CBSE Maths Question Paper (Delhi) Class 10th (2010)

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Series LRH/1                                                                                                                  Code No. 30/1/1


Time allowed : 3 hours                                                                                              Maximum marks . 80


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 2 marks each, Section C comprises of ten questions of 3 marks each and Section D comprises of five questions of 6 marks each.



                                                                              Section A


1.    Has the rational number  image a terminating or a non-terminating  decimal representation ?


2.    If image are the zeroes of a polynomial, such that image = 6 and image = 4, then write the polynomial.


3.    If the sum of first p terms of an A.P., is image, find its common difference.


4.    In Fig.  1, S and T are points on the sides PQ and PR, respectively of image PQR, such that PT = 2 cm, TR = 4 cm and ST is parallel to QR. Find the
ratio of the areas of image PST and A PQR.



5.    In Fig.    2, image AHK is similar to image ABC. If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find AC.



6. If 3x = cosec 0 and 3 = cot 0, find the value of image


7.    If P(2, p) is the mid-point of the line segment joining the points A(6, -5) and B(--2, 11), find the value of p.


8.    If A(1, 2), B(4, 3) and C(6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of the fourth vertex D.


9.    The slant height of a frustum of a cone is 4 cm and the perimeters (circumferences) of its circular ends are    18 cm and 6 cm. Find the curved surface area of the frustum. image


10.    A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting a red face card.



                                                                                             Section B


11.    If two zeroes of the polynomial image , then find its third zero.


12.    Find the value of k for which the following pair of linear equations have infinitely many solutions :

         2x + 3y = 7; (k 1)x + (k + 2)j, = 3k


13.    In an A.P., the first term is 2, the last term is 29 and sum of the terms is 155. Find the common difference of the A.P.


14.    If all  the  sides  of a parallelogram touch  a  circle,  show that the parallelogram is a rhombus.


15.    Without using trigonometric tables, find the value of the following expression 
        sec (90°- 0).cosec 0 - tan (90° - 0) cot 0 + cos2 25° + cost 65°
                                         3 tan 27°. tan 63°


        Find the value of cosec 30°, geometrically.


16.    Prove that 2 - 3image is an irrational number.


17.    The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes 1/2 . Find the fraction.

Solve the following pair of.equations image


18.    In an A.P., the sum of first ten terms is -150 and the sum of its next ten terns is -550. Find the A.P.


19.    In Fig. 3, ABC is a right triangle, right angled at C and D is the mid-point of BC. Prove that image



20.    Prove the following :


Prove the following :



21.    Construct a triangle ABC in which BC = 8 cm, image = 45° and image = 30°. Construct another triangle similar to imageABC such that its sides are 3/4 of the corresponding sides of imageABC.


22.    Point  P  divides  the  line  segment joining the  points  A(2, 1) and B(5, -8) such that image . If P lies on the line 2x - y + k = 0, find the value of k.


23.    If R(x, y) is a point on the line segment joining the points P(a, b) and Q(b, a), then prove that x + y = a + b.


24.    In Fig. 4, the boundary of shaded region consists of four semicircular arcs, two smallest being equal. If diameter of the.largest is 14 cm and that of the smallest is 3.5 cm, calculate the area of the shaded region. image


Find the area of the shaded region in Fig. 5, if AC = 24 cm, BC = 10 cm and O is the centre of the circle. image




25.    Cards bearing numbers 1, 3, 5, _ _ _ , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing
(i)    a prime number less than 15.
(ii)    a number divisible by 3 and 5.


                                                                                     Section D


26.    Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46, find the integers.

The difference of squares of two numbers is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.


27.     Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Using the above, prove the following :
If the areas of two similar triangles are equal, then prove that the triangles
are congruent.


28.    From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of the foot of the tower is 30°. Find the height of the tower.


29.    A milk container is made of metal sheet in the shape of frustum of a cone whose volume is  image. The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in

making the container at the rate of Rs. 1.40 per square centimeter. image

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of base of the cone is 21 cm and its volume is 3 of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy . image


30.    Find the mean, mode and median of the following frequency distribution:

Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 4 4 7 10 12 8 5

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