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How many numbers with no more than three digits can be formed using only the digits 1 through 7 with no digit used more than once in a given number?

(a) 259 (b) 249 (c) 257 (d) 252 Solution: Numbers can be with 1 digit, 2 digits and 3 digits... View Article

A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :

(a) 40 (b) 41 (c) 16 (d) 32 Solution: The committee should include at least 1 lady. at least 1... View Article

Four couples (husband and wife) decide to form a committee of four members. Find the number of different committees that can be formed in which no couple finds a place.

(a) 12 (b) 14 (c) 16 (d) 24 Solution: The number of committees of 4 gentlemen = 4C4 = 1... View Article

There are three men and seven women taking a dance class. Number of different ways in which each man is paired with a woman partner, and the four remaining women are paired into two pairs each of two is

(a) 105 (b) 315 (c) 630 (d) 450 Solution: 3 women can be selected in 7C3 ways and can be... View Article

Three boys and three girls are to be seated around a table, in a circle. Among them, the boy X does not want any girl neighbour and the girls Y does not want any boy neighbour. The number of such arrangements possible is

(a) 4 (b) 6 (c) 8 (d) None of these Solution: Consider the figure. 1, 2 and X are the... View Article

The graph of the function y = f(x) is symmetrical about the line x = 2, then

(a) f(x) = -f(-x) (b) f(2+x) = f(2-x) (c) f(x) = f(-x) (d) f(x+2) = f(x-2) Solution: Consider a graph... View Article

Which of the following statements is incorrect.

(a) x sgn x = |x| (b) |x| sgn x = x (c) x (sgn x) (sgn x) = x... View Article

Let f(x) = x/(1- x) and ‘a’ be a real number. If x₀ = a, x₁ = f(x₀), x₂ = f(x₁), x₃ = f(x₂)……. If x₂₀₀₉= 1, then the value of a is

(a) 0 (b) 2009/2010 (c) 1/2009 (d) 1/2010 Solution: Given f(x) = x/(1- x) x0 = a, x1 = f(x0)... View Article

If f(x) and g(x) are periodic functions with periods 7 and 11, respectively, then the period of F(x) = f(x) g(x/5) – g(x) f(x/3)

(a) 177 (b) 222 (c) 433 (d) 1155 Solution: Given F(x) = f(x) g(x/5) – g(x) f(x/3) Period of f(x)... View Article

Let f(x) = [x], where [x] denotes the greatest integer less than or equal to x. If a = √(2011²+2012), then the value of f(a) is equal to

(a) 2010 (b) 2011 (c) 2012 (d) 2013 Solution: Given f(x) = [x], where [x] denotes the greatest integer less... View Article

If f and g are two functions defined as f(x) = x + 2, x ≤ 0; g (x) = 3, x ≥0, then the domain of f + g is

(a) {0} (b) [0, ∞) (c) (-∞, ∞) (d) (-∞, 0) Solution: f(x) = x + 2, x ≤ 0 ... View Article

If f(x) = x/(x-1), then f(a)/f(a+1) is equal to:

(a) f(a2) (b) f(1/a) (c) f(-a) (d) f(-a/a-1) Solution: Given f(x) = x/(x-1) f(a) = a/(a-1) f(a+1) = (a+1)/(a+1-1) =... View Article

If a function F is such that F(0) = 2, F(1) = 3, F(x + 2) = 2 F(x) – F(x + 1) for x ≥ 0, then F(5) is equal to

(a) -7 (b) -3 (c) 17 (d) 13 Solution: Given F(0) = 2, F(1) = 3 F(x + 2) =... View Article

Which of the following functions are periodic?

(a) f(x) = log x, x > 0 (b) f(x) = ex, x ∈ R (c) f(x) = x –... View Article

Sansad TV Perspective: Budget 2022-23: Economic lifelines in focus’

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

31 Jan 2022: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 31 Jan 2022. Important news and... View Article

consider-the-bcc-unit-cells-of-the-solids-1-and-2-with-the-position-of-atoms-as-shown-below-the-radius-of-atom-b-is-twice-that-of-atom-a-the-unit-cell-edge-length-is-50-more-in-solid-2-than-in-1-what-is-the-approximate-packing-efficiency-in-solid-2

Image (A) 45 % (B) 65 % (C) 75 % (D) 90 % The Correct Answer is (D) 90 %... View Article

csbr-crystallises-in-a-body-centred-cubic-lattice-the-unit-cell-length-is-4366-pm-given-that-the-atomic-mass-of-cs-is-133-br-is-80-amu-and-avogadro-number-is-602-1023-mol-1-what-will-be-the-density-of-csbr

(A) 8.5 g/cm3 (B) 4.25 g/cm3 (C) 42.5 g/cm3 (D) 0.425 g/cm3 The Correct Answer is (A) 8.5 g/cm3. Solution:... View Article

assertion-through-the-central-atom-of-both-nh3-and-h2o-molecules-are-sp3c-hybridised-yet-the-h-n-h-bond-angle-is-greater-than-that-of-h-o-hreason-this-is-because-the-nitrogen-atom-has-a-lone-pair-and-the-oxygen-atom-has-two-lone-pairs

(A) Assertion is true, but Reason is false. (B) Both Assertion and Reason are false. (C) Both Assertion and Reason... View Article

Consider the following statements: 1. Cs+ is more highly hydrated than the other alkali metal ions.2. Lithium has the highest melting point among the alkali metals Li, Na, K, and Rb.3. Only lithium forms a stable nitride by direct combination among the alkali metals.Which of these statements are correct.

(A) 1 and 2 are correct (B) 2 and 3 are correct (C) 1 and 3 are correct (D) 1,... View Article

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