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CBSE Home page 2008 CBSE MATH SET - 1

 

1) Complete the missing entries in the following factor tree :

 

2) If (x + a) is a factor of 2x2 + 2ax + 5x + 1O , find a .

 

3) Show that x = -3 is a solutionof x2 + 6x + 9 = 0 .

 

4) The first term of an A.P. is p and its common difference is q. Find its 10th term.

 

5) If tanA = 5/12, find the value of (sinA + cosA)secA

 

6) The 1engths of the diagonals of a rhombus are 30 cm and 40 cm. Find the side of the rhombus.

 

7) In figure-1, PQ||BC and AP:PB = 1:2 .
Find   ar(ΔAPQ)
ar(ΔABC)

 
 

 

8) The surface area of a sphere is 616 cm2. Find its radius.

 

9) A die is thrown once. Find the probability of getting a number less than 3.

 

10) Find the class marks of classes 10-25 and 35-55.

 

11) Find all the zeros of the polynomial x4 + x3 -34x2 -4x + 120, if two of its zeros are 2 and -2.

 

12) A pair of dice is thrown once. Find the probability of getting the same number on each dice.

 

13) If sec4A = cosec (A - 20°), where 4A is an acute angle, find the value of A.

OR

In a ΔABC , right-angled at C, if tanA = 1/ find the value of
sinA cosB + cosA sinB.

 

14) Find the value of k if the points (k, 3), (6, -2) and (-3, 4) are collinear.

 

15) E is a point on the side AD produced of a ||gm ABCD and BE intersects CD at F. Show that ΔABE ~ ΔCFB.

 

16) Use Euclid's Division Lemma to show that the square of any positive integer is either of the form
3m or (3m + 1) for some integer m.

 

17) Represent the following pair of equations graphically and write the coordinates of points where the lines intersect y-axis
x + 3y = 6
2x - 3y = 12

 

18) For what value of n are the nth terms of two A.P.'s 63, 65, 67, ... and 3, 10, 17, .... equal?

OR

If m times the mth term of an A.P. is equal to n times its nth term, find the (m + n)th term of the A,P.

 

19) In an A.P., the first term is 8, nth term is 33 and sum to first n terms is 123. Find n and d, the common difference.

 

20) Prove that
(1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A.

OR

Without using trigonometric tables, evaluate the following
2(   cos58° ) - (   cos38° cosec52° )
sin32° tan15° tan60° tan75°

 

21) If P divides the join of A(-2, -2) and B(2, -4) such that
AP/AB = 3/7 ,
find the coordinates of P

 

22) The mid-points of the sides of a triangle are (3, 4), (4, 6) and (5, 7). Find the coordinates of the vertices of the triangle.

 

23) Draw a right triangle in which the sides containing the right angle are 5 cm and 4 cm. Construct a similar triangle whose sides are 5/3 times the sides of the above triangle.

 

24) Prove that a parallelogram circumscribing a cirde is a rhombus.

OR

In Figure 2, AD⊥BC. Prove that AB2 + CD2 = BD2 + AC2.

 

25) In Figure 3, ABC is a quadrant of a circle of radius 14 cm and a semi-circle is drawn with BC as diameter. Find the area of the shaded region.

 

26) A peacock is sitting on the top of a pillar, which is 9 m high. From a point 27 m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snüe the peacock pounces on it. If their speeds are equal, at what distance from the hole is the snake caught ?

OR

The difference of two numbers is 4. If the difference of their reciprocals is 4/21 , find the two numbers.

 

27) The angle of elevation of an aeroplane from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation changes to 300. If the plane is flying at a constant height of 3600 m, find the speed, in km/hour, of the plane.

 

28) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio.
Using the above, prove the following :
In Figure 4, AB || DE and BC || EF. Prove that AC || DF.

OR

Prove that the lengths of tangents drawn from an external point to a circle are equal. Using the above, prove the following :
ABC is an isosceles triangle in which AB = AC, circumscribed about a circle, as shown in Figure 5. Prove that the base is bisected by the point of contact.

 

29) If the radii of the circular ends of a conical bucket, which is 16 cm high, are 20 cm and 8 cm, find the capacity and total surface area of the bucket.
[Use π 22/7 ]

 

30)
Classes Frequency
0-20 6
20-40 8
40-60 10
60-80 12
80-100 6
100-120 5
120-140 3

ANSWERS

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