AILET entrance exam Question Bank Solutions for Mathematics

In the expansion of `(2^4 - 1/"x"^7)` the term independent of x is:

If A = `[(2,4),(0,3)]` and B = `[(1,2),(0,5)]` , then 4A - 3B is equal to:

Cos³x dx is equal to: 

If A = `(("cos x","sin x"),(-"sin x","cos x"))` then A^-1 is equal to:

If the sum of two unit vector is also a unit vector then the magnitude of their difference will be:

The differential coefficient of sin^-1 x w.r.t. cos^-1 `sqrt (1-"x"^2)` is :

If x = a (t + sin t) and y = a (1 – cos t) then `"dy"/"dx"` is equal to:

The differential coefficient of sin^-1 `((1-"x"^2)/(1+"x"^2))` w.r.t. x is:

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

d (sec^-1x) is equal to: 

The differential coefficient of tan^-1 `sqrt((1-"x"^2)/(1 + "x"^2))` w.r.t. is:

If the lines x + y = 1, 2x – y = 0 and x + 2y +λλ is equal to:

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: