Mathematics questions
18011 published questions with worked solutions.
- The area of the region R = (x,y) : xy≤27, 1≤y≤x² is equal to:
- The product of all possible values of α, for which _ x 0 ( 1- ( x) (( +1)x) (( +2)x) ^2(( +1)x) )=2, is:
- Let f : ℝ → ℝ be a differentiable function such that f ( x+y 3 )= f(x)+f(y) 3 for all x,y∈ℝ, and f′(0)=3. Then the minimum value...
- The value of the integral _ /6 ^ /3 ( 4- ^2x ^4x )dx is:
- Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no...
- If the sum of the coefficients of x⁷ and x¹⁴ in the expansion of ( 1 x^3 -x^4 )^n, x≠0, is zero, then the value of n is _______.
- If 4+ _ p=1 ^ 11 ^ -1 ( 2^ p-1 1+2^ 2p-1 )= , then tanα is equal to _______.
- Let y=y(x) be the solution of the differential equation x ( yx )dy= (y ( yx )-x )dx, y(1)=π/2 and let = ( y(e^ 12 ) e^ 12 ). Then...
- Let f : ℝ → ℝ be defined as f(x)= 2x^2-3x+2 3x^2+x+3 . Then f is:
- Consider the quadratic equation (n²−2n+2)x²−3x+(n²−2n+2)²=0, n∈ℝ. Let α be the minimum value of the product of its roots and β be...
- Let S= z∈ℂ : z²+√6 iz−3=0 . Then _ z S z^8 is equal to:
- The sum of all possible values of θ∈[0,2π], for which the system of equations: x cos3θ−8y−12z=0, x cos2θ+3y+3z=0, x+y+3z=0 has a...
- The sum 1+ 12(1^2+2^2)+ 13(1^2+2^2+3^2)+ upto 10 terms is equal to:
- A building has ground floor and 10 more floors. Nine persons enter a lift at the ground floor. The lift goes up to the 10th...
- Let C be a circle having centre in the first quadrant and touching the x-axis at a distance of 3 units from the origin. If the...
- The eccentricity of an ellipse E with centre at the origin O is √3/2 and its directrices are x=±4√6/3. Let H : x²/a²−y²/b²=1 be a...
- Let x=9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is 1/3. Let P(α,0), α>0, be a focus of E...
- If ( ^ -1 (x 2))= ( ^ -1 1-x^2 ), x∈(0,1), then the value of x is:
- The shortest distance between the lines x-4 1= y-3 2= z-2 -3 and x+2 2= y-6 4= z-5 -5 is:
- Let a=2 i+3 j+3 k and b=6 i+3 j+3 k. Then the square of the area of the triangle with adjacent sides determined by the vectors (2...