Mathematics questions
18011 published questions with worked solutions.
- The area (in sq. units) of the region, given by the set (x,y) R R|x 0,2x^2 y 4-2x is :
- The sum of all values of x in [0, 2 ], for which x+ 2x+ 3x+ 4x=0, is equal to :Not in JEE Main syllabus
- Let f:[0, ) [0, ) be defined as f(x)= _0^x[y]dy where [x] is the greatest integer less than or equal to x. Which of the following...
- The values of a and b, for which the system of equations 2x + 3y + 6z = 8, x + 2y + az = 5, 3x + 5y + 9z = b has no solution, are...
- Let a parabola P be such that its vertex and focus lie on the positive x–axis at a distance 2 and 4 units from the origin,...
- Let an ellipse E: x^2 a^2 + y^2 b^2 =1, a^2>b^2, passes through ( 3 2 ,1 ) and has eccentricity 1 3 . If a circle, centered at...
- Let the foot of perpendicular from a point P(1, 2, –1) to the straight line L : x 1 = y 0 = z -1 be N. Let a line be drawn from P...
- Let y = y(x) be solution of the following differential equation e^y dy dx -2e^y x+ x ^2x=0, y ( 2 )=0 If y(0) = _e( + e^ -2 ),...
- Consider the following frequency distribution class: 10–20, 20–30, 30–40, 40–50, 50–60; Frequency: , 110, 54, 30, If the sum of...
- Let p =2 i +3 j + k and q = i +2 j + k be two vectors. If a vector r =( i + j + k ) is perpendicular to each of the vectors ( p +...
- The ratio of the coefficient of the middle term in the expansion of (1+x)^ 20 and the sum of the coefficients of two middle terms...
- Let M = A= pmatrix a&b &d pmatrix :a,b,c,d 3, 2, 1,0 Define f:M Z, as f(A) = det(A), for all A , where Z is set of all integers....
- There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students...
- Let S= n N: pmatrix 0&i 1&0 pmatrix ^n pmatrix a&b &d pmatrix ^n= pmatrix a&b &d pmatrix a,b,c,d R , where i= -1 . Then the...
- Let [t] denote the greatest integer less than or equal to t. Let f(x) = x – [x], g(x) = 1 – x + [x], and h(x) = min f(x), g(x) ,...
- Let A= pmatrix 1&0&0 0&1&1 1&0&0 pmatrix . Then A^ 2025 -A^ 2020 is equal to:
- The local maximum value of the function f(x)= ( 2 x )^ x^2 , x > 0, is
- If the value of the integral _0^5 x+[x] e^ x-[x] dx= e^ -1 + . where , R, 5 +6 =0, and [x] denotes the greatest integer less than...
- The point P(-2 6, 3) lies on the hyperbola x^2 a^2 - y^2 b^2 =1 having eccentricity 5 2 . If the tangent and normal at P...
- Let y(x) be the solution of the differential equation 2x^2dy+(e^y-2x)dx=0, x > 0. If y(e) = 1, then y(1) is equal to: