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}

MCQ - Real Number - Class 10 - Part 2

11. A number which can be expressed in the form of p/q, where q ≠ 0 is a rational number is:-

                a) p and q are co- prime number              

                b) p and q are real numbers

                c) p and q are irrational numbers

                d) p and q are integers

12. n² – 1 is divisible by 8, if n is

                a) an integer                                                      b) a natural number                       

c) an odd number                                            d) an even number

13. If a non- zero rational number is multiplied by an irrational number then we always get –

                a) an irrational number                                 b) a rational number

                c) zero                                                                  d) one

14.  The largest number which divides 70 and 125 leaving remainder 5 and 8 respectively is –

                a) 13                      b) 65                      c) 875                    d) 1750

15. The product of a non-zero rational and an irrational number is –

                a) always irrational                          b) always rational

                c) rational or irrational                   d) one

16. If we write 0  as a rational number, we get

                a) 9/10                  b) 1                        c) 5/10                  d) 0

17. Write an irrational number between 2 and 3 is –

                a) 2.5                     b) 2.001                                c) 2.1333333456…                             d) 2.1

18. The least number that is divisible by all numbers from 1 to 10 (both inclusive) is –

                a) 10                      b) 100                                    c) 504                                    d) 2520

19. if the HCF of 65 and 117 is expressible in the form of 65m – 117 then the value of m is –

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

20. The greatest number that divides 87 and 97 leaving 7 as remainder is –

                a) 10                      b) 1                                        c) 87 x 97                             d) 6300

Dr Rajesh Kumar Thakur

NB :- Answer is written with red colour