If sin4 Aa+cos4 Ab=1a+b, then the value of sin8 Aa3+cos8 Ab3 is equal to
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The number of terms common to the series 3+7+11+⋯+2019 and 1+6+11+⋯+2021 is
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The sum of series 1.2.4 + 2.3.5 + 3.4.6 + ----------- 20 terms. __
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If p⇒(q∨r) is false, then the truth values of p,q,r are respectively
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The value of 5log15(12)+log√2(4√3+√7)+log12(110+2√21) is
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For every natural number n, n(n2−1) is divisible by
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The distances of the roots of the equation |sinθ1|z3+|sinθ2|z2+|sinθ3|z+|sinθ4|=3, from z=0, are
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The number of real roots of the equation esin x−e−sin x−4=0 are
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Let [k] denotes the greatest integer less than or equal to k. Then the number of positive integral solutions of the equation [x[π2]]=⎡⎢⎢⎣x[1112]⎤⎥⎥⎦ is
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Three integers a,b,c are in G.P. If a,b,c−64 are in A.P., and a,b−8,c−64 are in G.P., then (a+b+c) is equal to
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If two roots of the equation x3−3x+2=0 are same, then the roots will be
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If sin A = 45 and cos B = - 1213, where A and b lie in first and third quadrant respectively, then cos(A + B) =
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Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 12,16 and 13, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games. P(X=Y) is
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If 2sec(2α)=tanβ+cotβ ,then one of the values of α+βis
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