Arithmetic Progression CBSE Class X Self Evaluation Tests For Mathematics

1. 0, –4, –8, –12, ............

2.. 1, 2, 4, 8, 16, ...............

3. 6, 6, 6, 6, 6, ............

4. 5, 5 +Ö 3, 5  2 Ö3, 5+3Ö3,...........

7. Find the sequence whose of nth term is given by :

(a) 2n – 7 (b) –3 + 5n² (c) 4/3 - 6n  Also, determine which of these sequences are A.P’s.

8. Find the A.P. whose nth term is given by :

(a) 9 – 5n (b) –n + 6 (c) 2n + 7

9. Find the 8th term of an A.P. whose 15th term is 47 and the common difference is 4.

10. The 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term and the general term.

11. The 7th term of an A.P. is – 4 and its 13th term is –16. Find the A.P. [CBSE 2004]

12. Which term of the A.P. 3, 10, 17, .... will be 84 more than its 13th term? [CBSE 2004]

13. Find the A.P. whose third term is 16 and the seventh term exceeds its fifth term by 12.

14. For what value of n is the nth term of the following A.P.’s the same?

1, 7, 13, 19, ..... and 69, 68, 67............... [CBSE 2006C]

15. If the 10th term of an A.P. is 52 and 17th term is 20 more than the 13th term, find the A.P.

16. If seven times the seventh term of an A.P. is equal to nine times the ninth term, show that 16th term is zero.

17. (a) Which term of the A.P. 2, 6, 10, 14, ....... is 78?

(b) Which term of the A.P. 5, 9, 13, 17, ....... is 125?

(a) Which term of the A.P. –4, –1, 2, 5, ....... is 119?

(a) Which term of the A.P. Ö2, Ö18, Ö50 ....... is 21 Ö2 ?

18. How many terms are there in each of the following finite A.P.’s?

(a) –3, –4, –5, –6, ....., – 107

(b) 7, 13, 19, ........, 211

(c) 8, 13, 18, ......., 208

19. (a) Is 216 a term of A.P. 3, 8, 13, 18, ......?

(b) Is 271 a term of A.P. 1, 4, 7, 10, .....?

(c) Is –52 a term of A.P. 10, 7, 4 ......?

(d) Is –190 a term of A.P. –3, –8, –13, ......?

20. Find the 8th term from the end of the A.P. 7, 10, 13, ..... , 184. [CBSE 2005]

21. Find the 20th term from the end of the A.P. 3, 8, 13, ....., 253.

22. Find the value of k so that k – 3, 4k – 11 and 3k – 7 are three consecutive terms of an A.P.

23. Find the value of x so that 3x + 2, 7x – 1 and 6x + 6 are three consecutive terms of an A.P.

24. The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the

first term and the common difference.

25. The 9th term of an A.P. is equal to 7 times the 2nd term and 12th term exceeds 5 times the 3rd term by 2. Find

the first term and the common difference.

26. Find the middle term of an A.P. with 17 terms whose 5th term is 23 and the common difference is –2.

27. For what value of n, the nth terms of the two A.P.’s are same? 2, –3, –8, –13, ...... and –26, –27, –28, –29, .......

28. For what value of n, the nth terms of the two A.P.’s are same? 3, 10, 17, ...... and 63, 65, 67, .....

29. Find the number of integers between 200 and 500 which are divisible by 7.

30. How many numbers of three digits are exactly divisible by 11?

31. The angles of a triangle are in A.P. If the greatest angle equals the sum of the other two, find the angles.

32. Three numbers are in A.P. If the sum of these numbers is 27 and the product is 648, find the numbers.

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

zero.

34. A sum of Rs. 1000 is invested at 8% simple interest per annum. Calculate the interest at the end of 1, 2, 3,

......years. Is the sequence of interest an A.P.? Find the interest at the end of 30 years.

35. Two A.P.’s have the same common difference. The difference between their 100th terms is 111222333.

X Mathematics Sample Paper March _2014

Science Sample Paper Links -2014                                      

Section A

1. If the equation kx2+ 4x+ k=0 has two equal roots, then

(a) k = ±2 (b) k = 0 (c) k = 2 (d) none of these

2. If the sum of n terms of an A.P., is 2n2 +4n, then its nth term is

(a) 4n + 2 (b) 4n + 5 (c) 10n - 4 (d) none of these

3. If tangents TA and TB from a point T to a circle with center O are inclined to each other at an angle of 70° then <TOA is equal to

(a)80° (b) 70° (c) 55° (d) 50°

4. To divide a line segment AB in the ratio 5:3, first a ray AX is drawn so that < BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is

(a) 12 (b) 11 (c) 10 (d) 8

5. If the circumference and area of a circle are numerically equal, then diameter of the circle is 

(a)2x (b) 2 (c) 4 (d) 4x

6. The number of solid spheres, each of diameter 2 cm that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm is

(a)14 (b) 15 (c) 135 (d) none of these

7. From the top of a cliff 20 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is

(a)40 m (b) 60 m (c) 90 m (d) none of these

8. If the distance between the points (5, r) and (1, 0) is 5, then r is

(a)5 (b) -5 (c) 0 (d)  + - 3

9. The area of a triangle with vertices A(4, 0), B(7,0) and C(9, 5) is

a)14 sq. units (b) 28 sq. units (c) 17.5 sq. units (d) none

10. If A(5, -1),B(-3, -2) and C(-1,8) are the vertices of triangle ABC, then the length of the median through A is

(a) √50 units (b) √60 units (c) √62 units (d) √65 units

                                                            Section B

11. Does there exist a equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

12. The nth term of an A.P., cannot be 2n² +1. Justify your answer.

13. AB is a chord of the circle and AOC is its diameter such that <ACB = 50°. If AT is the tangent to the circle at the point A, then <BAT is equal to 50°. Justify your answer.

14. Write True or False and give reason for your answer for the following: A pair of tangents can be constructed from a point P to a circle of radius 6 cm situated at a distance of 5 cm from the centre.

15. Is it true that the distance travelled by a circle wheel of diameter x cm in one revolution is 2px cm? Why?

16. A circle is inscribed in a square of side x cm and another circle is circumscribing the square. Is it true to say that area of the outer circle is two times the area of the inner circle? Give reasons for your answer.

17. Write True or False and justify you answer for the following:

A spherical steel ball is melted to make 10 new identical balls. Then, the radius of each new ball is 1/10th radius of the original ball.

18. A hemisphere is cut out from the top of the cylinder with radius equal to the radius of cylinder. Taking radius as r and height of cylinder as h. find total surface area of solid?

                                                         Section C

19. 50 circular plates, each of radius 7 cm and thickness 1/2 cm are placed one above another to form a Solid right circular cylinder. Find the total surface area and the volume of the cylinder so formed

20. A bag contains cards which are numbered from 2 to 100. A card is drawn at random from the bag. Find the probability that it bears (i) a two digit number (ii) a number which is a perfect square

21. In an AP, the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP.22. Construct a triangle ABC in which BC=9 cm, <B=60° and AB=6 cm. then construct another triangle whose sides are 2/3 of the corresponding sides of tri. ABC.

23. If (1,2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find the values of x and y.

24. Two tangents PA and PB are drawn to a circle with centre O from an external point P. prove that <APB=2 <OAB.

25. A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole as observed from a point A on the ground is 60° and angle of depressionof point A from the top of the tower is 45°.Finf the height of the tower. [Take p =1.73].26. A coin is tossed 3 times. List the possible outcomes. Find the probability of getting at least 2 heads.27. ABC is a triangle right angled at A. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.28. A canal is 300 cm wide and 120 cm deep. The water in the canal is following with a speed of 20 km/h. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?

                                                             Section D

29. The interior of building is in the form of a cylinder of diameter 4 cm and height 3.5 m, surmounted by a cone of the same base with vertical angle as a right angle. Find the surface area (curved) and volume of the interior of the building.

30. An AP consists of 37 terms. The sum of three middlemost terms is 225 and sum of last three terms is 429. Find AP.

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

32. The angles of depression of the top and bottom of a building 60 metres high as observed from the top of a tower are 30° and 60°, respectively. Find the height of the tower and also the horizontal distance between the building and the tower.

33. A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?

34. The mid-points D, E, F of the sides AB, BC and CA respectively of a triangle ABC are (3, 4), (8, 9), and (6, 7). Find the coordinates of the vertices of the triangle.

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Sample Paper X Mathematics CBSE SA 2 2014

SAMPLE PAPER X SUBJECT MATHEMATICS CBSE SA – 2  March 2014

SECTION-A
1. The circumference of two circles are in the ratio 2: 3 then the ratio of the areas is:
(a) 2 : 4 (b) 2 : 9 (c) 4 : 9 (d) 4 : 6

2. A silver rod of diameter 2 cm and length 12 cm is drawn into a thin wire of length 24 m of uniform thickness, and then the thickness of the wire is:
(a) 0. 183 (b) 0.173 (c) 0.186 (d) 0.175

3. In two concentric circles, the length of tangent to inner circle is 8cm. Find the radius of outer circle, if the radius of inner circle is 3 cm.
(a) 5 cm (b) 4 cm (c) 3 cm (d) 2 cm

4. A point P is 13 cm from the centre of a circle. Find the length of the tangent drawn to the circle from the point P, if the radius of the circle is 5 cm.
(a) 12 cm (b) 10 cm (c) 8cm (d) 6 cm

5. If PA and PB are tangents from a point playing outside the circle such that PA = 10cm and angle APB, then the length of chord AB is:
(a) 5 cm (b) 4 cm (c) 3 cm (d) 2 cm

6. If 17th term of an A.P. exceeds its 9th term by 64, then the difference is:
(a) 8 (b) 6 (c) 4 (d) 12

7. One coin is tossed three times. The probability of getting 2 heads and 1 heads and 1 tail is:
(a) 1/8 (b) 2/5 (c) 3/8 (d) ¼

8. A vertical stick 20 m long casts a shadow 16 m long. At the same time a tower casts a shadow 48 m long. Then the height of the tower is:
(a)40 m (b) 32 m (c) 96 m (d) 60 m

9. A cone is divided into two parts by drawing a plane through mid – point of its axis, parallel to its base. The ratio of volumes of two parts is:
(a) 2: 3 (b) 1: 2 (c) 1: 3 (d) 1: 7

10. From a point Q , the length of the tangent to a circle is 24cm and the distance of Q from the centre is 25cm. The radius of the circle is:
(a) 7 cm (b) 12 cm (c) 15 cm (d) 24.5 cm

SECTION – B

11. For what value of P, are 2p -1, 7 and 3p three consecutive terms of an A.P.?

12. The length of the minute hand of a clock is 14 cm. Find the area swept out by the minute hand in 1 hour.

13. Find the roots of the quadratic equation 3x – 8/x = 2 ; x does not equal 0

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

15. A letter is drawn at random form the word ‘MATHEMATICS’. Find the probability of drawing each of the different letters in the given word.

16. How many balls each of radius 1 cm can be made from a solid sphere of lead of radius 8cm?

17. It is known that a box of 500 electric tubes contains 15defective electric tubes. One tube is taken out at this box. What is the probability that is a non – defective electric tube?

18. Find the coordinates of the points P,Q and R which divided the line segment joining A (5 , 4) and B (11 , 6) into four equal parts.

SECTION – C

19. The sum of two natural numbers is 8. Determine the numbers, if sum of their reciprocal is 8/15.

20. Draw a right triangle ABC in which AC = AB = 4.5 cm and angle = 90 degree. Draw a triangle similar to triangle to ABC with its sides equal to 5/4th of the corresponding sides of angle ABC.

21. Prove that the tangents drawn at the ends of a chord of circle make equal angles with the chord.

22. In an A.P. the sum of first ten is – 150 and the sum of its next ten terms is – 550.

23. PA and PB are two tangents from an exterior point P to a circle of radius 5 m. If length of the chord AB is 8 cm, then find the length of the tangent.

24. Three cows are tethered with 10 m long rope at the three corners of a triangular field having sides 42 mm 20 m and 34 m. Find the area of the plot which can be grazed by the cows, also find the area of the remaining field (unglazed).

25. The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is ¼. The probability of selecting a blue ball at random from the same jar is 1/3. If this jar contains 10 orange balls, then what is the total number of balls in the jar?

26. 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.

27. The internal and external diameters of a hollow hemispherical shell are 6cm and 10cm respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.

28. A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle the angle of elevation of the top of the light house from 60degree to 45 degree. Find the speed of the boat.

SELECTION-D

29. If the radii of the ends of a bucket 45 cm high, are 28 cm and 7 cm. Find the capacity of bucket.

30. The side of a square exceeds the side of another square by 4 cm and the sum of the areas of the two squares is 400 sq. cm. Find the dimensions of the squares.

31. The speed of a boat in still water is 11 km/ h. It can go 12 km upstream and return downstream to the original point in 2 hours and 45 minutes. Find the speed of the stream.

32. An iron sphere of radius ‘a’ unites is immerse completely in water contained in a right circular cone of semi – vertical angle 30 degree , water is drained off from the cone till its surface touches the sphere. Find the volume of water remaining in the cone.

33. The sum of first 8terms of an arithmetic progression is 156. The ratio of its 12th tern to its 68th is 1: 5 Calculate the first term and the fifteenth term.

34. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
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