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The area bounded by the curve y = x² + 4x + 5, the axes of co-ordinates and the minimum ordinate is

Solution: Given y = x2 + 4x + 5 dy/dx = 2x+4 dy/dx = 0 => x = -2 When x = -2, y = 1 When x = 0, y = 5 Required area = ∫-20 (x2 + 4x... View Article

An article was purchased for Rs. 1239 including GST of 18%. Find the price of the article before GST was added?

Solution: Let the price of the article before adding GST be x. So x + (18/100)x = 1239 => x + 0.18x = 1239 => 1.18x = 1239 => x =... View Article

The number of non-negative integral solutions to the system of equations x+y+z+u+t = 20 and x+y+z = 5.

(a) 336 (b) 246 (c) 346 (d) none of these Solution: Given x+y+z+u+t = 20 ..(i) x+y+z = 5 ..(ii) Put (ii)in (i) => 5 + u + t = 20... View Article

Let x₁, x₂, x₃,…, x_n, be n observations and a be the arithmetic mean. then the formula for the standard deviation is given by

Solution: We know that the standard deviation of n observations x1, x2, …xn is given by the formula σ = √[(1/n)∑i=1n (xi... View Article

If a and b are two numbers such that a²+b² = 7 and a³+b³ = 10, then which is the wrong statement.

(a) greatest value of |a+b| is 5 (b) greatest value of a+b is 4 (c) greatest value of a+b is 1 (d) least value of |a+b| is 1 Solution: Given... View Article

Which of the following is the correct formula for the sum and products of the zeroes of a quadratic polynomial p(x) = ax² + bx + c = 0.

(a) -b/a, c/a (b) -b/c, a/c (c) a/b, -c/b (d) none of these Solution: Given polynomial is ax2+bx+c = 0 We know the roots of quadratic... View Article

Find the product of all the prime factors of 616.

(a) 154 (b) 300 (c) 144 (d) none of the above Solution: Prime factorisation of 616 = 23 × 71 × 111 Prime factors are 2, 7, and 11. Product... View Article

Find the value of x, if the two lines, through a = (5, 6) and b = (2, -3) and through c = (-3, 3) and d = (6, x) are perpendicular.

(a) 1 (b) 3 (c) 0 (d) 2 Solution: Given a(5, 6), b(2, -3), c(-3, 3) and d(6, x). When lines are perpendicular, the product of slopes = -1... View Article

Line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

(a) 1 (b) 4 (c) -4 (d) 2 Solution: Let the point be A(-2, 6) and B(4, 8). Other two points be C(8,12) and D(x, 24). When lines are... View Article

A piece of wire 7/8 metre long broke into two pieces. One-piece was 1/4 metre long. How long is the other piece?

Solution: Total length of wire = 7/8m Length of one piece = 1/4m Length of remaining piece = 7/8 - ¼ = (7-2)/8 = 5/8m Hence the... View Article

In the figure shown neglecting friction and mass of pulleys, what is the acceleration of mass B?

a) g/3 b) 5g/2 c) 2g/2 d) 2g/5 Answer: d) 2g/5 Solution: aA = (aB + 0)/2 2aA = aB ------(1) From A, mg - TA = maA mg = maA + TA... View Article

The moments of inertia of two freely rotating bodies A and B are I_A and I_B respectively. I_A>I_B and their angular momenta are equal. If K_A and K_B are their kinetic energies, then.

a) KA = KB b) KA ≠ KB c) KA < KB d) KA = 2KB Answer: b.c Solution: Kinetic energy E=L2/2I If angular momenta are equal,... View Article

A small hole of an area of cross-section 2mm² is present near the bottom of a fully filled open tank of height 2 m. Taking g=10m/s², the rate of flow of water through the open hole would be nearly

a) 2.23 x 10-6 m3/s-1 b) 6.4 x 10-6 m3/s-1 c) 12.6 x 10-6 m3/s-1 d) 8.9 x 10-6 m3/s-1 The correct answer is c) 12.6 x 10-6 m3/s-1 The... View Article

The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. above. Choose the correct entries in the brackets below:

(a) (A/B) lives closer to the school than (B/A) (b) (A/B) starts from the school earlier than (B/A) (c) (A/B) walks faster than (B/A) (d) A... View Article

A 0.1m long conductor carrying a current of 50A is perpendicular to a magnetic field of 1.21 mT. The mechanical power to move the conductor with a speed of 1ms⁻¹ is

a) 0.25 mW b) 6.25 mW c) 0.625 W d) 1 W Answer: b) 6.25 mW Solution: Mechanical power required = electrical power expended due to the... View Article

A straight tunnel is dug into the earth as shown in the figure at a distance d from its
centre. A ball of mass m is dopped from one of its ends.The time it takes to reach the other end is approximately

a) 42 min b) 84 min c) 84 (d/R) min d) 42 (d/R) min Answer: a) 42 min Solution: The gravitational field inside the earth's surface g=... View Article

The wavelengths of 60 cm and 61 cm, produces 9 beats/ second. The velocity of sound is (approximately)

(1) 330 m/s (2) 335 m/s (3) 340 m/s (4) 325 m/s Answer: (1) 330 m/s Solution: Number of beats produced per second v1 - v2 =... View Article

In the circuit shown, the reading of the ammeter (ideal) is the same with both switches open as with both closed. Find the value of resistance R in ohm

Answer: 600 Ω Solution: i0 = 1.5/[300 + (100R/(100 + R)] i1 = i0 (R/(100 + R)) i1 = 1.5/[300 + (100R/(100 + R))] (R/100 + R) i = i1 1.5/400... View Article

A ring of radius R is having two charges q and 2q distributed on its two half parts. The electric potential at a point on its axis at a distance of 2√2 from its centre is (k= 1/4πε₀)

a) 3kq/R b) kq/3R c) kq/R d) kq/√3R Answer; c) kq/R Solution: r = √R2 + (2√2R)2 r = 3R vp = kqnet/r =... View Article

To a fish underwater, viewing obliquely a fisherman standing on the bank of a lake, the man looks

a) taller than what he actually is b) shorter than what he actually is c) The same height as he actually is d) Depends on the obliquity... View Article