Poornima: November 2020

Monday, 9 November 2020

Arithmetic Progression @5 (Grade 10)

1. Find the sum of the first 35 terms of an Arithmetic Progression whose third term is 7 and seventh term is two more than thrice of its third term.

2.If the 5th term and 12th term of an Arithmetic Progression are 30 and 65 respectively, find the sum of its 26 terms.

3.Find the sum of first 25 natural numbers.

4. Find the sum of first 100 natural numbers.

5.Which term of the sequence 6, 11, 16, 21, 26, ....... is 126?

6. Find the seventeenth term of the Arithmetic Progress {31, 25, 19, 13, ................}

7.Find the sum of the following Arithmetic series:

1 + 8 + 15 + 22 + 29 + 36 + ………………… to 17 terms.

8.Find the sum of the series: 7 + 15 + 23 + 31 + 39 + 47 + ……….. + 255

9.Show that the sequence 7, 11, 15, 19, 23, ......... is an Arithmetic Progression. Find its 27th term and the general term.

10.The 5th term of an Arithmetic Progression is 16 and 13th term of an Arithmetic Progression is 28. Find the first term and common difference of the Arithmetic Progression.

11.The sum of three numbers in Arithmetic Progression is 12 and the sum of their square is 56. Find the numbers.

12.The sum of four numbers in Arithmetic Progression is 20 and the sum of their square is 120. Find the numbers.

ANSWERS

Grade 3, 4 : Numbers( Fractions)

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1. Write three fractions equivalent to:

(i) ²/₅

(ii) ⁷/₁₀

2. Arrange the following fractions in ascending order:

(i) 10/11, ⁷/₁₁, ⁹/₁₁

(ii) ⁴/₅, ⁴/₈, ⁴/₆, ⁴/₉

3. Arrange the following fractions in descending order:

(i) ²/₅, ⁴/₅, ³/₅, ¹/₅

(ii) 7/10, ⁷/₁₃, ⁷/₈, ⁷/₁₁

4. Find the value of:

(i) ³/₉ + ²/₉ + ⁴/₉

(ii) ¹¹/₄ - ⁷/₁₄

5. Sort out the smallest four-digit number made by 3, 5, 6 and 0 out of the given numbers:

(i) 6053

(ii) 3056

(iii) 5036

(iv) 0356

6. Write the greatest number of four digits made by 9, 2, 0, 8 out of the given numbers:

(i) 2089

(ii) 9820

(iii) 8902

(iv) 0982

7. Tick the true fact:

(i) 5 x 0 = 0

(ii) 5 x 0 = 5

(iii) 5 x 0 = 50

(iv) 5 x 0 = 05

8. Which fact is false:

(i) 5 x 1 = 5

(ii) 5 x 0 = 0

(iii) 5 + 0 = 0

(iv) 5 + 0 = 50

9. Write the place value of 8 in the number 3873.

10.Write the place value of 5 in the number 3859

Percentage % (Grade 7,8)

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1.In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :

2. A student multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation ?

3.If 20% of a = b, then b% of 20 is the same as :

4.The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :

5.A man has a certain unknown sum of money, 60 % of that sum is ₹ 4800. What is the sum of money?

6 . Find 71% of 3600m

7.What percent of 60 m is 9 m ?

8. What percent of 80 kg is 28 kg ?

9.What percent of 30 litres is 6 litres ?

10.A number when decreased by 10 % gives 45 . The number is?

11.A number, when increased by 40 % gives 84 . The number is?

12. A man has a certain unknown sum of money, 35 % of that sum is ₹ 700. What is the sum of money?

13. What percent of 90 m is 27 m ?

14.Find 30 % of 1550 metres

15.Express 38 % as a ratio.

ANSWERS

Saturday, 7 November 2020

Arithmetic Progression (AP) @4

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1. Write the common difference of an A.P. whose nth term is 3n + 5.

2. Write the value of x for which x + 2, 2x, 2x + 3 are three consecutive terms of an A.P.

3. For what value of k, are the numbers x, (2x + k) and (3x + 6) three consecutive terms of an A.P.?

4. If

a, 2 are three consecutive terms of an A.P., then find the value of a?

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

6. For what value of p are 2p + 1, 13 and 5p – 3 three consecutive terms of an A.P.?

7. Find the next term of the A.P.

8. Which term of the A.P.:

21, 18, 15, .... is zero?

9. If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of n terms.

10. Find the sum of all three digit numbers which are divisible by 7.

11. Find the sum of all the three digit numbers which are divisible by 9.

12. If Sn the sum of n terms of an A.P. is given by Sn = 3n2 – 4n, find the nth term.

13. The sum of 4th and 8th terms of an A.P. is 24, and the sum of 6th and 10th terms is 44. Find the A.P.

14. The Sum of n terms of an A.P. is 5n2 – 3n. Find the A.P. Hence find its 10th term.

15. The sum of 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the first three terms of the A.P.

Arithmetic Progression (AP)@3

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1. The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

(a) 5

(b) 6

(d) 8

2. If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is

(a) 13

(b) 9

(d) 17

3. If 7th and 13th term of an A.P. are 34 and 64 respectively, then its 18th term is

(a) 87

(b) 88

(d) 90

4. If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is

5. If the sum of n terms of an A.P. is then its nth term is

(a) 4n – 3

(b) 3n – 4

(d) 3n + 4

6. If 3 times the third term of an A.P. is equal to 5 times the fifth term. Then its 8th term is

(a) 0

(b) 1

(d) 3

7. In an A.P., am+n + am-n is equal to

(a) 0

(b) 1

(d) am

8. If pth term of an A.P.

is and qth term is

then the sum of pq terms is

9. If the sum of first n even natural number is equal to k times the sum of first n odd natural number then value of k will be

10. If in an A.P., Sn = n2 p, Sm = m2 p and Sr denotes the sum of r terms of the A.P., then is equal to

11. The number of terms of an A.P. 3, 7, 11, 15... to be taken so that the sum is 406 is

(a) 5

(b) 10

(d) 14

12. Sum of n terms of the series

13. The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is

(a) 508th

(b) 502th

(d) none of these

14. If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of (p + q) terms will be

(a) p + q

(b) –(p + q)

(d) 0

15. If are in A.P. then the value of x is

(a) 6

(b) 2

(d) 0

16. If sum of n terms of an A.P. is then common difference of the A.P. is

(a) 3

(b) 4

(d) 7

17. Sum of first n natural number is

18. If nth terms of the APs 63, 65, 67, ... and 3, 10, 17, ... are equal, then n is

(a) 27

(b) 23

(d) 13

19. If pth term of an A.P.

is then sum of first n terms of A.P. is

20. Sum of all natural numbers lying between 250 and 1000 which are exactly divisible by 3 is

(a) 157365

(b) 153657

(d) 155637

ANSWERS

Arithmetic Progression (AP) @2

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1. Find the ‘6th’ term of the A.P.:

2. If the numbers a, b, c, d and e form an A.P., then find the value of a – 4b + 6c – 4d + e.

3. If

is the arithmetic mean between ‘a’ and ‘b’, then, find the value of ‘n’.

4. If pth term of an A.P. is

prove that the sum of the first ‘pq’ terms is

5. If

are in A.P., prove that a2, b2, c2 are also in A.P.

6. Solve the equation:

1 + 4 + 7 + 10 + ... + x = 287

7. Find three numbers in A.P. whose sum is 21 and their product is 231.

8. Find p and q such that: 2p, 2p, q, p + 4q, 35 are in AP

9. If

are three consecutive terms of an AP, find the value of a.

10. For what value of p, are (2p – 1), 7 and

three consecutive terms of an AP?

Arithmetic Progression (AP) Class 10

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1. The nth term of an A.P. is given by an = 3 + 4n. The common difference is
(a) 7
(b) 3
(c) 4
(d) 1

2. If p, q, r and s are in A.P. then r - q is
(a) s - p
(b) s - q
(c) s - r
(d) none of these

3.If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are

(a) 2, 4, 6
(b) 1, 5, 3
(c) 2, 8, 4
(d) 2, 3, 4

4. The (n - 1)th term of an A.P. is given by 7,12,17, 22,... is

(a) 5n + 2
(b) 5n + 3
(c) 5n - 5
(d) 5n - 3

5. The nth term of an A.P. 5, 2, -1, -4, -7 ... is

(a) 2n + 5
(b) 2n - 5
(c) 8 - 3n
(d) 3n - 8

6. Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4

(a) 262
(b) 272
(c) 282
(d) 292

7. The sum of all two digit odd numbers is

(a) 2575
(b) 2475
(c) 2524
(d) 2425

8.If 2x, x + 10, 3x + 2 are in A.P., then x is equal to

(a) 0
(b) 2
(c) 4
(d) 6

9.The sum of all odd integers between 2 and 100 divisible by 3 is

(a) 17
(b) 867
(c) 876
(d) 786

10.If the numbers a, b, c, d, e form an A.P., then the value of a - 4b + 6c - 4d + e is

(a) 0
(b) 1
(c) -1
(d) 2

11. If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then 18th term is

(a) 18
(b) 9
(c) 77
(d) 0

12. If p, q, r are in AP, then p3 + r3 - 8q3 is equal to

(a) 4pqr
(b) -6pqr
(c) 2pqr
(d) 8pqr

13. Two APs have the same common difference. . The first term of one of these is -1 and that of the other is -8. Then the difference between their 4th terms is

(a) -1
(b) -8
(c) 7
(d) -9

14. In an AP, if d = -2, n = 5 and an = 0, the value of a is

(a) 10
(b) 5
(c) -8
(d) 8

15.An AP consists of 31 terms. If its 16th term is m, then sum of all the terms of this AP is

(a) 16 m
(b) 47 m
(c) 31 m
(d) 52 m

ANSWERS

Friday, 6 November 2020

Triangles @2

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Triangles

1. If the triangle's sides are a base that is 10 inches, a height that is 4 inches, and the other side that is

5 inches, what is the area of that triangle?

2. A right triangle has an angle measuring 38 degrees. Which is the degree measure of another angle of

this triangle?

3.One angle of the triangle is $85^{\circ}$ and the other two angles are in the ratio $8 :11$ . Find the measures of each of the unknown angles.

4.Three angles of a triangle measures $(2x)^{\circ}, (4x-7)^{\circ} \ and\ (5x-11)^{\circ}$ . Find the value of $x$ and the measures of all the angles.

5.In $\Delta ABC, \angle A=3\ \angle B=6 \ \angle C$ . Find the angles of the triangle.

6.Using the information given in the adjoining figure, find the value of $x \ and\ y.$ P12

7. In the adjoining figure, $DCBE$ is a straight line, $\angle ABD=135^{\circ} \ and\ \angle ACE=125^{\circ}$ .

Find $\angle BAC.$

P13