NDA || Mathematics || Mini_Mock

If sin x + sin y = a and cos x + cos y = b, then  is equal to

The value of  is equal to

The value of  is equal to

Two poles are 10 m and 20 m high. The line joining their tips makes an angle of 15^o with the horizontal. The distance between the poles is approximately equal to

A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, tip of the flag staff are 30 degree and 45 degree respectively. Which one of the following gives the best approximation to the height of the tower?

The angle of elevation of the top of a tower from a point 20 m away from its base is 45°. What is the height of the tower?

Let X be the set of all persons living in a city. Persons x, y in X are said to be related as x < y if y is at least 5 years older than x. Which one of the following is correct?

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then the number of subsets of A containing exactly two elements is

Which one of the following matrices is an elementary matrix?

If  then what is A + 3A^-1 equal to? where I is the identity matrix of order 2.

Consider the following statements in respect of the matrix  :

1) The matrix A is skew-symmetric.

2) The matrix A is symmetric.

3) The matrix A is invertible.

Which of the above statements is/are correct?

Consider two matrices  and  . Which one of the following is correct?

Let A= {x, y, z) and B= {p, q, r, s}. What is the number of distinct relations from B to A?

Consider the following statements :

1) f(x) = [x], where [.] is the greatest integer function, is discontinuous at
x = n, where n ∈ Z.

2) f(x) = cot x is discontinuous at x =nπ, where n ∈ Z.

Which of the above statements is/are correct?

If   and g o f(t) = g(f(t)), then what is  equal to?

Solve

If  = ?

If z = f o f(x) where f(x) = x², then what is  equal to?

At what value of x does f(x) attain minimum value?

What is the minimum value of f(x)?