TTA Solved Model question Paper

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[Arun Vats]

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1. If the matrix A = is singular, then ? =
a) 3 b) 4 c) 2 d) 5
2. A = is symmetric, then x =
a) 3 b) 4 c) 2 d) 5
3. If A is a 3 x 3 matrix and det(3 A) = k det(A) then k =
a) 9 b) 6 c) 1 d) 27
4. If A = , then A-1 =
a) b) c) d)
5. If A = then A2 is equal to
a) A b) –A c) Null Matrix d) I
6. is a
a) rectangular matrix b) singular matrix
b) non-singular matrix d) skew-symmetric matrix
7. The slope of the straight line whose inclination with negative x-axis is 120º is
a) b) c) 1 d) infinity
8. If two lines whose slopes are m1 and m2 are perpendicular iff
a) m1 = m2 b) m1m2 = 0 c) m1m2 = -1 d) m1 + m2 = -1
9. The rate of increase of the radius of a circle is 1 cm/sec, the rate of increase of its area is 4? cm2/sec at a particular instant. The radius at that instant is
a) 2 cm b) 3 cm c) 4 cm d) 6 cm
10.If the side of a square is increasing at the rate of 0.02 cm/min, the rate at which its area is increasing at the instant when the length of the side is 5 cm is
a) 0.2 cm 2/min b) 0.4 cm 2/min c) 0.1 cm 2/min d) 0.6 cm 2/min
11.A particle is moving on a plane according to the distance-time relationship is given by s = t3 + 6t2 + 8t – 4. When its acceleration is 8 m/sec2, its velocity is
a) 8 m/sec b) 11 m/sec c) 23 m/sec d) -1 m/sec
12.A stone moves vertically upwards according to the distance-time equation s = 16t – 2t2.The greatest height reached by the stone is
a) 4 b) 64 c) 32 d) 96
13.The distance moved by a particle traveling in a straight line in t seconds is given by s = 45t + 11t2 – t3. The time taken by the particle to come to rest is
a) 9 sec b) 5 sec c) 3 sec d) 2 sec
14.The distance s described by a particle in time t is given by the relation s = aet + be-t. The acceleration is equal to
a) velocity b) the distance traveled
c) twice the distance traveled d) the square of the distance traveled
15.The slope of the normal to the curve y = at the point is
a) 9 b) -9 c) d)
17.The normal to the curve y = f(x) will be parallel to x-axis if
a) b) c) d)
18.The maximum point of the function 2×3 – 9×2 + 12x is
a) x = 0 b) x = 5 c) x = 1 d) x = 2
19.The minimum value of 2×3 – 9×2 + 12x – 4 is
a) 1 b) 3 c) 0 d) -2
20.The point of inflection of the function x3 – 3×2 + 3x is
a) (1,0) b) (1,1) c) (6,126) d) (-1,-7)
21.Velocity of sound is greatest in
a) Solids b) Liquids c) Gases d) None of these
22.If the phase difference between the two waves is 2? during superimposition, then the resultant amplitude is
a) Maximum b) Minimum c) Half of maximum d) None of these
23.If two waves of same frequency and same amplitude on superimposition produce a resultant disturbance of the same amplitude, the wave differ in phase by
a) b) c) d)
24.The equation of a plane progressive wave is given by y = 2sin?(0.5x – 200t) where x and y are expressed in cm and t in sec. The wave velocity is
a) 400 cm/sec b) 300 cm/sec c) 200 cm/sec d) 100 cm/sec
25.Equation of a plane progressive wave is given by y = 0.2 cos ?(0.04t + 0.02x – 1/6). The distance is expressed in cm and time in sec. The minimum distance between two particles separated by phase difference ?/2 is radian is
a) 25 cm b) 12.5 cm c) 8 cm d) 4 cm
26.Ultrasonic waves are those waves which
a) Human being can hear b) Human being cannot hear
c) Have high velocity d) Have large amplitude
27.It is possible to distinguish between the transverse and longitudinal waves by studying the property of
a) Interference b) Polarization c) Diffraction d) Reflection
28.The following phenomenon cannot be observed for sound waves
a) Refraction b) Polarization c) Diffraction d) Reflection
29.Doppler shift in frequency does not depend upon
a) Frequency of the wave produced b) Velocity of the source
c) Velocity of the listener/observer d) Distance between source and listener
30.A source of sound of frequency 450 cycles/second is moving towards a stationary observer with 34 m/s speed. If the speed of sound is 340 m/s then the apparent frequency will be
a) 410 cps b) 550 cps c) 500 cps d) 450 cps
31.An observer moves towards a stationary source of sound of frequency n. The apparent frequency heard by him is 2n. If the velocity of sound in air is 332 m/s, then the velocity of observer is
a) 166 m/s b) 664 m/s c) 332 m/s d) 1328 m/s
32.The equation of a wave traveling in a string can be written as y = 3 cos ?(100t – x).Its wavelength is
a) 100 cm b) 5 cm c) 3 cm d) 2 cm
33.Sound velocity is maximum in
a) O2 b) H2 c) He d) N2
34.Phon is the unit of
a) Pitch b) Quality c) Timbre d) Loudness
35.Loudness of sound L and corresponding intensity of sound I are related as
a) L = KI2 b) L = KI c) L = K d) L = K log I
36.The index of refraction of a medium is 1.5. If the speed of light in air is 3 x 108 m/s, then its speed in the medium will be
a) 2 x 108 m/s b) 1.2 x 108 m/s c) 4 x 108 m/s d) 3.2 x 108 m/s
37.The ratio of intensities of the two waves is given by 4:1. The ratio of amplitudes of two waves is
a) 2:1 b) 1:2 c) 4:1 d) 1:4
38.Two source of waves are called coherent if
a) Both have the same amplitude by vibrations
b) Both produce waves of different wavelength having constant phase difference
c) Both produce waves of same wavelength having constant phase difference
d) Both produce waves having the same velocity
39.Which of the following does not support the wave nature of light?
a) Interference b) Diffraction c) Polarization d) Photoelectric effect