AILET entrance exam Question Bank Solutions

Which terms of the series `1/2,-1/2,1-2`, .... is -128:

`(("cos"  30  theta + "i" "sin" 30  theta)^5 ("cos"  20  theta + "i"  "sin" 20 theta)^4)/(("cos"  theta + "i"  "sin"  theta)^-4("cos"  theta  "i"   "sin"  theta)^6)` is equal to:

The vertex of the parabola x2 – y + 6x + – = 0 is:

`lim_(x->0) ("x"^2 - 3"x" + 2)/("2x"^2 + "x" - 3)` is equal to:

If (θ) = tan θ, then the value of `("f"(θ) - "f"(phi))/(1+"f"(θ) + "f"(phi))` is 

If f(x) = `"x-3"/"x+1"`, then f [f {f (x)}] is equal to:

`lim_(x->0) (sqrt(1+"x")- sqrt (1 - "x"))/"x"` is equal to:

`(1-2"i")/("2 + i") + "4 - i"/"3 + 2i"` is equal to:

The value of `(4 sqrt (sqrt3))/7 - sqrt (sqrt3)/7` is :

The modules of `"1 + i"/"1 + i"` is:

The imaginary part of `"1 - i"/"1 + i"` is:

If z = 5 + 3i then the value of |z - 2| will be:

If z₁ = 1 + 2i and z₂ = I – 1, then z₁/z₂ is equal to: 

The amplitude of `1 -sqrt "3i"`  is:

If a = I 2j and b = 2i + λλ the parallel vectors then λλ equal to:

If z = `((1 + "i")(2 + "i"))/(3 + "i")` then [z] is equal to:

The real part of cos h (αα - iββ) is

For Z₁, Z₂ ∈ C the valuer of |Z₁ + Z₂ |² + |Z₁ - Z₂ |² will be:

`lim_(x->0) |"x - b"|/"x - b"` is equal to:

Vertical angles that are opposite to each other are also