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A curve is represented parametrically by the equation x= t+eat and y = -t + eat when t belongs to R and a> 0.. If the curve touches the axis of x at the point A, then the coordinates of the point A are 1. (1,0) 2 (1/e, 0) ...
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for a sufficiently large value of n the sum of the square roots of the first n positive integers i.e. √1 + √2 + .... √n is approximately equal to?? ...
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let a, b be the distinct positive roots of the equation tanx = 2x then evaluate ∫(sin(ax).sin(bx)) dx independent of a and b. lower limit = 0 upper limit = 1 ...
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find the moment of inertia of a cylinder of mass M, radius R and length L about an axis passing through its centre and perpendicular to its symmetry axis. Do this by integrating an elemental disc along the length of the cylin ...
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Calculate the packing fraction of closed cylinders. ...
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5.35 g of a salt ACl ( of weak base AOH) is dissolved in 250 ml of solution. The pH of the resultant solution was found to be 4.827. Find the ionic radius of A+ and Cl- if ACl forms CsCl type crystals having density 2.2 g/cc. ...
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let f(x) = ([a]2-5[a]+4)x3 - (6{a}2-5{a} + 1)x - (tanx)sgnx, be an even function for all x belongs to R, then sum of all possible values of "a" is (where [] and {} denotes greatest integer function and fractional part functio ...
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There are n containers having volumes V, 2V, ......., nV. A fixed mass of a gas is filled in all containers connected with stopcock. All containers are at the same temperature if pressure of first container is P then What is ...
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A mixture of two gases A and B in the mole ratio 2:3 is kept in a 2 litre vessel. A second 3 litre vessel has the same two gases in the mole ratio 3:5. Both gas mixtures have the same temperature and same total pressure. They ...
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The expression wherever defined, sec4x - 4tan3x+ 4tanx is always : 1. positive 2. negative 3. non- positive 4. non negative ...
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The number of solution of the equation e2x + ex + e-2x + e-x = 3(e-2x+ ex) is 1. 0 2. 2 3. 1 4. more than 2 ...
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let f1(x) = x for 0≤x≤1 1 for x>1 0 otherwise and f2(x) = f1(-x) for all x f3(x) = -f2(x) for all x f4(x) = f3(-x) for all x Which of the following in necessarily true? 1. f4(x) = f1(x) for all x 2. f1(x) = - f3(-x) fo ...
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Solve the inequality sin2x > 2 sin2x + (2- 2 ) cos2x. ...
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Find general value of x which satsfies the equation 2sin(3x+ π/4 ) = 1+8sin2x cos22x . ...
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If two circle touch each other, at their highest or lowest points, and a straight line be drawn through that point to meet both circles, show that the time of sliding down form rest down the portion of this line intercepted b ...
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Suppose p(x) is a polynomial with integer coefficients. The reminder when p(x) is divided by x-1 is 1 and the remainder when p(x) divided by x-4 is 10. If r(s) is the remainder when p(x) is divided by (x-1)(x-4), find the val ...
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Let f(x) = x135 + x125 - x115 + x5 + 1. If f(x) is divided by x3 - x, then the remainder is some function of x say g(x). Find the value of g(10). ...
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A horizontal tube, open at both ends, contains a column of liquid. the length of the liquid column does not change with temperature. Let γ = coefficient of volume expansion of the liquid and α= coefficient of volume expansi ...
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What is the exact value of cos 5° + cos 77° + cos 149° + cos 221° + cos 293°? ...
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If a and b are positive numbers and each of the quations x2+ax+2b = 0 and x2+2bx+a = 0 has real roots, then the smallest possible value of (a+b) is 1. 3 2. 4 3. 5 4. 6 ...
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The set of values of 'a' for which the equations cos2x + a sin x = 2a-7 posses a solution is 1. (-∞,2) 2. [2.6] 3. (6, ∞) 4. (-∞, ∞) ...
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Number of quadratic equations with real roots which remain unchanged even after sqaring their roots is 1. 1 2. 2 3. 3 4. 5 ...
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If x be the real number such that x3+4x = 8 then the value of the expression x7 + 64x2 is 1. 124 2. 125 3. 128 4. 132 ...
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number of possible ordered pair (s) (a,b) for each of which the equality a(cos x - 1) + b2 = cos(ax+b2) - 1 holds true for all x belonging to R are 1. 0 2. 1 3. 2 d. infinite ...
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What is the sum of the roots of the equation (x+1) = 2log2(2x + 3) - 2log4(1980 - 2-x)?? ...
