X Maths Sqp1 Qp

An

Educomp Initiative

Mock Test Paper – I Mathematics Class X

m o .r c u o H g n i n r a e .L w w w

General Instructions 1. 2.

3.

All questions are compulsory.

The question paper consists of 30 questions divided into 4 sections A, B, C and D. Section A comprises of 10 questions of 1 mark, Section B is of 5 questions of 2 marks each. Section C is of 10 questions of 3 marks each and section D is of 5 question of 6 marks each. There is no overall choice. Internal choice has been provided with.

Section A

1.

Find without actual division whether the rational number is a terminating or non-terminating repeating decimal :

2.

3.

17 . 90

Find the number of zeroes of the polynomial as depicted in the figure below:

State whether the pair of linear equation is consistent / inconsistent. 3x + y = 1

2y = 2 – 6x

4.

Determine whether x  3 is a solution of the equation or not, x 2  3 3 x  6  0 .

5.

In a right angled ABC, right angled at C, if tan  = 1, then verify that 2 sin  cos  = 1.

6.

In a ABC, AD is the bisector of A meeting side BC at D, if AB = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC.

www.learninghour.com India's No. 1 Tutoring Company

1 [email protected] Ph: 011-26121440, 011-26897579

An

Educomp Initiative

P

7.

If TP and TQ are the two tangents to a circle with centre O, so that POQ = 110°,then PTQ is equal to x°. Find x°.

x°

o

T

m o .r c u o H g n i n r a e .L w w w Q

8. 9. 10.

The difference between circumference and diameter of circle is 105 cm. Find the radius of the circle. If P(not E) =

1 then P(E) is given by a, find a. 6

The mean of five numbers is 10. If each number is decreased by 3, find the mean of new numbers.

Section B

11.

12. 13.

Find the sum of the product of the zeroes of the following quadratic polynomial. x2 – (c – ab)x – abc Or 2 Find the quotient and the remainder, when 6x – 31x + 47 is divided by 2x – 5. If sin 5A = cos 4A, where 5A and 4A are acute angles, find the value of A. C

D

Q

P

A

B

ABCD is a parllelogram and APQ is a straight line meeting BC at P and DC produced at Q. Prove that the rectangle contained by BP and DQ is equal to the rectangle contained by AB and BC.

14.

15.

The circle is divided into three regions - I, II and III. A spinner is fixed at the centre O of the circle of ROQ = 45°, find the probability that the spinner will land in the region II.

If A(6, –1), B(1, 3) and C(K, 8) are three points such that AB = BC, find the value of K.

www.learninghour.com India's No. 1 Tutoring Company

2 [email protected] Ph: 011-26121440, 011-26897579

An

Educomp Initiative

Section C 16.

The length of the hypotenuse of a right angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1cm. Find the length of each side of the triangle.

17.

m o .r c u o H g n i n r a e .L w w w

18. 19. 20.

Solve 4x2 + 4bx – (a2 – b2) = 0 by method of completing the squares.

Find the sum of n terms of an A.P. whose nth term is given by tn = 5 – 6n.

Prove that the square of any positive integer of the form 5q + 1 is of the same form. Prove that

cos A sin A   sin A  cos A 1  tan A 1  cot A

Or

4 cos 70.cosec20  3cos 55  7 sin 35 7 tan 5.tan 25. tan 45. tan 65.tan 85 

21. 22. 23. 24.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Find the coordinates of the circumcentre of a  whose vertices are A (4, 6) , B(0, 4) and C (6, 2). Find the point on the y-axis which is equidistant from (–5, –2) and (3, 2).

A circle touches the side BC of ABC, at P and touch AB and AC produced at a Q and R respectively. Prove that AQ 

1 Perimeter of ABC. 2

Or

In a quad – ABCD , CA = CD, B = 90° and AD² = AB2 + BC² + CA². Prove that ACD = 90°. D

C

A

www.learninghour.com India's No. 1 Tutoring Company

B

3 [email protected] Ph: 011-26121440, 011-26897579

An

25.

Educomp Initiative

Find the area of the shaded region.

m o .r c u o H g n i n r a e .L w w w o

m 7c

40°

B

D

14 cm

A

C

OR

A field is in the form of a circle. The cost of ploughing the field at Rs. 1.50 per m² is Rs. 5775. Find the cost of fencing the field at Rs. 8.50 per metre.

Section D

26.

C

State and prove Thales Theorem. In the figure LM | | AB. If AL = x – 3, AC = 2x,

L

M

BM = x – 2 and BC = 2x + 3, find the value of x.

A

27.

B

A shuttle cock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere. The external diameter of the frustum are 5 cm and 2 cm and the height of the entire shuttle cock is 8 cm. Find its external surface area. Or

A juice seller serves his customer using glasses (as shown in the figure). The inner diameter of these cylindrical glasses is 7 cm and height is 12 cm. The bottom of the glass has a raised hemispherical portion. Find the apparent and actual capacities of the glass.

12 cm

7 cm

www.learninghour.com India's No. 1 Tutoring Company

4 [email protected] Ph: 011-26121440, 011-26897579

An

28.

29.

30.

Educomp Initiative

There are two class rooms A and B containing students. If 5 students are shifted from room A to room B, the resulting number of students in the two rooms become equal. If 5 students are shifted from room B to room A, the resulting number of students in room A becomes double the number of students left in room B. Represent this situation algebraically and solve graphically.

m o .r c u o H g n i n r a e .L w w w From a window, h metres high above the ground of a house in a street, the angles of elevation of the top and angle of depression of the foot of another house on the opposite side of the street are  and  respectively. Show that the height of the opposite house is h (1 + tan  cot ) metres.

The mean of the following frequency table is 50, but the frequencies f1 and f2 in class 20-40 & 60-80 are missing. Find the missing frequencies if the total frequencies are 120. Class

0-20

20-40

40-60

60-80

80-100

Frequency

17

f1

32

f2

19

Or

The following distribution shows the height of students of certain school. Height(in cm)

No.of students

160-162

15

163-165

118

166-168

142

169-171

127

172-174

18

Find the modal height of students.

........End of Paper........

www.learninghour.com India's No. 1 Tutoring Company

5 [email protected] Ph: 011-26121440, 011-26897579