1. On division by 6, a2 cannot leave remainder ............ (a N)(a) 1 (b) 4 (c) 5 (d) 3

2. Every even integer is of the form ............... .(a) q (b) 2q (c) 3q (d) 4q

3. At x = 0, value of polynomial 8x2 + 6x - 3 is .............. .(a) 8 (b) 6 (c) 0 (d) -3

4. The zero of p(x) = -x2 + 2x - 1 is _______ .(a) 1 (b) -1 (c) 0 (d) 2

5. If the zeros of polynomial p(x) = 3x3 - x2 - ax - 45 is 3, then a = _______ .(a) 3 (b) 6 (c) 9 (d) 12

6. The product of the zeros of a quadratic polynomial p(x) = 3x2 + 7x + 4 is _______ .

(a) 4 (b)34

(c)73 (d)

43

7. Pair of equations 2x + y = 3 and x + 2y = 4 is _______ .(a) consistent (b) not consistent(c) linearly dependent (d) is the same

8. For a pair of equations 13x - 7y = 19 and 7x - 13y = 31, x + y = _______ .(a) 2 (b) -2 (c) 5 (d) 40

9. If5x +

3y = 4 and

3x +

5y = 2, then

1x -

1y = _______ .(x, y 0)

(a) 6 (b) 5 (c) 3 (d) 1

10. After x years, the sum of the ages of sachin and sehwag will be y years, then thesum of the ages before 3 years was _______ years.(a) y - 2x - 6 (b) y + 2x + 6 (c) x - 2y + 6 (d) x + 2y + 6

11. If -3 is a root of a qudratic equation x2 + 3(k + 2)x - 9 = 0, thn k = _______ .(a) 2 (b) -2 (c) 3 (d) -3

PART - AInstructions : [1] All 1 to 50 objective questions are compulsory. (Write your

answer in the OMR Answer Sheet given separately.)[2] All objective questions carry equal marks. Each of 1 mark.[3] A O, B O, C O, D O are given for each questions in the given

separate OMR Answer Sheet. You have to dark compulsory the circle(O) with pen to the correct answer from the given

alternatives.

MAHESH TUTORIALSSUBJECT : Maths(012)Third Preliminary Exam

Question Paper

Date:Marks : 50Time: 1 Hrs.

GSEB Batch : 10th Std. Eng. Medium

SET - B

12. The roots of a quadratic equation x +2x

= 3 are _______ . (x 0)

(a) 2 and 1 (b) -2 and -2 (c) 2 and -1 (d) -2 and 1

13. For a quadratic equation, if _______ , then both the roots are equal.(a) D < 0 (b) D > 0 (c) D = 1 (d) D = 0

14. x = _______ is a solution of a quadratic equation x2 + 7x + 12 = 0.(a) 7 (b) -3 (c) 4 (d) 3

15. If one of the roots of quadratic equation x2 + 4x + m = 0 is 2, then other root is_______.(a) -6 (b) 6 (c) 4 (d) 3

16. For the A.P. 0.1, 0.4, 0.7, 1, ... the common differece is _______ .(a) 3 (b) 0.5 (c) 0.3 (d) -0.3’

17. For a given A.P. the first term is -4 and the common difference is -5. Then, the12th term of the A.P. is _______ .(a) -24 (b) -240 (c) -59 (d) -50

18. The sum of first 16 terms of the A.P. 1, 1.5, 2, ... is _______ .(a) 96 (b) 76 (c) 160 (d) 80

19. ABC DEF is a similarity in ABC and DEF, m A = 40. Then,m E + m F = _______ .(a) 40 (b) 80 (c) 140 (d) 180

20. In ABC, A - M - B, A - N - C and MN|| BC . If AM : AB = 2 : 3 and AC = 15, then NC= _______.(a) 3 (b) 6 (c) 9 (d) 5

21. In ABC, the bisector of A intersects BC at D. If AB : AC = 3 : 4 and BD = 4.5,then BC = _______ .(a) 4.5 (b) 6 (c) 10.5 (d) 12

22. In ABC, m B = 90 and BM is an altitude. If AM - MC = 7 and AB2 - BC2 = 175,then AC =_______.(a) 224 (b) 126 (c) 25 (d) 20

23. In XYZ, m X : m Y : m Z = 1 : 2 : 3. If XY = 15, YZ = _______.

(a)15 3

2(b) 17 (c) 8 (d) 7.5

24. In ABC, m B = 45 and AM is an altitude, M BC . If BC = 7 and AM = 4 thenAC = _______.(a) 4 (b) 2.5 (c) 5 (d) 10

25. One of the end points of a circle having centre at origin is A(3, -2), then the otherend point of the other end point of the diameter has the coordinates_______ .

(a) (-3, 2) (b)3 ,12 (c)

3 , 12 (d) (-3, -2)

26. Points (3, 4), (-1, 4) and _______ are collinear.(a) (-5, 4) (b) (2, 3) (c) (4, 3) (d) (4, 2)

27. A(3, 5) and B(7, 5), then the mid point of AB is _______.

(a) (5, 5) (b)53,2 (c)

3 ,52 (d) (4, 9)

28. Y-axis divides the line segment joining A(-3, -4) and B(1, -2) from A in ratio_______.(a) 2 : 1 (b) 1 : 2 (c) 3 : 1 (d) 3 : 2

29.2 2

2 2cos 40+cos 50sin 40+sin 50 = _______ .

(a) 2 (b) 4 (c) 1 (d) 0

30. sin2 (3x + 30) + cos2 (2x + 45) = 1, then x = ______ .(a) 0 (b) 15 (c) 30 (d) 60

31.4 4

2 2sin θ -cos θsin θ -cos θ = ______ .

(a) 1 (b) 0 (c) 2 sin2 (d) 2 cos2

32. sin21 + sin23 + sin287 + sin289 = ______ .(a) 0 (b) 1 (c) 2 (d) 4

33. The angle of elevation of the top of the tower from a point P on the ground hasmeasure 45. The distance of the tower from the point P is a and height of thetower is b. Then ...........(a) a > b (b) a < b (c) a = b (d) a = 2b

34. If the angles of elevation of a tower from two points at distance a and b (a > b)from its foot on the same side of the tower have measure 30 and 60, then theheight of the tower is .......

(a) a + b (b) ab (c) a - b (d)a

b

35. From the top of a building h metre high, the angle of depression of an object onthe ground has measure . The distance (in metres) of the object from the foot ofthe building is .............(a) h sin (b) h tan (c)h cot (d) h cos

36. A chord of (O, 5) touches (O, 3). Therefore the length of the chord = ______ .(a) 8 (b) 10 (c) 7 (d) 6

37. PA and PB are tangents to (O, 5). If OP = 13, then PB = ______ .(a) 5 (b) 10 (c) 12 (d) 13

38. If the area and the circumference of a circle are numerically equal, then r =______ .

(a) (b) 2 (c) 1 (d) 2

39. The perimeter of a semicircular table-top is 3.60m. Then, its radius is ______cm.(a) 35 (b) 70 (c) 105 (d) 140

40. The circumference of the wheels of a truck is 440 cm. They make 250 rotationsper minute. Then, the speed of the truck is ______ km/h.(a) 50 (b) 60 (c) 66 (d) 88

41. In a circle, the ratio of the areas of two distinct minor sector is 1 : 4. Then, theratio of the angles at the centre for those minor sector is ______ .(a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 4

42. The ratio of radii of tweo spheres is 3 : 4. then, the ratio of their volume is_______.(a) 64 ; 27 (b) 9 : 16 (c) 16 : 9 (d) 27 : 64

43. CSA of a hemisphere with diameter 20 cm is ______ cm2.(a) 20 (b) 200 (c) 100 (d) 40

44. The radii of a frustum of a cone are 5 cm and 9 cm and height is 6 cm, then thevolume is _______ cm3.(a) 320 (b) 151 (c) 302 (d) 98

45. CSA of a cylindrical tank with diameter 2.1 m and height 5 m is ______m2.(a) 22 (b) 44 (c) 66 (d) 33

46. The median class of the frequency distribution given in 9, is ________ .(a) 40 - 50 (b) 30 - 40 (c) 20 - 30 (d) 10 - 20

47. If Z + M = 34 and m + x = 40, then M = _______ .(a) 15 (b) 17 (c) 19 (d) 21

48.Z-MM-x = _______ .

(a) 3 (b)13 (c) 2 (d)

12

49. If P(A) : P A = 3 : 2, then P(A) = _______.

(a)35

(b)25

(c)34

(d)12

50. The probability that a tree of babool bears mangoes naturally is _______.

(a)12 (b)

11000

(c) 1 (d) 0

PART - BSECTION - A

Solve the following sums : [2 marks] 161. Find l.c.m.(105, 91) using g.c.d.(a, b) l.c.m.(a, b) = ab.2. 3 is zero of p(x) = 3x3 - x2 - ax - 45. Find ‘a’.3. The difference between two natural numbers is 6. Adding 10 to the twice of the

larger number, we get 2 less than 3 times of the smaller number. Find these numbers.4. Find the 15th term from end for A.P. 10, 15, 20, 25, ......., 1000.

OR4. Which term of A.P., 100, 97, 94, 91, ...... will be its first –ve term ?5. The correspondence ABC ZXY is a similarity in ABC and XYZ. If AB = 12,

BC = 9, CA = 7.5 and ZX = 10, then YZ + XY = ...... .6. A(3, 5) and B(2, – 7) and C are the collinear points such that B–A–C and BA = AC. Find

the coordinates of C.7. Evaluate : 2 sin2 30 cot 30 - 3 cos2 60 sec2 30

OR7. Prove that If sin + cos = p and sec + cosec = q, show that q(p2 – 1) = 2p8. Daily wages of 90 employees of a factory are as follows :

Daily wages (in Rs) 150-250 250-350 350-450 450-550 550-650 650-750Number of employees 4 6 8 12 33 17

Daily wages (in Rs) 750-850 850-950Number of employees 8 2

SECTION - BSolve the following sums : [3 marks] 12

9. The difference of lengths of sides forming right angle in right angled triangle is 3cm. If the perimeter of the triangle is 36 cm. Find the area of the triangle.

10. A bridge across a valley is h metres long. There is a temple in the valley directlybelow the bridge. The angles of depression of the top of the temple from the two endsof the bridge have measures and . Prove that the height of the bridge above the

top of the temple ish (tan . tan )tan tan

.

11. Two balance dice are thrown once. Write down all the possible outcomes of thisexperiment. What is the probability that the sum of number on two dice is.(i) 7 (ii) 11 (iii) more than 10(iv) less than 2 (v) less than 13 (vi) a prime number

PART - B

Instructions : [1] There are four sections in this question paper and total17 questions.

[2] All questions are compulsory.[3] Take care of internal options in the question paper.[4] Draw neat, clean and labelled diagram as directed.[5] The number on the right-hand indicates marks.[6] Write the answer of questions according to the section.

MAHESH TUTORIALSSUBJECT : Maths(012)Third Preliminary Exam

Question Paper

GSEB Batch : 10th Std. Eng. Medium

SET - B

Date:Marks : 50Time: 2 Hrs.

12. The mean of the following frequency distribution of 200 observations is 332. Findthe values of x and y.

Class 100-150 150-200 200-250 250-300 300-350 350-400Frequency 4 8 x 42 50 y

Class 400-450 450-500 500-550Frequency 32 6 4

OR12. Find the mean wage of 200 workers of a factory where wages are classified as follows:

Class 100-150 150-200 200-250 250-300 300-350 350-400Frequency 4 8 14 42 50 40

Class 400-450 450-500 500-550Frequency 32 6 4

SECTION - CSolve the following sums : [4 marks] 12

13. P lies in the exterior of (0, 5) such that OP = 13. Two tangents are drawn to thecircle which touch circlein A and B. Find AB

14. On a circular table top of radius 30cm a design is formed leaving an equilateraltriangle inscribed in a circle. Find the area of the design.( = 3.14)

O3030

60

M C

A

D

B

15. A hemispherical tank full of water is emptied by pipe at the rate of2147 litres per

second. How much time will it take to empty three fourth of the tank, if it is 4 m indiameter ?

OR15. A tent is in the shape of cylinder surmounted by a conical top. If the height and the

radius of the cylinder part are 3.5 m and 2 m respectively and the slant height ofthe top is 3.5 m, find the area of the canvas used for making the tent. Also find thecost of canvas of the tent at the rate of ` 1000 per m2.

SECTION - DAnswer the following questions : [5 marks] 15

16. (P , 4) is given. Draw a pair of tangents through A which is in the exterior of (P , 4) such that the measure of an angle between the tangents is 60.

17. Areas of two similar triangles are proportional to squares of corresponding sides.(Prove it for acute angled triangles)

OR17. In ABC , mB = 90. and BE is a median. Prove that AB2 + BC2 + AC2 = 8 BE2.

**** Best of Luck ****