a, b, c are in G.P. with 1 < a < b < n, and n > 1 is an integer. loga n, logb n, logc n form a sequence. This sequence is which one of the following? (a) Harmonic progression (b) Arithmetic progression (c) Geometric progression (d) None of these Solution: Given that a, b, c are in... View Article
The value of the infinite product 61/2 ×61/4× 61/8×61/16×…is (a) 6 (b) 36 (c) 216 (d) ∞ Solution: 61/2 ×61/4× 61/8×61/16×… = 6(1/2 + 1/4 + 1/8 + 1/16 +... View Article
Let Sn (1 ≤ n ≤ 9) denotes the sum of n terms of series 1 + 22 + 333 + ……………..+ 9999999999, then for 2 ≤ n ≤ 9 (a) Sn - Sn-1 = (1/9)(10n - n2 + n) (b) Sn = (1/9)(10n - n2 + 2n - 2) (c) 9(Sn - Sn-1) = n(10n -1) (d) none of these Solution: Given... View Article
Given that α, γ are the roots of the equation Ax2 – 4x + 1 = 0, and β, δ the roots of the equation Bx2 – 6x + 1 = 0, the values of A and B such that α, β, γ, and δ are in H. P. are (a) A = 3, B = 8 (b) A = - 3, B = 8 (c) A = 3, B = - 8 (d) None of these Solution: α, β, γ, and... View Article
If (1 – P) (1 + 3x + 9x2 + 27x3 + 81x4 + 243x5) = 1 – P6, P ≠ 1, then find the value of P/x is (a) 1/3 (b) 3 (c) 1/2 (d) 2 Solution: (1 - P) (1 + 3x + 9x2 + 27x3 + 81x4 + 243x5) = 1 - P6 (1 + 3x + 9x2 + 27x3 + 81x4 +... View Article
What is the greatest value of the positive integer n satisfying the condition 1 + ½ + ¼ + â…› + …..+ 1/2n-1< 2 – 1/1000? (a) 8 (b) 9 (c) 10 (d) 11 Solution: Given 1 + ½ + ¼ + â…› + …..+ 1/2n-1< 2 - 1/1000 LHS... View Article
If a = 1 + (√3-1) + (√3-1)2 + (√3-1)3 + …. and ab = 1, then a and b are the roots of the equation (a) x2 + 4x - 1 = 0 (b) x2 - 4x - 1 = 0 (c) x2 + 4x + 1 = 0 (d) x2 - 4x + 1 = 0 Solution: Given a = 1 + (√3-1) + (√3-1)2 +... View Article
If a, b, c are positive numbers, then least value of (a + b + c)(1/a + 1/b + 1/c) is (a) 1 (b) 6 (c) 9 (d) None Solution: We use A.M ≥ H.M (a+b+c)/3 ≥ 3/[(1/a) + (1/b) + (1/c)] => (a + b +... View Article
Consider the sequence 8A + 2B, 6A + B, 4A, 2A – B, ……., Which term of this sequence will have a coefficient of A which is twice the coefficient of B? (a) 10th (b) 14th (c) 16th (d) None of these Solution: Given sequence 8A + 2B, 6A + B, 4A, 2A - B, ....... This is an AP... View Article
ABC is a right angled triangle in which ∠B = 900 and BC = a. If n points L1, L2, …, Ln on AB are such that AB is divided in n + 1 equal parts and L1M1, L2M2,…, LnMn are line segments parallel to BC and M1, M2,…., Mn are on AC, then the sum of the lengths of L1M1, L2M2,…., LnMn is (a) a(n+1)/2 (b) a(n-1)/2 (c) an/2 (d) none of these Solution: AL1/AB = L1M1/BC 1/(n+1) = L1M1/a =>L1M1 = a/(n+1) AL2/AB = L2M2/BC... View Article
If |r|>1 and x = a + (a/r) + (a/r2) + … to ∞, y = b – (b/r) + (b/r2) – …to ∞ and z = c + (c/r2) + (c/r4) + …∞ then xy/z = (a) ab/c (b) ac/b (c) bc/a (d) 1 Solution: Sum of infinite GP, S = a/(1-r) where a is the first term and r is the common ratio. Given... View Article
Let An be the sum of the first n terms of the geometric series 704 + (704/2) + (704/4) + (704/8) + … and Bn be the sum of the first n terms of the geometric series 1984 – (1984/2) + (1984/4) – (1984/8) + …If An = Bn, then the value of n is (where n ∈ N). (a) 4 (b) 5 (c) 6 (d) 7 Solution: We know sum of n terms of G.P = a(1 - rn)/(1 - r) Given An = 704 + 704/2 + 704/4... View Article
Which range of frequencies is suitable for sky wave propagation? 1) 1 KHz to 500 KHz 2) 1 MHz to 2 MHz 3) 2 MHz to 20 MHz 4) Above 20 MHz Answer: 3) 2 MHz to 20 MHz Solution: 2 MHz to 20 MHz... View Article
In radio and television broadcasts, the information signal is in the form of 1) Analog signal 2) Digital signal 3) Both analog and digital signals 4) Neither analog nor digital signal Answer: 1) Analog signal... View Article
Ground waves are polarised at ___________direction. 1) Vertically upward 2) Horizontal 3) Tangential direction to the surface of the earth 4) In all four Answer: 1) Vertically upward... View Article
___________is used as a medium an space communication 1) Two wireline 2) Space 3) Amplifier 4) Optical fibre Answer: 2) Space Solution: Space is used as a medium an space... View Article
Type of communication possible by Modem duplex is ………………… 1) Half duplex 2) Simplex 3) Doudle Duplex 4) Full duplex Answer: 4) Full duplex Solution: Type of communication possible by... View Article
Which of the following is the disadvantage of FM over AM? 1) Larger bandwidth requirement 2) Larger noise 3) Higher modulation power 4) Low efficiency Answer: 1) Larger bandwidth requirement... View Article
Basically, the product modulator is 1) An amplifier 2) A mixer 3) A frequency separator 4) A phase separator Answer: 2) A mixer Solution: The product modulator... View Article
Maximum usable frequency (MUF) in F-region layer is x, when the critical frequency is 60 MHz and the angleof incidence is 70°. Then x is 1) 150 MHz 2) 170 MHz 3) 175 MHz 4) 190 MHz Answer:3) 175 MHz Solution: From Snell's law μ1sini=μ2sinr Maximum usable frequency in... View Article
