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The differential equation of the family of straight lines whose slope is equal to \( y \) intercept.
A \( \cdot(x+1) \frac{d y}{d x}-y=0 \)
B. \( \left(x+1 \frac{d y}{d x}+y=0\right. \)
c. \( \frac{d y}{d x}=\frac{x-1}{y-1} \)
D. \( \frac{d y}{d x}=\frac{x+1}{y+1} \) | 2 | Maths |
\( \sqrt[*]{\frac{x}{1+x^{4}}} d x \)
\( \mathbf{A} \cdot \tan ^{-1} x^{2} \)
B. \( 2 \tan ^{-1} x^{2} \)
c. \( \frac{1}{2} \tan ^{-1} x^{2} \)
D. \( \frac{1}{2} \tan ^{-1} x \) | 2 | Maths |
The following graph represents:
\( \mathbf{A} \cdot \cot ^{-1}(x+1) \)
\( B \cdot \sin ^{-1}\left(x^{4}+1\right) \)
\( \mathbf{c} \cdot \tan ^{-1}\left(x^{3}+1\right) \)
\( D \cdot \cos ^{-1}\left(x^{2}+1\right) \) | 2 | Maths |
\( 2 \mu F \) capacitance has P.D across its two terminals of \( 200 \mathrm{V} . \) It is disconnected
from the battery and when another uncharged capacitance is connected in parallel to it, P.D becomes 20 V. The capacity of another capacitance will be:
A \( .2 \mu F \)
в. \( 4 \mu F \)
c. \( 10 \mu F \)
\( \mathbf{D} \cdot 16 \mu F \) | 3 | Physics |
Two non-reactive gases A and B are present in a container with partial pressures 200 and \( 180 \mathrm{mm} \) of Hg. When
a third non - reactive gas \( C \) is added then total pressure becomes 1 atm then mole fraction of \( \mathrm{C} \) will be:
A . 0.225
B. 0.75
\( c \cdot 0.5 \)
D. none of these | 1 | Chemistry |
An optically active halide when allowed
to react with \( C N^{\ominus} \) gives a racemic mixture, the halide is most likely:
A. primary halide
B. sec. halide
c. tert. halide
D. none of these | 1 | Chemistry |
If \( \triangle A B C \) is right angled at \( B \) and
\( B C=7 c m, A C-A B=1 \mathrm{cm}, \) then
find the value of \( \cos A+\sin A \) | 2 | Maths |
Range of vision of a normal human eye
is from:
\( A \cdot 100 \mathrm{m} \) to \( 25 \mathrm{cm} \)
B. \( 1 \mathrm{km} \) to \( 25 \mathrm{cm} \)
c. Infinity to 25 m
D. Infinity to 25 cm | 3 | Physics |
In the situation shown in figure, what
should be the relation between \( Q \) and \( q \)
so that electric potential at centre of the
square is zero:
A. \( Q=q \)
в. \( Q=3 q \)
c. \( Q=2 q \)
D. \( Q=-3 q \) | 3 | Physics |
A wire of resistance \( 20 \Omega \) is bent to form
a closed square. What is the resistance
across a diagonal of the square. | 3 | Physics |
and mass m. A particle also of mass \( \mathrm{m} \) is fixed at a point \( A \) on the wedge of the disc as in fig. The disc can rotate freely
about a fixed horizontal chord PQ that is
at a distance \( \mathrm{R} / 4 \) from the centre \( \mathrm{C} \) of
the disc. The line AC is perpendicular to
PQ. Initially the disc is held vertical with
the point \( A \) at its highest position. It is
then allowed to fall so that it starts
rotating about PQ.
If the linear speed of the particle as it
reaches its lowest position is \( \boldsymbol{v}= \)
\( \sqrt{x g R} \) Find \( x \) | 3 | Physics |
State the given statement is true or false.
Statement: Mercuric oxide is reduced
by thermal decomposition.
A. True
B. False | 1 | Chemistry |
Assertion
Capital formation in India has been low
due to population explosion.
Reason Rising population has led to increased spending on consumption, while very little part of the national income is available for savings and investments
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 |
Write general formula of Grignard
reagent. | 1 | Chemistry |
If \( \cos (\alpha+\beta)=\frac{4}{5} \) and \( \sin (\alpha-\beta)=\frac{5}{13} \)
where \( \alpha, \beta \) lie between \( 0^{\circ} \) and \( 45^{\circ}, \) then
the value of \( \tan 2 \alpha \) is
A \( \cdot \frac{56}{33} \)
в. \( \frac{46}{33} \)
c. \( \frac{14}{33} \)
D. \( \frac{16}{33} \) | 2 | Maths |
Fill in the blank.
It becomes \( _{-}-_{-}-_{-}-_{-} \) to cut vegetable with a sharp edged knife because the pressure is
A. easy, more
B. difficult, more
c. easy, less
D. difficult, less | 3 | Physics |
The Young's double slit experiment is
done in a medium of refractive index
4/3. A light of 600 nm wavelength is falling on the slits have \( 0.45 \mathrm{mm} \)
separation. The lower slit \( S_{2} \) is covered
by a thin glass sheet of thickness 10.4
mm and refractive index 1.5. The
interference pattern is observed on a
screen placed at \( 1.5 \mathrm{m} \) from the slits as
shown in the fig.
(All wavelength in this problem are for
the given medium of refractive index
4/3. Ignore dispersion.) Find the location
of central maxima (bring fringe with
zero path difference ) on the y-axis. | 3 | Physics |
Find the sin angle between the vectors \( A=3 i-4 j+5 k \) and \( B=i-j+k ? \) | 2 | Maths |
In a meter bridge, the balance point is obtained at \( 40 \mathrm{cm} . \) If a resistance equal
to that in the left gap is shunted across
itself, the new balance point is:
\( \mathbf{A} \cdot 40 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 25 \mathrm{cm} \)
D. \( 32 \mathrm{cm} \) | 3 | Physics |
Number of primary carbon atoms in the given compound is:
\( \boldsymbol{C}-\underbrace{\boldsymbol{C}}_{\boldsymbol{C}}-\boldsymbol{C}-\dot{\boldsymbol{C}}-\boldsymbol{C} \)
\( A \cdot 2 \)
B. 5
\( c \cdot 4 \)
\( D \) | 1 | Chemistry |
The number of molecules present in 2
grams of helium at \( 273^{\circ} \mathrm{C} \) and 1520
mm Hg pressure are:
\( \left[N_{A}=6.02 \times 10^{23}\right] \)
A. \( 3.01 \times 10^{23} \)
B. \( 6.02 \times 10^{23} \)
c. \( 3.01 \times 10^{22} \)
D. \( 6.02 \times 10^{22} \) | 1 | Chemistry |
Two stones are thrown up
simultaneously from the edge of a cliff
\( 200 \mathrm{m} \) high with initial speeds of \( 15 \mathrm{m} \)
\( s^{-1} \) and \( 30 \mathrm{m} s^{-1} \) respectively. The time
variation of the relative position of the
second stone with respect to the first as
shown in the figure. The equation of the
liner part is
\( \mathbf{A} \cdot x_{2}-x_{1}=50 \mathrm{t} \)
B \( \cdot x_{2}-x_{1}=10 t \)
\( \mathbf{c} \cdot x_{2}-x_{1}=15 t \)
D. \( x_{2}-x_{1}=20 t \) | 3 | Physics |
The total number of amino acids in a
molecule of the Hypoglycemic hormone is:
A . 30
B . 21
\( c \cdot 5 \)
D. 27 | 1 | Chemistry |
Electrovalent bond or ionic bond is
formed by:-
A. Sharing of electrons
B. Donation of electrons
c. Transfer of electrons
D. None of these | 1 | Chemistry |
Which of the following statement is not
correct about Ellingham diagram?
A. \( \Delta G \) increases with an increase in temperature
B. It consists of plots of \( \Delta_{f} G^{\circ} \) vs \( T \) for formation of oxides
C. A coupling reaction can be well expressed by this diagram
D. It express the kinetics of the reduction process | 1 | Chemistry |
If the eccentricity of an ellipse is \( \frac{5}{8} \) and the distance between its foci is \( 10, \) then
its latus rectum is
A \( \cdot \frac{39}{4} \)
B. 12
c. 15
D. \( \frac{37}{2} \) | 2 | Maths |
The production of saleable steel in some of the steel plants of our country during 1999 is given below:
Plant \( \quad \) Bhilai Durgapur \( \quad \) Rourke
Production
In thousand tonnes
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big division = 20 thousand
tonnes. | 2 | Maths |
Phytotron is
A. A controlled condition chamber for plants
B. Leaf culture process
C . Special culture of seeds
D. Root culture process | 1 | Chemistry |
Magnification produced by spherical
lens is \( +2.5 . \) What is the nature of
image?
A. Virtual, erect
B. Real, invented
c. Real, erect
D. None | 3 | Physics |
For the fuel cell reaction, \( 2 H_{2}+O_{2} \rightarrow \)
\( 2 H_{2} O, \Delta G=-475 k J \)
The value of \( \boldsymbol{E}^{o} \) cell is:
A . \( 1.23 \mathrm{v} \)
B. 2.46
c. \( 0.615 \mathrm{v} \)
D. 0.31 | 1 | Chemistry |
Find the vector equation of the line joining (1,2,3) and (-3,4,3) and show pependicular to the z-axis | 2 | Maths |
What is the oxidation number of \( C l \) in
the \( C l O_{3}^{-} \) ion?
\( A \cdot-1 \)
B. +5
\( c \cdot-5 \)
\( D \cdot+7 \) | 1 | Chemistry |
The number of \( s p^{2} \) hybridized carbon
atoms in the given compound is:
\[
\mathbf{H C} \equiv \mathbf{C}-\mathbf{C H}_{2}-\mathbf{U}-\mathbf{C H}_{2}-\mathbf{C H}=\mathbf{C H}_{2}
\]
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
\( D \) | 1 | Chemistry |
\( \int \frac{t^{2}+t}{t} d t \) | 2 | Maths |
The notation for an isotope of sodium
\( _{11}^{23} N a . \) Which row gives the composition
of a neutral atom of this isotope of
sodium?
\( \begin{array}{lll}\text { number } & \text { number } & \text { number } \\ \text { of } & \text { of } & \text { of } \\ \text { protons } & \text { neutrons } & \text { electrons } \\ \text { A } & 11 & 12 & 11 \\ \text { B } & 11 & 12 & 12 \\ \text { C } & 11 & 23 & 11 \\ \text { D } & 12 & 11 & 12\end{array} \)
\( A \)
B. B
\( c \cdot c \)
\( D . \) | 3 | Physics |
Which type of wave is produce in a
resonance tube?
A. longitudinal
B. transverse
c. transverse stationary
D. longitudinal stationary | 3 | Physics |
Calculate the de Brogile wavelength of a photon whose linear momentum has a magnitude of \( 3.3 \times 10^{-23} k g m / s \)
A. 0.0002 nm
B. \( 0.002 \mathrm{nm} \)
c. \( 0.02 \mathrm{nm} \)
D. \( 0.2 \mathrm{nm} \)
\( E \cdot 2 \mathrm{nm} \) | 3 | Physics |
Among \( N_{2} O, S O_{2}, I_{3}^{+} \) and \( I_{3}^{-}, \) the linear
species are \( N_{2} O \) and \( I_{3}^{-} \)
A . True
B. False | 1 | Chemistry |
Plants, but not animals, can convert fatty acids to sugars by a series of reactions called
A. photosynthesis
B. Krebs cycle
c. glycolysis
D. glyoxylate cycle | 0 | Biology |
The number of lines which pass through point (2,-3) and are at a distance 8 from point (-1,2) is
\( A \cdot \infty \)
B. 4
\( c \cdot 2 \)
D. | 2 | Maths |
For the reaction \( \mathbf{H}_{2}(\mathbf{g})+\mathbf{I}_{2}(\mathbf{g}) \rightleftharpoons \)
\( 2 H I(g) \)
\( \mathbf{K}_{\mathbf{c}}=\mathbf{6 6 . 9} \) at \( \mathbf{3 5 0}^{\circ} \mathbf{C} \) and \( \mathbf{K}_{\mathbf{c}}=\mathbf{5 0 . 0} \mathbf{a t} \)
\( 448^{\circ} \mathrm{C} . \) The reaction has:
\( \mathbf{A} \cdot \Delta H=+v e \)
B. \( \Delta H=-v e \)
c. \( \Delta H=Z \) ero
D. \( \Delta H= \) Not found the signs | 1 | Chemistry |
The degree of dissociation of
\( \boldsymbol{C a}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) in a dilute aqueous solution
containing 7 g of salt per 100 g of water at \( 100^{\circ} \mathrm{C} \) is \( 75 \% \). The vapour pressure of solution in \( \mathrm{mm} \) is \( x, \) then find the
value of \( x / 150 \) to the nearest integer. | 1 | Chemistry |
According to the Arrhenius concept
formation of \( \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \) ions in solution
is responsible for
A. basic substance.
B. acidic substance
c. neutral substance
D. slightly acidic substance | 1 | Chemistry |
Very short answer type. Name the monomer(s) of the following dimers/polymers proteins | 1 | Chemistry |
Let \( n \) be an odd integer greater than 1
and let \( c_{1}, c_{2}, \cdots, c_{n} \) be integers. For
each permutation \( \boldsymbol{a}=\left(\boldsymbol{a}_{1}, \boldsymbol{a}_{2}, \cdots, \boldsymbol{a}_{n}\right) \)
of \( (1,2, \cdots, n) \) define \( S(a)=\sum_{i=1}^{n} c_{i} a_{i} \)
Prove that there exist permutations
\( a \neq b \) of \( \{1,2, \cdots, n\} \) such that \( n ! \) is a
divisor of \( \mathrm{S}(\mathrm{a})-\mathrm{S}(\mathrm{b}) \)
A \( \cdot \frac{1}{2} n !(n !-1) \equiv \frac{1}{2}(n+1) ! \sum_{i=1}^{n} c_{i}(\bmod n !) . \) Because \( n>1 \)
is odd, the right-hand side is congruent to 0 mod \( n ! \) while the lefthand side is not, a contradiction
B \( \cdot \frac{1}{2} n !(n !+1) \equiv \frac{1}{2}(n+1) ! \sum_{i=1}^{n} c_{0}(\text { modn! }) . \) Because \( n>1 \)
is odd, the right-hand side is congruent to 0 mod \( n ! \) while the lefthand side is not, a contradiction.
c. \( \frac{1}{2} n !(n !-1) \equiv \frac{1}{2}(n-1) ! \sum_{i=1}^{n} c_{0}(\text { modn! }) . \) Because \( n> \)
is odd, the right-hand side is congruent to 0 mod \( n ! \) while the lefthand side is not, a contradiction.
D. None of the above | 2 | Maths |
\( A \) and \( B \) are events with \( P(A)= \) \( \mathbf{0 . 6}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 7} \) then compute \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( B) \) | 2 | Maths |
Aerosols, decrease primary productivity by
A. Decreasing \( O_{2} \) concentration
B. Preventing \( N_{2} \) fixation
c. Reducing photosynthesis
D. None of the above | 1 | Chemistry |
A monochromatic beam of light falls on Young's double slit experiment
apparatus as shown in figure. A thin
sheet of glass is inserted .in front of
lower slit \( S_{2} \)
The central bright fringe can be
obtained:
\( A \cdot A t O \)
B. Above \( O \)
c. Below \( O \)
D. Anywhere depending on angle \( \theta \), thickness of plate \( t \), and refractive index of glass \( \mu \) | 3 | Physics |
Find \( \frac{d y}{d x}, \) when \( y=\frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}} \) | 2 | Maths |
The odds against a certain event are 5 to 2 and the odds in a fvour of another
event independent to the former are 6 to
5. Find the probability that none of the events will occur. | 2 | Maths |
Find the equation of parabola with vertex (0,0)\( \& \) focus at (0,2) | 2 | Maths |
Equations relating to acidic properties of an aq. solution of HCl gas is/are:
A \( \cdot H C l(g)+H_{2} O \rightleftharpoons H_{3} O^{+}+C l \)
в. \( Z n(O H)_{2}+2 H C l \rightarrow Z n C l_{2}+2 H_{2} O \)
c. \( M n O_{2}+4 H C l \rightarrow M n C l_{2}+C l_{2}+2 H_{2} O \)
D. all of the above | 1 | Chemistry |
Study involving both electricity and magnetism is called
A. electromagnetism
B. magnetoelectricism
c. electricmagnetism
D. magneticelectromerism | 3 | Physics |
The frequency of generator \( (\mathrm{AC}) \) is measured using:
A. multimeter
B. AVO meter
c. tachometer
D. speedometer | 3 | Physics |
Ergocalciferol is name of vitamin:
A. \( A \)
в. \( B \)
c. \( C \)
\( D \cdot D_{2} \) | 1 | Chemistry |
Which is the correct sequence of the
components of a reflex arc?
A. Receptors - Muscle - Sensory neuron - Motor neuron Spinal cord
B. Receptors - Motor neuron - Spinal cord - Sensory neuron - Muscle
C. Receptors - Spinal cord - Sensory neuron - Motor neuron- Muscle
D. Receptors - Sensory neuron - Spinal cord - Motor neuron - Muscle | 0 | Biology |
Find the integrals of the functions.
i) \( \sin ^{3} x \cos ^{3} x \)
ii) \( \sin x \sin 2 x \sin 3 x \)
iii) \( \sin 4 x \sin 8 x \)
iv \( \frac{1-\cos x}{1+\cos x} \)
v) \( \frac{\cos x}{1+\cos x} \) | 2 | Maths |
A gas \( X \) bleaches the colour of flowers
by reduction while the other gas \( Y \) bleaches by oxidation. These two gases
\( X \) and \( Y \) are respectively:
A. \( C O \) and \( C O_{2} \)
B. \( N H_{3} \) and \( S O_{3} \)
\( \mathrm{c} \cdot \mathrm{CO}_{2} \) and \( \mathrm{Br}_{2} \)
D. \( S O_{2} \) and \( C l_{2} \) | 1 | Chemistry |
Considre the sequence \( \left(a_{n}\right) n \geq 0 \) given
by the following relation: \( a_{0}=4, a_{1}= \)
\( 22, \) and for all \( n \geq 2, a_{n}=6 a_{n-1}- \)
\( a_{n-2} . \) Prove that there exist sequences
of positive integers \( \left(x_{n}\right) n \geq \)
\( \mathbf{0},\left(\boldsymbol{y}_{n}\right) \boldsymbol{n} \geq \mathbf{0} \) such that \( \boldsymbol{a}_{\boldsymbol{n}}=\frac{\boldsymbol{y}_{\boldsymbol{n}}^{\boldsymbol{2}}+\boldsymbol{7}}{\boldsymbol{x}_{\boldsymbol{n}}-\boldsymbol{y}_{\boldsymbol{n}}} \)
for all \( n \geq 0 \) | 2 | Maths |
Which of the following doesn't show that
air has pressure?
A. Ball falling to the ground
B. Flying a kite
c. Riding a bicycle against the wind
D. none of these | 3 | Physics |
At \( 380^{\circ} C, \) the half life period for the first
order decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is \( \boldsymbol{3} \boldsymbol{6} \boldsymbol{0} \)
min. The energy of activation of the
reaction is \( 200 k J \) mol \( ^{-1} \). Calculate the
time required for \( 75 \% \) decomposition at
\( 450^{\circ} \mathrm{C} \) | 1 | Chemistry |
If the source is now changed to green light of wavelength \( 10^{-7} m \) and a new glass plate is placed in place of the previous glass plate, the central fringe shifts to a position initially occupied by the sixth bright fringe due to red light without the glass plate. What is refractive index of new glass plate?
A \( .2 .6 \mu m \)
в. \( 1.6 \mu m \)
c. \( 1.2 \mu m \)
D. \( 2.2 \mu m \) | 3 | Physics |
For the function \( \boldsymbol{f}(\boldsymbol{x})=\left|\boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\boldsymbol{6}\right| \)
the right hand derivative \( f^{\prime}(2+) \) is
equal to. | 2 | Maths |
Is this device feasible?
A. Yes
B. no
C. depends on the availability of material
D. maybe or may not be | 3 | Physics |
For constant non zero mass, momentum
versus velocity graph is a:
A. straight line parallel to \( x \) - axis
B. straight line parallel to y- axis
C. straight line passing through origin
D. straight line passing through y- axis with an intercept | 3 | Physics |
The value of
\( \lim _{x \rightarrow \infty} \frac{\cot ^{-1}\left(x^{-a} \log _{a} x\right)}{\sec ^{-1}\left(a^{x} \log _{x} a\right)},(a>1) \) is equal
to
A . 1
B.
c. \( \pi / 2 \)
D. does not exist | 2 | Maths |
Which of the following is NOT soluble in
water?
A. Salt
B. Sugar
c. oxygen
D. sand | 1 | Chemistry |
Assertion
\( \boldsymbol{S} \boldsymbol{c}(\boldsymbol{Z}=\mathbf{2 1}) \) is placed in d-block
elements.
Reason
Last filling electron goes into \( 3 d- \) suborbit.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct | 1 | Chemistry |
According to 1st law of Thermodynamics,
A. Energy can be created but not destroyed
B. Energy cannot be created but can be destroyed
C. Energy can be created and destroyed
D. Energy can not be created nor destroyed | 3 | Physics |
Select the correct statement.
This question has multiple correct options
A. At radioactive equilibrium, the number of atoms of \( A \) and \( B \) are in the inverse ratio of their average life.
B. In beta decay, all the emitted electrons have altogether different energy.
C. If \( n / p \) is lower than required for the belt of stability, either positron emission or \( \mathrm{K} \) -electron capture must be shown.
D. Like electrons energy level in atoms, nuclear energy level also exist. | 1 | Chemistry |
If this enzyme were to be absent in our small intestine, digestion of proteins in our body would be severely affected.
A. Pancreatic amylase
B. Maltase
c. Lipase
D. Enterokinase | 0 | Biology |
Match the List I with the List II. | 1 | Chemistry |
If \( y=e^{m \sin ^{-1} x}, \) then show that \( (1- \)
\( \left.x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-m^{2} y=0 \) | 2 | Maths |
Which element is considered
radioactive among the options given below?
A. Sodium
B. Gold
c. Thorium
D. Neon | 1 | Chemistry |
Find the domain of the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\sqrt{|\boldsymbol{x}|-\boldsymbol{x}}} \)
A. \( [0, \infty) \)
(n)
в. \( (-\infty, 0) \)
\( c \cdot[1, \infty) \)
D. \( (-\infty, 0 \) | 2 | Maths |
Which of the following is wrong
statement?
A \( \cdot D=\frac{1}{f} \) where \( f \) is focal length and \( D \) is optical power of lens.
B. Power is in diopter when \( f \) is in meters.
C. Power is in diopter and does not depend upon the system of unit used to measure \( f \)
D. \( D \) is positive for convergent lens and \( D \) is negative for divergent lens. | 3 | Physics |
According to periodic law elements with similar properties fall in the vertical column called a
A. same, group
B. same, period
c. different, group.
D. none of these | 1 | Chemistry |
If the sum to \( n \) terms of an AP is
\( \frac{4 n^{2}-3 n}{4} \) then the \( n^{t h} \) term of the AP is equal to
A \( \cdot \frac{5 n-1}{4} \)
в. \( \frac{8 n-7}{4} \)
c. \( \frac{3 n^{2}-2}{4} \)
D. \( \frac{7 n-8}{4} \) | 2 | Maths |
Equation of two equal sides of a triangle are the lines \( 7 x-y+3=0 \) and \( x+ \)
\( y-3=0 \) and the third side passes
through the point \( (1,-10), \) then the equation of the third side can be
This question has multiple correct options
A . \( x-3 y=31 \)
B. \( 3 x+y+7=0 \)
c. \( x+3=0 \)
\( \mathbf{D} \cdot y=3 \) | 2 | Maths |
The value of \( c \) in Lagranges mean value
theorem for \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{l} \boldsymbol{x}^{2}+\boldsymbol{m} \boldsymbol{x}+ \)
\( \boldsymbol{n},(\boldsymbol{l} \neq \mathbf{0}) \) on \( [\boldsymbol{a}, \boldsymbol{b}] \) is
A \( \cdot \frac{a}{2} \)
B. \( \frac{b}{2} \)
c. \( \frac{(a-b)}{2} \)
D. \( \frac{(a+b)}{2} \) | 2 | Maths |
An electron in the ground state of
hydrogen has an angular momentum \( L_{1} \)
and an electron in the first excited state
of lithium has an angular momentum
\( \boldsymbol{L}_{2} . \) Then
A \( \cdot L_{1}=L_{2} \)
В. \( L_{1}=4 L_{2} \)
\( \mathbf{c} \cdot L_{2}=2 L_{1} \)
D. \( L_{1}=2 L_{2} \) | 3 | Physics |
Which of the following is a restatement of first law of thermodynamics:
A. Guy-Lassac's Law
B. The principle of entropy
C. The principle of enthalpy
D. conservation of energy
E. Avogadro's hypothesis | 3 | Physics |
Given: Parallelogram \( A B C D \) in which
diagonal \( A C \) and \( B D \) intersect at \( M \)
Prove \( M \) is the mid-point of \( L N \) | 2 | Maths |
Diazomethane was photolysed to
generate singlet carbine which was
treated with cis-2-butene. The main
product(s) of the reaction is/are:
A. cis-1, 2-dimethylcyclopropane
B. trans-1, 2-dimethylcyclopropane
c. mixture of \( (A) \) and \( (B) \)
D. Ethylcyclopropane | 1 | Chemistry |
Pressure exerted by a body on a surface
is
A. force \( \times \) area
B. force \div area
c. area \( \div \) force
D. force \div volume | 3 | Physics |
What is the magnitude of the total force
on a driver by the racing car he operates, as it accelerates horizontally along a straight line from rest to \( 60 m / s \) in \( 8.0 s \text { (mass of the driver }=80 k g) \) | 3 | Physics |
Which of the following statements
about ozone is true?
A. Ozone layer is benifical to us because ozone cuts the ultraviolet radiationof the sun
B. The conversion of ozone to oxygen is an endothermic reaction
C. Ozone is triatomic linear molecule
D. Ozone layer is harmul as it cuts out radiation useful for photosynthesis | 1 | Chemistry |
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \frac{N a N O_{2}+\boldsymbol{H} C l, \mathbf{0}^{o} \boldsymbol{C}}{\longrightarrow} \)
\( \boldsymbol{X} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{w} \boldsymbol{a} \boldsymbol{r} \boldsymbol{m}}{\boldsymbol{Y}} \boldsymbol{Y} \)
In the above reaction, \( \boldsymbol{Y} \) is:
\( \mathbf{A} \cdot C_{6} H_{5} C l \)
в. \( C_{6} H_{6} \)
c. \( C_{6} H_{5} O H \)
D. \( C_{6} H_{5} C H O \) | 1 | Chemistry |
mRNA part that codes for the amino acid serine, is:
A. AMP
B. ADP
c. uca
D. d ATP | 1 | Chemistry |
The distance of the point (1,-5,9) from the planer. \( (\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\boldsymbol{k}})=\mathbf{5} \)
measured long the line \( r=\hat{i}+\hat{j}+\hat{k} \) is
A \( 3 \sqrt{5} \)
5
B. \( 10 \sqrt{3} \)
\( c \cdot 5 \sqrt{3} \)
D. \( 3 \sqrt{10} \) | 2 | Maths |
Match the column I with Column II and
select the correct option from the codes
given below.
(a) \begin{tabular}{l|l|l}
column I & & Column II \\
& \\
Hottest zone of candle flame & (i) & Zone of unburunt wax vapours. \\
Yellow zone of candle flame & (ii) & Nonluminous zone \\
Black innermost zone of the candle flame & (iii) & Incomplete combustion zone/ \\
\hline
\end{tabular}
(b)
\( (c) \)
\( A \)
(a) - (i), (b) - (ii), (c) - (iii)
B. (a) - (ii), (b) - (i), (c) - (iii)
c. (a) - (i), (b) - (iii), (c) - (ii)
D. (a) - (ii), (b) - (iii), (c) - (i) | 1 | Chemistry |
If the Vant Hoff factor for \( \mathbf{0 . 1} \mathbf{M} \)
\( B a\left(N O_{3}\right)_{2} \) solution is 2.74 , the degree of dissociation is:
A . 0.87
в. 0.74
c. 0.91
D. 87 | 1 | Chemistry |
\( = \)
\( u \)
\( \delta \) | 1 | Chemistry |
An atom 'X' has a mass number of 12
and contains 6 electrons. State the
atomic number of 'X' and the number of
neutrons it contains.
\( A \cdot 6,6 \)
B. 6, 12
\( c \cdot 12,6 \)
D. 12, 12 | 1 | Chemistry |
Define self inductance of a coil. Derive
the expression for magnetic energy stored in the inductor of inductance \( L \)
carrying current \( \boldsymbol{I} \) | 3 | Physics |
Very Short Answer Type Question. How is atmosphere important for us? | 0 | Biology |
Solve \( \lim _{x \rightarrow 0} \frac{\sin x}{\sqrt{x^{2}}} \)
\( \mathbf{A} \cdot 1 \)
B . -1
\( \mathbf{c} \cdot 0 \)
D. doesn't exist | 2 | Maths |
What will be the radius of curvature of a
concave mirror whose focal length is 25
\( \mathrm{cm} ? \) | 3 | Physics |
Which of the following is the cell reaction that occurs when the following half-cells are combined?
\( \boldsymbol{I}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{I}^{-}(\boldsymbol{1} \boldsymbol{M}) ; \boldsymbol{E}^{o}=+\boldsymbol{0 . 5 4} \mathbf{V} \)
\( \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{B} \boldsymbol{r}^{-}(\boldsymbol{1} \boldsymbol{M}) ; \boldsymbol{E}^{o}=+\mathbf{1} . \boldsymbol{0} \boldsymbol{9} \)
\( \mathbf{V} \)
A \( \cdot 2 B r^{-}+I_{2} \rightarrow B r_{2}+2 I^{-} \)
В \( \cdot I_{2}+B r_{2} \rightarrow 2 I^{-}+2 B r^{-} \)
c. \( 2 I^{-}+B r_{2} \rightarrow I_{2}+2 B r \)
D. \( 2 I^{-}+2 B r^{-} \rightarrow I_{2} B r_{2} \) | 1 | Chemistry |
If \( \lim _{x \rightarrow \infty} f(x) \) exists and is finite and nonzero and if \( \lim _{x \rightarrow \infty}\left\{f(x)+\frac{3 f(x)-1}{f^{2}(x)}\right\}=3, \) then the
value of \( \lim _{x \rightarrow \infty} f(x) \) is
A . 2
B.
\( c \cdot-1 \)
D. 3 | 2 | Maths |
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