22

UNIT TEST II (JULY, 2022)
SUBJECT: MATHEMATICS
CLASS X
SET-A

Time: 55 Min
M.M.: 30

1. If tanθ=√3, then what is the value of secθ? (1 mark)

2. From a well shuffled pack of cards, a card is drawn at random. What is the probability of getting a black queen? (1 mark)

3. If the probability of an event is p, then find the probability of its complimentary event. (1 mark)

4. Evaluate: 4(sin⁴30°+cos⁴60°)-3(cos²45°-sin²90°) (2 marks)

5. In a musical chair game, the person playing the music has been advised to stop playing the music at any time within two minutes after playing. What is the probability that the music will stop within the first half minute after starting? (2 marks)

6. Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has
i) an even number.
ii) a perfect square number. (2 marks)

7. The probability of selecting a red ball at random from a jar that contains only red blue and orange balls is 1/4. The probability of selecting a blue ball at random from the same jar is 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar. (3 marks)

8. If sin(A-B)=1/2; cos(A+B)=1/2, 0°<(A+B)≤90°, A>B, then find A & B. (3 marks)

9. If tanθ=4/3, show that √[(1-sinθ)/(1+sinθ)] + √[(1+sinθ)/(1-sinθ)]=10/3 (3 marks)

10. Prove that : cosA/1-tanA + sin²A/sinA-cosA = sinA+cosA (4 marks)

11. In the figure of ΔPQR, ∠P=θ & ∠R= φ

Find
i) [√(x+1)] cotφ
ii)[√(x³+x²)] tanφ
iii) cosθ

12. Case-Study

Two friends were playing a game with two dice. Pratima has blue dice and Riya has grey dice. They decided to throw the dice simultaneously appearing on the top of both dice. On the basis of the above information, answer the following questions.

i) Note down all the possible outcomes. What is the probability of getting the sum of numbers on two dice is 19? (2 marks)
ii) What is the probability that both the numbers are odd numbers? (1 mark)
iii) What is the probability that sum of two numbers is even? (1 mark)