Mathematics questions
18011 published questions with worked solutions.
- Let _ ^ _e4 dx e^x - 1 = 6. Then eᵅ and e⁻ᵅ are the roots of the equation:
- Let A = 2, 3, 6, 8, 9, 11 and B = 1, 4, 5, 10, 15 . Let R be a relation on A × B define by (a, b) R (c, d) if and only if 3ad −...
- For a, b > 0, let f(x) = cases ((a + 1)x) + b x x , & x < 0 3, & x = 0 ax + b^2x^2 - ax b a ,x x , & x > 0 cases be a continuous...
- If the term independent of x in the expansion of ( a ,x^2 + 1 2x^3 )^ 10 is 105, then a² is equal to:
- Let A be the region enclosed by the parabola y² = 2x and the line x = 24. Then the maximum area of the rectangle inscribed in the...
- If α = _ x 0^+ ( e^ x - e^ x x - x ) and β = _ x 0 (1 + x)^ 12 x are the roots of the quadratic equation ax² + bx − √e = 0, then...
- Let S be the focus of the hyperbola x^2 3 - y^2 5 = 1, on the positive x-axis. Let C be the circle with its centre at A(√6, √5)...
- The number of distinct real roots of the equation |x + 1||x + 3| − 4|x + 2| + 5 = 0, is ________ .
- Let a ray of light passing through the point (3, 10) reflects on the line 2x + y = 6 and the reflected ray passes through the...
- Let a, b, c ∈ N and a < b < c. Let the mean, the mean deviation about the mean and the variance of the 5 observations 9, 25, a,...
- Let α|x| = |y|e^ xy − β , α, β ∈ N be the solution of the differential equation x dy − y dx + xy(x dy + y dx) = 0, y(1) = 2. Then...
- If 1 [5] (x - 1)^4(x + 3)^6 dx = A ( x - 1 x + 3 )^B + C, where C is the constant of integration, then the value of α + β + 20AB...
- Given the following two statements : (S₁) : (q ∨ p) → (p ↔ q) is a fallacy. Then :Not in JEE syllabus
- If (a+ 2 b x)(a- 2 b y)=a^2-b^2 where a > b > 0, then dx dy at ( 4 , 4 ) is :
- The integral ( x x x+ x )^2dx is equal to (where C is a constant of integration) :
- A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If ∠BAC = 90°, and ar(ΔABC) = 5 5 sq. units,...
- The value of _ r=0 ^ 20 ^ 50-r C_6 is equal to :
- Let P(3, 3) be a point on the hyperbola, x^2 a^2 - y^2 b^2 =1. if the normal to it at P intersects the x-axis at (9, 0) and e is...
- Let y = y(x) be the solution of the differential equation, xy'-y=x^2(x x+ x), x > 0. if y( ) = , then y'' ( 2 )+y ( 2 ) is equal...
- Let [t] denote the greatest integer ≤ t. Then the equation in x, [x]^2+2[x+2]-7=0 has :