AILET entrance exam Question Bank Solutions

The max. value of sin x + cos x:

x² sin³ dx is equal to: 

If x `sqrt(1 + "y") + "y" sqrt (1 + "x") = 0  "then"  "dy"/"dx"` is equal to: 

If y = `"sin"^-1 (- 1/(1 + "x"^2)) , "then" "dy"/"dx"` is equal to:

The value of 1 + `1/4 + 1.3/4.8 + (1.3.5)/(4.8.12) + ........` is :

If `|(1,2,4),(3,6+x,7),(5,10,4+x)| = 0`, then the value of x will be:

If (1 + x)ⁿ = C₀ + C₂x + C₂Xⁿ then `"C"_1/"C"_0 + "2C"_2/"C"_1 + "3C"_3/"C"_2+ .......+ "nC"_"n"/"C"_"n-1"` is equal to:

If A = `(("d"_1,0,0),(0,"d"_1,0),(0,0,"d"_3))` then adj A =

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: