Question Paper (Section wise)

1) 
y = x^{2 }+ constant

y^{2 }= x + constant

y^{2 }= x^{2 }+ constant

xy = constant


2) Rod of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient if linear expansion α/°C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod when it temperature rises △TK. Young’s modulus, Y for this metal is


3) Two masses m and are connected at the two ends of a massless rigid rod of length ℓ. The rod is suspended by a thin wire of torsional constant k at the center of mass of the rodmass system (see figure). Because of torsional constant k, the restoring torque is τ = k θ for angular displacement θ. If the rod is rotated by θ_{0} and released, the tension in it when it passes through its mean position will be


4) A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is:

11 × 10^{5 }W

11 × 10^{3} W

11 × 10^{4 }W

11 × 10^{5 }W


5) The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1cm and 34.2±0.1cm, respectively. What will be the value of its volume in appropriate significant figures?

4264 ± 81cm^{3}

4264 ± 81.0cm^{3}

V = 4260 ± 80 cm^{3}

4300 ± 80cm^{3}


6) A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity is SI units equal to that of its acceleration. Then, its periodic time in seconds is:


7) In the circuit shown, The switch S_{1 }is close at time t = 0 and the switch S_{2} is kept open. At some later time (t_{0}), the switch S_{1} is opened and S_{2} is closed. The behaviour of the current I as a function of time‘t’ is given by:


8) An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be:

2.26×10^{3} m/s away from the lens

0.92×10^{3} m/s away from the lens

3.22×10^{3} m/s towards the lens

1.16×10^{3} m/s towards the lens


9) In the figure shown below, the charge on the left plate of the μF Capacitor is 30μC. The charge on the right place of the 6μF capacitor is

12μC

+12μC

18μC

+18μC


10) An alphaparticle of mass m suffers 1deminisional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is:

2 m

3.5 m

1.5 m

4 m


11) In the given circuit diagram, the currents, I_{1} = 0.3 A, I_{4} = 0.8 A and I_{5} = 0.4 A, are flowing as shown. The currents I_{2}, I_{3} and I_{6}, respectively are:

1.1 A, 0.4 A, 0.4A

1.1 A, 0.4 A, 0.4A

0.4 A, 1.1 A, 0.4A

0.4 A, 0.4 A, 0.4A


12) A simple harmonic motion is represented by:
The amplitude and time period of the motion are:


13) A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when:

R = 0.001 r

R = 1000 r

R = 2r

R = r


14) The magnetic field of an electromagnetic wave is given by:
The associated electric field will be:


15) Calculated the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelenght 500 nm coming from a star.

457.5 × 10^{9} radian

610 × 10^{9}radian

305 × 10^{9} radian

152.5 × 10^{9} radian


16) If ‘M’ is the mass of water that rises in a capillary tube of radius ‘r’, then mass of water which will rise in a capillary tube of radius ‘2r’ is:

4 M


M

2 M


17) For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be:

80 m/s

80 m/s

100 m/s

100 m/s


18) A solid sphere of mass ‘M’ and radius ‘a’ is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance ‘3a’ from the centre will be:


19) The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is: [Take µ_{0} = 4π × 10^{7} NA^{2}]

9µ T

1µ T

3µ T

18µ T


20) The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used?


21) A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic diploe moment of circular loop will be ______×

22) A galvanometer of resistance 100 Ω has 50 division on its scale and has sensitivity of 20 µ A/ division. It is to be converted to a voltmeter with three ranges, of 02 V, 010 V and 020 V. For the given case the closed value of total resistance when connected in series is ______ kΩ.

23) For the given circuit what will be the output for logic gate when both input A & B are 1 (high)?

24) A damped harmonic oscillator has a frequency of 5 oscillations per seconds. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop toof the original amplitude is closed to _______ sec.

25) The election field in a region is given by where E is in NC1 and x in meters. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = = 1 is V1 and that at x= 5 is V_{2} then V_{1} – V_{2} is ______ V.

 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15

 16
 17
 18
 19
 20
 21
 22
 23
 24
 25

1) The correct decreasing order for acidic strength is

NO_{2}CH_{2}COOH > FCH_{2}COOH > CNCH_{2}COOH > CICH_{2}COOH

FCH_{2}COOH > NCCH_{2}COOH > NO_{0}CH_{2}COOH > CICH_{2}COOH

CNCH_{2}COOH > O_{2}NCH_{2}COOH > FCH_{2}COOH > CICH_{2}COOH

NO_{2}CH_{2}COOH > NCCH_{2}COOH > FCH_{2}COOH > CICH_{2}COOH


2) Number of stereo centers present in linear and cyclic structures of glucose are respectively

4 & 5

5 & 5

4 & 4

5 & 4


3) For emission line of atomic hydrogen from n_{1}= 8 to n_{f }= n, the plot of wave number against will be (The Rydberg constant, R_{H} is in wave number unit)

Linear with intercept – R_{H}

Non linear

Linear with slope R_{H}

Linear with slope – R_{H}


4) An organic compound ‘A’ is oxidised with Na_{2}O_{2} followed by boiling with HNO_{3}. The resultant solution is then treated with ammonium molybdate to yield a yellow precipitate. Based on above observation, the element present in the given compound is:

Phosphorus

Sulphur

Nitrogen

Fluorine


5) The reaction that is NOT involved in the ozone layer depletion mechanism in the stratosphere is:



CH_{4} + 2O_{3} ⟶ 3CH_{2} = o + 3H_{2}O



6) The electrolytes usually used in the electroplating of gold and silver, respectively, are:

[Au(CN)_{2}]^{} and [Ag(CN)_{2}]^{}

[Au(CN)_{2}]^{} and [AgCl_{2}]^{}

[Au(OH)_{4}]^{} and [Ag(OH)_{2}]^{}

[Au(NH_{3})_{2}]^{+} and [Ag(CN)_{2}]^{}


7) For the cell different half cells and their standard electrode potentials are given below:
If = −0.76 V, Which cathode will give a maximum value of E^{⁰}_{cell }per electron transferred?

Ag^{+} / Ag

Fe^{3} +/Fe^{2+}

Au^{3} + /Au

Fe^{2+ }/ Fe


8) The amphoteric hydroxide is:

Be(OH)_{2}

Ca(OH)_{2}

Mg(OH)_{2}

Sr(OH)_{2}


9) Match the ores (column A) with the metals (column B)

I – a, II – b, III – c, IV  d

I – c, II – d, III – b, IV  a

I –c, II – d, III – a, IV  b

I – b, II – c, III – d, IV  a


10) Chlorine on reaction with hot and concentrated sodium hydroxide gives:

Cl^{} and ClO_{3}^{}

Cl^{} and ClO^{}

ClO_{3}^{} and ClO_{2}^{}

Cl^{} and ClO_{2}^{}


11) The element that shows greater ability to form pπ  pπ multiple bonds, is:

Sn

C

Ge

Si


12) Glucose and Galactose are having identical configuration in all the positions except position.

C – 4

C – 3

C – 5

C – 2


13) The major product obtained in the following reaction is:


14) The increasing order of basicity of the following compounds is:

(d) < (b) < (a) < (c)

(a) < (b) < (c) < (d)

(b) < (a) < (c) < (d)

(b) < (a) < (d) < (c)


15) For the solution of the gases w, x, y and z in water at 298 K, the Henrys law constants (K_{H}) are 0.5, 2 35 and 40 kbar, respectively. The correct plot for the given data is:


16) The ore that contains the metal in the form of fluoride is:

saphalerite

malachite

magnetite

cryolite


17) For any given series of spectral lines of atomic hydrogen, let ∆⊽ = ∆⊽_{max}  ∆⊽_{min} difference in maximum and minimum frequencies in cm^{1}. the ration ∆⊽_{Lymann / }∆⊽_{Balmer}

5 : 4

4 : 1

9 : 4

27 :5


18) C_{60}, an allotrope of carbon contains:

20 hexagons and 12 pentagons.

12 hexagons and 20 pentagons.

18 hexagons and 14 pentagons.

16 hexagons and 16 pentagons.


19) The correct match between ItemI and ItemII is:

a → III, b → I, c → II, d → IV

a → IV, b → II, c → I, d → III

a → II, b → IV. c → I, d → III

a → III, b → I, c → IV, d → II


20) The crystal field stabilization energy (CFSE) of [Fe(H_{2}O)_{6}]Cl_{2} and K_{2}[NiCl_{4}], respectively, are :

–0.4∆_{o} and –0.8∆_{t}

–0.4∆_{o} and –1.2∆_{t}

–2.4∆_{o} and –1.2∆_{t}

–0.6∆_{o} and –0.8∆_{t}


21) 20 mL of 0.1 M H2SO4 is added to 30 mL of 0.2 M NH4OH solution. The pH of the resultant mixture is [pkb of NH4OH = 4.7]

22) 5.1 g NH_{4}SH is introduced in 3.0 L evacuated flask at 327°C. 30% of the solid NH_{4 }SH decomposed to NH_{3 }and H_{2}S as gases. The K_{p} in atm^{2} of the reaction at 327°C is
(R = 0.082 L atm mol^{1 }k ^{1}, Molar mass of S = 32g mol^{1}, molar mass of N = 14g mol^{1})

23) If the de Brogile wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5πa0 (a0 is Bohr radius), then the value of n/z is:

24) The calculated spin only magnetic moments (BM) of the cationic species of is

25) The mole fraction of a solvent in aqueous solution of a solute is 0.8. The molality (in mol kg1) of the aqueous solution is

 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15

 16
 17
 18
 19
 20
 21
 22
 23
 24
 25

1) Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true?

The lines are concurrent at the point

Each line passes through the origin

The lines are all parallel

The lines are not concurrent


2) For any , the expression 3(sinθ – cosθ)^{4} + 6(sinθ + cosθ)^{2} + 4 sin^{6}θ equals:

13 – 4cos^{2}θ + 6 sin^{2} θcos^{2}θ

13 – 4 cos^{6} θ

13 – 4cos^{2}θ + 6cos^{4}θ

13 – 4 cos^{4}θ + 2sin^{2}cos^{2}θ


3) Let f : R → R be a function defined as
Then f is:

continuous if a = 5 and b = 5

continuous if a = 5 and b = 10

continuous if a = 0 and b = 5

not continuous for any values of a and b


4) If the area of an equilateral triangle inscribed in the circle, x^{2 }+ y^{2 }+ 10x + 12y + c = 0 is 27 sq. units then c is equal to:

13

20

25

25


5) The value of cot is:


6) With the usual notation, in ∆ABC, if ∠A + ∠B = 120°, then the ratio ∠A : ∠B, is:

7:1

5:3

9:7

3:1


7) The value of the integral (where [x] denotes the greatest integer less than or equal to x) is:

0

sin 4

4

4 – sin 4


8) The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of items is. Then the common ratio of this series is:


9) Equation of a common tangent to the parabola y^{2} = 4x and the hyperbola xy = 2 is:

x + y + 1 = 0

x – 2y + 4 = 0

x + 2y + 4 = 0

4x + 2y + 1 = 0


10) If a curve passes through the point (1, 2) and has slope of the tangent at any point (x, y) on it as then the curve also passes through the point:

(3, 0)


(1, 2)



11) The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is:

7

5

1

3


12) Let S and S’ be the foci of an ellipse and B be any one of the extremities of its minor axis. If ΔS’BS is a right angled triangle with right angle B and area (ΔS’BS) = 8 sq. units, then the length of a latus rectum of the ellipse is:

4



2


13) Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is. If the curve passes through the center of the circle x^{2 }+ y^{2}  2x  2y = 0, then its equation is:

x log_{e }y = x – 1

x log_{e} y = –2 (x – 1)

x^{2} log_{e} y= –2 (x – 1)

x log_{e} y= 2(x – 1)


14) If the eccentricity of the standard hyperbola passing through the point (4, 6) is 2, then the equation of the tangent to the hyperbola at (4, 6) is:

2x – 3y + 10 = 0

x – 2y + 8 = 0

2x – y – 2 = 0

3x – 2y = 0


15) If where C is a constant of integration, then the function f(x) is equal to:


16) If the tangent to the curve, y = x^{3} + ax – b at the point (1, 5) is perpendicular to the line, x + y + 4 = 0, then which one of the following points lies on the curve?

(2, 2)

(2, 2)

(2, 1)

(2, 1)


17) If the line is normal to the hyperbola , then the value of m is:


18) Let, where the function f satisfies f(x + y) = f(x)f(y) for all natural numbers x, y and f (1) = 2. Then the natural number ‘a’ is:

4

16

2

3


19) If where and then for all x, y, 4x^{2} – 4xy cos α + y^{2} is equal to:

4 sin^{2}α – 2x^{2}y^{2}

4 cos^{2} α + 2x^{2}y^{2}

2 sin^{2 }α

4 sin^{2} α


20) A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm^{2}/min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of ice decreases is:


21) If z and w are two complex numbers such that then is equal to ___________.

22) If the number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is 2m, then m is equal to ______________.

23) The value of p such that , is equal to _____________.

24) If the line intersects the plane 2x + 3y – z + 13 = 0 at a point P and the plane 3x + y + 4z = 16 at a point Q, then (PQ)^{2} is equal to ________________.

25) Let g(x) = cos x^{2}, f(x) = , and α, β (α < β) be the roots of the quadratic equation 18x^{2} – 9πx + π^{2} =0. If the area (in sq. units) bounded by the curve y = (gof)(x) and the lines x = α , x = β and y = 0, is then (a + b) is equal to _____________.

 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15

 16
 17
 18
 19
 20
 21
 22
 23
 24
 25