Mathematics Sample CBT

1. A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number.

2. In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?

3. Find the difference between the range and the variance of the following set of numbers 4,9,6,3,2,8,10,5,6,7 where εd2 = 60

4. An arc of a circle subtends an angle to at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle [π = 22/7]

5. A cone with the sector angle of 45o is cut out of a circle of radius rcm. Find the base radius of the cone.

6. Given that log_a⁡2 = 0.693 and log_a⁡3 = 1.097, find log_a⁡13.5

7. If 8^(x/2) = (2^(3/8)) 〖(4〗^(3/4)), find x.

8. Simplify ((2√3+3√5))/((3√5 -2√3 ))

9. Differentiate (6x^3-5x^2+1)/(3x^2 )

10. d/dx cos (3×2 – 2x) is equal to