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Given two points A = {2, 4} and B = {3, 6} in 2d plane. Euclidean distance between the points is

Solution: Given A = {2, 4} and B = {3, 6} The distance between two points is given by √((x2-x1)2 + (y2-y1)2) Distance between AB =... View Article

Convert 49 into binary number.

Solution: To convert decimal to binary we should divide the number successively by 2 until the quotient is 0. Keep the whole part for the next... View Article

In the given figure, D is the mid-point of BC, then the value of cot y⁰/cot x⁰ is

(a) 2 (b) 1/4 (c) ⅓ (d) ½ Solution: In ∆ ACD, cot x = AC/CD ..(i) In ∆ACB, cot y = AC/BC D is the midpoint of BC So CD = BC/2 So cot x =... View Article

If the area of the triangle formed by the points (2a, b) (a + b,2b + a) and (2b, 2a) is 2 sq. units, then the area of the triangle whose vertices are (a + b, a – b),(3b-a, b + 3a ), and (3a – b, 3b – a) will be

Solution: Area of triangle = Area of the triangle formed by the points (2a, b) (a + b, 2b + a) and (2b, 2a) = 2 => => 3ab - 3b2 = 4... View Article

A problem in statistics is given to four students A, B, C, and D. Their chances of solving it are ⅓, ¼, ⅕, and ⅙ respectively. What is the probability that the problem will be solved?

(a) 1/3 (b) 2/3 (c) 4/5 (d) none of these Solution: P(A) = ⅓ P(B) = ¼ P(C) = ⅕ P(D) = ⅙ P(A not solving) = ⅔ P(B not solving) =... View Article

The equation x²+2(m-1)+m+5 = 0 has equal and real root. Find the value of m.

Solution: Given x2+2(m-1)+m+5 = 0 For positive roots, b2-4ac = 0 => 4(m-1)2 - 4(m+5) = 0 => 4(m-1)2 = 4(m+5) => m2-2m+1 = m+5... View Article

If 2 is added to the numerator of a fraction, it reduces to (1/2) and if 1 is subtracted from the denominator, it reduces to (⅓). Find the fraction.

Solution: Let x be the numerator and y be the denominator of the fraction. (x+2)/y = ½ ..(i) x/(y-1) = ⅓ ..(ii) (i) => y = 2(x+2)... View Article

The bisector of ∠B and ∠C of triangle ABC intersect each other at the point O. Prove that ∠BOC = 90⁰+ ½ ∠A.

Solution: Consider ∆BOC. ∠1 + ∠2 + ∠BOC = 1800 ..(i) In ∆ABC, ∠A + ∠B + ∠C = 1800 ∠A + 2∠1 + 2∠2 = 1800 ½ ∠A + ∠1 + ∠2 = 900 ∠1 + ∠2 =... View Article

Find the middle term in the expansion of ((x/3) + 9y)¹⁰.

Solution: Here n = 10 Since n is even, middle term = ((n/2) + 1)th term = (10/2) + 1 = 6th term The general term of (a+b)n is Tr+1 = nCr... View Article

If A is a symmetric and B skew-symmetric matrix and A+B is non-singular and C =(A+B)⁻¹(A-B), then prove that (i) C^T(A+B)C =A+B (ii) C^T (A-B)C = A-B (iii) C^TAC = A

Solution: Since A is symmetric, AT= A B is skew-symmetric, BT = -B Given C = (A+B)−1(A-B) Multiply by (A+B) (A+B)C =... View Article

Determine the smallest positive value of x (in degrees) for which tan (x + 100⁰) = tan (x + 50⁰) tan x tan (x – 50⁰).

(a) 300 (b) 450 (c) 600 (d) 750 Solution: Given tan (x + 1000) = tan (x + 500) tan x tan (x - 500) tan (x + 1000)/tan (x - 500) = tan (x +... View Article

46 square equals

Solution: To find the square of a number, multiply the number by the same number. 462 = 46×46 = 2116... View Article

One end of a taut string of length 3m along the x-axis is fixed at x=0. The speed of the waves in the string is 100m/s. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

a) b) c) d) Answer: d Solution: The fixed end is a node while the free end is an... View Article

Two non-conducting spheres of radii R₁ and R₂ and carrying uniform volume charge densities +ρ and −ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,

(A) The electrostatic field is zero (B) The electrostatic potential is constant (C) The electrostatic field is constant in magnitude (D) The... View Article

A ladder is leaned against a smooth wall and allowed to slip on a frictionless floor. Which figure represents the trace of its COM?

Answer: (c) Solution: The center of mass will move downward and will shift horizontally... View Article

A coil has an inductance of 0.7H and is joined in series with a resistance of 220 Ω. When an alternating e.m.f. of 220V at 50 c.p.s. is applied to it, then the wattless component of the current in the circuit is

a) 5 ampere b) 0.5 ampere c) 0.7 ampere d) 7 ampere Answer: b) 0.5 ampere Solution: XL=ωL=2πfL=220Ω... View Article

Out of the following material whose elasticity is independent of temperature

a) steel b) copper c) invar steel d) glass Answer: c) invar steel Solutions: Elasticity decreases with temperature for steel, copper... View Article

A 40μF capacitor is connected to a 200V,50Hz ac supply. The RMS value of the current in the circuit is, nearly:

a) 1.7 A b) 2.05 A c) 2.5 A d) 25.1 A Answer: c) 2.5 A Solution: The RMS value of the current irms=Cωεrms... View Article

Two transparent media A and B are separated by a plane boundary. The speed of light in medium A is 2.0×10⁸ ms⁻¹ and in medium, B is 2.5×10⁸ ms⁻¹. The critical angle for which ray of light going from A to B suffers total internal reflection is

a) sin-1 (1/2) b) sin-1 (2/5) c) sin-1 (4/5) d) sin-1 (3/5) Answer: c) sin-1 (4/5) Solution:... View Article

An electric field of 300 V/m is confined to a circular area 10 cm in diameter. If the field is increasing at the rate of 20V/m-s, the magnitude of the magnetic field at a point 15 cm from the centre of the circle will be

a) 1.85 x 10-15 T b) 1.85 x 10-16 T c) 1.85 x 10-17 T d) 5.55 x 10-18 T Answer: d) 5.55... View Article