u \text { is more electropositive than } C) \)
B \( \cdot \) a. \( C H_{3}-S-C H_{3} \rightarrow \stackrel{\ominus}{C} H_{3}+\stackrel{\oplus}{S} C H_{3} \)
\( \mathrm{b} . \mathrm{CH}_{3}-\widetilde{\mathrm{C}} \mathrm{N} \rightarrow^{\oplus} \mathrm{CH}_{3}+^{\ominus} \mathrm{C} N \)
c. \( C \stackrel{\hat{H}_{3}}{-C u} \rightarrow \stackrel{\oplus}{C H_{3}}+C u \)
\( (C u \text { is more electropositive than } C) \)
\( \mathbf{c} \cdot \) а. \( C H_{3}-\tilde{S}-C H_{3} \rightarrow \stackrel{\oplus}{C} H_{3}+\stackrel{\ominus}{S} C H_{3} \)
\( \mathrm{b} . \mathrm{CH}_{3}-\widetilde{\mathrm{C}} \mathrm{N} \rightarrow \stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{3}+^{\ominus} \mathrm{C} N \)
c. \( C \hat{H}_{3}-C u \rightarrow \stackrel{\ominus}{C} H_{3}+C u \)
\( (C u \text { is more electropositive than } C) \)
D. a. \( C H_{3}-S-C H_{3} \rightarrow C H_{3}+S C H_{3} \)
b. \( C H_{3}-\tilde{C} N \rightarrow C H_{3}+\stackrel{\ominus}{C} N \)
c. \( C \stackrel{\Omega}{H}_{3}-C u \rightarrow \stackrel{\oplus}{C} H_{3}+C u \)
\( (C u \text { is more electronegative than } C) \)
| 1 |
Chemistry
|
Choose the correct alternative:
The tax on goods and services purchased and is usually a certain percentage added to buyer's cost.
A. vat
B. Sales tax
c. Property tax
D. None
| 2 |
Maths
|
A shopkeeper buys an article at a discount of \( 30 \% \) from the wholesaler
(the printed price of the article being \( R s .2,000) \) and paid sales-tax at the
rate of \( 8 \% \). The shopkeeper sells the article to a buyer at the printed price
and charges tax at the same rate. Find the VAT (Value Added Tax) paid by the shopkeeper
| 2 |
Maths
|
Evaluate the integral \( \int_{-3}^{3} \log (\sqrt{x^{2}+1}+x) d x= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \log 2 \)
c. \( -\log 2 \)
D. \( 2 \log 2 \)
| 2 |
Maths
|
Which term of the sequence
\( 114,109,104 \dots \dots \) is the first negative
term
| 2 |
Maths
|
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