UNIT TEST II (JULY, 2022)
SUBJECT: MATHEMATICS
CLASS X
SET-B
Time: 55 Min
M.M.: 30
1. If sinθ=√3/2, then what is the value of cosθ? (1 mark)
2. A card is selected at random from a well shuffled deck of 52 playing cards. What is the probability of its being a face card? (1 mark)
3. A bag contains 3 red balls, 5 white balls and 7 black balls. What is the probability that ball drawn from the bag at random will be neither red nor black? (1 mark)
4. Evaluate: (4cot²60°+sec²30°-2sin²45°)/(sin²60°+cos²45°) (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 one minute after she starts playing. What is the probability that the muusic will stop within the first half minute after starting? (2 marks)
6. Cards marked with numbers 3,4,5,…,50 are placed in a box and mixed thorougly. One card is drawn at random from the box. Find the probability that number on the drawn card is
i) divisible by 7.
ii) a number which is a perfect square.
7. A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is
i) not red.
ii) white. (3 marks)
8. If cosec(A-B)=2; cot(A+B)=1/√3, 0°<(A+B)≤90°, A>B, then find A & B. (3 marks)
9. If cosθ+sinθ=√2cosθ, show that cosθ-sinθ=√2sinθ. (3 marks)
10. Prove that: cos²θ/(1-tanθ)+sin³θ/(sinθ-cosθ)=1+sinθ.cosθ (4 marks)
11. In the figure of ΔABC, ∠C=θ & ∠A= φ
Find:
i) cosecθ √(x+1)
ii) cotφ√(x³+x²)
iii) cosθ
12.
Rahul and Ravi planned to platy Business (board game) in which they were supposed to use two dice. On the basis of above information, answer the following questions.
i) Note down all the possible outcomes. Ravi got first chance to roll the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 8? (2 marks)
ii) Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 13? (1 mark)
iii) Ravi got next chance. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is more than and equal to 7? (1 mark)