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Class 10 Class 12

Mathematics Pre Board Paper 2

Download this Mathematics Pre Board Paper 2 for taking the test offline or sharing with your friends. Once you are done with all the answers to the questions, Go ahead with answer key to check your answers.

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Pre Board Instructions

General Instructions:

All questions are compulsory.
The Question Paper consists of 30 Questions divided into Four sections A, B, C and D.
Section A contains 6 Questions of 1mark each.
Section B contains 6Questions of 2marks each.
Section C contains 10 Questions of 3marks each.
Section D contains 8 Questions of 4marks each.
There is no overall choice. However, an Internal choice has been provided in Four questions of 3 Marks each and Three questions of 4 Marks each. You have to attempt only one of the alternatives in all such questions.
Use of Calculators is not permitted.

Section A

Check whether the following are quadratic equations:
(x + 1)² = 2(x – 3)

[1]

For the following APs, write the first term and the common difference
0.6, 1.7, 2.8, 3.9, . . .

[1]

State Euclid’s division algorithm.

[1]

Find the distance between the following pairs of points :
(– 5, 7), (– 1, 3)

[1]

Write the value of sin (65° + θ) -cos (25° - θ).

[1]

Give two different examples of pair of
(i) similar figures.
(ii) non-similar figures.

[1]

Section B

The H.C.F. and L.C.M. of two numbers are 12 and 240 respectively. If one of these numbers is 48; find the other number.

[2]

Find the number of solutions of the follow ing pair of linear equations :
x + 2y - 8 = 0
2x + 4y = 16

[2]

A deck of 52 cards is shuffled. Tanvika draws a single card from the deck at random. What is the probability that the card is a Jack.

[2]

10.

Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear

[2]

11.

12 cards, numbered 1, 2,3......., 12 are put in a box and mixed throughly. A card is drawn at random from the box. Find the probability that the card drawn bears

(i) an even number
(ii) a number divisible by 2 or 3.

[2]

12.

Choose the correct choice in the following and justify :
30th term of the AP: 10, 7, 4, . . . , is

11th term of the A.P. is $space space minus 3 comma space 1 half comma space 2 comma space....$

[2]

Section C

13.

Kind a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.

[3]

14.

Find the distance between the points
(cos ө - sin ө), (-cos ө, sin ө)

[3]

OR

Find the distance between the points
Let the given points be A (a cos ө, 0) and B(0, a sin ө)

15.

The sets of Physics, Chemistry and Mathematics books have to be stacked in such a way that all the books are stored topic wise and the height of each stack is the same. The number of Physics books is 12, the number of Chemistry books 20 and the number of Mathematics books is 30. Assuming that the books are of the same thickness, determine the number of stacks of Physics, Chemistry and Mathematics books.

[3]

16.

For what value of k, the pair of linear equations 3x - ky + 7 = 0,x - 2y + 5 = 0 has unique solution.

[3]

17.

Evaluate without using trigonometric tables:

fraction numerator 3 space cos space 55 degree over denominator 7 space sin space 35 degree end fraction minus fraction numerator 4 left parenthesis cos space 70 degree. space cosec space 20 degree right parenthesis over denominator 7 left parenthesis tan space 5 degree. space tan space 25 degree. space tan space 45 degree. space space tan space 65 degree. space tan space 85 degree right parenthesis end fraction.

[3]

OR

Without using trigonometric tables, evalutate the following:

space space space left parenthesis sin squared 25 degree space plus space sin squared space 65 degree right parenthesis space plus space square root of 3 left parenthesis tan space 5 degree. space tan space 15 degree. space tan space 30 degree. space tan space 75 degree. space tan space 85 degree right parenthesis

18.

A conical flask is full of mater. The flask was base m radius r and height n. the mater is poored into a cylindrical flask of base radius mr. find the height of water in the cylindrical flask.

[3]

OR

A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?

19.

The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the side BC. Prove that DF × EF = FB × FA.

[3]

OR

The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, find AB.

20.

In Fig, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP=2r, show that ∠ OTS = ∠ OST = 30°.

[3]

21.

A chord of a circle of radius 14 cm subtends 60° at the centre. Find the area of the major sector.

[3]

22.

The marks obtained by 40 students of class X of a certain school in Science paper consisting of 10 marks are presented in the table below. Find the mean marks obtained by the students.

Marks obtained(x_i)	5	6	7	8	9
Number of students (f_i)	4	8	14	11	3

[3]

Section D

23.

Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75, if in the nth week, her weekly savings became Rs. 20.75, find n.

[4]

24.

Represent the following problem situations in the form of quadratic equations:
The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

[4]

OR

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

25.

Prove the following identities:
(1 + cot θ- cosec θ) (1 + tan θ+ sec θ) = 2.

[4]

26.

A hemispherical tank full of water is emptied by a pipe at the rate of litres per second. How much time will it take to half empty the tank, if the tank is 3 m in diameter.

[4]

27.

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

[4]

OR

In an equilateral ABC, D is a point on side BC such that

BD equals 1 third BC.

Prove that 9AD² = 7AB².

28.

Construct a triangle ABC in which AB = 5 cm, ∠B = 60° and altitude CD = 3 cm. Construct a triangle AQR similar to ΔABC, such that each side of ΔAQR is 1.5 times that of the corresponding side of ΔABC.

[4]

29.

The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 15 seconds the angle of elevation changes to 30°. If the jet plane is flying at a constant height of

bold 1500 square root of bold 3 bold space bold m

find the speed of the jet plane.

[4]

30.

Find the value of P, if the mean of the following distribution is 18.

x:	13	15	17	19	20 + p	23
f:	8	2	3	4	5p	6

[4]

OR

The median of the following data is 52.5. Find the values of x and y if the total frequency is 100.

Class Interval	Frequency
0-10	2
10-20	5
20-30	x
30-40	12
40-50	17
50-60	20
60-70	y
70-80	9
80-90	7
90-100	4
	Total 100