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A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio

1) 1 : 2 2) 3 : 4 3) 2 : 1 4) 4 : 3 Solution: Let the equation of the straight line passing through origin O is y = mx …(i) Given 4x + 2y... View Article

The equation of one of the lines parallel to 4x – 3y = 5 and at a unit distance from the point (-1, -4) is

1) 3x + 4y - 3 = 0 2) 3x + 4y + 3 = 0 3) 4x - 3y + 3 = 0 4) 4x - 3y - 3 = 0 Solution: Given line is 4x - 3y = 5 => y = (4/3)x - 5/3 Here... View Article

The line L given by x/5 + y/b = 1 passes through the point (13, 32). The line K is parallel to L and has the equation x/c + y/3 = 1. Then, the distance between L and K is

1) 23/√15 2) √17 3) 17/√15 4) 23/√17 Solution: Given L: x/5 + y/b = 1 …(i) It passes through (13, 32). So 13/5 + 32/b = 1 32/b = 1 - 13/5 =... View Article

The equation of second degree x² + 2√2xy + 2y²+ 4x + 4√2y + 1 = 0 represents a pair of straight lines. The distance between them is

1) 2√3 2) 2√5 3) 2 4) 10 Solution: Distance between pair of straight lines ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 is d = 2√((g2 - ac)/a(a +... View Article

If a, b, c ≠ 0 and belong to the set {0,1,2,3…9}, then log₁₀ [(a + 10b + 10² c) / (10^-4 a + 10^-3 b + 10^-2 c)] =

1) 1 2) 2 3) 3 4) 4 Solution: (4) 4 log10 [(a + 10b + 102 c) / (10-4 a + 10-3 b + 10-2 c)] = log10 {[a + 10b + 102c] / [a + 10b + 102c]} *... View Article

The value of

1) 0 2) 1 3) 2 4) 100! Solution: (2) 1... View Article

The solution set of the equation [4 (1 – (1 / 3) + (1 / 9) + (1 / 27) + ….)]^{log₂ (x)} = [54 (1 + (1 / 3) + (1 / 9) + (1 / 27) + ….)]^{log_x (2)} is

1) {4, 1/4} 2) {2,1/2} 3) {1,2} 4) {8,1/8} Solution: (1) {4, 1 / 4} [4 (1 - (1 / 3) + (1 / 9) + (1 / 27) + ….)]log_2 (x) = [54 (1 + (1 / 3)... View Article

If log x / (a – b) = log y / (b – c) = log z / (c – a), then xyz =

1) 0 2) 1 3) - 1 4) 2 Solution: (2) 1 log x / (a - b) = log y / (b - c) = log z / (c - a) log x / (a - b) = log y / (b - c) = log z / (c -... View Article

If n = 2006!, then [1 / log₂ n] + [1 / log₃ n] + …. + [1 / log₂₀₀₆ n] =

1) 2006 2) 2005 3) 2005! 4) 1 5) 0 Solution: (4) 1 n = 2006! then [1 / log2 n] + [1 / log3 n] + …. + [1 / log2006 n] = log2 n + log3 n +... View Article

The value of a = log₂ log₂ log₄ 256 + 2 log_√2 2 then a is

1) 1 2) 2 3) 3 4) 4 5) 5 Solution: (5) 5 a = log2 log2 log4 256 + 2 log√2 2 = log2 log2 log4 44 + 2 log√2 (√2)2 = log2 log2 log4 4 + 4... View Article

If log_0.3 (x – 1) < log_0.09 (x – 1), then x lies in the interval

1) (2, ∞) 2) (1, 2) 3) (-2, -1) 4) None of these Solution: (1) (2, ∞) log0.3 (x - 1) < log0.09 (x - 1) Here x - 1 > 0 log0.3 (x - 1)... View Article

If a^x = b^y = c^z = d^w, then the values of x [(1 / y) + (1 / z) + (1 / w)] is

1) loga (abc) 2) loga (bcd) 3) logb (cda) 4) logc (dab) Solution: (2) loga (bcd) ax = by = cz = dw log ax = log by x log a = y log b (x /... View Article

If log_e [a + b] / 2 = (1 / 2) [log_e a + log_e b] then

1) a = b 2) a = b / 2 3) 2a = b 4) a = b / 3 Solution: (1) a = b loge [a + b] / 2 = (1 / 2) [loge a + loge b] loge [a + b] / 2 = (1 / 2)... View Article

If y = 2^1/[log_x(8)], then x =

1) y 2) y2 3) y3 4) None of these Solution: (3) y3 y = 21/[log_x(8)] y = 2log (8^x) = 2log (2^3)x = 2(⅓)log_2 (x) = 2log 2x^(⅓) y =... View Article

If a, b, c are distinct positive numbers each being different form 1 such that (log_b a . log_c a – log_a a) + (log_a b . log_c b – log_b b) + (log_a c . log_b c – log_c c) = 0, then abc is equal to

1) 0 2) e 3) 1 4) 2 5) 3 Solution: (3) 1 (logb a . logc a - loga a) + (loga b . logc b - logb b) + (loga c . logb c - logc c) = 0 (loga b... View Article

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