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Section A

Objective (1 mark each)

10 × 1 mk

A1

P

(even) on a die.

From: Probability · 1 mark

A2

Two similar triangles have perimeters

30

cm and

20

cm. If one side of first is

12

cm, find the corresponding side of the second.

From: Triangles · 1 mark

A3

A kite is flying at height

60

m; string makes

60^\circ

with ground. Length of string?

From: Some Applications of Trigonometry · 1 mark

A4

Pole

15

m, sun

45^\circ

: shadow length.

From: Some Applications of Trigonometry · 1 mark

A5

Discuss nature of roots of

2x^2 - 6x + 3 = 0

.

From: Quadratic Equations · 1 mark

A6

\dfrac{2}{x} + \dfrac{3}{y} = 13,\; \dfrac{5}{x} - \dfrac{4}{y} = -2

.

From: Pair of Linear Equations in Two Variables · 1 mark

A7

Area of a quadrant of a circle with

r = 14

.

From: Areas Related to Circles · 1 mark

A8

A quadrilateral

ABCD

is drawn to circumscribe a circle. Prove

AB + CD = AD + BC

.

From: Circles · 1 mark

A9

TSA of cuboid

l=8, b=6, h=5

.

From: Surface Areas and Volumes · 1 mark

A10

Show that any positive odd integer is of the form

4q+1

or

4q+3

.

From: Real Numbers · 1 mark

Section B

Very short answer (2 marks each)

6 × 2 mk

B1

If

\sin A = 3/5

, find

\cos A, \tan A

.

From: Introduction to Trigonometry · 2 marks

B2

P

(leap year has

53

Sundays).

From: Probability · 2 marks

B3

Similar triangles side ratio

2:3

. Area ratio?

From: Triangles · 2 marks

B4

Volume of cylinder

r = 7, h = 10

.

From: Surface Areas and Volumes · 2 marks

B5

Sum of first

n

terms is

3n^2 + 5n

. Find

n^{th}

term.

From: Arithmetic Progressions · 2 marks

B6

Find HCF of

180

and

252

using Euclid's algorithm.

From: Real Numbers · 2 marks

Section C

Short answer (3 marks each)

8 × 3 mk

C1

From top of a

50

m tower, angle of depression of two objects on ground on same side are

30^\circ

and

60^\circ

. Find distance between them.

From: Some Applications of Trigonometry · 3 marks

C2

\triangle ABC\sim\triangle DEF

:

AB=4, DE=6

, area

(ABC)=32

. Find area

(DEF)

.

From: Triangles · 3 marks

C3

Solve

x^2 - 5x = 0

.

From: Quadratic Equations · 3 marks

C4

Value of

\tan^2 60 + 4\cos^2 45 + 3\sec^2 30 + 5\cos^2 90

.

From: Introduction to Trigonometry · 3 marks

C5

Can the number

6^n

end with the digit

0

?

From: Real Numbers · 3 marks

C6

Prove

(1 - \cos^2\theta)\csc^2\theta = 1

.

From: Introduction to Trigonometry · 3 marks

C7

Solve

x + y = 7,\; x - y = 3

.

From: Pair of Linear Equations in Two Variables · 3 marks

C8

A ladder

\sqrt 3

m leans against a wall; foot is

1

m from the wall. Angle with ground?

From: Some Applications of Trigonometry · 3 marks

Section D

Long answer (5 marks each)

6 × 5 mk

D1

The 7th term of an AP is 34 and 13th is 64. Find the AP.

From: Arithmetic Progressions · 5 marks

D2

Are

(1, 2), (2, 3), (3, 4)

collinear?

From: Coordinate Geometry · 5 marks

D3

Two dice thrown,

P

(sum

= 8

).

From: Probability · 5 marks

D4

Section formula:

(2, 4)

and

(6, 8)

divided in

1:3

.

From: Coordinate Geometry · 5 marks

D5

S_{20}

of

5, 8, 11, \ldots

From: Arithmetic Progressions · 5 marks

D6

Wheel makes

200

revolutions to cover

88

m. Diameter?

From: Areas Related to Circles · 5 marks

Class-wide Mock Paper