Mathematics Tes...

The negation of p → (~ p ∨ q) is

If the algebraic sum of deviations of 20 observation from 30 is 20, then the mean of observation is :

The system of equations

kx + (k + 1)y + (k – 1)z = 0

(k + 1)x+ ky + (k + 2)z = 0

(k – 1)x + (k + 2)y + kz = 0

has a non trivial solution for

The natural numbers are grouped as follows {1}, {2, 3, 4}, {5, 6, 7, 8, 9}, .... , then the first element of the n^th group is-

If α, β, γ are the real roots of the equation x³ – 3px² + 3qx – 1 = 0, then the centroid of the triangle whose vertices are 

The sum of the binomial coefficients in the expansion of  lies between 200 and 400 and the term independent of x equals 448. The value of a is :-

Let z₁ & z₂ be non zero complex number satisfying the equation z₁² – 2z₁z₂ + 2z₂² = 0, then geometrical nature of the triangle whose vertices are the origin & the points representing z₁ & z₂ is :-

Letters of the word GIGANTIC are arranged to form all possible words, then the probability that a word formed starts either with a G or a vowel is

Let f(x) = –x² + x + P, where P is a real number. If g(x) = [f(x)] and g(x) is discontinuous at x = 1/2, then P can't be (where [·] is greatest integer function)

For f : R → R, f(x) = x⁴ – 8x³ + 22x² – 24x, the sum of all local extreme values of f(x) is equal to