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P(x) = `{(1/"k" ((5),(x))"," (x=0,1,2,3,4,5); k > 0),(0 "," "otherwise"):},`
is p.m.f. of a r.v. X. Then `1/"k"` is equal to
Concept: undefined >> undefined
The differential equation having y = (cos-1 x)2 + P (sin-1 x) + Q as its general solution, where P and Q are arbitrary constants, is
Concept: undefined >> undefined
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The maximum value of P = 7x + 6y subject to constraints x + 2y ≤ 24, 2x + y ≤ 30 and x ≥ 0, y ≥ 0 is ______.
Concept: undefined >> undefined
The mean and variance of a binomial distribution are 2 and 1 respectively, then the probability of getting exactly three successes in this distribution is ______.
Concept: undefined >> undefined
The family of curves y = `e^("a" sin x)`, where a is an arbitrary constant, is represented by the differential equation.
Concept: undefined >> undefined
If z1 and z2 are z-coordinates of the points of trisection of the segment joining the points A (2, 1, 4), B (–1, 3, 6) then z1 + z2 = ______.
Concept: undefined >> undefined
`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?
Concept: undefined >> undefined
(q v r) v (~ p v ~ q) is a ______.
Concept: undefined >> undefined
The value of `tan^-1 (1/3) + tan^-1 (1/5) + tan^-1 (1/7) + tan^-1 (1/8)`is ______.
Concept: undefined >> undefined
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
Concept: undefined >> undefined
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
Concept: undefined >> undefined
cos (36° - A) cos (36° + A) + cos(54° + A) cos (54° - A) = ?
Concept: undefined >> undefined
`int_0^1 ((x^2 - 2)/(x^2 + 1))`dx = ?
Concept: undefined >> undefined
If a = `3hat"i" + hat"j" - hat"k"`, b = `2hat"i" - hat"j" + 7hat"k"` and c = `7hat"i" - hat"j" + 23 hat"k"` are three vectors, then which of the following statement is true.
Concept: undefined >> undefined
The rate of disintegration of a radio active element at time t is proportional to its mass, at the time. Then the time during which the original mass of 1.5 gm. Will disintegrate into its mass of 0.5 gm. is proportional to ______.
Concept: undefined >> undefined
∫ log x · (log x + 2) dx = ?
Concept: undefined >> undefined
The c.d.f, F(x) associated with p.d.f. f(x) = 3(1- 2x2). If 0 < x < 1 is k`(x - (2x^3)/"k")`, then value of k is ______.
Concept: undefined >> undefined
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
Concept: undefined >> undefined
If `x^2 y^2 = sin^-1 sqrt(x^2 + y^2) + cos^-1 sqrt(x^2 + y^2)`, then `"dy"/"dx"` = ?
Concept: undefined >> undefined
`int_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e2x dx = ?
Concept: undefined >> undefined
