class 10th Maths Exempler ( Trigo, Real, Stats and Probability)

Question 1  The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is

(A) 13 (B) 65

(C) 875 (D) 1750

Question 2. If cos A = 45 , then the value of tanA is

Question 3 If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is
(A) 1
(B) 12
(C) 2
(D) 3

Question 4. lf 4tanθ = 3, then (4sinθ−cosθ4sinθ+4cosθ) is equal to

Question 5. A pole 6m high casts a shadow 2√3 m long on the ground, then the Sun’s elevation is
(A) 600
(B) 45°
(C) 30°
(D) 90°

Question 6. If two positive integers a and b are written as a = x3y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is
(A) xy
(B) xy2
(C) x3y3
(D) x2y2

Question 7  If two positive integers p and q can be expressed as p = ab2, and q = ab; a, b being prime numbers, then LCM (p, q) is

(A) ab
(B) a2b2
(C) a3b2
(D) a3b3

Question 8. Prove that √3 + √5 is irrational.

Question 9. On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

Question 10. Consider the following frequency distribution

Question 11. The upper limit of the median class is
(a) 7                                (b) 17.5                      (c) 18                                 (d) 18.5

Question 12. While computing mean of grouped data, we assume that the frequencies are
(a) evenly distributed over all the classes
(b) centred at the class marks of the classes
(c) centred at the upper limits of the classes
(d) centred at the lower limits of the classe

Question 13.

Question 14. For the following distribution,

the modal class is
(a) 10-20                             (b) 20-30            (c) 30-40                           (d) 30-40

Question 15. If an event cannot occur, then its probability is
(a) 1                          (b) 34                          (c) 12                 (d) 0

Question 16. The probability expressed as a percentage of a particular occurrence can never be
(a) less than 100                                        (b) less than 0
(c) greater than 1                                       (d) anything but a whole number

Question 17. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
(a) 4                           (b) 13                        (c) 48                       (d) 51

Question 18. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7                           (b) 14                        (c) 21                       (d) 28

Question 19.

Question 20.If tanA = 34 , then sinA cosA = 1225 .

Question 21. (√3 +1)(3 – cot 30°) = tan3 60° – 2 sin 60°

Question 22. A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.

Question 23. An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Question 24. The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

Question 25. If 1 + sin2θ = 3sinθ cosθ, then prove that tanθ = 1 or 12 .

Question 26. A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are α and β , respectively. Prove that the height of the tower is ( htanαtanβ−tanα)

Question 27. If a sinθ + b cosθ = c, then prove that acosθ – bsinθ = a2+b2+c2−−−−−−−−−√.

Question 28. The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the other tower.

Question 29. A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Prove that the height of the other house is h (1 + tan α cot β) metres.

Question 30. The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be 60° and 30°, respectively. Find the height of the balloon above the ground.

Question 31. I toss three coins together. The possible outcomes are no heads, 1 head,2 head and 3 heads. So, I say that probability of no heads is 14. What is wrong with this conclusion?

Question 32. Sushma tosses a coin 3 times and gets tail each time. Do you think that the outcome of next toss will be a tail? Give reasons.

Question 33. Calculate the mean of the following data

Question 34. The daily income of a sample of 50 employees are tabulated as follows.

Find the mean daily income of employees.

Question 35. Size of agricultural holdings in a survey of 200 families is given in the following
Compute median and mode size of the holdings.

Question 36. The median of the following data is 50. Find the values of p and q, if the sum of all the frequencies is 90.

Question 37. Find the mean marks of students for the following distribution

Question 38. Box A contains 25 slips of which 19 are marked  ₹ 1 and other are marked  ₹ 5 each. Box B contains 50 slips of which 45 are marked  ₹ 1 each and others are marked  ₹ 13 each. Slips of both boxes are poured into a third box and resuffled. A slip is drawn at random. What is the probability that it is marked other than  ₹ 1?

Question 39. the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value.
(i) 7                              (ii) greater than 7                                      (iii) Less than 7

Question 40. A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since, this situation has only two possible outcomes, so the 1 probability of each is 

12. Justify.