APDCL OFFICE CUM FIELD ASSISTANT SOLVED PAPER 2019:- MATHEMATICS SECTION

APDCL OFFICE CUM FIELD ASSISTANT  SOLVED PAPER 2019:- MATHEMATICS SECTION

1.The quotient and remainder of 17 when divided by 6  is
A. 2 and  5    B. 2 and 1
C. 5 and 2     D. 1 and 2

Answer:-

            17 / 6=

quotient = 2 and remainder = 5

therefore correct answer is A) 2 and 5

2.HCF of 272 and 148 is

A. 1    B. 2
C. 4    D. 6

Answer :

     272 = 2×2×2×2×17

     148 = 2×2×37

HCF= 2×2 =4

Correct answer is 4

3.which one of the following  is not irrational

A.√5           B. 2√5
C. 2+√5      D. √4

Answer √4 because √4=2

4. the Discriminate of the equation 3x^2-2√3+1=0
A.1       B. -1
C.0       D. 12

Answer :-

b^2-4ac=(-2√3)^2-4×3×1

      =4×3-12

=0

5. Probability of an event E+ Probability of the event 'not E'
A. 0     B. 1/2
C.1/4    D.1

ANSWER-

We know that

P(not E) = 1- P(E)

P(not E)+P(E) =1

Therefore Probability of a event E+ Probability of the event 'not E'=1

6. For what value of A and B below sin(A+B)= Sin(A)+Sin(B)
A.  A=0=B    B. A=30=B
C. A=45=B   D. A=60=B

Answer

sin(A+B)= Sin(A)+Sin(B

Sin(0+0)= 0+0= 0

Since Sin(0)= 

Therefore Correct Answer is A) A=0=B

7. Which of the following cannot be the probability of an event?

A.1/3       B. -1/2

C. 0.5        d. 20

Answer- B. -1/2

Because probability of an event cannot be negative.

8.Let Sn = 1+2+3+....+n then

A. Sn = n(n-1)/2      B. Sn= n(n+1)/2

C. Sn=n(1-n)/2         D. Sn=n(n-2)/2

Answer- B. Sn= n(n+1)/2

9.Consider  the number 3ⁿ When n is a natural number . Then 3ⁿ ends with the digit zero for

A. Any value of n       B.  For Unique value of n

C. For some value of n   D. No Value of n

Answer-  D. No Value of n

If the number  3ⁿ for any n, were to end with the digit zero, then it would be

divisible by 5. That is, the prime factorisation of  would  3ⁿ contain the prime 5.

This is not possible because 3ⁿ =(1x3)ⁿ. So there is no natural number n for which 4n

ends with the digit zero.

10. consider The lines 2x-y=0 and 4x+3y=20 .then the only common point of the both lines is

A. (4,2)      B. (0.0)

C. (2,4)      D. (4,3)

Answer- C. (2,4)     

Here x=2 then for the line 2x-y=0

=>2x2-y=0

=> y=4

Again 4x+3y=20

  ð   4x2+3y=20

  ð   3y=20-8

  ð  3y=12
  ð  y=12/3=4

11. Which of the following pairs of lines is parallel

A. x-2y=0 and 3x+4y-20=0   B.3x+2y-5=0 and 6x+4y-10=0

C. 3x+2y-5=0 and 2x+3y-5=0  D.x+2y-4=0 and 2x+4y-16=0

Answer- D.x+2y-4=0 and 2x+4y-16=0

Here a₁=1 a₂₌2 b₁=2 b₂=4 c₁=-4 c₂=-16

a₁/ a₂= b₁/ b₂≠ c₁/ c₂

Hence this pairs of lines is parallel

12.In a right angle triangle with right angle at B and ACB=60⁰ .If AB =3 cm , then the lengh of BC is

A. 3           B. 1/3

C. 1/ √3     D.  √3

Answer- D.  √3

tan (60⁰)= AB/BC

√3  = 3/C

C=3/√3=√3

13. The tangent  PQ at  the point P of a circle of radius 6 cm meets a line through the center O at a point Q so that OQ=12. Then the length of PQ is

A.    6√3   

B.    18

C.   3√6

D.   36

Answer-  A.6√3

OQ²=OP²+PQ²

12²= 6²+PQ²

=>144=36+PQ²

=> PQ²=144-36=108

=>PQ=√4x3x9=6√3

14. Jadhu and madhu are two friends . what is the probability that both will have different birthday (in a non- leap year)

A. ½    B.1/364

C.1/365  D. 364/365

Answer- D. 364/365

15. For what value of K following pairs of linear equations have no equations 3x+2y=1

(3k-1)x+(2k-1)y=2k+1

A.  K=1

B.  K= ½

C.  K=2

D.  K=-1

Answer- this question is wrong

16. If α,β,γ are the zeros of the cubic polynomial ax³+bx³+cx+d then

a)   αβ+βγ+ γα=-b/a

b)   αβ+βγ+ γα=-d/a

c)   αβ+βγ+ γα=-b/d

d)   αβ+βγ+ γα=c /a

Answer- αβ+βγ+ γα=c /a
17. The pairs of linear equations in two variables a₁x+b₁y+c₁= 0 and a₂x+b₂y+c₂= 0

 Has infinitely many solutions if

A.  a₁/a₂ ≠b₁/b₂

B.  a₁/a₂=b₁/b₂≠c₁/c₂

C.  a₁/a₂≠b₁/b₂=c₁/c₂

D.  a₁/a₂=b₁/b₂=c₁/c₂

Answer - D.  a₁/a₂=b₁/b₂=c₁/c₂

18. There are two classrooms A and B. If 5 students are sent from A to B , then the numbers of students in each class room is same . If 10 students are sent from B to A, then the numbers of students in A is double the numbers of students in B . Then the Numbers of students in A is

A. 20 B. 30

C. 40  D. 50

Answer – D. 50

19. Consider the points A(1,0) B(4,0) and C  (1,4) . Then the triangle ABC is a

A. Right angled triangle   B. Equilateral triangle

Isosceles triangle   D. Isosceles right triangle

Answer- A. Right angled triangle  

AB= √(4-1)²+(0-0)²= √3²=3

BC= √ (1-4)²+(4-0)²=√9+16=√25=5

CA= √(1-1)²+(4-0)²=√4²=4

Here AB²+CA²= BC²

Hence the triangle is A. Right angled triangle   .

20.If the sum of the reciprocals of a person A’s age in years 3 years back and 5 years from now is 1/3 then his present age is

A. 7    B. -7

C. 3    D. -3

 Answer- 7