NDA I - Mathematics Question Paper 2013 - Defence MCQ

If a and b are rational and b is not perfect square, then the quadratic equation with rational coefficients whose one root is  is

If A is a finite set having n elements, then the number of relations which can be defined in A is

If the positive integers a, b, c, d are in AP, then the numbers abc, abd, acd, bcd are in

Which one of the following is an example of non-empty set ?

What is one of the square roots of 3 + 4i, where i = √-1 ?

The number 83 is written in the binary system as

The relation R in the set Z of integers given by R = {(a, b): a-b is divisible by 5} is

what is equal to ?

What is 0.9 + 0.09 + 0.009 +.... equal to ?

How many real roots does the quadratic equationf(x) = x² + 3|x| + 2 = 0 have ?

In a group of 50 people, two tests were conducted, one for diabetes and one for blood pressure. 30 people were diagnosed with diabetes and 40 people were diagnosed with high blood pressure, what is the minimum number of people who were having diabetes and high blood pressure ?

Consider the following statements:

1. The product of two non-zero matrices can never be identity matrix.

2. The product of two non-zero matrices can never be zero matrix.

Q. Which of the above statements is/are correct ?

Consider the following statements:

Q. Which of the above statements is/are correct ?

The cofactor of the element 4 in the determinant

If A is a square matrix of order 3 with |A|  , then which one of the following is correct ?

Let A = {a, b,c, d) and B = {x, y, z }. W hat is the num ber o f elements in A * B ?

If C (28 ,2r) = C (28 , 2r - 4), then w hat is r equal to ?

If A is a subset of B, then which one of the following is correct ?

Let f be a function from the set of natural numbers to the set o f even natural num bers given by f(x) = 2x. Then f is

 ,then what is λ equal to ?

What is the angle (in circular measure) between the hour hand and the minute hand of a clock when the time is half past 4 ?

The angle of elevation of the top of a tower from two places situated at distances 21m. and x m. from the base of the tower are 45° and 60° respectively. What is the value of 7x ?

What is equal to ?

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite of bank is 60°. When he retires 40 m. from the bank, he finds the angle to be 30°. What is the breadth of the river ?

If the angles of a triangle are 30° and 45° and the included side is (√3 +1), then what is the area of the tringle ?