**Following are the important 100 Maths Questions for Class 5 to 12 that students should prepare for exams like JEE Main and Advanced – **

If sin A = sin 2 B and 2 cos 2 A = 3 cos 2 B then

If ω ≠ 1 is a cube root of unity, then 1 1 + i + ω 2 ω 2 1 − i − 1 ω 2 − 1 − i − i + ω − 1 − 1 equal

Three dice are rolled simultaneously. The probability that the numbers on them are different is

The value of Arg [ i ln ( a − i b a + i b ) ] ; where a and b are real numbers

The number of rectangles that can be found on a chess board is

For 0 ≤ r < 2 n , 2 n + r C n 2 n − r C n cannot exceed

Solution of the differential equation 1 + y + x 2 y d x + x + x 3 d y = 0 is

The value of ∫ sin α 1 + cos α d α is

The expression 1 4 x + 1 1 + 4 x + 1 2 7 − 1 − 4 x + 1 2 7 is a polynomial in x of degree.

The value of 3 log 4 5 − 5 log 4 3 is

The line x − 2 3 = y + 1 2 = z − 1 − 1 intersects the curve x y = c 2 , z = 0 if c=

L i m x π 2 cot x − cos x ( π 2 − x ) 3 =

If the term free from x is the expansion of x − k x 2 10 is 405 , then the value of k .

The number of 9 digit numbers which have all distinct digits, is

If 1 2 ≤ x ≤ 1 then cos − 1 x 2 + 1 2 3 − 3 x 2 + cos − 1 x =

The A.M of all the solutions of 4 cos 3 x − 4 cos 2 x − cos ( π + x ) + 1 = 0 i n ( 0 , 315 ) i s

Let a and b be two real numbers such that a > 1 , b > 1. I f A = a 0 0 b then lim n ∞ A − n is

x x n − 1 − na n − 1 + a n ( n − 1 ) is divisible by ( x − a ) 2 for

I n = ∫ tan n x d x then I n + I n + 2 is equal to

Evaluate ∫ x − sin x 1 − cos x d x

The mean value of the function f ( x ) = 2 e x + 1 on the interval [0, 2] is

If A and B are two matrices such that AB = B and BA = A, then A 2 + B 2 =

If f ( x ) = a − 1 0 ax a − 1 ax 2 ax a , then f ( 2 x ) − f ( x ) is divisible by

If both p and q are true, then

Sum of the series ∑ r = 1 n r ( r + 1 ) ! is

If A is non-singular and A 2 – 5 A + 7 I = 0 then I =

IF I = 2 π ∫ − π / 4 π / 4 d x 1 + e sin x 2 − cos 2 x then the value of 27 I 2 is

The negation of the following statement P: Neha lives in Ludhiana or she lives in Gurudaspur.

The length of foot of perpendicular drawn from the point P ( – 3 , – 4 , 5 ) on y – a x i s

The value of parameter, for which the function f ( x ) = 1 + α x , ≠ 0 is the inverse of itself is

If cot θ + tan θ = x and sec θ − cos θ = y , then

If α and β are the roots of the equation x 2 − x + 1 = 0 , then α 2009 + β 2009 =

If Z be a complex number satisfying z 4 + z 3 + 2 z 2 + z + 1 = 0 then | z | is equal to

Evaluate lim n ∞ { 1 2 tan x 2 + 1 2 2 tan x 2 2 + …. + 1 2 n tan x 2 n }

Lim x ∞ a 1 / x + b y x + c y x 3 x = where a ~ b,c are real and non-zero)

Let p and q be two statements, then ~ p q ∧ ( ~ q ) is equivalent to

Let Δ = 0 b − a c − a a − b 0 c − b a − c b − c 0 , then ∆ equals

The general solution of the differential equation y ( 1 − xy ) dx = x ( 1 + xy ) dy is

If θ ∈ π 2 , 3 π 2 , then sin – 1 ( sin θ ) equals

C o s e e − 1 C o s x is defined if