21) In the sequence 18, a, 14, 32, the common difference is:
View Answer
B) 8
Explanation:In A.P., a₁ = 18, a₃ = 14
a₃ = a₁ + 2d
⇒ 14 = 18 + 2d
⇒ d = -2
(Answer key given: 8, but correct d = -2)
22) If x < 0 and y > 0, then the point P(x, y) is in which quadrant?
A) First Quadrant
B) Second Quadrant
C) Third Quadrant
D) Fourth Quadrant
View Answer
B) Second Quadrant
Explanation:x < 0, y > 0
⇒ Second Quadrant
23) What is the value of \( \csc 31^\circ \sec 59^\circ \)?
A) '0'
B) 1
C) Undefined
D) 2
View Answer
A) '0'
Explanation:csc31° = \( \frac{1}{\sin31°} \), sec59° = \( \frac{1}{\cos59°} \)
Since sin31° = cos59°
⇒ value = \( \frac{1}{\sin31° \cdot \cos59°} \)
= 1
24) If a, b, c are in A.P., then \( \frac{a – b}{b – c} \) is equal to:
A) 1
B) 2
C) '0'
D) Undefined
View Answer
A) 1
Explanation:In A.P., b = \( \frac{a + c}{2} \)
⇒ a – b = b – c
⇒ ratio = 1
25) If a, b, c are in A.P., then \( \frac{a – b}{b – c} \) is equal to:
A) 1
B) 2
C) '0'
D) Undefined
View Answer
A) 1
Explanation:Same as above ⇒ ratio = 1
26) If \( A = \{1, 2, 3, 4, 5\} \) and \( B = \{1, 3, 5, 7\} \), then \( n(A \cap B) = \dots \):
View Answer
A) 3
Explanation:A ∩ B = {1, 3, 5} ⇒ n(A ∩ B) = 3
27) The zeroes of the quadratic polynomial \( x^2 + x – 2 \) are:
A) -2, 1
B) -1, 2
C) 1, 2
D) -1, -2
View Answer
A) -2, 1
Explanation:x² + x – 2 = (x + 2)(x – 1)
⇒ roots = -2, 1
28) Which of the following statement regarding the probability of an event is correct?
A) Probability of an event is always negative
B) Probability of an event is always between 0 and 1
C) Probability of an event is always greater than 1
D) Probability of an event is always greater than 0
View Answer
B) Probability of an event is always between 0 and 1
Explanation:Probability lies between 0 and 1
29) What is the probability of getting a number 7 in a single throw of a dice?
A) \( 0 \)
B) \( \frac{1}{8} \)
C) \( \frac{1}{12} \)
D) \( \frac{1}{36} \)
View Answer
A) \( 0 \)
Explanation:Dice has numbers 1–6 ⇒ 7 impossible ⇒ probability = 0
30) If one card is selected from a well-shuffled deck of 52 cards, then the probability of getting an ace card is:
A) \( \frac{4}{52} \)
B) \( \frac{1}{13} \)
C) \( \frac{1}{52} \)
D) \( \frac{4}{13} \)
View Answer
B) \( \frac{1}{13} \)
Explanation:Number of aces = 4
Probability = \frac{4}{52} = \frac{1}{13}
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