Mathematics questions
18011 published questions with worked solutions.
- If the function f(x) = cases a| - x| + 1, & x 5 b|x - | + 3, & x > 5 cases is continuous at x = 5, then the value of a − b is:
- Let z ∈ C be such that |z| < 1. If = 5 + 3z 5(1 - z) , then:
- The domain of the definition of the function f(x) = 3 4 - x^2 + _ 10 (x^3 - x) is:
- Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of...
- If m is chosen in the quadratic equation (m^2 + 1)x^2 - 3x + (m^2 + 1)^2 = 0 such that the sum of its roots is greatest, then the...
- The value of the integral _0^1 x ^ -1 (1 - x^2 + x^4) ,dx is:
- Let P be the plane, which contains the line of intersection of the planes, x + y + z − 6 = 0 and 2x + 3y + z + 5 = 0 and it is...
- If some three coefficients in the binomial expansion of (x + 1)^n in powers of x are in the ratio 2 : 15 : 70, then the average...
- A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is ^ -1 ( 12 ). Water is poured into it...
- The value of sin 10° sin 30° sin 50° sin 70° is:
- If p (q r) is false, then the truth values of p, q, r are respectively:Not in JEE syllabus
- The vertices B and C of ΔABC lie on the line, x+2 3 = y-1 0 = z 4 such that BC = 5 units. Then the area (in sq. units) of this...
- If x dy dx - y x = 6x, (0 < x < 2 ) and y ( 3 ) = 0, then y ( 6 ) is equal to:
- If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its 11th term is:
- The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35...
- If the two lines x + (a − 1)y = 1 and 2x + a^2y = 1 (a ∈ R − 0, 1 ) are perpendicular, then the distance of their point of...
- The area (in sq. units) of the region A = (x, y) : y^2 2 x y + 4 is:
- The region represented by |x − y| ≤ 2 and |x + y| ≤ 2 is bounded by a:
- All the pairs (x, y) that satisfy the inequality 2^ ^2x - 2 x + 5 1 4^ ^2y 1 also satisfy the equation:Not in JEE Main syllabus
- If α and β are the roots of the quadratic equation, x^2 + x - 2 = 0, (0, 2 ), then ^ 12 + ^ 12 ( ^ -12 + ^ -12 ) ( - )^ 24 is...