NDA Mock Test - 6 - NDA MCQ

Sets A and B have n elements in common. How many elements will (A x B) and (B x A) have in common?

then what is |z| equal to

What is the modulus of 

If is the imaginary cube root of unity, then what is (2 – ω + 2ω²)²⁷ equal to

If x = (1101)₂ and y = (110)₂, then what is the value of x² – y²

If (10 x010)₂ – (11y1)₂ = (10z11)₂, then what are the possible values of the binary digits x, y, z respectively

If a, b, c are in GP, then  is equal to 

If x², y², z² are in AP, then y + z, z + x, x + y are in

If the sum of the first two terms and the sum of the first four terms of a geometric progression with positive common ratio are 8 and 80 respectively, then what is the 6th term?

If x > 1 and log₂ x, log₃ x, log_x 16 are in GP, then what is x equal to? 

The harmonic mean of two numbers is 21.6.  If one of the numbers is 27, then what is the other number?

If α and β are the roots of the equation x² – 2x + 4 = 0, then what is the value of α³ + β³?

If a, b and c are real numbers, then roots of the equation (x – a) (x – b) + (x – b) (x – c) + (x – c) (x – a) = 0 are always

If x = 2 + 2^1/3 + 2^2/3, then what is the value of x³ – 6x² + 6x?

Using the digits 1, 2, 3, 4 and 5 only once, how many numbers greater than 41000 can be formed? 

A, B, C, D and E are coplanar points and three of them lie in a straight line.  What is the maximum number of triangles that can be drawn with these points as their vertices?

What is the number of ways of arranging the letters of the word 'BANANA', so that no two N's appear together?

What is the middle term in the expansion of 

What is the number of terms in the expansion of (a + b + c)ⁿ, n ∈ N?

What is the coefficient of x4 in the expansion of ?

The value of is equal to

The value of (yz)^{log  y – log z} x (zx)^{log z – log x} x (xy)^{log x – log y} is equal to 

then x is equal to

Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15^o with the horizontal. What is the approximate distance between the poles? 

From the top of a lighthouse 120 m above the see, the angle of depression of a boat is 15^o. What is the (approx) distance of the boat from the lighthouse? 

then a, b, c are in 

then AT  is equal to