Q) The median of the marks scored by 100 students in a 25 marks Unit test is
| Marks | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 |
| No. of students | 10 | 18 | 42 | 13 | 7 |
B) 12.3
C) 12.6
D) 12.7
Explanation: n/2 = 90/2 = 45
45 lies in the class = 10 — 15
∴ Median class = 10 – 15; h = 5
n/2 – c.f
median =
x h=
x 5= 10 + 17/42 x 5
= 10+85/42
= 10+2.023
= 12.023 = 12.3
Q) A number chosen from 1 to 100. Find the probability that it is a prime number.
A) 1/2
B) -1/4
C) 1/4
D) -1/2
Q) In hundred numbers 20 are fours, 40 are fives, 30 are sixes remaining are tens arithmetic mean is
A) 3.5
B) 5.6
C) 4.7
D) 5.8
Explanation: Arithmetic mean =
= 560/100 = 5.6
Q) If a coin is tossed 3 times, then the probability of getting at least one head is
A) 
B) 
C) 
D) 
Explanation: n(S) = 23 = 8
A = {(H HH), (H HT), (HTH), (T HH), (H T T), (T H T), (T T H)}
= n (A) = 7
∴ P(A) = n(A)/n(S) = 7/8
Q) A bag contains 6 red balls, 12 green balls and 8 black balls. Find the probability that the ball drawn is either a black or a red ball.
A) 
B) 
C) 
D) 
Explanation: n(S) = 26C1 = 26
n(A) .= 8C1 = 8
P(A) = n(A)/ n(S) = 8/26
N(B) = 6C1 = 6
P(B) = n(B)/n(S) = 6/26
∴ P(A u B) = P(A) + P(B) – P(A n B)
= 8/26+6/26 -0
=14/26 = 7/13
Q) The mean of 17, 4, 8, 6 and 15 in m, the median of 8, 14,10, 5, 7, 5, 20, 19 and n is (m – 1). Then the values of m and n are
A) m = 9, n = 10
B) m = 10, n = 9,
C) m = 5, n = 9
D) None of these
Explanation: Mean = m
=
= mM = 50/5 = 10
∴ m = 10
Median (n) = m-1
N = 10-1 (∴ m = 10)
∴ n = 9
∴ m = 10, n = 9
Q) If two dice are rolled simultaneously, then the probability that the numbers on them are different is
A) 
B) 
C) 
D) 
Explanation: n(S) = 62 = 36
n(A) = 30
∴ P(A) =
= 30/36 = 5/6
Q) Ratio of volume of cylinder and cone whose radii are equal and having same heights
A) 1 : 3
B) 1 : 2
C) 3 : 1
D) 2 : 1
Q) If A = 45°, B = 60°, then sin A + cos B =
A) 
B) 
C) 
D) 
Explanation: A = 45°, B = 60°
sin A + cos B = sin 45° + cos 60°
=
Q) If A = π/4, then (1 + tan A) (1 + tan2A) (1 + tan3A) =
A) 6
B) 4
C) 8
D) 2
nice