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int {frac{{dx}}{{4{{sin }^2}x + 5{{cos }^2}x}}} ...
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The least positive integer n which will reduce {left( {frac{{i - 1}}{{i + 1}}} ight)^n} to a real number, is ...
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If x + frac{1}{x} = sqrt 3 , then x = ...
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{i^2} + {i^4} + {i^6} + ..... upto (2n+1) terms = ...
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Solve the equation cos 4θ+sin5θ=2. (cos4θ=1....and sin5θ=1...using this i got θ= nπ/2 and θ= nπ/5 +(-1)n π/10 ....how should i proceed further??) ...
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∫f(x)/f'(x) dx ...
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The sum of 1+3+5+7+..... upto n terms is ...
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If {left( {frac{{1 + i}}{{1 - i}}} ight)^m} = 1, then the least integral value of m is ...
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The values of x and y satisfying the equation frac{{(1 + i),x - 2i}}{{3 + i}} + frac{{(2 - 3i),y + i}}{{3 - i}} = i, are ...
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Find the next term: 521, 612, 343, 215, ____ ...
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Find the next term: 0, 7, 26, 63, 124, _____ ...
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The roots of the equation {7^{{{log }_7}}}^{({x^2} - 4x + 5)} = x - 1 are ...
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If sin-1x + tan -1x = frac{pi }{2} , then 2x2 + 1= ...
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For real values of x, range of the function y=frac{1}{2-sin 3x} is ...
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If 3+3alpha +3{{alpha }^{2}}+........infty =frac{45}{8}, then the value of alpha will be ...
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If {a^x} = bc,{b^y} = ca,,{c^z} = ab, then xyz = ...
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The roots of the given equation (p-q){{x}^{2}}+(q-r)x+(r-p)=0 are ...
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If the {{p}^{th}},,{{q}^{th}}, and {{r}^{th}} term of an arithmetic sequence are a, b and c respectively, then the value of [a (q – r)+b(r – p)+ c (p – q)]= ...
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If {9^x} - 4 imes {3^{x + 2}} + {3^5} = 0, then the solution pair is ...
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If x = sqrt {7 + 4sqrt 3 } , then x + frac{1}{x} = ...
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If {log _{12}}27 = a, then {log _6}16 = ...
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If the 10th term of a geometric progression is 9 and 4th term is 4, then its 7th term is ...
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The set of values of x which satisfy 5x + 2 < 3x + 8 and frac{{x + 2}}{{x - 1}} < 4 , is ...
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AB is a secant which intersects a circle with centre O at the points C and D such that AC=BD. From A, B two tangents AR and BS are drawn to meet the circle at the points P and Q respectively( as given in the diagram). PQ join ...
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2 sin -1x = cos-1 (1 -2x2) is true for ...
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If sin-1x+sin-1y= frac{2pi}{3} , cos-1x–cos-1y= frac{pi}{3} , the number of ordered pairs (x, y) is ...
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tan(cos-1x) = sin(cot-11/2), x is ...
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If x ≥ 1, then 2 tan -1x + sin-1 frac{2x}{1+{{x}^{2}}} is ...
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If cosec-1x = 2 cot-12 + cos-1 (frac{3}{5}) , then x = ...
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In a third order determinant, each element of the first column consists of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of four terms. Then it can b ...
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