Mathematics AssignmentsClass X

ARITHMETIC PROGRESSION

Q1 If a, b, c and d are in A.P. then show that d – b = c – a

Q2 Which term in the A.P. 5, 2, –1, ... is –22?

Q3 The fourth term of an A.P. is equal to three times the first term and the seventh term exceedstwice the third by 1. Find the first term and the common difference.

Q4 Find x such that x + 2, 4x – 6 and 3x – 2 are three consecutive terms of an A.P.

Q5 The 6th term of an A.P. is 12 and 8th term is 22. Find the 50th term of this A.P.

Q6 How many terms of the sequence –2, 3, 8, 13, ... make the sum 568?

Q7 Find the sum of thea) First 100 terms of the A.P. 90, 91, 92, 93, ...b) First 50 terms of the A.P. –12, –9, –6, –3, ...c) First 10 terms of the A.P. x, x + y, x + 2y, x + 3y ...

Q8 Find the suma) 72 + 70 + 68 + 66 + ... + 2b) (–1) + (–3) + (–5) + (–7) + ...+ (–99)

Q9 For an A.P. if a = 2, d = 4, Sn = 162, find n.

Q10 If 7 times the 7th term of an A.P. is equal to 11 times the 11th term, show that 18th term of theA.P. is zero.

Q11 Find the 20th term from the end of the A.P. 5, 9, 13, ..., 161

Q12 How many multiples of 9 lie between 10 and 250?

Q13 Find 20th term of an A.P. whose 11th term is 74 less than the 13th term, first term being –339

Q14 If the sum of first n terms of an A.P. is 2n2 + 3n, write the sum of first ten terms.

Q15 Find an A.P. whose third term is 16 and seventh term exceeds its 5th term by 12.

Q16 In an A.P. the 24th term is twice the 10th term. Prove that the 30th term is twice the 13th term.

Q17 The sum of 4th and 8th terms of an A.P. is 24. The sum of 6th and 10th term is 44. Find the firstthree terms of the A.P.

Q18 The sum of 5th and 7th terms of an A.P. is 52 and the 10th term is 46. Find the A.P.

Q19 Determine k so that 4k + 8, 2k2 + 3k + 6, 4k2 + 4k + 4 are three consecutive terms of an A.P.

Q20 Find the first negative term of the A.P. 159, 152, 145, ...Q21 If P times the pth term of an A.p is equal to q times the 9th term, show that its (p+q)th term is zero.Q22 If pth term of an A.P is q, and 9th term is p, prove that its nth term is (p+q-n).Q23 In am A.P, the 6th term is (11a+16b) and 14th term is (27a+40b) find its 27th term.Q24 If the sum of 1st mth terms of an A.P n same as that of 1st nth terms, then show that sum of the first(m+n)th terms of the A.P is zero.Q25. The 6th term of an A.P is zero, prove that its 21st term is triple its 11th term.

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1 1 11

) , 4,74 7 30

h xx x

1 1 1 1)d

a b x a b x

Mathematics AssignmentsClass X 2018 – 19

QUADRATIC EQUATIONS

Q1 For what value of k, x = ⅓ is a solution of the equation kx2 – x + 1 = 0?

Q2 If x = 2 and x = 3 are the roots of the equation 3x2 – 2mx + 2n = 0, find the values of m and n.

Q3 Form a quadratic whose roots are –3 and 7.

Q4 For what value of k, x = a is a solution of equation x2 – (a + b) x + k =0?

Q5 Find the roots of the quadratic equationsa) 2x2 – x + ⅛ = 0 f) a2x2 + (a2 + b2) x + b2 = 0 ; a≠0b) abx2 + (b2 – ac) x – bc = 0 g) y2 – (p + q) y + pq = 0

2) 2 7 5 2 0c x x

22 2) 5 7 5 6 0i x x x x

2 2 2 2 2) 1 0e m n x n m x

Q6 Find the value of ‘k’ so that the equation x2 – 4x + k = 0 has two distinct real roots.

Q7 Find the value of ‘k’ so that the equation kx (x–2) + 6 = 0 has two real equal roots.

Q8 A plane left 30 minutes late than the scheduled time and in order to reach the destination1500km away in time, it had to increase the speed by 250km/hr from the normal speed. Findits usual speed.

Q9 Some students planned a picnic. The budget for food was `240. But four of them failed to goand thus the cost on food for each member increased by `5. How many students were there?

Q10 An express train makes a run of 240km at a certain speed. Another train whose speed is12km/hr less takes an hour longer to cover the same distance. Find the speed of the expresstrain in km/hr.

22 2) 3 4 0, 2

2 2

x xj x

x x

OptionalPolynomial

Q1. Find a cubic polynomial whose zeroes are , and such that2, 7 =14and

Q2. Find zeroes of polynomial x3+4x2-9x-36, if two of its zeroes are equal in magnitude butopposite in sign.

Q3. If the zeroes of the polynomial x3-3x2 + x + 1 are a-b, a and a+b, find a and b.Q4. What must be subtracted form polynomial 6x4+7x3+26x2-25x+25 so that the resulting

polynomial is exactly divisible by polynomial 3x2-x+4?Q5. If x+1 is factor of 2x3+ax2+2bx+1, find the values of a and b if 2a-3b=4.Q6. Find k so that x2+2x+k is factor of 2x4+x3-14x2+5x+6. Find the zeroes of the 2

Linear equation

Q1.

Q2.

Q3.

Q4.

Q5.

Q6. Students of a class are made to stand in rows. If 4 students are extra in a row, there wouldbe 4 rows less. If 2 students are less in a row, there would be 4 rows more. Find the numberof students in the class.

Q7. There are two examination rooms A and B. If 10 candidates are sent from A to B, thenumber of students in each room is the same. If 20 candidates are sent from B to A, thenumber of students in A is double the number of students in B. Find the number of studentsin each room.

Q8. A part of monthly expenses of a family is constant and the remaining varies with the priceof rice. When the cost of rice is Rs.250 per quintal, the monthly expenditure of the family isRs. 1000 and when the cost of rice is Rs. 240 per quintal, the monthly expenditure Rs. 980.Find the monthly expenditure of the family when the cost of rice is Rs. 300 per quintal.

Q9. 8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finishit in 14 days. Find the time taken by a single man and a single boy to do the same boy.

Quadratic Equations.Q1. If x=2 and x=5 are roots of px2-7x+5q=0 find the values of p and q.

Q2.

Q3.

Q4. Solve

Q5. Find the value of k for which the roots of the given equations are real and equal.

a)

b) 2 2(1 3 ) 7(3 2 ) 0x k x k

polynomials.Q7. If m and n are zeroes of polynomial kx2+4x+4 and (m + n )2 –2mn=24, find the values of k.

Q6. Rs. 6500 were divided equally among a certain number of persons. Had there been 15 morepersons, each would have got Rs. 30 less, Find the original number of persons.

Q7. An aeroplane left 30 minutes later than its scheduled time and in order to reach itsdestination 1500 km away in time, it had to increase its speed by 250km/h from its usualspeed. Find its usual speed.

Q8. The length of the hypotenuse of a right triangle is 3 5 cm. If the smaller side is tripled andthe larger side is doubled, the new hypotenuse will be 15 cm. Find the length of each side.

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LINEAR EQUATIONS IN TWO VARIABLES

Q1 The value of a and b for which the pair of linear equations 2x+3y–7 and 2ax+(a+b)y=28 has infinitely many solutions are:

a) 3 and 5 b) 4 and 5 c) 4 and 7 d) 4 and 8

Q2 The value of k for which the pair of linear equations 10x+5y–(k–5)=0 and 20x+10y–k=0 has infinitely many solution.

a) 2 b) 5 c) 10 d) 80 Q3 If x=a, y=b is the solution of the pair of linear equations x–y=5 and 4x–3y =17, then the values

of a and b are a) a=–3, b=3 b) a=2, b=–3 c) a=–2, b=3 d) a=3, b=–2

Q4 The pair x+2y=140 and 3x+4y=360 of linear equations represents two lines which are a) Parallel b) intersecting c) coincident d) either intersecting or parallel

Q5 If the lines represented by the pair of linear equations 4x+ky–8=0 and 3x–5y+7=0 are parallel then the value of k is

a) 20

3 b)

3

20 c)

5

10 d)

3

20

Q6 For what value of k the system of equations 2x+(k–2)y=k and 6x+(2k–1)y=2k+5 has infinite solutions?

Q7 Find a and b for which the following pairs of linear equations has infinite solutions a) 2x–(a–4)y=2b+1 b) 2x+3y=7

4x–(a–1)y=5b–1 2ax+(a+b)y=28

Q8 For what values of k the pair of linear equations have no solution? a) 3x–1y=k b) 8x+5y=9

(2k–1)x+(k+2)y=2k+1 kx+10y=8

Q9 Solve graphically a) 3x–4y=1 b) x–2y=5

6x–8y=–4 2x–4y=10 c) 3x+y=11, x–y=1 and x=0. Also find the area of triangle formed d) 2y–x=8, 5y–x=14, y–x=1. Write the coordinates of vertices of the triangle formed by the lines representing these equations

Q10 The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units. If we increase length by 3 units and breadth by 2 units, the area is increased by 67sq. Units. Find the length and breadth.

Q11 A boat covers 32km upstream and 36km downstream in 7 hours. Also it covers 40km upstream and 48k downstream in 9 hours. Find the speed of the boat in still water and that of the stream.

Q12 The ratio of incomes of two persons is 9:7 and the ratio of their expenditure is 4:3. If each of them manages to save `2,000 per month, find their monthly incomes.

Q13 Find the values of x and y if ABCD is a rectangle.

Mathematics Assignments Class X 2017-18

Mathematics Assignments Class X TERM 1 2016 – 17

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Q14 A and B each have certain number of oranges. A says to B, “If you give me 10 of your oranges, I will have twice the number of oranges left with you.” B replies “If you give me 10 of your oranges, I will have the same number of oranges as left with you.” Find the number of oranges with A and B separately.

Q15 Ram travels 760km to his home, partly by train and partly by car. He takes 8 hours if he travels 160km by train and the rest by car. He takes 12 minutes more if he travels 240km by train and the rest by car. Find the speed of the train and the car separately.

Q16 A two digit number is obtained by either multiplying sum of digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding2. Find the numbers.

Q17 In an examination, 2 marks are awarded for each correct answer while 1 mark is deducted for each wrong answer. Ram answered 150 questions and got 240 marks. How many questions did he answer correctly?

Q18 The sum of a two-digit number and the number obtained by reversing the order of its digit is 165. If the digits differ by 3, find the number.

Q19 Solve the following pair of equations

a) 2515

4210

yxyxyxyx

b) 154731633147 yxyx

c) 136

0,0;215

yx

yxyx

d) 3

163

20;

3

172

5 y

xxy

x

e) 2)(3

1

)(2

13

36

yxyxyxyx

f) 12

25

381

43

yxyx

Q20 Solve 2x+3y=11, 2x–4y=–24. Hence find the value of m for which y=mx+3

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POLYNOMIALS

Q1 Verify that –2, +1, +½ are zeroes of the polynomial P(x)=2x3+1x2–5x+2. Also verify the relationship between the zeroes and the coefficients of P(x)

Q2 Form the quadratic polynomial with zeroes

a) 4

3 and 3 b)

5

2 and

5

2 c) 3 and 2 d) 2 and

2

1

Q3 Find the value of b for which the polynomial 2x3 + 9x2 – x – b is exactly divisible by 2x +3

Q4 If two zeroes of the polynomial P(x) = x4 – 6x3 – 26x2 + 138x –35 are 32 and 32 find

other zeroes.

Q5 Write the sum and products of zeroes of polynomial without finding the zeroes. P(x) = 6x3 + 5x2 – 12x + 4

Q6 If sum of squares of zeros of polynomial P(x) = x2 – 8x + k is 40, find the value of k.

Q7 Give examples of polynomials f(x), g(x), q(x) and r(x) which satisfy division algorithm and (i) degree r(x)=0 (ii) degree q(x) = degree r(x) = 1

Q8 If polynomial x4–6x2+16x2–25x+10 is divided by x2–2x+k, the remainder is x + a, find k and a.

Q9 Find the value of P for which the polynomial x3+4x2–px+8 is exactly divisible by x–2.

Q10 Find the quotient and remainder in the division of the 1st polynomial by 2nd polynomial. a) 27x3–1 by 3x–1 b) x3–3x2+3x–5 by x2–x+1

Q11 Is x2+5x+6 a factor of x3–19x–30?

Q12 If a and b are zeroes of the polynomial f(x)=x2–5x+k and a–b=1, find k.

Q13 In dividing P(x)=x2+3x+2 by a polynomial g(x) the quotient q(x) and remainder are x–2 and 12. Find g(x).

Q14 On dividing 6x4+8x3+17x2+21x+7 by 3x2+4x+1 the remainder is px+q. Find p and q.

Q15 If and are zeroes of polynomial p(x)=4x2–5x–1, find the value of

a) 2 + 2 b) 2

+ 2

Q16 If and are zeroes of polynomial p(x)=x2–2x+3, find the value of

a) +2, + 2 b)

1,

1

Q17 If HCF and LCM of p(x) and q(x) are 2x–1 and 6x3+25x2–24x+5 respectively, if p(x)=2x2+9x–5 find q(x).

Q18 Find zeroes of polynomial: pqx2 + (q2–pr)x – qr and verify relationship between zeroes and coefficients.

Mathematics Assignments Class X 2017-18