Guess Paper – 2008
Class – X
Subject – Mathematics
Maximum Marks: 80 Time allowed: 3 Hours
Q1 to Q10 carry 1 mark; Q11 to Q15 carry 2 marks; Q16 to Q25 carry 3 marks; Q26 to Q30 carry 6 marks
- The reciprocal of √361 is a rational number. Is it true or false?
- The roots of ax2 + bx + c = 0 are real and unequal. What is b2 – 4ac?
- In the equation x + 2y = 10, if the value of x is –2, find the value of y.
- The graph of x = 5 is a line parallel to __________.
- What is the value of tan 2A – sec 2A?
- What is the distance between two parallel tangents of a circle of diameter 6 cm?
- Find the length of tangent drawn from an external point at a distance of 13cm from the centre of a circle of radius 5cm.
- Find the area of a sector of a circle of diameter 42 cm if the angle of the sector is 60˚.
- Which measure of central tendency can be obtained by the abscissa of the point of intersection of a more than ogive and a less than ogive?
- A card is drawn from a deck of playing cards. Find the probability of a spade or a face card.
- Find the 11th term from the end of the AP 10, 7, 4, ………….., – 62. OR
In a flower-bed, there are 23 rose plants in the first row, 21 in the second row, 19 in the third row and so on. There are 5 rose plants in the last row. How many rows are there in the flower-bed?
- If 12 sec A = 13, find the value of sin A and tan A.
- Find the value of ‘a’ if the distance between the points ( 3, a ) and ( 4, 1 ) is √10 units.
- Cards numbered from 30 to 59 are thoroughly shuffled and one card is drawn. Find the probability that the number on the card is
(i) not a prime number. (iii) a perfect square.
- In the given figure, D is a point on BC of the triangle ABC such that ÐADC = ÐBAC.
Prove that CA 2 = CB ´ CD A
B D C
- State Euclid’s Division Lemma. Using
’s division algorithm, find the HCF of 392 and 138420. Euclid
- Divide 8x4 + 8x3 – 12x2 + 21x – 30 by 3x –5 + 2x2 and verify division algorithm.
- A motor boat can travel 36 km upstream and 40 km downstream in 5½ hours. If the speed of the stream is 2 km per hour, find the speed of the boat in still water.
- Prove the identity (sin A + cosec A) 2 + (cos A + sec A) 2 = 7 + tan 2 A + cot 2 A OR
If sin q + cos q = p and sec q + cosec q = q, then prove that q. ( p2 –1 ) = 2.p
- Solve graphically: 2x – y + 2 = 0 ; 2x + y – 6 = 0.
Write the vertices of the triangle obtained by these lines and x-axis. Shade it and find its area.
- Draw a D ABC in which BC = 7cm, Ð B = 45° and Ð A = 75°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of the D ABC.
- The area of an equilateral triangle is 49√3 cm2. Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. OR
- If the three points ( x1, y1 ), ( x2, y2 ) and ( x3, y3 ) lie on the same line, prove that
y2– y3 y3– y1 y1– y2
______ + ______ + _____ = 0
x2 x3 x3 x1 x1 x2
- Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle, which touches the smaller circle. OR BL and CM are medians of a D ABC, right angled at A. Prove that 4.( BL2 + CM2 ) = 5 BC2
- If A and B are (–2, –2) and (2, –4), respectively, find the coordinates of P such that AP : AB = 3 : 8 and P lies on the line segment AB.
- Two circles touch each other internally. The sum of their areas is 116π cm 2 and the distance between their centres is 6 cm. Find the diameters of the two circles. OR
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boat in still water.
- Find the mean, median and mode of the following distribution.
- A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60˚ and the angle of depression of the base of the hill as 30˚.
31.Calculate the distance of the hill from the ship and the height of the hill. OR
The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 metres.
- State and prove Pythagoras Theorem. Using it, find the length of third side of a right triangle, if it has hypotenuse of length p cm and one side of length q cm such that p – q = 1.
- A solid toy is in the form of a hemisphere surmounted by a right circular cone. If the height of the cone is 2 cm and the diameter of the base is 4 cm, find the volume of the toy. If the right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy.
OR The diameters of the ends of a frustum of a cone 45 cm high are 56 cm and 14 cm. Find its volume, the curved surface area and the total surface area. ( use p = 22/7)
If you still have some time left, give it a thought:
Hard-work beats talent, when talent does not work hard.