General Instruction
1. All the questions are compulsory
2. The question paper consists of 40 question and it is divided into four sections A,B , C and D. SECTION A Comprises of 20 questions carrying 1 mark each. Section B comprises of 6 questions carrying 2 marks each, Second C comprises of 8 questions carrying 3 marks each. Section D comprises of 6 questions carrying 4 marks each.
3. There is no overall choice
4. Use of calculator is not permitted.
2. The question paper consists of 40 question and it is divided into four sections A,B , C and D. SECTION A Comprises of 20 questions carrying 1 mark each. Section B comprises of 6 questions carrying 2 marks each, Second C comprises of 8 questions carrying 3 marks each. Section D comprises of 6 questions carrying 4 marks each.
3. There is no overall choice
4. Use of calculator is not permitted.
Section A
1. What is the mean of first 12 prime number?
2. If the zeros of the quadratic polynomial x2+ (a+1)x + b are 2 and -3 , then
a) a=-7 ,b=-1
b) a=5 , b=-1
c) a=2 ,b=-6
d) a=0, b=-6
3. If the probability of an event is 'p' the probability of its complementary event will be
a) p-1
b) p
c ) 1-p
d) 1-1/p
4. The decimal expansion of the rational number 237/(23✕5) will terminate after
a) one decimal place
b) two decimal place
c) three decimal place
d) more than three decimal place
5. If x= 3m-1 and y= 4 is a solution of the equation x+y = 6 , then find the value of m.
6. If 1/2 is a root of x2 + px -5/4=0 then value of p is__________.
7. Find 5th term of an A.P. whose nth term is 3n+5.
8.In the given Fig., ∠M= ∠N= 46°, Express x in terms of a, b and c.
9. The distance between the line 2x + 4= 0 and x-5= 0 , is __________.
10. If 3x= cosecθ and 3/x = cotθ , then find 3( x2 -1/x2).
11. Which of these number always end with digits 6.
a) 4n
b) 2n
c) 6n
d) 8n
12.IF ∆ABC ∼ ∆QRP, Area(∆ABC)/Area (∆PQR)=9/4 ,AB= 18 cm ,BC = 15 cm , then find the length of PR.
13.The perimeter of triangle formed by the points (0,0) ,(2,0) and (0,2) ___________.
14. In fig. ,ABCD is a cyclic quadrilateral . If ∠BAC = 50° and ∠DBC = 60° , then ∠BCD_____
15.In the given Fig. ∆AHK ∼ ∆ABC If AK =10 cm, BC=3.5 cm and HK =7 cm, find AC.
16. If tanθ = cot (30°+ θ) , find the value of θ .
17. In fig. , O is the centre of a circle , PQ is a chord and the tangent PR at P makes an angles of 50° with PQ. Find ∠POQ.
18.It is given that ∆DEF ∼ ∆RPQ. Is it true to say that ∠D=∠R and ∠F=∠P?
19. Find the sum of first 10 even numbers.
20. Which of the following equation has 2 as a root
a) x2+4=0
b) x2-4= 0
c) x2+3x+12=0
d) 3x2 -6x -2= 0
2. If the zeros of the quadratic polynomial x2+ (a+1)x + b are 2 and -3 , then
a) a=-7 ,b=-1
b) a=5 , b=-1
c) a=2 ,b=-6
d) a=0, b=-6
3. If the probability of an event is 'p' the probability of its complementary event will be
a) p-1
b) p
c ) 1-p
d) 1-1/p
4. The decimal expansion of the rational number 237/(23✕5) will terminate after
a) one decimal place
b) two decimal place
c) three decimal place
d) more than three decimal place
5. If x= 3m-1 and y= 4 is a solution of the equation x+y = 6 , then find the value of m.
6. If 1/2 is a root of x2 + px -5/4=0 then value of p is__________.
7. Find 5th term of an A.P. whose nth term is 3n+5.
8.In the given Fig., ∠M= ∠N= 46°, Express x in terms of a, b and c.
10. If 3x= cosecθ and 3/x = cotθ , then find 3( x2 -1/x2).
11. Which of these number always end with digits 6.
a) 4n
b) 2n
c) 6n
d) 8n
12.IF ∆ABC ∼ ∆QRP, Area(∆ABC)/Area (∆PQR)=9/4 ,AB= 18 cm ,BC = 15 cm , then find the length of PR.
13.The perimeter of triangle formed by the points (0,0) ,(2,0) and (0,2) ___________.
14. In fig. ,ABCD is a cyclic quadrilateral . If ∠BAC = 50° and ∠DBC = 60° , then ∠BCD_____
17. In fig. , O is the centre of a circle , PQ is a chord and the tangent PR at P makes an angles of 50° with PQ. Find ∠POQ.
19. Find the sum of first 10 even numbers.
20. Which of the following equation has 2 as a root
a) x2+4=0
b) x2-4= 0
c) x2+3x+12=0
d) 3x2 -6x -2= 0
Section B
21. Find the median of the following distribution(click on image to zoom)
22. If the quadratic equation Px2-2√5Px +15=0 has two equal roots then find the value of P.
23. Find the 20th term from the last term of the A.P. 3,8,13,.....253.
24. If 7sin2θ + 3cos2θ = 4 then show that tan θ = 1/√3 .
25. If diameters of two concentric circle are d1 and d2 ( d2 >d1) and c is the length of chord of bigger circle which is tangent to the smaller circle . Show that d22 = c2 + d12.
26. If sin(A-B) = 1/2 , cos(A+B) = 1/2 then find the value of A and B
23. Find the 20th term from the last term of the A.P. 3,8,13,.....253.
24. If 7sin2θ + 3cos2θ = 4 then show that tan θ = 1/√3 .
25. If diameters of two concentric circle are d1 and d2 ( d2 >d1) and c is the length of chord of bigger circle which is tangent to the smaller circle . Show that d22 = c2 + d12.
26. If sin(A-B) = 1/2 , cos(A+B) = 1/2 then find the value of A and B
Section C
27. Prove that √3 + √5 is irrational.
28. A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball. Find the number of black balls in the bag.
29. Area of a sector of a circle of radius 36 cm is 54π cm2 .Find the length of the corresponding arc of the sector.
30. What must be added to 4x4 + 2x3 -2x2 + x -1 so that the resulting polynomial is divisible by x2 - 2x -3?
31. Find the value of K so that the area of triangle ABC with A ( K+ 1,1) , B(4,-3) and C(7, -K) is 6 sq. Units.
32. Prove that (tanθ + secθ-1 )/ (tanθ - secθ +1) = (1+ sinθ)/cosθ
33. Determine the A.P. where 4th term is 18 and the difference of 9th term from the 15 th term is 30.
34. The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6:05 am to 6:40 am.
Section D
35. The rain water from a roof 22m✕20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m . If the vessel is just full , find the rainfall in cm.
36. A and B are two points 150 km apart from on a highway. Two cars start with different speeds from A and B at same time. If they move in same direction, they meet in 15 hr. If they move in opposite direction , they meet in one hr. Find their speeds.
37. In ∆PQR PD QR such that D lies on QR. If PQ = a ,PR=b ,QD =c , DR= d and a,b,c ,d are positive units. Prove that (a+b)(a-b) = (c+d) (c-d).
38. If P(x,y) is any point on the line of the line joining A (a,0) and B(0,b) then show that x/a+ y/b =1.
39. AB is a line segment of length 8 cm. Locate a point C on AB such that AC= 1/3 CB.
40.Find the mean, median and mode of the following data:(click on image to zoom)
36. A and B are two points 150 km apart from on a highway. Two cars start with different speeds from A and B at same time. If they move in same direction, they meet in 15 hr. If they move in opposite direction , they meet in one hr. Find their speeds.
37. In ∆PQR PD QR such that D lies on QR. If PQ = a ,PR=b ,QD =c , DR= d and a,b,c ,d are positive units. Prove that (a+b)(a-b) = (c+d) (c-d).
38. If P(x,y) is any point on the line of the line joining A (a,0) and B(0,b) then show that x/a+ y/b =1.
39. AB is a line segment of length 8 cm. Locate a point C on AB such that AC= 1/3 CB.
40.Find the mean, median and mode of the following data:(click on image to zoom)
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