Polynomials - MCQ - Class 10

9. if α and β are the zeros of the polynomial f(x) = x² + x + 1 then what is the value of 1/α + 1/β ?

                a) 1                         b) – 1                     c) 2                         d) -2

10. if one zero of the polynomial f(x) = (k² + 4) x² + 13x + 4k is reciprocal of the other then find the value of k?

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

11 If the zeros of the polynomial f(x) = x³ – 3px² + qx – r are in AP then

                a) 2p³ = pq – r                                                    b) 2p³ = pq + r   

                c) 2p³ = pq /r                                                      d) p³ = pq /2 – r

12. if if α and β are the zeros of the polynomial f(x) = x² – p(x+1) x – c such that (α + 1) (β+ 1) = 0 then what is the value of c?

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

13. A quadratic polynomial whose one zero is 6 and sum of the zeroes is 0, is

      (a)   x² – 6x + 2                   (b)   x² – 36                  (c)   x² – 6                     (d)   x² – 3

14. If graph of a polynomial does not intersect the x-axis but intersects y-axis in one point, then no, of zeroes of the polynomial is equal to

      (a)   0                                              (b)   1                                     (c)   0 or 1                            (d)   none of these

15 . Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial

      (a)   intersects y-axis                                                                (b)   intersects x-axis

      (c)   intersects y-axis or intersects x-axis                          (d)   none of these

16. The zeros of the quadratic polynomial x² + 7x + 12 are –

                a) -2, - 5                                b) – 3 , -4                             c) – 5, - 2                              d) -6, -1

17 . Find p and q , if the zeros of the polynomial x³ – 3 x² + x + 1 are p – q , p and p + q

                a) p = ± √2 , q = 1              b) p = √2 , q = 2                  c) p = 2, q = √2                   d) p = 1, q = ±√2

18. if two zeros of the polynomial f(x) = x³ – 4x² – 3x + 12 are sqr root 3 and  - (sqr root 3) then find the third zero?

                a) 2                         b) 4                        c) -5                       d) -1

19 . If p and q are the zeros of the quadratic polynomial 4x² – 1 = 0 , find the value of p² + q²

                a) 3/2                    b) ¼                       c) ½                        d) 1

20. Form a quadratic polynomial of which one zero is 6 - sqr root 5 and the sum of the zeros is 12?

                a) x² – 4x + 30                     b) x² + 4x – 31                     c) x² - 12x – 31                    d) x² - 12x + 31

21. Find the remainder when 2t⁴ – 6t³ + 2t² – t + 2 is divided by t + 2?

                a) 90                                      b) 91                                      c) 92                       d) 93

22. If the sum of the zeros of the polynomial p (x) = 2x³ – 3kx² + 4x – 5 is 6 then the value of k is

                a) 2                         b) 4                        c) -4                       d) 6

23. What is the difference between the values of the polynomial x² - 12x + 31 at x = 1 and x = 2?

                a) 6                         b) 9                        c) -5                       d) 0

24 . If x¹⁰⁰ + 2.x⁹⁹ + k is divisible by x + 1 then the value of k is

                a) 1                         b) 2                        c) 3                         d) -2

NB :- Answer is marked with red colour

Dr Rajesh Kumar Thakur

Polynomials - MCQ - Class -10

Polynomials

1.     1.   Fill in the blank

a)       A polynomial of degree 0 is called a ------------- polynomial.    (Constant)

b)      A polynomial of degree 1 is called a ------------ polynomial.     (linear)

c)       A polynomial of degree 2 is called a ------------ polynomial.     (Quadratic)

d)      A polynomial of degree 3 is called a ------------ polynomial.     (Cubic)

e)      A polynomial of degree 2 is called a ------------ polynomial.     (bi -Quadratic)

f)        The number of zeros of a quadratic polynomial is -----.            (2)

g)       The number of zeros of a cubic polynomial is -----.                    (3)

h)      The graph of a quadratic polynomial is a -----------. (Parabola)

i)        A quadratic equation can have ------------- two roots. (exactly/ at least / at most)  - at most

j)        If α is a zero of p(x) then ------------- is a factor of p(x)   { x – α )

                2.  if a, b, c are the zeros of the polynomials 2x³ – x² + 3x – 1, find the value of (abc) + (ab + bc + ca)                                                                                                                                                                 

a)       2                      b) 1.5                     c) ½                        d) 0

2           3. The value of p for which 2x³ + 9x² – x – p is exactly divisible by 2x + 3 is –

a)       – 15                b) 15                      c)9                          d) – 9

3     4.   If one of the zeros of the quadratic polynomial (k -1) x² + kx + 1 is – 3 , then the value of k is –

a)       4/3                 b) -4/3                  c) 2/3                    d) -2/3

4     5.   If P(x) and D(x) are two polynomials such that D(x) ≠ 0, there exist unique polynomials Q(x) and R(x) such that P(x) = D(x). Q(x) + R(x) where: -

a)       R(x) = 0 and deg R(x) > deg Q(x)

b)      R(x) = 0 or deg R(x) > deg Q(x)

c)       R(x) = 0 or deg R(x) < deg Q(x)

d)      R(x) = 0 and deg R(x) > deg Q(x)

5 6.  Write a polynomial with the sum, sum of product of its zeros taken two at a time and the product of its zeros as -2, +5 and – 3 respectively.

a)       2x³ + 3x² – 5x + 3                      

 b) 4x³ + 7x² – 5x + 3                                                                               

c) x³ + 2x² + 5x + 3                       

 d) 2x³ - 3x² + 7x + 3

6.     If 2 + sqr root 3 and 2 - sqr root 3 are  the two zeros of a polynomials then which of the polynomial you can make with these roots?

a)       x² – 4x + 1                                    b) x² + 4x + 1

c) 4x² – 4x + 3                                     d) x² – 4x + 3

7.  If one zero of the polynomial ax³ + bx² + cx + d is zero, then the product of other two zeros is –

                a) a                         b) b/a                    c) -c/a                   d) d/a

8  If the polynomials ax³ + 4x² + 3x – 4 and x² – 4x + a, leave the same remainder when divided by           x -3, then value of a is –

                a) 20                      b) -1                       c) 1                         d) -2b

Dr Rajesh Kumar Thakur

MCQ - Real Number - Class 10 - Part 4

31. If a and b are positive integers, then HCF(a,b) x LCM (a,b) =

                a) a x b                  b) a + b                 c) a – b                  d) a/b

32. π is –

                a) a natural number                        b) not a real number

                c) a rational number                       d) an irrational number

33.  The missing number in the factor tree is-

a)       4                                      b) 5                                        c) 6                         d) 8

34. 91/625   , when written in decimal form terminates; as the factor of denominator are in the form of 2^m x 5ⁿ. This number will terminate after how many digits?

                a) 1                         b) 2                        c) 3                         d) 4

35.  Decimal representation of rational number 8/27 is –

                a) 0.                b) 0.29                 c) 0.2                 d) none of these

36. The HCF and LCM of two numbers are 4 and 9696, then the product of two numbers is –

                a) 9696                  b) 24242               c)38784                                 d) 4848

37. A number p/q when expressed in decimal form terminates after 7 digits then factor of q are of the form of x^m × yⁿ; the value of x + y should be –

                a) 7                         b) 14                      c) 9                         d) 26

38. The HCF of two numbers is 8, which one of the following can never be their LCM

                a) 24                      b) 48                      c) 56                       d) 60

39. The LCM of two co-prime number is 638. One number is 29, find the other number

                a) 16                      b) 22                      c) 36                       d) 17

40. IF A, B and C are three numbers such that LCM of A and B is B and the LCM of B and C is C then LCM of A, B and C is

                a) A                        b) B                        c) C                         d)

NB :- Answer is marked with red


DR RAJESH KUMAR THAKUR

MCQ - Real Number - Class 10 - Part 3

21. The rational number that corresponds to 0.6 + 0.  + 0.4  is –

                a) 83/90                b)7/9                                     c) 43/90                                d) 167/90

22.  The HCF of two consecutive rational number p and p + 1 is

                a) p                        b) p+ 1                                  c) 1                                         d) 0

23. If pⁿ = ( a x 5)ⁿ, for pⁿ to end with the digit zero a = ---- for any natural number n is –

                a)  any natural number                  b) any even number                      

                c) any odd number                          d) none

24. 2 -  is –

                a) a rational number                       b) a natural number                       

                c) an irrational number                  d) a whole number

25. The number given below which always ends with the digit 6 for all-natural numbers n is –

                a) 4ⁿ                                                       b) 6ⁿ

                c) 2ⁿ                                                       d) 8ⁿ

26. There is a circular path around a field. Nilabh takes 22 minutes to complete one round while Nishtha takes 20 minutes to complete the same. If they both start at the same time and move in the same direction, after how many minutes will they meet again at the starting point?

                a) 220                    b) 3.4                     c) 440                    d) 4.4

27.  If two positive integers p and q can be expressed as p = ab² and b = xy² ; a, b being prime number then LCM( p ,q) is –

                a) ab                      b) a²b²                  c)a³b²                    d)a²b³

28.  Any one of number m, m + 2 and m + 4 is a multiple of –

                a) 2                         b) 3                        c) 4                         d) 5

29. If p is a prime number and p divides k² , then p divides :-

                a) 2k²                     b) k                        c) 3k                       d) none of these

30. If p = HCF (100, 190) and q = LCM (100,190) then p²q² is

                a)3.61 x 10⁶         b)3.61 x 10³         c) 3.61 x 10⁵        d)3.61 x 10⁸

^{NB :- Answer is marked with red colour}