The more you solve Mathematics problem, more you gain chances of reaching towards perfection. Always when you start solving sample or exam paper first have a look a complete question paper and marks allotted to every question. It takes hardly five minutes to go through paper and then accordingly decide what you will solve first. Following is the example of CBSE sample paper for class X for the year 2011:
M.M: 80, TIME: 3hrs
1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections, namely
Section A : 10 questions (1 mark each)
Section B : 8 questions (2 marks each)
Section C : 10 questions (3 marks each)
Section D : 6 questions (4 marks each)
3. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks and 2 questions of four marks each.
4. Use of calculators is not allowed.
Q1. The quadratic equation 2×2- 5x +1=0 has
(a) Two distinct real roots
(b) two equal real roots
(c) no real roots
(d) more than two real roots
Q2. The 9th term of an AP is 449 and 449th term is 9. The term which is equal to zero is
(a)501th (b) 502th (c) 458th (d) 459th
Q3. Two circles touch each other externally at C and AB is a common tangent to the circles. Then, ?ACB=(a) 600 (b) 450 (c) 300 (d) 90 degree
Q4. The length of an arc that subtends an angle of 24o at the centre of a circle with 5 cm radius is
(a) 2/3p cm (b) 3/2p cm (c) 3/1p cm (d) 5/3p cm
Q5. An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 450. The height of the tower is
(a) 10 m (b) 20 m (c) 30 m (d) 40 m
Q6. The probability that a randomly chosen number from one to twelve is a divisor of twelve is (a) 1/12 b) 1/2 (c) 1/4(d) 1/6
Q7. The value of x, for which the points (x,-1), (2,1) and (4,5) lie ona line is
(a) 0 (b) 1 (c) 2 (d) 3
Q8. The ratio in which the point R (2/7,20/7) divides the join of P(-2,-2) and Q(2,-4) is
(a) 3:4 (b) 4:3 (c) 2:1 (d) 1:2
Q9. A pendulum swings through an angle of 300 and describes an arc 8.8cm in length. The length of the pendulum is
(a) 8.8 cm (b) 15.8 cm (c) 16.8 cm (d) 17 cm
Q10. Three cubes whose edges measure 3cm, 4cm and 5 cm respectively are melted to recast a single cube. The surface area of the new cube is
(a) 216 cm2 (b) 200 cm2 (c) 215 cm2 (d) 220 cm2
Q11. If the centroid of the triangle formed by points P(a, b),Q(b, c)and R(c, a) is at the origin, then find the value of a + b + c.
Find the area of the quadrilateral ABCD whose vertices are A(1,1), B(7,-3), C(12,2) and D(7,21) respectively.
Q12. An A.P. consists of 60 terms. If the first and the last term be 7 and 125 respectively, find the 32nd term.
Q13. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) A two digit number (ii) a perfect square number
Q14. Find two consecutive positive integers, sum of whose squares is 25.
Q15. Prove that the tangents at the extremities of any chord make equal angles with the chord.
Q16. The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm, find the area of the sector.
Q17. A circle touches all the four sides of a quadrilateral ABCD. Prove that
AB + CD = BC + DA
Q19. If a ??b ??c, prove that the points (a,a2), (b,b2) and (c,c2) can never be collinear.
Q20. A body falls 8 metres in the first second of its motion, 24 metres in the second, 40 metres in the third second and so on. How long will it take to fall 2048 metres?
Q21. Draw a pair of tangents to a circle of any convenient radius,which are inclined to the line joining the centre of the circle and the point at which they intersect at an angle of 45°. Also write the steps of construction.
Q22. From a balloon vertically above a straight road, the angles of depression of two cars at an instant are found to be 450 and 600.If the cars are 100m apart, find the height of the balloon.
The angles of elevation of the top of a tower from two points at a distance a and b metres from the base and in the same straight line with it are complementary. Prove that the height of the tower is ab metres.
Q23. A bag contains 12 balls out of which x are white.
(i) If one ball is drawn at random, what is the probability that it will be a white ball?
(ii) If 6 more white balls are put in the bag, then the probability of drawing a white ball will be double than that in (i). Find x.
Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any day of the week. What is the probability that both will visit the shop on
(i) the same day? (ii) two different days? (iii) consecutive days?
Q24. In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. Find the area of the remaining portion of the triangle. (take 3=1.732)
A round table cover has six equal designs as shown in the figure.If the radius of the cover is 28 cm, find the cost of making the design at the rate of Rs. 0.35 per cm2.
Q25. A canal is 300cm wide and 120cm deep. The water in the canal is flowing with a speed of 20km/h. How much area will it irrigate in 20 minutes if 8cm of standing water is desired?
Q26. From a solid cylinder whose height is 2.4 cm and diameter 1.4cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.(use ?=3.1416)
Q27. Solve for x, using the quadratic formula: abx2 -(a2+b2)x + ab=0
Q28. If D, E and F are the mid points of sides BC, CA and AB respectively of a ?ABC, whose vertices are A(-4,1), B(6,7) and C(2,-9), then prove that,Ar. ?DEF = 1/4(Ar ?ABC).
Q29. Find the value of the middle most term (s) of the A.P.:-11, -7, -3, …., 49
The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, find the AP.
Q30.The base of right angled triangle 2cm less than the perpendicular .the length of hypotenuse is10cm.Find other two sides of triangle.
Q31.In a class test, the sum of the marks obtained by a student P in Mathematics and Science is 28. Had he got 3 more marks in Mathematics and 4 marks less in Science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately.
Q32. Prove that the lengths of tangents drawn from an external point to a circle are equal.
From a window, h metres high above the ground, of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are ? and ? respectively. Show that the height of the opposite house is h(1+tan?.cot?) metres.
Q33The length and breadth of cuboid are 4cm ,3cm respectively .The total surface area is 52cm2.Find the height of the cuboid.
Q34. A solid consisting of a right circular cone, standing on a hemisphere, is placed upright, in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having been given that the radius of the cylinder is 3 cm and its height is 6 cm, the radius of the hemisphere is 2 cm and the height of the cone is 4 cm.