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Which of the following reduction
reactions are actually employed in
commerical extraction of metals?
This question has multiple correct options
\( \mathbf{A} \cdot F e_{2} O_{3}+2 A l \rightarrow A l_{2} O_{3}+2 F e \)
B. \( C r_{2} O_{3}+2 A l \rightarrow A l_{2} O_{3}+2 C r \)
\( \mathbf{c} \cdot 2 N a\left[A u(C N)_{2}\right]+Z n \rightarrow N a_{2}\left[Z n(C N)_{4}\right]+2 A u \)
\( \mathbf{D} \cdot C u_{2} S+P b \rightarrow C u+P b S \downarrow \)
| 1 |
Chemistry
|
A sink, that is the system where heat is rejected, is essential for the conversion of heat into work. From which law does
the above inference follow?
A. zeroth
B. First
c. second
D. Third
| 3 |
Physics
|
If \( 2 A-\left[\begin{array}{ll}1 & 2 \\ 7 & 4\end{array}\right]=\left[\begin{array}{cc}3 & 0 \\ 0 & -2\end{array}\right], \) then \( A \) is
equal to
\( \mathbf{A} \cdot\left[\begin{array}{cc}2 & 1 \\ 7 / 2 & 1\end{array}\right] \)
В. \( \left[\begin{array}{cc}4 & 4 \\ 7 / 2 & 1\end{array}\right] \)
c. \( \left[\begin{array}{ll}3 & -1 \\ 7 & 2\end{array}\right] \)
D. None of these
| 2 |
Maths
|
Show that \( (\sqrt{3}+\sqrt{5})^{2} \) is an irrational.
| 2 |
Maths
|
More than \( 70 \% \) of world's freshwater is
contained in
A. Polarice
B. Glaciers and mountains
C. Antartica
D. Greenland
| 0 |
Biology
|
Living cells of xylem are
A. Xylem parenchyma
B. Xylem fibres
c. Vessels
D. Tracheids
| 0 |
Biology
|
Who discovered Java ape man?
A . Leakey
B. Mayr
C. Davidson Black
D. Dubois
| 0 |
Biology
|
What is acid rain?
| 1 |
Chemistry
|
A radioactive element X disintegrates successively as under:
\( \boldsymbol{X} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{X}_{1} \stackrel{\boldsymbol{\beta}}{\rightarrow} \boldsymbol{X}_{2} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{X}_{3} \stackrel{\gamma}{\rightarrow} \boldsymbol{X}_{4} \)
If the atomic number and atomic mass.
Number of \( X \) are 72 and \( 180 . \) What are
the corresponding values for \( \boldsymbol{X}_{\mathbf{4}} \)
A .69,176
B. 69,172
c. 71,176
D. 71,172
| 3 |
Physics
|
The numerator of the rational number is
less than its denominator by 3 . If the numerator becomes three times and
the denominator is increased by \( 20, \) the new number becomes \( \frac{1}{8} . \) Find the original number.
| 2 |
Maths
|
The velocity-time graph of a linear
motion is shown in Fig. The distance
from the origin 0 after 8 seconds is :
\( \mathbf{A} \cdot 18 m \)
B. \( 16 m \)
\( c .8 m \)
D. \( 6 m \)
| 3 |
Physics
|
Given a uniform electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{5} \times \)
\( \mathbf{1 0}^{3} \hat{\mathbf{i}} \mathbf{N} / \mathbf{C}, \) find the flux of this field
through a square of \( 10 \mathrm{cm} \) on a side whose plane is parallel to the \( \boldsymbol{Y}-\boldsymbol{Z} \)
plane. What would be the flux through the same square if the plane makes a
\( 30^{\circ} \) angle with the \( \$ \$ X \) -axis?
| 3 |
Physics
|
The probability distribution function of a random variable \( \boldsymbol{X} \) is given by
\( \boldsymbol{x}_{i}: \quad 0 \quad 1 \quad 2 \)
\[
\begin{array}{lll}
3 c & 4 c & c-1
\end{array}
\]
where \( c>0 . \) Find \( c \)
| 2 |
Maths
|
When a test charge is brought in from infinity along the perpendicular bisector of an electric dipole, the work done is
A. positive
B. zero
c. Negative
D. None of theses
| 3 |
Physics
|
Which one of the following noble gas has an unusual property of diffusing through the materials such as rubber,
glass or plastic?
A. не
B. Kr
c. Ne
D. Ar
| 1 |
Chemistry
|
Green house effect is due to
A. X-rays
B. UV rays
c. Green rays
D. Infra-red rays
| 0 |
Biology
|
The tenth term in the expansion of
\( \left(2 x^{2}+\frac{1}{x}\right)^{12} \)
A \( \cdot \frac{1760}{x^{3}} \)
в. \( -\frac{1760}{x^{3}} \)
c. \( \frac{1760}{x^{2}} \)
D. none of the above
| 2 |
Maths
|
\( \boldsymbol{a} \neq \boldsymbol{p}, \boldsymbol{b} \neq \boldsymbol{q}, \boldsymbol{c} \neq \boldsymbol{r} \) and \( \left|\begin{array}{lll}\boldsymbol{p} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{q} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{r}\end{array}\right|=0 \)
then the value of \( \frac{\boldsymbol{p}}{\boldsymbol{p}-\boldsymbol{a}}+\frac{\boldsymbol{q}}{\boldsymbol{q}-\boldsymbol{b}}+ \)
\( \frac{r}{r-c} \) is equal to
\( A \)
B. 2
\( c \cdot 3 \)
D.
| 2 |
Maths
|
Wavelength is expressed in:
A . \( N \)
в. \( e \) го \( g \)
c. dyne
D. \( A^{0} \)
| 3 |
Physics
|
The presence or absence of hymen is not reliable indicator of virginity or sexual experience.
A. True
B. False
| 0 |
Biology
|
In the given figure, two identical regular
hexagons are placed side by side as
shown.
Find the value z.
\( \mathbf{A} \cdot 60^{\circ} \)
\( \mathbf{B} \cdot 90^{\circ} \)
\( \mathbf{C} \cdot 120^{\circ} \)
D. \( 160^{\circ} \)
| 2 |
Maths
|
Construct a \( \triangle \boldsymbol{A B C}, \boldsymbol{A B}= \)
\( \mathbf{6 c m}, \boldsymbol{B C}=\mathbf{7} \mathbf{c m} \) and \( \angle \boldsymbol{A}=\mathbf{6 0}^{\circ} \)
| 2 |
Maths
|
Choose the correct answer from the
alternatives given By anticlinal divisions, an organ increases in:
A. circumference
B. volume
c. area
D. length
| 0 |
Biology
|
Fibres can be classified as natura
fibres and synthetic fibres.
A. True
B. False
| 1 |
Chemistry
|
Three coins are tossed. Find the
probability of getting atleast two head.
| 2 |
Maths
|
Which among the following group 15 element forms most stable pentavalent compound?
A. Phosphorus
B. Antimony
c. Bismuth
D. Arsenic
| 1 |
Chemistry
|
If 10 g of ice at \( 0^{\circ} \mathrm{C} \) mixes with 10 g of water at \( 10^{\circ} \mathrm{C} \), then the final
temperature \( t \) is given by
A \( \cdot(10 \times 80)+10(t-0)=10(10-t) \)
в. \( 10 \times 80=10(10-t)+10(t-0) \)
\( \mathbf{c} \cdot t=5^{\circ} C \)
D. \( t=0^{\circ} \mathrm{C} \)
| 3 |
Physics
|
Which of the following is an antihistamine?
A. Brompheniramine
B. Rantidine
c. cimetidine
D. None of the above
| 1 |
Chemistry
|
Male heterogametic, XX-XO type of sex determination is found in
A. Butterflies
B. Moth
c. Grasshoppers
D. Drosophila
| 0 |
Biology
|
Calculate the force of gravitation between the earth and the sun, given that the mass of the earth \( =6 \times 10^{24} k g \)
and of the \( \operatorname{Sun}=2 \times 10^{30} k g . \) The
average distance between the two is
\( 1.5 \times 10^{11} m \)
| 3 |
Physics
|
What is ecological succession?
| 0 |
Biology
|
Factorise \( : 8 x^{3}-27 y^{3}-2 x+3 y \)
A \( \cdot(2 x+3 y)\left(4 x^{2}-x y+9 y^{2}+1\right) \)
В \( \cdot(2 x+y)\left(4 x^{2}-6 x y-9 y^{2}\right) \)
C \( \cdot(x-3 y)\left(4 x^{2}-3 x y+9 y^{2}\right) \)
D \( \cdot(2 x-3 y)\left(4 x^{2}+6 x y+9 y^{2}-1\right) \)
| 2 |
Maths
|
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{i} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{i} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{i}\end{array}\right] \) then \( \boldsymbol{n} \in \boldsymbol{N}, \boldsymbol{A}^{4 n+1}= \)
| 2 |
Maths
|
For \( x, t \in R \) let
\( \boldsymbol{p}_{1}(\boldsymbol{x})=(\sin t) \boldsymbol{x}^{2}-(2 \cos \boldsymbol{t}) \boldsymbol{x}+\sin \boldsymbol{t} \)
be a family of quadratic polynomials in \( x \) with variable co efficients. Let \( A(t)= \) \( \int_{0}^{1} p_{t}(x) d x . \) Which of the following
statements are true?
(I) \( A(t)<0 \) for all \( t \)
(II) \( A(t) \) has infinitely many critica points.
(III) \( A(t)=0 \) for infinitely many t.
(IV) \( A^{\prime}(t)<0 \) for all \( t \)
A. (I) and (II) only
B. (II) and (III) only
C. (III) and (IV) only
\( D \cdot(I V) \) and (1) only
| 2 |
Maths
|
A man standing on the road has to ho!d his umbrella at \( 30^{\circ} \) with the vertical to
keep the rain away. He throws the umbrella and starts running at 10 k \( m / h r . \) He find that rain drops are
hitting his head vertically, then the speed of the rain drops with respect to moving man.
A. \( 20 k m / h r \)
в. \( 10 \sqrt{3} k m / h r \)
c. \( \frac{10}{\sqrt{3}} k m / h r \)
D. \( 10 k m / h r \)
| 3 |
Physics
|
Identify the products.
\[
\mathrm{NaBH}_{4} \quad \mathrm{Me}-\mathrm{CONH}_{2} \quad \mathrm{LiAlH}_{4}
\]
| 1 |
Chemistry
|
Substances that break just after elastic
limit is reached are known as
A. brittle substances
B. breakable substances
c. ductile substances
D. elastic substances
| 3 |
Physics
|
The domain of \( f(x)=\log (\sin x) \) is
A \( \cdot(-\pi, \pi) \)
В. \( (2 n \pi,(2 n+1) \pi) \) and \( n \in Z \)
с. \( [0,2 \pi] \)
]
D. \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
| 2 |
Maths
|
The reference electrode is made from
which of the following?
A. \( Z n C l_{2} \)
в. \( \mathrm{CuSO}_{4} \)
c. \( H g_{2} C l_{2} \)
D. \( H g C l_{2} \)
| 1 |
Chemistry
|
Write Chemical equation when \( X e F_{4} \) disproportionates to \( \mathrm{Xe}(0) \) and \( \boldsymbol{X} e(\boldsymbol{V} \boldsymbol{I}) \)
compounds through \( X e(I I) \) and \( \boldsymbol{X} \boldsymbol{e}(\boldsymbol{V} \boldsymbol{I} \boldsymbol{I} \boldsymbol{I}) \)
| 1 |
Chemistry
|
Describe briefly the underlying principle of a transistor amplifier working as an oscillator. Hence, use the necessary circuit diagram to explain how self sustained oscillations are achieved in
the oscillator.
| 3 |
Physics
|
If \( 1 \mathrm{kg} \) wt \( =10 \mathrm{N}, \) the value of gravitational intensity will be
A \( \cdot 10 m / s^{2} \)
в. \( \frac{1}{10} m / s^{2} \)
c. \( 1 m / s^{2} \)
D. \( \frac{1}{100} m / s^{2} \)
| 3 |
Physics
|
Given that \( A \subset B, \) then identify the
correct statement
\( \mathbf{A} \cdot P(A / B)=P(A) \)
B \( . P(A / B) \leq P(A) \)
\( \mathbf{c} \cdot P(A / B) \geq P(A) \)
D \( \cdot P(A / B)=P(A)-P(B) \)
| 2 |
Maths
|
The decision of cell division occurs at
A. starting of \( G_{1} \)
B. End of G \( _{1} \)
c. Initial stage of prophase
D. End of telophase
| 0 |
Biology
|
What is common between given cations
and anions :
\( \boldsymbol{O}^{2-}, \boldsymbol{F}^{-}, \boldsymbol{N} \boldsymbol{a}^{+}, \boldsymbol{M} \boldsymbol{g}^{2+}, \boldsymbol{A} \boldsymbol{l}^{3+} ? \)
A. All have same ionic radii
B. All are isoelectronic species having 10 electrons
c. All of them belong to the third period
D. The nature of oxides of all the ions is basic
| 1 |
Chemistry
|
The given structure show bondline
formula of 2, 3-Dimethylbutanal
A. True
B. False
| 1 |
Chemistry
|
Let \( \boldsymbol{f}(\boldsymbol{x}) \) be a continuous function
whose range is \( [2,6,5] . \) If \( h(x)= \) \( \left[\frac{\cos x+f(x)}{\lambda}\right], \lambda \in N \) be continuous
where [.] denotes the greatest integer
function, then the least value of \( \lambda \) is
\( A \cdot 6 \)
B. 7
c. 8
D. None of these
| 2 |
Maths
|
Assertion
In any transition series, the magnetic
moment of \( M^{2+} \) ion first increases and
then decreases.
Reason
In any transition series, the number of unpaired electrons first increases, afterwards decrease
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
| 1 |
Chemistry
|
The convex lens used in a simple microscope produces a magnification of
5. The image is formed at the least
distance of distinct vision. What is the
focal length of the lens?
| 3 |
Physics
|
A thin circular loop of radius R rotates about its vertical diameter with an angular frequency \( \omega . \) Show that a small bead on the wire loop remains at its lower most point for \( \omega \leq \sqrt{g / R} \). What
is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for \( \omega= \)
\( \sqrt{2 g / R} ? \) Neglect friction.
| 3 |
Physics
|
At what distance should an object be
placed in front of a convex lens of focal length \( 0.4 m \) so that the image is thrice the size ofthe object?
| 3 |
Physics
|
The focus of a conic is the origin and its
corresponding directrix is \( 7 x-y- \)
\( \mathbf{1 0}=\mathbf{0 .} \) If length of its latus rectum is 2
then its eccentricity is:
A \( \cdot \sqrt{2} \)
B. 1
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{1}{2} \)
| 2 |
Maths
|
An ideal gas with adiabatic exponent \( =1.5 \) ) undergoes a process in which work done by the gas is same as increase in internal energy of the gas. The molar heat capacity of gas for the process is:
\( A \cdot C=4 R \)
B. \( c=0 \)
\( c \cdot c=2 R \)
D. \( c=R \)
| 3 |
Physics
|
A tunnel is dug along a chord of the earth at a perpendicular distance R/2
from the earth's centre. The wall of the
tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass \( \mathrm{m} \) when it is at a distance \( x \) from the centre of the
tunnel.
| 3 |
Physics
|
The precipitate of \( M_{2} S_{3} \) obtained on
mixing equal volumes of solutions \( \boldsymbol{S}_{1} \)
having \( \left[M^{3+}\right]=4 \times 10^{-5} M \) and \( S_{2} \)
having \( \left[S^{2-}\right]=2 \times 10^{-3} M . \) Calculate
its solubility product.
| 1 |
Chemistry
|
A child is standing in tront ot a straight plane mirror. His father is standing
behind him, as shown in the fig. The
height of the father is double the height
of the child. What is the minimum
length of the mirror required so that the
child can completely see his own image
and his fathers image in the mirror?
Given that the height of father is \( 2 H \)
\( \mathbf{A} \cdot H / 2 \)
B. \( 5 H / 6 \)
c. \( 3 H / 2 \)
D. None of these
| 3 |
Physics
|
If \( X=\{2,3,5,7,11\} \) and \( Y=\{4,6,8,9,10\} \) then find the number of one-one functions
from \( X \) to \( Y \)
A . 720
B. 120
\( c \cdot 24 \)
\( D \cdot 12 \)
| 2 |
Maths
|
Differentiate \( \sin ^{2} 3 x \cdot \tan ^{3} 2 x \)
| 2 |
Maths
|
If \( I_{0} \) is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity
when the slit width is doubled
A. \( I_{0} \)
B. \( \frac{I_{0}}{2} \)
\( c \cdot 2 I_{0} \)
D. \( 4 I_{0} \)
| 3 |
Physics
|
Evaluate \( \lim _{x \rightarrow 0} \frac{\sin ^{-1}[\cos x]}{1+[\cos x]} \)
denotes the greatest integer function)
A . 0
B. -
\( c . \)
D. \( \infty \)
| 2 |
Maths
|
The ultra-high frequency band of radio waves in electromagnetic wave is used
as in:
A. television waves
B. cellular phone communication
c. commercial FM radio
D. both (a) and (c)
| 3 |
Physics
|
The frequency of light of wave length
\( 5000 A^{\circ} \) is :
A \( \cdot 1.5 \times 10^{3} \mathrm{Hz} \)
B \( \cdot 6 \times 10^{8} \mathrm{Hz} \)
c. \( 6 \times 10^{14} \mathrm{Hz} \)
D. \( 7.5 \times 10^{15} \mathrm{Hz} \)
| 3 |
Physics
|
Find \( \boldsymbol{f}^{\prime}(\boldsymbol{3}) \) if \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{5} \boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{x}+\mathbf{5} \)
A . 28
B. 54
\( c .32 \)
D. None
| 2 |
Maths
|
Assertion
Pulling a lawn roller is easier than
pushing it.
Reason
Pushing increases the apparent weight
and hence the force of friction.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
| 3 |
Physics
|
Ketone bodies are byproducts in the metabolism of
A. carbohydrate
B. Protein
\( c . \) Fat
D. All the above
| 0 |
Biology
|
The wavelength associated with 1 Me \( V \)
proton is
A. \( 28.6 p m \)
B. 2.86 \( p m \)
c. \( 2.86 \mathrm{fm} \)
D. 28.6 \( f m \)
| 3 |
Physics
|
With due regard to significant figures, add the following:
a. 953 and 0.324
b. 953 and 0.625
c. 953.0 and 0.324
d. 953.0 and 0.374
A . a. \( 953 ; \) b. 954 c. 953.3 d. 953.4
B. a. \( 953 ; \) b. 955 c. 953.3 d. \( 953 . \)
c. a. \( 952 ; \) b. 954 с. 953.3 d. 953.4
D. a. \( 953 ; \) b. 954 c. 953.3 d. 952.4
| 3 |
Physics
|
If \( a \neq 0 \) and \( a-\frac{1}{a}=4, \) find:
\( a^{3}-\frac{1}{a^{3}} \)
A . 76
B. 71
c. 45
D. 16
| 2 |
Maths
|
Muscles of heart are
A. Striated and voluntary
B. Nonstriated and voluntary
C. Striated unbranched and involuntary
D. Nonstriated and involuntary
E. Striated, branched and involuntary
| 0 |
Biology
|
If \( x \) and \( y \) are positive integers, the
value of \( p \) in the equation \( p x=y \) is
always
A. positive
B. negative
c. one
D. zero
| 2 |
Maths
|
For a weak electrolyte molar conductance in dilute solution
increases sharply as its concentration in solution is decreased. Give reason.
| 1 |
Chemistry
|
The magnetic materials having negative magnetic susceptibility are
A. non-magnetic
B. para magnetic
c. dia magneticc
D. ferro magnetic
| 3 |
Physics
|
A point on the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}=\frac{\boldsymbol{y}-\mathbf{2}}{\mathbf{2}}= \)
\( \frac{z+1}{3} \) at a distance \( \sqrt{6} \) from the origin
is
This question has multiple correct options
\( \mathbf{A} \cdot\left(\frac{-5}{7}, \frac{-10}{7}, \frac{13}{7}\right) \)
в. (1,2,-1)
\( ^{\mathbf{C}} \cdot\left(\frac{5}{7}, \frac{10}{7}, \frac{-13}{7}\right) \)
D. (-1,-2,1)
| 2 |
Maths
|
The nuclear reactor at Kaiga is a :
A. research reactor
B. fusion reactor
c. breedor reactor
D. power reactor
| 3 |
Physics
|
What is the name given to energy which must be provided in order for a chemical change to occur?
A. Gibbs free energy
B. Activation energy
c. Potential energy
D. Bond energy
E. Kinetic energy
| 1 |
Chemistry
|
The circumference of a circle is \( 22 \mathrm{cm} \)
Then the area is
| 2 |
Maths
|
A compound \( X \) on heating gives a colorless gas. The residue is dissolved
in water to obtain \( Y . \) Excess \( C O_{2} \) is
bubbled through aqueous solution of \( Y \) and \( Z \) is formed. \( Z \) on gentle heating
gives back \( X . \) The \( X \) is:
A \( \cdot C a C O_{3} \)
в. \( C a\left(H C O_{3}\right)_{2} \)
c. \( N a_{2} C O_{3} \)
D. \( N a H C O_{3} \)
| 1 |
Chemistry
|
Find the ratio in which the line \( 2 x+ \)
\( 3 y-5=0 \) divides the line segment
joining the points (8,9) and \( (2,1) . \) Also, find the coordinates of the point of
division.
| 2 |
Maths
|
The first element of group number 15 is:
A. carbon
B. nitrogen
c. oxygen
D. beryllium
| 1 |
Chemistry
|
The resistance of an iron wire is \( 10 \Omega \)
and its temperature coefficient of
resistance is \( 5 \times 10^{-3} /^{o} C . \) A current of
\( 30 \mathrm{mA} \) is flowing in it at \( 20^{\circ} \mathrm{C} \). Keeping potential difference across its ends constant, if its temperature is
increased to \( 120^{\circ} \mathrm{C} \) then the current
flowing in the wire will be (in \( \mathrm{mA} \) )
A . 20
B . 35
c. 10
D. 40
| 3 |
Physics
|
Which of the following conclusions can be drawn from the Rutherford alpha
scattering model?
I. The atom is mostly empty space.
II. Electrons orbit the nucleus of the
atom.
III. The atom has a dense, positively charged nucleus.
A. I only
B. Il only
c. I and II only
D. II and III only
E. I, II, and III
| 3 |
Physics
|
Expand the following using identities \( (x+7)(y+5) \)
| 2 |
Maths
|
What is the black circular aperture in
our eyes and why does it appear black?
A. The aperture is known as iris and it appears black as no light is reflected from it.
B. The aperture is known as pupil and it appears black as all light is reflected from it.
C. The aperture is known as iris and it appears black as all light is reflected from it.
D. The aperture is known as pupil and it appears black as no light is reflected from it.
| 3 |
Physics
|
\( \operatorname{Let} f(x)=\cos 2 x \cdot \cot \left(\frac{\pi}{4}-x\right) \) If \( f \) is
continuous at \( x=\frac{\pi}{4} \) then the value of \( f\left(\frac{\pi}{4}\right) \) is equal to
A . 2
B. -
c. \( \frac{-1}{2} \)
D.
| 2 |
Maths
|
If \( f(x)=\sin 2 x-\cos 2 x, \) find \( f^{\prime}\left(\frac{\pi}{6}\right) \)
| 2 |
Maths
|
A force \( \overrightarrow{\boldsymbol{F}}=\mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}-\mathbf{3} \hat{\boldsymbol{k}} \) is applied at
the point \( P, \) whose position vector is \( \vec{r}=2 \hat{i}-2 \hat{j}-3 \hat{k} . \) What is the
magnitude of the moment of the force about the origin?
A . 23 units
B. 19 units
c. 18 units
D. 21 units
| 2 |
Maths
|
Which condition is not satisified by an
ideal solution?
A \( \cdot \Delta H_{\operatorname{mixing}}=0 \)
B. \( \Delta V_{\text {mixing}}=0 \)
C. \( \Delta S_{\text {mixing}}=0 \)
D. obeyance of Raoult's law
| 1 |
Chemistry
|
Tidal energy works using:
A. average of sea levels of high and low tides.
B. resisting the formation of tides.
C. difference in sea levels between high and low tides
D. using heat energy in tides.
| 3 |
Physics
|
Angular momentum of the disc will be
conserved about
A. centre of mass
B. point of contact
C. a point at a distance \( 3 R / 2 \) vertically above the point of contact
D. a point at a distance \( 4 R / 3 \) vertically above the point of contact
| 3 |
Physics
|
Find the general solution of the
equation \( 4 \cos ^{2} x=1 \)
| 2 |
Maths
|
If \( \left(x^{2}+x y+3 y^{2}\right)=1, \) what will be the
value of \( (x+6 y)^{3} \cdot \frac{d^{2} y}{d x^{2}} ? \)
| 2 |
Maths
|
The sporophyte of Bryophyte is
A. Parasitic
B. Autotrophic
c. Saprophytic
D. Semiparasitic or parasitic
| 0 |
Biology
|
Sum of all the values of \( x \) in the interval
\( [0,100 \pi] \) satisfying the equation
\( \sin x=0 \) is
\( \mathbf{A} \cdot 4950 \pi \)
B. \( 5050 \pi \)
c. \( 5151 \pi \)
D. none of these
| 2 |
Maths
|
\( A D \) is an altitude of an isosceles
triangle \( A B C \) in which \( A B=A C \)
Show that, \( A D \) bisects \( B C \)
| 2 |
Maths
|
Which of the elements below is most
likely to form compounds in which it has an incomplete octet?
A. \( B \)
в. \( C \)
c. \( N \)
D.
E. \( F \)
| 1 |
Chemistry
|
Select correct options.
This question has multiple correct options
A. In hitting or kicking a ball we decrease the time of contact so that large force acts on the ball producing greater acceleration.
B. In catching a ball by drawing hands backwards, increases the time of contact and so, lesser force acts on hands and hands are saved from getting hurt.
C. An athlete is advised to come to stop slowly after finishing a fast race. So that time of stop increases and hence force experienced by him decreases.
D. None of these
| 3 |
Physics
|
The potential energies of first, second
and third Bohr's orbits of \( H e^{+} \) cation
are \( E_{1}, E_{2} \) and \( E_{3} . \) The correct sequence
of these energies is:
A \( . E_{1}>E_{2}>E_{3} \)
B . \( E_{1}=E_{2}>E_{3} \)
c. \( E_{1}=E_{2}=E_{3} \)
D. \( E_{3}>E_{2}>E_{1} \)
| 1 |
Chemistry
|
Let \( [t] \) denote the greatest integer \( \leq t \) and \( \lim _{x \rightarrow 0} x\left[\frac{4}{x}\right]=A . \) Then the function,
\( f(x)=\left[x^{2}\right] \sin (\pi x) \) is discontinuous,
when \( x \) is equal to:
\( A \cdot \sqrt{A} \)
B. \( \sqrt{A+1} \)
c. \( \sqrt{A+5} \)
D. \( \sqrt{A+21} \)
| 2 |
Maths
|
In funaria, the meiosis occurs in
A. capsule/sporangium
B. Gametophore
c. Protonema
D. Gametangia
| 0 |
Biology
|
The sex ratio is the highest in
A. Punjab
B. Harayana
c. Kerala
D. Karnataka
| 0 |
Biology
|
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