Mathematics Tes...

Let z₁ and z₂ be the nth roots of unity which are ends of a line segment that subtend a right angle at the origin. Then, n must be of the form

If A is a square matrix of order 3 with |A| = 2, then the value of |(A − A^T)⁵| + |(A^T − A)³| is

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dP/dx = 100 − 12√x. If the firm employs 25 more workers, then the new level of production of items is

AB is a vertical tower. The point A is on the ground and C is the middle point of AB. The part CB subtends an angle α at a point P on the ground. If AP = nAB, then the correct relation is

If x = −1 and x = 2 are points of extrema of f(x) = α log|x| + βx² + x, then

If a,b,c,d,e,f are in arithmetic progression. Then e − c is equal to

The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together, is

Fifteen coupons are numbered 1, 2, 3,…..,15 respectively. Seven coupons are selected at random one at a time with replacement. The probability, that the largest number appearing on selected coupons is at most 9, is

If O is the origin, OP and OQ are distinct tangents to the circle x² + y² + 2gx + 2fy + c = 0, then the circumcentre of the triangle OPQ is