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21 June 2021: PIB Summary & Analysis

June 21st, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. International Yoga Day 2. Food security (Assistance to State Government Rules)... View Article

If the Boolean expression is a tautology

If the Boolean expression (p ∧ q) ⍟ (p ⊗ q) is a tautology, then ⍟ and ⊗ are respectively given by : a. ∧, → b. →, → c. ∨, → d. ∧, ∨ Answer:... View Article

If [latex]\vec{a}=\alpha i+\beta j+3k,\vec{b}=-\beta i-\alpha j-k \text \ and \ \vec{c}=i-2j-k,[/latex] such that[latex]\vec{a}.\vec{b}=1[/latex] and [latex]\vec{b}.\vec{c}=-3[/latex], then [latex]\frac{1}{3}((\vec{a}\times\vec{b}).\vec{c})=[/latex] is equal to

Answer: 2... View Article

The maximum value of z in the following equation

The maximum value of z in the following equation z = 6xy + y2, where 3x + 4y ≤ 100 and 4x + 3y ≤ 75 for x ≥ 0 and y ≥ 0 is... View Article

If the function f (x) = [cos (sinx) – cosx] / x⁴ is continuous at each point in its domain and f (0) = 1 / k, then k is

Answer: 6 (1 / k) = limx→0 [{2 sin (sinx + x) / 2} sin {x - sinx} / 2] / x4 = limx→0 [(sinx + x) (x - sinx)] / 2x4 = {limx→0... View Article

If f (x) = sin [cos^-1 (1 – 2^2x) / (1 + 2^2x)] and its first derivative with respect to x is (- b / a) log_e 2 when x = 1, where a and b are integers, then the minimum value of |a² – b²| is

Answer: 481 cos-1 [1 - 4x] / [1 + 4x] Let 2x = t > 0 cos-1 [(1 - t2) / (1 + t2)], t > 0 and t = tan θ cos-1 (cos 2θ) =... View Article

If [ ^.] represents the greatest integer function, then the value of |∫₀^√π/2 [[x²] – cosx] dx| is

Answer: 1 ∫0√π/2 [[x2] - cosx] dx = ∫01 [- cosx] dx + ∫1√π/2 [1 - cosx] dx = ∫01 - 1 - [cosx] dx +... View Article

If (2021)³⁷⁶² is divided by 17, then the remainder is

Answer: 4 (2021)3762 = (2023 – 2)3762 = multiple of 17 + 23762 = 17λ + 22 (24)940 = 17λ + 4 (17 – 1)940 =... View Article

The minimum distance between any two points

The minimum distance between any two points P1 and P2 while considering point P1 on one circle and point P2 one the other circle for the given... View Article

If [latex]A=\begin{bmatrix} 2 &3 \\ 0&-1 \end{bmatrix}[/latex], then the value of det (A⁴) + det (A¹⁰– Adj (2A))¹⁰) is equal to

Answer: 16 |A10 - adj (2A)10| = 0... View Article

If the equation of the plane passing through the line of intersection

If the equation of the plane passing through the line of intersection of the planes 2x - 7y + 4z - 3 = 0, 3x - 5y + 4z + 11 = 0 and the point... View Article

Let there be three independent events

Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is ɑ, only E2 occurs is β and only E3 occurs is .... View Article

The value of the limit

The value of limx→0+ [cos-1 (x - [x]2) . sin-1 (x - [x]2)] / [x - x3], where [x] denotes the greatest integer ≤ x is: a. 0 b.... View Article

The area of the triangle with vertices A (z), B (iz) and C (z + iz) is:

a. (1 / 2) |z + iz|2 b. 1 c. 1 / 2 d. (1 / 2) |z|2 Answer: (d) Area of triangle = (1 / 2) (area of square) = (1 / 2) |z|2... View Article

In a school, there are three types of games to be played.

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all three games. Which Venn... View Article

The inverse of y = 5^logx is

a. x = 5logy b. x= ylog5c. x = y1/log5 d. x = 51/logy Answer: (c) y = 5logx log5 y = loge x x = elog5y... View Article

Two dice are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is:

a. 17 / 36 b. 4 / 9 c. 5 / 12 d. 1/2 Answer: (a) n (S) = 36 The possible ordered pairs are (1, 1), (1, 2), (1, 3), (1, 5), (1, 7), (2, 1),... View Article

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