# IMO Level 2 Class 10 Year 2012 − 2013 Higher Questions and Answers Part 4

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21. The value of is ________.

(A)

(B) 0

(C)

(D) 1

22. If and then ________.

(A)

(B)

(c)

(D)

23. A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs ₹ 216 and one full and one half reserved first class tickets cost ₹ 327. What is the cost of basic first class full fare and the reservation charge?

(a) ₹ 105 and ₹ 6

(B) ₹ 216 and Rs12

(c) Rs210 and ₹ 12

(D) ₹ 210 and ₹ 6

24. if p and q are the roots of the equation , then what is the equation if the roots are and

(A)

(B)

(C)

(D)

25. Given intersecting chords, find x.

(A)

(B)

(C)

(D)

26. If ABC is a right angled triangle with and , where and notations have their usual meanings, then which one of the following is correct?

(A)

(B)

(C)

(D)

27. Six fruit baskets contain peaches, apples, and oranges. Three of the baskets contain two apples and one orange each, two other baskets contain three apples and one peach each, and the last basket contains two peaches and two oranges. You select a basket at random and then select a fruit at random from the basket. Which of the following is the probability that the fruit is an apple?

(A) 0.32

(B) 0.4

(C) 0.46

(D) 0.58

28. A is three times as old as B. Four years ago, C was twice as old as A. in four years՚ time, A will be 31. What are the present ages of B and C respectively?

(A) 9,46

(B) 9,50

(C) 10,46

(D) 10,50

29. If and γ are in A. P. , then ________.

(A)

(B)

(C)

(D)

30. Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

(A) 60 mins 15 secs

(B) 50 mins 15 secs

(C) 51 mins 12 secs

(D) 49 mins 8 secs

31. Points A, B, C and D are midpoints of the sides of square JETS. If the area of JETS is 36 sq. cm, then the area of ABCD is ________.

Fig: …

(A) 3 sq. cm

(B) 7.5 sq. cm

(C) 9 sq. cm

(D) 18 sq. cm

32. The mean of and 4 is m. the numbers and p have mean and median q, then ________.

(A) 7

(B) 6

(C) 5

(D) 4