AILET entrance exam Question Bank Solutions for Mathematics

Solve the following question and mark the best possible option.
Using the digits 1,2 find the number of natural numbers, which are smaller than 2 × 10⁸.

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Consider positive integers x and y such that the difference between x² + y and x + y² is a prime number. How many different values can the ordered pair (x, y) take?

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a, b, c and d are positive real numbers such that a + b + c + d = p, where ‘p’ is a constant. Find the maximum value of (p – a) (p – b) (p – c) (p – d)?

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Find 3x²y² if x and y are integers such that y² + 3x²y² = 30x² + 517.

If (1+ x)ⁿ = C₀ + C₁x + C₂x² + …..C_nxⁿ , then C₀C² + C₁C³ + C₂C⁴ + …..=C_n-2 C_n is equal to:

If (1 + x)ⁿ = c₀ + c₁x + C₂x² +……+ C_nxⁿ , then C₀ + `"C"_1/2 + "C"_1/3 + ……+ "C"_1/("n" + 1)` is equal to:

If ωω the cube root of unity then the value of `|(1, ωω, ωω^2),(ωω,ωω^2,1),(ωω^2,1,ω)|` will be:

The value of the determination `|("cos" alpha,"sin" alpha , 0),(-"sin" alpha , "cos" alpha , 0),(0,0,1)|` is :

If a + b = a – b , then the angle between a and b will be:

`pi pi^2 0 "sin x"/sqrt(1 + "sin 2x")`dx is equal to :

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

x e^x dx is equal to: 

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 =