Time Allowed: 3 hours Maximum Marks: 80
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
Section A
1. (125)
−1/3
=? [1]
a) − 1
5
b) -5
c) d) 5
1
5
2. If the line represented by the equation 3x + ky = 9 passes through the points (2, 3), then the value of k is [1]
a) 2 b) 1
c) 3 d) 4
3. In which quadrant does the point (-7, -4) lie? [1]
a) IV b) I
c) II d) III
4. A histogram is a pictorial representation of the grouped data in which class intervals and frequency are [1]
respectively taken along
a) horizontal axis only b) horizontal axis and vertical axis
c) vertical axis and horizontal axis d) vertical axis only
5. The equation x - 2 = 0 on number line is represented by [1]
a) infinitely many lines b) two lines
c) a point d) a line
6. The basic facts which are taken for granted, without proof, are called [1]
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, a) theorems b) axioms
c) propositions d) lemmas
7. In the adjoining figure, AOB is a straight line. If x : y : z = 4 : 5 : 6, then y = ? [1]
a) 72° b) 48°
c) 60° d) 80°
8. In Triangle ABC which is right angled at B. Given that AB = 9cm, AC = 15cm and D, E are the mid-points of [1]
the sides AB and AC respectively. Find the length of BC?
a) 13cm b) 13.5cm
c) 12cm d) 15cm
9. (x2 - 4x - 21) = ? [1]
a) (x - 7) (x + 3) b) ( x - 7) ( x - 3)
c) (x + 7) (x + 3) d) (x + 7) (x - 3)
10. Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form [1]
a) (− 9
, m) b) (-9 , 0)
2
c) (0, − 9
) d) (n, −
9
)
2 2
11. ABCD is a parallelogram in which diagonal AC bisects ∠ BAD. If ∠ BAC = 35o, then ∠ ABC = [1]
a) 70o b) 120o
c) 110o d) 90o
12. If bisector of ∠A and ∠B of a quadrilateral ABCD intersect each other at p , ∠B and ∠C at Q , ∠C and ∠D [1]
at R and, ∠D and ∠A at S then PQRS is a
a) Rectangle b) Parallelogram
c) Rhombus d) Quadrilateral whose opposite angles are
supplementary
13. In the given figure, AB and CD are two intersecting chords of a circle. If ∠CAB = 40° and ∠BCD = 80°, then [1]
∠CBD = ?
a) 60° b) 50°
c) 70° d) 80°
−−−
14. The simplest rationalising factor of 3
√500 , is [1]
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, – 3 –
a) √3 b) √2
– 3 –
c) 2√3 d) √5
15. If a linear equation has solutions (1, 2), (-1, -16) and (0, -7), then it is of the form [1]
a) y = 9x - 7 b) 9x - y + 7 = 0
c) x - 9y = 7 d) x = 9y - 7
16. Line sgements AB and CD intersect at O such that AC||DB. If ∠ CAB = 45° and ∠ CDB = 55°, then ∠ BOD = [1]
a) 135° b) 80°
c) 100° d) 90°
17. To draw a histogram to represent the following frequency distribution : [1]
Class interval 5-10 10-15 15-25 25-45 45-75
Frequency 6 12 10 8 15
The adjusted frequency for the class 25-45 is
a) 6 b) 5
c) 2 d) 3
18. The number of spherical bullets each 5 dm in diameter which can be cast from a rectangular block of lead 11 m [1]
long, 10 m broad and 5 high is
a) 8400. b) 5600.
c) 6300. d) 4200.
19. Assertion (A): The side of an equilateral triangle is 6 cm then the height of the triangle is 9 cm. [1]
√3
Reason (R): The height of an equilateral triangle is 2
a.
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
20. Assertion (A): The point (1, 1) is the solution of x + y = 2. [1]
Reason (R): Every point which satisfy the linear equation is a solution of the equation.
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
Section B
21. The perimeter of an isosceles triangle is 42 cm and its base is 1 1
2
times each of the equal sides. Find the height [2]
–
of the triangle. (Given, √7 = 2.64.)
22. In given figure, if OA = 10, AB = 16 and OD ⊥ to AB. Find the value of the CD. [2]
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General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
Section A
1. (125)
−1/3
=? [1]
a) − 1
5
b) -5
c) d) 5
1
5
2. If the line represented by the equation 3x + ky = 9 passes through the points (2, 3), then the value of k is [1]
a) 2 b) 1
c) 3 d) 4
3. In which quadrant does the point (-7, -4) lie? [1]
a) IV b) I
c) II d) III
4. A histogram is a pictorial representation of the grouped data in which class intervals and frequency are [1]
respectively taken along
a) horizontal axis only b) horizontal axis and vertical axis
c) vertical axis and horizontal axis d) vertical axis only
5. The equation x - 2 = 0 on number line is represented by [1]
a) infinitely many lines b) two lines
c) a point d) a line
6. The basic facts which are taken for granted, without proof, are called [1]
Page 1 of 17
, a) theorems b) axioms
c) propositions d) lemmas
7. In the adjoining figure, AOB is a straight line. If x : y : z = 4 : 5 : 6, then y = ? [1]
a) 72° b) 48°
c) 60° d) 80°
8. In Triangle ABC which is right angled at B. Given that AB = 9cm, AC = 15cm and D, E are the mid-points of [1]
the sides AB and AC respectively. Find the length of BC?
a) 13cm b) 13.5cm
c) 12cm d) 15cm
9. (x2 - 4x - 21) = ? [1]
a) (x - 7) (x + 3) b) ( x - 7) ( x - 3)
c) (x + 7) (x + 3) d) (x + 7) (x - 3)
10. Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form [1]
a) (− 9
, m) b) (-9 , 0)
2
c) (0, − 9
) d) (n, −
9
)
2 2
11. ABCD is a parallelogram in which diagonal AC bisects ∠ BAD. If ∠ BAC = 35o, then ∠ ABC = [1]
a) 70o b) 120o
c) 110o d) 90o
12. If bisector of ∠A and ∠B of a quadrilateral ABCD intersect each other at p , ∠B and ∠C at Q , ∠C and ∠D [1]
at R and, ∠D and ∠A at S then PQRS is a
a) Rectangle b) Parallelogram
c) Rhombus d) Quadrilateral whose opposite angles are
supplementary
13. In the given figure, AB and CD are two intersecting chords of a circle. If ∠CAB = 40° and ∠BCD = 80°, then [1]
∠CBD = ?
a) 60° b) 50°
c) 70° d) 80°
−−−
14. The simplest rationalising factor of 3
√500 , is [1]
Page 2 of 17
, – 3 –
a) √3 b) √2
– 3 –
c) 2√3 d) √5
15. If a linear equation has solutions (1, 2), (-1, -16) and (0, -7), then it is of the form [1]
a) y = 9x - 7 b) 9x - y + 7 = 0
c) x - 9y = 7 d) x = 9y - 7
16. Line sgements AB and CD intersect at O such that AC||DB. If ∠ CAB = 45° and ∠ CDB = 55°, then ∠ BOD = [1]
a) 135° b) 80°
c) 100° d) 90°
17. To draw a histogram to represent the following frequency distribution : [1]
Class interval 5-10 10-15 15-25 25-45 45-75
Frequency 6 12 10 8 15
The adjusted frequency for the class 25-45 is
a) 6 b) 5
c) 2 d) 3
18. The number of spherical bullets each 5 dm in diameter which can be cast from a rectangular block of lead 11 m [1]
long, 10 m broad and 5 high is
a) 8400. b) 5600.
c) 6300. d) 4200.
19. Assertion (A): The side of an equilateral triangle is 6 cm then the height of the triangle is 9 cm. [1]
√3
Reason (R): The height of an equilateral triangle is 2
a.
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
20. Assertion (A): The point (1, 1) is the solution of x + y = 2. [1]
Reason (R): Every point which satisfy the linear equation is a solution of the equation.
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
Section B
21. The perimeter of an isosceles triangle is 42 cm and its base is 1 1
2
times each of the equal sides. Find the height [2]
–
of the triangle. (Given, √7 = 2.64.)
22. In given figure, if OA = 10, AB = 16 and OD ⊥ to AB. Find the value of the CD. [2]
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