NDA || 25 day challenge || Math part I

If , then what is (cos θ – sin θ) equal to?

If  and  is an acute angle, then the value of is

Once the angle of elevation of top of a tree was 45° from 400m away from the tree. After 2 months, the tree grew up and now from same point angle of elevation becomes 60°. The tree grew by-

(take )

If 2 sin θ – 8 cos²θ + 5 = 0, 0^o < θ < 90^o, then what is the value of cot 2θ ?

The number of real roots of the equation

, is

The roots of the equation  are

Find the total number of solutions of the equations  and

Number of real roots of the equation  is :

Let z be a complex number such that |z| = 8 and  What is z equal to?

Convert (300.65625)₁₀ in its binary equivalent.

If A is an identity matrix of order 3, then its inverse (A^-1)

Find the number of ways in which letters of word “HINDUSTAN” can be arranged such that none of the vowels can not be together?

In a certain population 10% of the people are rich, 5% are the famous and 3% are rich and famous. The probability that a person picked at a random from the population is either famous or rich but not both, is equal to:

The 7^th term of a G.P. is 8 times the 4^th term. Find the G.P. when its 5^th term is 64 .

A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is