Assistant Director FIA Batch 1 Past Paper MCQs - Page 8 of 10

The sum of the first seventy positive even integers is?

A) 4960

B) 4970

C) 4980

D) None of these

The sum of the first seventy positive odd integers is?

A) 4910

B) 4920

C) 4900

D) None of these

The population of a city increases by 700 each year If the population grows to 25000 in five years. its initial population was?

A) 21000

B) 21500

C) 22000

D) None of these

Every year population increase = 700

after five year population increase = 5 x 700= 3500

So intial population = 25000-3500=21500

The moment about a point p(0, 0, 0) of the force F = 21-i-k applied at Q(1, 1,1) is?

A) 3i-3j

B) 3j+3j

C) 3j-3k

D) None of these

The work done by a force F = i+j+k in moving an object from a point p(1,1,1) to the point Q(1,2,2) is?

A) 1

B) 2

C) 0

D) None of these

The projection of a vector a= i+j+k on anther vector b= 3jk+3k is?

A) 2/√2

B) 1/√2

C) 3/√2

D) None of these

The centroid of a Wangle LMN with vertices L(1,1,1), M(3, 3, 3), N(5, 5, 5) is the point?

A) (3,3,3)

B) (2,2,2)

C) (25, 2.5, 2.5)

D) None of these

Solve:

A = [a_ij] be n square matrix If a_2i = 0 for all j 1, 2, 3, …, n, then the matrix A is?

A) Regular

B) Diagonal

C) Singular

D) None of these

If z – a is a factor of polynomial P(z), then P(a) is always?

A) z

B) 0

C) a

D) None of these

P(z)=z-a

P(a)=a-a=0

Imaginary Part of the multiplicative inverse of a number 6-5i is?

A) 5/61

B) 6/61

C) -5/61

D) None of these

Multiplicative inverse of 6-5i is 1/6-5i so,

= (1/6-5i) x (6+5i/6+5i)

= (6+5i)/ 6²- 5i² ∴ (a² – b²) = (a-b)(a+b)

By sloving we get

= 6/61 + 5i/61