Practice Questions

Q80.Two integers x and y are chosen with replacement from the set {0, 1, 2, 3, … . . , 10}. Then the probability that |x −y| > 5 is : (1) 30 (2) 62 121 121 (3) 60 (4) 31 121 121

Q80.The coefficients a, b, c in the quadratic equation ax2 + bx + c = 0 are chosen from the set {1, 2, 3, 4, 5, 6, 7, 8} . The probability of this equation having repeated roots is : (1) 1 (2) 1 128 64 (3) 3 (4) 3 256 128

Q80.An integer is chosen at random from the integers 1 , 2, 3, . . . . . , 50. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is (1) 8 (2) 21 25 50 (3) 9 (4) 14 50 25 is equal to _______. +

Q80.An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is : (1) 5 (2) 5 256 715 3 3 (3) (4) 715 256 1

Q80.If the shortest distance between the lines x−41 = y+12 = −3z and x−λ2 = y+14 = z−2−5 is √56 , then the sum of all possible values of λ is : (1) 5 (2) 8 (3) 7 (4) 10

Q80.Bag 𝐴 contains 3 white, 7 red balls and bag 𝐵 contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn in white, is : 1 1 (1) (2) 4 9 (3) 1 (4) 3 3 10

Q80.Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is : (1) 5 (2) 5 18 16 (3) 4 (4) 7 17 18 1C0+1C1 2C0+2C1+2C2 3C0+3C1+3C2+3C3 , b = 1 +

Q80.A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is: (1) 2 (2) 2 5 7 1 1 (3) (4) 7 5

Q81.The number of real solutions of the equation x|x + 5| + 2|x + 7| −2 = 0 is_________

Q81.The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is _________

Q81.The sum of the square of the modulus of the elements in the set {z = a + ib : a, b ∈Z, z ∈C, |z −1| ≤1, |z −5| ≤|z −5i|} is ________

Q82.All the letters of the word GTWENTY are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word GTWENTY IS 11C2 11C9

Q1. A cylindrical wire of mass (0. 4 ± 0. 01) g has length (8 ± 0. 04) cm and radius (6 ± 0. 03) mm . The maximum error in its density will be (1) 3. 5% (2) 5% (3) 1% (4) 4%

Q1. Two trains A and B of length l and 4l are travelling into a tunnel of length L in parallel tracks from opposite directions with velocities 108 km h−1 and 72 km h−1, respectively. If train A take 35 s less time than train B to cross the tunnel then, length L of tunnel is: (Given L = 60 l) (1) 1200 m (2) 900 m (3) 1800 m (4) 2700 m

Q1. Match List I with List II List I List II A. Torque I. M L−2 T−2 B. Stress II. M L2 T−2 C. Pressure gradient III. M L−1 T−1 Coefficient of D. IV. M L−1 T−2 viscosity Choose the correct answer from the options given below : (1) A-II, B-I, C-IV, D-III (2) A-IV, B-II, C-III, D-I (3) A-II, B-IV, C-I, D-III (4) A-III, B-IV, C-I, D-II

Q1. Two resistance are given as 𝑅1 = ( 10 ± 0 . 5 ) Ω and 𝑅2 = ( 15 ± 0 . 5 ) Ω . The percentage error in the measurement of equivalent resistance when they are connected in parallel is (1) 6 . 33 (2) 2 . 33 (3) 5 . 33 (4) 4 . 33

Q1. In the equation 𝑋+ 𝑎 𝑏] = 𝑅𝑇, 𝑋 is pressure, 𝑌 is volume, 𝑅 is universal gas constant and 𝑇 is 𝑌2[𝑌- temperature. The physical quantity equivalent to the ratio 𝑎 is: 𝑏 (1) Pressure gradient (2) Energy (3) Impulse (4) Coefficient of viscosity

Q1. If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is: 2 c 2 G1] (2) h1c1G−1 (1) [h 1 1 2 c 2 G 2 ] (4) [h 2 c 2 G−12 ] (3) [h−1 1 1 1 1

Q1. A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution in 4 s. At the end of 3rd second, the displacement of body (in m) from its starting point is: (1) 30 (2) 15 π (3) 5 π (4) 10√2

Q1. Three forces F1 = 10 N, F2 = 8 N, F3 = 6 N are acting on a particle of mass 5 kg. The forces F2 and F3 are applied perpendicularly so that particle remains at rest. If the force F1 is removed, then the acceleration of the particle is (1) 7 m s–2 (2) 0. 5 m s–2 (3) 4. 8 m s–2 (4) 2 m s–2

Q2. As shown in the figure, a particle is moving with constant speed π m s−1 . Considering its motion from A to B, the magnitude of the average velocity is: (1) √3 m s−1 (2) π m s−1 (3) 1. 5√3 m s−1 (4) 2√3 m s−1

Q2. The speed of a wave produced in water is given by ν = λagbρc . Where λ, g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are (1) 1, −1, 0 (2) 12 , 0, 12 (3) 1, 1, 0 (4) 21 , 12 , 0

Q2. The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as: ν = raρbsc . The values of a, b and c respectively are (1) (−32 , −12 , 12 ) (2) (−32 , 12 , 12 ) (3) ( 23 , 12 , −12 ) (4) ( 32 , −12 , 12 )

Q2. The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is (1) 192 m (2) 136 m (3) 272 m (4) 68 m

Q2. If force (F), velocity (V ) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be : (1) F V 4 T −6 (2) F V −4 T −2 (3) F 2 V −2 T 6 (4) F V −2 T 2