Mathematics questions
18011 published questions with worked solutions.
- Given b + c 11 = c + a 12 = a + b 13 for a ΔABC with usual notation. If A = B = C , then the ordered triad (α, β, γ) has a value:Not in JEE syllabus
- A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the...
- If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the...
- The value of the integral _ -2 ^ 2 ^2x [ x ] + 12 dx (where [x] denotes the greatest integer less than or equal to x) is:
- In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x^2 - c^2 = y,...Not in JEE syllabus
- Let f(x) = cases -1, & -2 x < 0 x^2 - 1, & 0 x 2 cases and g(x) = |f(x)| + f(|x|). Then, in the interval (−2, 2), g is:
- The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is 27 19 . Then the common...
- The value of r for which ^ 20 C_r , ^ 20 C_0 + ^ 20 C_ r-1 , ^ 20 C_1 + ^ 20 C_ r-2 , ^ 20 C_2 + + ^ 20 C_0 , ^ 20 C_r is...
- Equation of a common tangent to the parabola y^2 = 4x and the hyperbola xy = 2 is:
- If the system of linear equations 2x + 2y + 3z = a, 3x − y + 5z = b, x − 3y + 2z = c where a, b, c are non zero real numbers, has...
- The sum of the real values of x for which the middle term in the binomial expansion of ( x^3 3 + 3x )^8 equals 5670 is:
- Let a = i + 2 j + 4 k, b = i + j + 4 k and c = 2 i + 4 j + ( ^2 - 1) k be coplanar vectors. Then the non-zero vector a c is:
- The plane containing the line x-3 2 = y+2 -1 = z-1 3 and also containing its projection on the plane 2x + 3y − z = 5, contains...
- The maximum value of the function f(x) = 3x^3 - 18x^2 + 27x - 40 on the set S = x R : x^2 + 30 11x is:
- The outcome of each of 30 items was observed; 10 items gave an outcome 12 - d each, 10 items gave outcome 12 each and the...
- The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of...
- If one real root of the quadratic equation 81x^2 + kx + 256 = 0 is cube of the other root, then a value of k is:
- A square is inscribed in the circle x^2 + y^2 - 6x + 8y - 103 = 0 with its sides parallel to the coordinate axes. Then the...
- If y(x) is the solution of the differential equation dy dx + ( 2x + 1 x )y = e^ -2x , x > 0, where y(1) = 12e^ -2 , then:
- Let [x] denote the greatest integer less than or equal to x. Then _ x 0 ( ^2x) + (|x| - (x[x]))^2 x^2