Mathematics questions
18011 published questions with worked solutions.
- Let f : ℝ → ℝ be a function defined by f(x) = 4ˣ/(4ˣ + 2) and M = _ f(a) ^ f(1-a) x ^4(x(1-x))dx, N = _ f(a) ^ f(1-a)...
- Let a⃗ and b⃗ be two vectors such that |a⃗| = 1, |b⃗| = 4, and a⃗·b⃗ = 2. If c⃗ = (2a⃗ × b⃗) − 3b⃗ and the angle between b⃗ and...
- Let f : R R be a continuous function. Then _ x 4 _ /4 ^ ^2x f(x)dx x^2- ^2 16 is equal to :
- ^ -1 ( (-5))+ ^ -1 ( (6))- ^ -1 ( (12)) is equal to : (The inverse trigonometric functions take principal values)
- Consider the system of linear equations –x + y + 2z = 0, 3x – ay + 5z =1, 2x – 2y – az = 7. Let S_1 be the set of all a R for...
- Let the acute angle bisector of the two planes x – 2y – 2z + 1 = 0 and 2x – 3y – 6z + 1 = 0 be the plane P. Then which of the...
- Which of the following is equivalent to the Boolean expression p ?Not in JEE syllabus
- If y = y (x) is the solution curve of the differential equation x^2dy+ (y- 1 x )dx=0, x > 0 and y(1) = 1, then y ( 1 2 ) is equal...
- If n is the number of solutions of the equation 2 x (4 ( 4 +x ) ( 4 -x )-1 )=1, x [0, ] and S is the sum of all these solutions,...Not in JEE Main syllabus
- The function f(x)=x^3-6x^2+ax+b is such that f(2) = f(4) = 0. Consider two statements. (S_1) there exists x_1, x_2 (2,4),...
- Let J_ n,m = _0^1 x^n x^m-1 dx, n>m and n,m . Consider a matrix A=[a_ ij ]_ 3 3 where a_ ij = cases J_ 6+i,3 -J_ i+3,3 , & i j 0,...
- The area, enclosed by the curves y = x+ x and y = | x- x| and the lines x = 0, x = 2 , is :
- Consider the parabola with vertex ( 1 2 , 3 4 ) and the directrix y = 1 2 . Let P be the point where the parabola meets the line...
- The numbers of pairs (a, b) of real numbers, such that whenever is a root of the equation x^2+ax+b=0, ^2-2 is also a root of this...
- Let S_n=1 (n-1)+2 (n-2)+3 (n-3)+ +(n-1) 1, n 4. The sum _ n=4 ^ ( 2S_n n! - 1 (n-2)! ) is equal to :
- Let P_1, P_2, ….., P_ 15 be 15 points on a circle. The number of distinct triangles formed by points P_i, P_j, P_k such that i +...
- The range of the function, f(x)= _ 5 (3+ ( 3 4 +x )+ ( 4 +x )+ ( 4 -x )- ( 3 4 -x ) ) is :
- Let a_1, a_2,......,a_ 21 be an AP such that _ n=1 ^ 20 1 a_na_ n+1 = 4 9 . If the sum of this AP is 189, then a_6a_ 16 is equal...
- Let be the acute angle between the tangents to the ellipse x^2 9 + y^2 1 =1 and the circle x^2+y^2=3 at their point of...
- Let X be a random variable with distribution. x: –2, –1, 3, 4, 6 P(X=x): 1/5, a, 1/3, 1/5, b If the mean of X is 2.3 and variance...