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If both the roots of the equation x² – 6ax + 2 – 2a + 9a² = 0 exceed 3, then

1) a < ½ 2) a > ½ 3) a < 1 4) a > 11 / 9 Solution: (4)... View Article

A value of b for which the equations x² + bx – 1 = 0, x² + x + b = 0 have one root in common, is

1) – √2 2) ± √3i 3) i√5 4) √2 Solution: (2) ± √3i x2 + bx – 1 =... View Article

Let a, b and c be real numbers, a ≠ 0, if α ≠ 0. If α is a root of a²x² + bx + c = 0, β is a root of a²x² – bx – c = 0 and 0 < α < β. Then, the equation a²x² + 2bx – c = 0 has a root γ that always satisfies

1) γ = a 2) α < β < γ 3) α < γ < β 4) γ = [α... View Article

If the equations x² + 2x + 3 = 0 and ax² + bx + c = 0; a, b, c ∈ R, have a common root, then a : b : c is equal to

1) 1: 2 : 3 2) 3 : 2 : 1 3) 1 : 3 : 2 4) 3 :... View Article

Let p and q be real numbers. If α is the root of x² + 3p² x + 5q² = 0, β is the root of x² + 9p²x + 15q² = 0 and 0 < α< β, then the equation x² + 6p²x + 10q² = 0 has root γ that always satisfies

1) ɣ = (ɑ / 4) + β 2) β < γ 3) γ = (ɑ / 2) + β... View Article

If the roots of the equation λ² + 8λ + μ² + 6μ = 0 are real, then μ lies between

1) – 2 and 8 2) – 3 and 6 3) – 8 and 2 4) – 6 and 3... View Article

If a = cos (2π / 7) + i sin (2π / 7), then the quadratic equation whose roots are α = a + a² + a⁴ and β = a³ + a⁵ + a⁶, is

1) x2 – x + 2 = 0 2) x2 + 2x + 2 = 0 3) x2 + x... View Article

If one of the roots of equation x² + ax + 3 = 0 is 3 and one of the roots of the equation x² + ax + b = 0 is three times the other root, then the value of b is

1) 3 2) 4 3) 2 4) 1 Solution: (1) 3 Let 3 and α be the roots of the... View Article

If a, b and c are distinct positive real numbers in AP, then the roots of the equation ax² + 2bx + c = 0 are

1) imaginary 2) rational and equal 3) rational and distinct 4) irrational Solution: (3) rational and distinct Given that 2b... View Article

The roots of the equation x³ – 3x – 2 = 0 are

1) – 1, – 1, 2 2) – 1, 1, – 2 3) – 1, 2, – 3 4) –... View Article

E₁ : a + b + c = 0 , if 1 is root of ax² + bx + c = 0, E₂ : b² – a² = 2ac, if sin θ and cos θ are the roots of ax² + bx + c = 0, which of the following is correct ?

1) E1 is correct E2 is correct 2) E1 is correct E2 is incorrect 3) E1 is incorrect E2 is... View Article

28 Apr 2021: UPSC Exam Comprehensive News Analysis

CNA 28th April 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY AND... View Article

27 Apr 2021: PIB Summary & Analysis

April 27th, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. ‘Large Area Certification’ scheme 2. Waste Management 3. Aditya-L1... View Article

27 Apr 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 27th April 2021. Important news and... View Article

Agriculture Infrastructure Fund (AIF)

The Agriculture Infrastructure Fund (AIF) was announced in May 2020 by the Government of India for farm-gate infrastructure for farmers.... View Article

If for some reason, the vasa efferentia in the human reproductive system get blocked, the gametes will not be transported from

A) epididymis to vas deferens B) testes to epididymis C) vagina to uterus D) ovary to uterus Answer:B) testes to... View Article

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