Mathematics questions
18011 published questions with worked solutions.
- If the shortest distance between the lines r = (- i + 3 k ) + ( i - a j ) and r = (- j + 2 k ) + ( i - j + k ) is 2/3 , then the...
- Let x * y = x^ 2 + y^ 3 and (x * 1) * 1 = x * (1 * 1). Then a value of 2 ^ -1 ( x^4 + x^2 - 2 x^4 + x^2 + 2 ) is
- The sum of all the real roots of the equation (e^ 2x - 4)(6e^ 2x - 5e^ x + 1) = 0 is
- Let the system of linear equations x + y + z = 2, 3x + y + z = 4, x + 2z = 1 have a unique solution (x*, y*, z*). If ( , x*),...
- Let x, y > 0. If x^ 3 y^ 2 = 2^ 15 , then the least value of 3x + 2y is
- Let f(x) = cases (x - [x]) x - [x] , & x (-2, -1) 2x, 3[|x|] , & |x| < 1 1, & otherwise cases where [t] denotes greatest integer...
- The value of the integral _ - /2 ^ /2 dx (1 + e^x)( ^6x + ^6x) is equal to
- _ n ( n^2 (n^2+1)(n+1) + n^2 (n^2+4)(n+2) + n^2 (n^2+9)(n+3) + + n^2 (n^2+n^2)(n+n) ) is equal to
- A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P...
- Let the maximum area of the triangle that can be inscribed in the ellipse x^ 2 /a^ 2 + y^ 2 /4 = 1, a > 2, having one of its...
- Let the area of the triangle with vertices A(1, ), B( , 0) and C(0, ) be 4 sq. units. If the points ( , - ), (- , ) and ( ^ 2 , )...
- The number of distinct real roots of the equation x^ 7 - 7x - 2 = 0 is
- A random variable X has the following probability distribution: | x | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | k |...
- The number of solutions of the equation (x + 3 ) ( 3 - x ) = 14 ^22x, x [-3 , 3 ] isNot in JEE Main syllabus
- If the shortest distance between the lines (x − 1)/2 = (y − 2)/3 = (z - 3)/ and (x − 2)/1 = (y − 4)/4 = (z − 5)/5 is 1/ 3 , then...
- Let the points on the plane P be equidistant from the points (−4, 2, 1) and (2, −2, 3). Then the acute angle between the plane P...
- Let a and b be two unit vectors such that |( a + b ) + 2( a b )| = 2. If (0, ) is the angle between a and b , then among the...
- If y = ^ -1 ( x^3 - x^3 ), 2 < x^3 < 3 2, then
- The slope of normal at any point (x, y), x > 0, y > 0 on the curve y = y(x) is given by x^ 2 /(xy - x^ 2 y^ 2 - 1). If the curve...
- Let * be the largest value of for which the function f _ (x) = 4 x^ 3 - 36 x^ 2 + 36x + 48 is increasing for all x ℝ. Then f _ *...