CLASS X CBSE MATH MOCK TEST

Time allowed: 3 Hours Max. Marks: 80

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 30 questions divided into four sections A, B, C and D.

(iii) Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each.

(iv) Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each.

(v) Use of calculators is not permitted

Section A

1. If the common difference of an AP is 3 then what is a15 –a9

2. The ratio between the length of the shadow of a tower and its height is √3:1. Find the angle of elevation

3. The circumference of the base of the cone is 44cm and slant height is 25cm. Find the curved surface area of the cone.

4. One end of the diameter of the circle is (2, 3) and the center is (-2,5). What are the coordinates of the other end of the diameter?

5. A card is drawn from a pack of 52 cards. What is the probability of drawing a red king?

6. Find the median using an empirical relation, when it is given that mode and mean are 8 and 9 respectively.

Section B

7. Find the roots of the quadratic equation 3x²-2√6+2=0

8. In fig.1, if length of AB is 9 cm, then find the length of CP

9. In a triangle ABC, Angle B = 90°. BD perpendicular to AC. AD = 10cm, CD = 2AD. Find the length of BD.

10. Which term is the first negative term in the series 184,181,178, 175,172….

11. Find the value of k so that the equation 3x-4y=2 and 7x+ky=12 has unique solutions

12. What point on the x axis is equal distance from (7,6) and (-3,4)

Section C

13. A coin is tossed 2 times. Find the probability of getting

At least one head

At most one head

Exactly one head

14. Prove that √2+√7 is irrational

15. Draw a pair of tangents to the circle of radius 3 cm which are inclined to each other with an angle of 60°.

OR

Draw a right triangle in which the sides are of length 4cm and 3 cm (other than the hypotenuse). Construct another triangle whose sides are 5/3 times of the corresponding sides of the given triangle

16. In a triangle ABC, Angle B = 90°. AB =28cm and BC = 21 cm. A semi-circle is drawn with AC, as diameter and a quarter circle is drawn with BC as radius. Calculate the area of the shaded portion, correct to two places of decimals

17. Find the value of k for the col-linear points (7,-2), (5, 1) and (3, k)

18. Solve graphically 2x+3y=5 and 7x-5y=2

19. Evaluate:

20. Find the sum of all natural numbers between 250 and 1000 which are divisible by 11

21. The speed of the boat in still water is 15 km/hr. It goes 30 km upstream and returns downstream in 4 hrs and 30 mins. Find the speed of the stream.

22. If all the sides of a parallelogram touch a circle. Show that the parallelogram is a rhombus.

Section D

23. Solve:

OR

Solve by cross multiplication method: ax + by = a-b, bx – ay = a+b

24. Water is flowing at the rate of 5km/through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44m wide. Determine the time in which the level of the water in the tank will raise by 7 cm.

OR

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If volume of the small cone is 1/27 of the volume of the given cone, then what is the height above the base at which the section is made?

25. Prove that if the two sides and a median bisecting the third side of a triangle are respectively proportional to their corresponding sides and the median of another triangle then the two triangles are similar.

OR

Prove that if two tangents are drawn to the circle from an external point then,

I. The length of the tangents are equal

Using the above result solve the below:

ABCD is a quadrilateral such that D = 90°. A circle C (O,r) touches the sides AB, BC, CD and DA at P, Q, R and S respectively. If BC = 38 cm, CD = 25 cm and BP = 27 cm, Find r.

26. A vertical tower is surmounted by a flagstaff of height h meters. At a point on the ground the angle of elevation of the bottom and the top of the flagstaff are α and β respectively. Prove that the height of the tower is

OR

The angle of elevation of a cloud from a point 60 meters above a lake is 30 ° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud.

27. Prove that:

28. After covering a distance of 30 km with a uniform speed, the speed of the train is reduced to 4/5 of its original speed due to a defect. Consequently the train reaches its destination late by 45 mins. Had it happened after covering 18 Km more the train would have reached 9 mins earlier. Find the speed of the train and the distance of the journey.

29. Find the median using the graph by drawing both less than and more than ogive curves.

30. On environmental day, students of Class X were asked to get sapling and develop nursery in the triangular region allotted to them as in figure given below: I. Find the coordinates of the vertices P, Q, R II. Find the area of the nursery III. What values have been imbibed in the students in this initiative?

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