Archives

The straight line x/a + y/b = 2 touches the curve (x/a)ⁿ + (y/b)ⁿ = 2 at the point (a, b) for

(a) n = 1, 2 (b) n = 3, 4, -5 (c) n = 1, 2, 3 (d) any value of n Solution: Given curve is (x/a)n + (y/b)n = 2. nxn-1/an +... View Article

The number of solutions of the equation 3 tan x + x³ = 2 in (0, π/4) is

(a) 0 (b) 1 (c) 2 (d) 3 Solution: Let f(x) = 3 tan x + x3 - 2 Differentiate w.r.t.x => f’(x) = 3 sec2x + 3x2 > 0 f(x)... View Article

What is the minimum value of px + qy (p > 0, q > 0) when xy = r²?

(a) 2r√(pq) (b) 2pq√r (c) - 2r√(pq) (d) 2 rpq Solution:Given xy = r2 => y = r2/x Let S = px +qy = px +... View Article

The curve y = xe^x has minimum value equal to

(a) -1/e (b) 1/e (c) -e (d) e Solution: Given y = xex Differentiate w.r.t.x => dy/dx = ex + xex = ex(1+x) Put dy/dx = 0... View Article

The number of tangents to the curve x^3/2 + y^3/2 = 2a^3/2, a > 0, which are equally inclined to the axes, is

(a) 2 (b) 1 (c) 0 (d) 4 Solution: Given curve x3/2 + y3/2 = 2a3/2 ..(i) Differentiate w.r.t.x => (3/2)... View Article

The motion of a particle is described as s = 2 – 3t + 4t³. What is the acceleration of the particle at the point where its velocity is zero?

(a) 0 (b) 4 unit (c) 8 unit (d) 12 unit Solution: Given s = 2 - 3t + 4t3 Velocity, V = ds/dt = -3 + 12t2... View Article

The function f (x) = x²/e^x monotonically increasing if

(a) x < 0 only (b) x > 2 only (c) 0 < x < 2 (d) x ∈ (-∞, 0) ⋃ (2, ∞) Solution: Given f(x) =... View Article

The cost of running a bus from A to B is Rs. (av + b/v) where v km/h is the average speed of the bus. When the bus travels at 30 km/h, the cost comes out to be Rs. 75 while at 40 km/h, it is Rs. 65. Then the most economical speed (in km/ h) of the bus is :

(a) 45 (b) 50 (c) 60 (d) 40 Solution: Given that cost, C = av+b/v When the bus travels at 30 km/h, the cost comes... View Article

If the curve y = ax² – 6x + b passes through (0, 2) and has its tangent parallel to the x-axis at x = 3/2 then

(a) a = b = 0 (b) a = b = 1 (c) a = b = 2 (d) a = b = -1 Solution: y = ax2 - 6x + b passes through (0, 2). => 2 = 0 -... View Article

05 Feb 2022: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 05 Feb 2022. Important news and views to boost... View Article

Sansad TV Perspective: Decoding Budget 2022-23

In the series Sansad TV Perspective, we bring you an analysis of the discussion featured on the insightful programme ‘Perspective’ on Sansad TV,... View Article

UPSC 2022: Weekly GK and Current Affairs Quiz Feb 05 – Feb 11

UPSC 2022: Weekly GK and Current Affairs Quiz Feb 05 - Feb 11 with Multiple Choice Questions and answers for IAS Exam Preparation other... View Article

04 Feb 2022: PIB Summary for UPSC

TABLE OF CONTENTS 1. Swachhta Saarthi Fellowship 2022 2. Rashtriya Yuva Sashaktikaran Karyakram (RYSK) 3. Blue Revolution 4. Towns of Export... View Article

05 Feb 2022: UPSC Exam Comprehensive News Analysis

CNA 05 Feb 2022:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related INTERNATIONAL RELATIONS 1. India’s diplomatic boycott of... View Article

04 Feb 2022: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 04 Feb 2022. Important news and views to boost... View Article

04 Feb 2022: UPSC Exam Comprehensive News Analysis

CNA 04 Feb 2022:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related C. GS 3 Related ECONOMY 1. The need to boost labour income... View Article

03 Feb 2022: PIB Summary for UPSC

TABLE OF CONTENTS 1. New methods to transform phenol into key essential ingredients 2. Incentives for adoption of renewable energy 3. Punaura... View Article

SDG India Index 2020-21

The NITI Aayog released the third edition of the Sustainable Development Goals (SDG) India Index 2020-21. What does the SDG India Index indicate?... View Article

The attenuation in optical fibre is mainly due to

1) absorption 2) scattering 3) Neither absorption nor scattering 4) Both (1) and (2) Answer: 4) Both (1) and (2) Solution: Due... View Article

Antenna is

1) inductive 2) capacitive 3) resistive above its resonant frequency 4) resistive at resonant frequency Answer: 1) inductive... 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