Three randomly chosen nonnegative integers x,yandzare found to satisfy the equation x+y+z=10.Then the probability that zis even, is:125 (b) 21 (c) 116 (d) 5536
Which of the following is (are) NOT the square of a 3×3 matrix with real entries? (a)⎣⎡10001000−1⎦⎤ (b) ⎣⎡−1000−1000−1⎦⎤ (c)⎣⎡100010001⎦⎤ (d) ⎣⎡1000−1000−1⎦⎤
A farmer F1has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1)and R(2, 0). From this land, a neighbouring farmer F2takes away the region which lies between the side PQand a curve of the form y=xn (n>1). If the area of the region taken away by the farmer F2is exactly 30% of the area of PQR, then the value of nis _______.
A box B1, contains 1 white ball, 3 red balls and 2 black balls. Another box B2, contains 2 white balls, 3 red balls and 4 black balls. A third box B3, contains 3 white balls, 4 red balls and 5 black balls.
Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let xi be the number on the card drawn from the ith box, i = 1, 2, 3.The probability that x1+x2+x3 is odd isThe probability that x1,x2,x3 are in an aritmetic progression is
In R', consider the planes P1,y=0 and P2:x+z=1. Let P3, be a plane, different from P1, and P2, which passes through the intersection of P1, and P2. If the distance of the point (0,1,0) from P3, is 1 and the distance of a point (α,β,γ) from P3 is 2, then which of the following relation is (are) true ?
Let f:[0,2]→R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1Let:F(x)=∫0x2f(t)dtforx∈[0,2]I˙fFprime(x)=fprime(x) . for all x∈(0,2), then F(2) equals (a)e2−1 (b) e4−1(c)e−1 (d) e4