Non-terminating recurring decimals (like 1/3 = 0.333…) are rational numbers. Therefore, the statement ‘All non-terminating decimals are irrational’ is false.
Q. 117. A right circular cone has radius and slant height . Its total surface area equals:
(A)
(B)
(C)
(D)
Answer:
(C)
Explanation:
The total surface area of a cone is . Substituting radius and slant height gives .
Q. 118. What is the length of the longest pole that fits inside a 10 m × 10 m × 5 m room?
(A) 8 m
(B) 12 m
(C) 13 m
(D) 15 m
Answer:
(D) 15 m
Explanation:
The longest pole is the space diagonal of the cuboid room: .
Q. 119. The mean of five numbers is 30. If one number is excluded, the mean of the remaining four is 28. What is the excluded number?
(A) 28
(B) 30
(C) 35
(D) 38
Answer:
(D) 38
Explanation:
The sum of the 5 numbers is . The sum of the remaining 4 numbers is . The excluded number is .
Q. 120. One end of a circle’s diameter is (2, 3); its centre is (-2, 5). What is the other end?
(A) (-6, 7)
(B) (4, 2)
(C) (5, 3)
(D) (6, 7)
Answer:
(A) (-6, 7)
Explanation:
Let the other end be . The center is the midpoint: and . The other end is .