MCQ - Probability - Class 10 - By Mr Anjan Kr. Thakur

Here are 45 objective questions on Probability prepared by Mr. Anjan Kumar Thakur who is a mathematics teacher at  L K Singhania School, Ghotan (Rajasthan),

                                                                                 MCQ –

1.       On rolling a die, how many outcomes we may have?

a.       3

b.       6

c.       7

d.       9

2.       Tossing 2 coins together the outcomes are –

a.       (H,T)

b.       (H,H), (T,T )

c.       ( T,H )

d.       All of these

3.       Which of the following is not a suit of a deck of playing cards ?

a.       Diamond

b.       Club

c.       Hearts

d.       Wine

4.       The probability any event can’t be greater than –

a.       ½

b.       ¾ 

c.       0

d.       1

5.       If P(E) = 0, it will be –

a.       A random event

b.       A sure event

c.       A impossible event

d.       A scheduled event

6.       If a coin is tossed once , what will be the probability of getting a HEAD is

a.       0

b.       ½

c.       1

d.       ¾

7.       What is the probability of getting a joker in a well shuffled deck of 52 playing cards –

a.       2/52

b.       1/52

c.       ½

d.       0

8.       What is the probability of getting a queen in a well shuffled deck of  playing cards –

a.       1/52

b.       1/13

c.       1/26

d.       4/13

9.       What is the probability of getting a prime number by rolling a fair die once –

a.       5/6

b.       ½

c.       ¾

d.       ¼

10.   What is the probability of getting a perfect  number by rolling a fair die once –

a.       1/6

b.       2/6

c.       1

d.       0

11.   What is the probability of getting a perfect square  number by rolling a fair die once –

a.       1

b.       2/6 0r 1/3

c.       0

d.       ½

12.   One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a face card  –

a.       1/13

b.       4/13

c.       1/52

d.       3/13

13.   Which of the following is not a face card ?

a.       Ace

b.       King

c.       Queen

d.       Jack

14.   One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a Seven card  –

a.       4/13

b.       1/13

c.       4/26

d.       1

15.   One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a red  card  –

a.       ¼

b.       1

c.       ½

d.       0

16.   One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a queen of heart  card  –

a.       1/13

b.       5/52

c.       1/26

d.       1

17.   A bag contains 5 balls of green colour, 7 balls of red colour and 13 balls of yellow colour. A ball is randomly picked up from the bag find the probability of getting a ball of red colour?

a.       13/20

b.       7/25

c.       10/25

d.        20/25

   

   18.   If the probability of the occurrence of an event be 3/7 what will be the probability of non-occurrence of the same event –

a.       1/7

b.       2/7

c.       4/7

d.       5/7

     19.   One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a king  –

a.       1/13

b.       2/52

c.       10/52

d.       None of the above

20.   One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a non-face card   –

a.       48/52

b.       10/13

c.       16/52

d.       54/52

21.   Which of the following number can’t be the probability of any event ?

a.       2/3

b.       ¾

c.       8/7

d.       ½

e.       0

22.   There are 100 cards on which the numbers from  1 to 100 is printed on them. Find the probability of getting ZERO if any one card is drawn after fairly reshuffling them –

a.       1/100

b.       2/100

c.       11/100

d.       NOTA

23.   In tossing two coins together what is the probability of getting 2 heads ?

a.       ½

b.       ¼

c.       ¾

d.       1

24.   In the above case find the probability of getting at least 1 tail –

a.       1

b.       ½

c.       ¾

d.       ¼

   25.   In a well shuffled deck of 52 cards what is the probability of getting a RED card if one card is drawn randomly ?

a.       ½

b.       1/13

c.       2/13

d.       ¼

26.   In a throw a pair of dice, what is the probability of getting a doublet -

a.       ¼

b.       5/6

c.       1/6

d.       14/36

27.   One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a queen or a black card  –

a.       1/2

b.       28/52

c.       24/26

d.       4/52

28.   One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting neither  queen or a king  –

a.       11/13

b.       10/13

c.       15/26

d.       NOTA

29.   A bag contains 6 red balls and 14 white balls find the probability of getting 1 white ball if randomly a ball be chosen –

a.       3/10

b.       7/10

c.       13/20

d.       7/20

30.   In a wheel of fortune there are 1 to 10 numbers printed on it. If I win after getting any perfect square number, find the probability of my victory ?

a.       7/10

b.       3/10

c.       1/10

d.       9/10

31.   Find the probability of getting the smallest positive integer –

a.       1

b.       ½

c.       0

d.       NOTA

32.   Find the probability of getting the biggest natural number  –

a.       1

b.       ½

c.       0

d.       NOTA

33.   In a class there are 20 girls and 15 boys, find the probability of getting a boy if a student be randomly selected –

a.       3/7

b.       4/7

c.       15/20

d.       5/15

34.   The probability of a sure event is

a.       ½

b.       ¾

c.       1/1000

d.       1

35.   The probability of an impossible  event is

a.       ½

b.       ¾

c.       1/1000

d.       1

36.   If the probability of an event A be ¼ and that of event B be ¾ , then both the events A and B are called –

a.       Sure event

b.       Impossible event

c.       Complementary event

d.       Supplementary event

37.   A die is thrown once , what is the probability of getting a perfect cube number ?

a.       ½

b.       ¼

c.       1

d.       1/6

38.   A die is thrown once , what is the probability of getting a composite  number ?

a.       ½

b.       1/3

c.       ¼

d.       1/6

39.   If a pair of dice be thrown , what is the probability of getting a sum greater than 10 of numbers appearing of both dice –

a.       5/36

b.       1/12

c.       4/36

d.       10/30

40.   A coin has ……. Faces .

a.       1

b.       2

c.       0

d.       3

41.   How many suits are there in a deck of playing cards ?

a.       1

b.       2

c.       3

d.       4

42.   How many faces does a die have ?

a.       1

b.       2

c.       4

d.       6

43.   P(E) indicates –

a.       Total outcome

b.       Favourable outcome

c.       Probability of occurrence of favourable events

d.       NOTA

44.   Getting a number less than 7 is a –

a.       Sure event

b.       Random event

c.       Impossible event

d.       Complementary event

45.   If 3 coins be tossed once together find the probability of getting all HEADS –

a.       ½

b.       ¼

c.       1/8

d.       1

Linear Equation in two variables - Class 10 - MCQ- by Dr Rajesh Kumar Thakur

Linear Equation in Two Variable

1.      Fill in the blank

a)      A system of simultaneous linear equations is said to be constant, if it has at least ------------ solution.  (one)

b)      A system of simultaneous linear equations is said to be in-consistent if it has ---------- solution. (no)

c)       The graphical representation of the system of linear equations will be ------ if it is consistent with unique solution. (intersecting)

d)      The graphical representation of the system of linear equations will be ------ if it is consistent with infinite many solutions. (parallel)

2.      The system of equations 3x – 5y = 20 and 6x - 10y = 40 has -                                                        

   a) one solution                b) exactly two solutions                                             

c) infinite many solutions            d) no solutions

3.      For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky + 16 = 0 represent coincident lines?                                                                                                                                  

  A) ½                 b) -1/2                   c) 2                  d) -2

4.      The value of k for which the system of equations kx – y = 2 and 6x – 2y = 3 has a unique solution is                                                                                                                                  

   a) -= 3              b) ≠ 3                      c) ≠0                d) = 0

5.      If the system of equations 2x + 3y = 7 and (a + b)x + (2a – b) y = 21 has infinite many solutions, then -                                                                                                                             

       a) a = 1, b = 5                           b) a = 5, b = 1                                                      

        c) a = -1, b = 5                          d) a = 5, b = -1

6.      The value of k for which the system of equations x + 2y = 5 and 3x + ky + 15 = 0 has no solution is                                                                                                                                          

       a) 6                  b) -6                 c) 3/2               d) none of these

7.      The area of triangle formed by the line x/a + y/b = 1 with the co-ordinate axes is    

                       a) ab                        b) 2ab              c) ½ ab             d) ¼ ab

8.      The area of triangle formed by the lines x = 3, y = 4 and x = y is -                      

                               a) ½ sq. unit            b) 1 sq. unit     c) 4 sq. unit      d) none of these

9.      The line 3x + 2y = 12 meets x- axis at

a)      (0,1)                       b) (4,0)             c) (2,3)             d) (0,6)

10.   The solution of the system of equations x – y + 1 = 0 , 3x + 2y – 12 = 0 is -               

                       a) (0,1)                             b) (4, 0)            c) (2, 3)            d) (0,6)

Note :- Answer written with red colour

Dr Rajesh Kumar Thakur

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