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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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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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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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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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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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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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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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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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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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Assume that p is a real number. In order for x+3p+1 - x =1 to have real solutions it is necessary that 1. p≥1/4 2. p≥-1/4 c. p≥1/3 4. p≥-1/3 ...
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What is the minimum value of 9sec2x + 10cosec2x for all x belongs to R?? ...
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What is the minimum value of 9sec2x + 10cosec2x for all x belongs to R?? ...
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Find the values of α and β, 0<α, β < Π/2, satisfying the eqn - cos α cos β cos (α+β) = -1/8. ...
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If cos π/7 , cos 3π/7 , cos 4π/7 are the roots of the equation 8x3-4x2-4x+1 = 0 then the What are the values of expressions sin π/14 sin 3π/14 sin 5π/14 and cos π/14 cos 3π/14 cos 5π/14 ???? ...
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IF K1 = tan 27θ - tan θ and K2 = sin θ/cos 3θ + sin 3θ/cos 9θ + sin 9θ/cos 27θ , then 1. K1 = 2K2 2. K1 = K2 + 4 3. K1 = K2 4. none of these ...
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Find the values of α and β, 0<α, β < Π/2, satisfying the eqn - cos α cos β cos (α+β) = -1/8. ...
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If α, β are the roots of the equation x2-2x-a2+1 = 0 and γ, δ are the roots of the equation x2-2(a+1)x+a(a-1)=0 such that α, β belongs to (γ,δ) , then find the values of ‘a’. ...
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A student appears for test I, II and II. The student is successful if he passes either in tests I and II or test I and III. The probabilities of the student passing in tests I, II and III are p, q and 1/2 respectively. If the ...
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The probability that a man aged x years will die in a year is p. The probability that out of n men M1, M2, M3, . . . . . . , Mn each aged x years, M will die and be the first to die is a. 1/n2 b. 1-(1-p)n c. 1/n2[1-(1-p)n] d. ...
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A circle of radius 5 units has diameter along the angle bisector of the lines x+y = 2 and x - y = 2. If chord of contact from origin makes an angle of 45° with the positive direction of x axis then the equation of the circle ...
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I n the fig. shown a point object O is placed in air . A spherical boundary separates 2 media.AB is principal axis.The refractive index above AB is 1.6 & below AB is 2 The separation b/w the images formed due to refraction at ...
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(y3-2x2y)dx + (2xy2 - x3)dy =0, then the value of xy√(y2-x2) is 1. y2 +x 2. xy2 3. any constant 4. none of these ...
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Find the value(s) of the parameter 'a' (a>0) for each of which the area of the figure bounded by the straight line, y = a2-ax/1+a4 and the parabola y = x2+2ax+3a2/1+a4 is the greatest. ...
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1. ∫cos2x/ (1+tanx) dx 2. ∫[(x/e)x+(e/x)x] lnx dx ...
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A charge of 200 μC is imparted to each of the 2 identical parallel plate capacitor connected in parallel. At t=0, the plates of both capacitors are placed 1 m apart. The paltes of 1st capacitor moves towards each other with ...
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A charge of 200 μC is imparted to each of the 2 identical parallel plate capacitor connected in parallel. At t=0, the plates of both capacitors are placed 1 m apart. The paltes of 1st capacitor moves towards each other with ...
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A capacitor of capacitance C is charnged to a potential difference V from a cell and then disconnected. A charge +Q is now given to its +ve plate. The potential difference across the capacitor is now: (a) V (b) V+Q/C (c) V+Q/ ...
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limn→∞(nαsin2n!/n+1), where 0<α<1 ...
