# 10th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2008

General Instructions:
1. All questions are compulsory.
2. The question paper consists of 30 questions divided into four sections - A, B, C and D. Section A comprises of ten questions of 1 mark each, Section B comprises of five questions of 2marks each, Section C comprises of ten questions of 3 marks each and Section D comprises of five questions of 6marks each.
3. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
There is no overall choice. However, an internal choice has been provided in one question of 2 marks each, three questions of 3 marks each and two questions of 6 marks each. You have to attempt only one of the alternatives in all such questions.
4. In question on construction, the drawing should be neat and as per the given measurements.
5. Use of calculators is not permitted.
Q1 :

Write a rational number between and.

The approximate values of and are:

= 1.414

= 1.732

We know that the decimal representation of a rational number may be either terminating or non-terminating repeating. Since the terminating decimal 1.5 lies between 1.414 and 1.732, 1.5 is a rational number between and.

Q2 :

Write the number of zeroes of the polynomial y= f(x) whose graph is given in figure.

The graph of the polynomial y= f(x) intersects x-axis at three points. Thus, the polynomial y= f(x) has three zeroes.

Q3 :

Is x= −2 a solution of the equation x2− 2x+ 8 = 0?

Onsubstituting x= −2 in the L.H.S. of the given equation, we obtain

x2− 2x+ 8 = (−2)2− 2(−2) + 8

= 4 + 4 + 8

= 16 0

Thus, x= −2 is not a solution of the given equation.

Q4 :

Write the next term of the A.P. .

Q5 :

D, E, and F are the mid-points of the sides AB, BC, and CA respectively of ΔABC. Find.

Q6 :

In figure, if ATO = 40°, then find AOB.

Q7 :

If sin θ= cos θ, then find the value ofθ.

Q8 :

Find the perimeter of the given figure, where AED is a semi-circle and ABCD is a rectangle.

Q9 :

A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. Find the probability of getting a black ball.

Q10 :

Find the median class of the following data:

 Marks obtained 0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 Frequency 8 10 12 22 30 18

Q11 :

Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.

Q12 :

In figure, OP is equal to diameter of the circle. Prove that ABP is an equilateral triangle.

Q13 :

Without using trigonometric tables, evaluate the following:

Q14 :

For what value of kare the points (1, 1), (3, k), and (−1, 4) collinear?

OR

Find the area of ΔABC with vertices A (5, 7), B (4, 5), and C (4, 5).

Q15 :

Cards, marked with numbers 5 to 50, are placed in a box and shuffled thoroughly. A card is drawn from the box at random. Find the probability that the number on the taken card is

1. a prime number less than 10

2. a number which is a perfect square

Q16 :

Prove that is an irrational number.

Q17 :

Use Euclid’s Division Lemma to show that the square of any positive integer is either of the form 3mor 3m+ 1 for some integer m.

Q18 :

The sum of the 4thand 8thterms of an A.P. is 24 and the sum of 6thand 10thterms is 44. Find the first three terms of the A.P.

Q19 :

Solve for xand y:

(a b) x+ (a+ b) y=a2− 2ab b2

(a+ b) (x+ y) = a2+ b2

OR

Solve for xand y:

37x+ 43y= 123

43x + 37y= 117

Q20 :

Prove that:

OR

Prove that:

Q21 :

If the point P(x, y) is equidistant from the points A(3, 6) and B(−3, 4), then prove that 3x+ y− 5 = 0.

Q22 :

The point R divides the line segment AB, where A(−4, 0) and B(0, 6) are such that . Find the coordinates of R.

Q23 :

In figure, ABC is a right-angled triangle, right-angled at A. Semi-circles are drawn on AB, AC, and BC as diameters. Find the area of shaded region.

Q24 :

Draw a ΔABC with side BC = 6 cm, AB = 5 cm, and ABC = 60°. Construct a ΔAB'C' similar to ΔABC such that sides of ΔAB'C' are of the corresponding sides of ΔABC.

Q25 :

D and E are points on the sides CA and CB respectively of ΔABC right-angled at C. Prove that AE2+ BD2= AB2+ DE2

OR

In the following figure, DB BC and AC BC. Prove that

Q26 :

A motor boat whose speed is 18 kmph in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

OR

Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Q27 :

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Using the above, do the following:

The diagonals of a trapezium ABCD, with ABCD, intersect each other at the point O. If AB = 2CD, then find the ratio of the area of ΔAOB to the area of ΔCOD.

OR

Prove that the lengths of the tangents drawn from external point to a circle are equal.

Using the above, do the following:

In the following figure, TP and TQ are the tangents drawn from T to the circle with centre O and R is any point on the circle. If AB is a tangent to the circle at R, then prove that TA + AR = TB + BR.

Q28 :

A tent consists of frustum of a cone, surmounted by a cone. If the diameter of the upper and lower circular ends of the frustum are 14 m and 26 m respectively, the height of the frustum is 8 m and the slant height of the surmounted conical portion is 12 m, then find the area of the canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal.)

Q29 :

The angle of elevation of a jet fighter 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 is flying at a speed of 720 km/hour, then find the constant height at which the jet is flying. [Use = 1.732]