The interval of the decreasing function f (x) = x3 – x2 + x – 4 is
1) (1 / 3, 1) 2) (- 1 / 3, 1) 3) (- 1 / 3, 1 / 3) 4)... View Article
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The least value of k for which the function x2 + kx + 1 is an increasing function in the interval 1 < x < 2 is
1) -4 2) -3 3) -1 4) -2 Solution: (4) -2 f (x) = x2 + kx + 1 f... View Article
For all real values of x, increasing function f (x) is
1) x-1 2) x2 3) x3 4) x4 Solution: (3) x3 f (x) = x3 f’ (x) = 3x2 It... View Article
If f (x) = 2x + cot-1 (x) + log [√1 + x2 – x], then f (x)
1) Increases in [0, ∞] 2) Decreases in [0, ∞] 3) Neither increases nor decreases in (0, ∞) 4) Increases... View Article
The values of ‘a’ for which the function (a + 2)x3 – 3ax2 + 9ax – 1 decreases monotonically throughout for all real x, are
1) a < -2 2) a > -2 3) -3 < a < 0 4) – ∞ < a ≤... View Article
The interval in which the function x3 increases less rapidly than 6x2 + 15x + 5, is
1) (-∞, -1) 2) (-5, 1) 3) (-1, 5) 4) (5, ∞) Solution: (3) (-1, 5) Increase rate = d... View Article
The value of a in order that f (x) = sin x – cos x – ax + b decreases for all real value of x is given by
1) a ≥ √2 2) a < √2 3) a ≥ 1 4) a < 1 Solution: (1) a ≥ √2... View Article
If the function f (x) = [k sinx + 2 cos x] / [sin x + cos x] is increasing of x, then
1) k < 1 2) k > 1 3) k < 2 4) k > 2 Solution: (4) k >... View Article
The function f (x) = log (1 + x) – (2x / [2 + x]) is increasing for all values of x, then
1) (0,∞) 2) (-∞,0) 3) (-∞,∞) 4) None of these Solution: (1) (0, ∞) f (x) = log (1 +... View Article
The function f (x) = tan x – x
1) Always increases 2) Always decreases 3) Never decreases 4) Sometimes increases and sometimes decreases Solution: (1) Always increases f... View Article
Economy This Week (21st Dec to 27th Dec 2020)
Economy is an important part of the UPSC prelims and mains exams; this series titled ‘Economy This Week’ has been initiated to... View Article
22 Jan 2021: UPSC Exam Comprehensive News Analysis
CNA 22 Jan 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY 1.... View Article
21 Jan 2021: PIB Summary & Analysis
January 21st, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. Statehood Day 2. Raksha Mantri Padak 3. Indian Telecom... View Article
What are residuary subjects?
Answer: Residuary Subjects are recognised as subjects that are not present in any of the lists stated in the constitution.... View Article
Write is the difference between terrace farming and contour ploughing.
Answer: Terrace farming and contour ploughing are both used to reduce soil erosion on slopes from tilled fields. The differences... View Article
How will you explain the term unemployment?
Answer: Unemployment is a condition in which skilled and abled individuals do not get gainful jobs at a decent wage.... View Article
Design Thinking is a lean and ______ process.
Answer: Design Thinking is a Lean and Agile Process. Design Thinking is nothing but an investigation of the problem. Design... View Article
Natural Gas, petroleum and coal are examples of (1) Rocks (2) Minerals (3) Fossils
Answer: (3) Fossils Natural Gas, Petroleum, Coal are examples of Fossils. Coal is formed when dead plant matter decays into... View Article
What is the importance of dates in history? explain.
Answer: Dates are significant, since they mention when certain events have occurred. This is really important since it chronologically documents... View Article
What did Bastille symbolise as? (1) The military strength of France (2) Humanity (3) Despotic rule of Louis XVI (4) Louis XVIs cowardice act
Answer: (3) Despotic rule of Louis XVI A sign of social injustice, inequality and the absolute monarchy was the Bastille.... View Article
