Archives

Gist of Kurukshetra April 2021 Issue: Folk Art and Culture

Kurukshetra Magazine is a vital source of study material for the UPSC IAS exam. It is a monthly magazine that gives information about important... View Article

26 Apr 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 26th April 2021. Important news and views to... View Article

Economy This Week (17th Apr to 23rd Apr 2021)

Economy is an important part of the UPSC prelims and mains exams; this series titled ‘Economy This Week’ has been initiated to address the need... View Article

CPTPP – Comprehensive and Progressive Agreement for Trans-Pacific Partnership

Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP)—a free trade agreement between Canada and 10 other countries in the... View Article

The polynomial (ax² + bx + c) (ax² – dx – c), ac ≠ 0 has

1) four real roots 2) at least two real roots 3) at most two real roots 4) no real roots Solution: (2) at least two real roots ac ≠ 0 ac... View Article

The coefficients of x in the quadratic equation x² + bx + c = 0 was taken as 17 in place of 13, its roots were found to be – 2 and -15. The correct roots of the original equation are

1) - 10, - 3 2) - 9, - 4 3) - 8, - 5 4) - 7, - 6 Solution: (1) - 10, - 3 The given equation is x2 + bx + c = 0 and b = 17 x2 + bx + c = 0... View Article

The solution set of the equation pqx² – (p + q)² x + (p + q)² = 0 is

1) {p / q, q / p} 2) {pq, p / q} 3) {q / p, pq} 4) {[p + q] / p, [p + q] / q} 5) {[p - q] / p, [p - q] / q} Solution: (4) {[p + q] / p, [p +... View Article

Let a, b be the solutions of x² + px + 1 = 0 and c, d be the solutions of x² + qx + 1 = 0. If (a – c) (b – c) and (a + d) (b + d) are the solutions of x² + αx + β = 0, then β equals

1) P + q 2) p - q 3) p2 + q2 4) q2 - p2 Solution: (4) q2 - p2 Since a + b = - p; ab = 1 and c + d = - q, cd = 1 It is given that (a - c) (b... View Article

The roots of the equation x⁴ – 2x³ + x = 380 are

1) 5, - 4, [1 ± 5 √- 3] / 2 2) - 5, 4, [- 1 ± 5 √- 3] / 2 3) 5, 4, [- 1 ± 5 √- 3] / 2 4) - 5, - 4, [1 ± 5 √3] / 2 Solution: (1) 5, - 4, [1 ±... View Article

If sin A, sin B and cos A are in GP, then the roots of x² + 2x cot B + 1 = 0 are always

1) real 2) imaginary 3) greater than 1 4) equal Solution: (1) real sin A, sin B, cos A are in GP. sin 2B = sin A cos A ⇒ cos 2B = 1 - sin 2B... View Article

If the cube roots of unity are 1, ω and ω² then the roots of the equation (x – 1)³ + 8 = 0, are

1) - 1, 1 + 2ω , 1 + 2ω2 2) - 1, 1 - 2ω, 1 - 2ω2 3) - 1, - 1, - 1, 4) - 1, - 1 + 2ω, - 1 - 2ω2 Solution: (2) - 1, 1 - 2ω, 1 - 2ω2 (x - 1)3 +... View Article

The roots of the equation x³ – 3x² – 6x + 8 = 0 are in arithmetic progression, then the roots of the equation are

1) 3, 4 , 5 2) 4, 7, 10 3) - 2, 1, 4 4) 1, 4, 7 Solution: (3) - 2, 1, 4 Sum of the roots = - b / a = - (- 3 / 1) = 3 -2, 1, 4 satisfies this... View Article

The difference between two roots of the equation x³ – 13x² + 15x + 189 = 0 is 2. Then, the roots of the equation are

1) -3, 7, 9 2) -3, - 7, - 9 3) -3, - 5, 7 4) -3, -7, 9 Solution: (1) -3, 7, 9 Let ɑ, ɑ + 2, β be the 3 roots of the equation x3 - 13x2 + 15x... View Article

If f (x) = 2x³ + mx² – 13x + n and 2, 3 are the roots of the equation f (x) = 0, then the values of m and n are

1) -5 , - 30 2) -5 , 30 3) 5 , 30 4) None of these Solution: (2) -5 , 30 The function f (x) = 2x3 + mx2 - 13x + n has three roots. Let the... View Article

The roots of the equation (q – r) x² + (r – p) x + (p – q) = 0 are

1) [r - p] / [q - r], 1 2) [p - q] / [q - r], 1 3) [p - r] / [q - r], 2 4) [q - r] / [p - q], 2 5) [r - p] / [p - q], 1 Solution: (2) [p -... View Article

If a, b and c are the sides of ∆ABC such that a ≠ b ≠ c and x² – 2(a + b + c ) x + 3λ (ab + bc + ca ) = 0 has real roots, then

1) λ < (4 / 3) 2) λ > (5 / 3) 3) λ ∈ (4 / 3, 5 / 3) 4) λ ∈ (1 / 3, 5 / 3) Solution: (1) λ < (4 / 3) The roots are real, hence D... View Article

M	T	W	T	F	S	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30