Mathematics Tes...

The negation of the boolean expression ~ s ∨ (~ r ∧ s) is equivalent to :

The angle of elevation of the top of vertical tower standing on a horizontal plane is observed to be 45° from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30°, then the distance (in m) of the foot of the tower from the point A is:

If a ∈ z, and the equation (x – a) (x – 10) + 1 = 0 has integral roots, then the values of a are :-

Consider the series

1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4...... such that value r repeats upto r² times, then,

If then locus of z is :-

The number of 5 digit numbers which are divisible by 3, using digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 when repetition of digit is allowed is :-

If ¹⁷C₁ 2¹⁶ + ¹⁷C₂ 2¹⁶ + 3.¹⁷C₃ 2¹⁴ + 4.¹⁷C₄.2¹³ +... ....... + 17.¹⁷C₁₇ = x.3^y then x + y is equal to –

A key bunch contains 100 keys exactly one of which open the door. A man tries to open the door by choosing a key random discarding the wrong key after each trial. The probability then door open in 25^th trial is –

Let P(h, k) be a point on the curve y = x² + 7x + 2, nearest to the line y = 3x – 3. Then the equation of the normal to the curve at P is

Suppose f(x) is a polynomial of degree four, having critical points at –1, 0, 1. If T = {x ∈ R} f(x) = f(0), then the sum of squares of all the elements of T is