Mathematics questions
18011 published questions with worked solutions.
- The number of points, at which the function f(x) = 6x, 2+3x^2 + |x-1| | |x^2- 14 | |, x ∈ (−π, π), is not differentiable, is...
- For the function f : [1, ∞) → [1, ∞) defined by f(x) = (x−1)⁴ + 1, among the two statements: (I) The set S = x ∈ [1, ∞) : f(x) =...
- Let S = z ∈ ℂ : z² + 4z + 16 = 0 . Then _ z S |z+ 3 i|^2 is equal to:
- If the system of equations x+y+z=5, x+2y+3z=9, x+3y+λz=μ has infinitely many solutions, then the value of λ+μ is:
- If α = 1 and β = 1 + i√2, where i = √−1, are two roots of the equation x³+ax²+bx+c=0, a,b,c ∈ ℝ, then _ -1 ^ 1 (x^3+ax^2+bx+c)dx...
- If the quadratic equation (λ+2)x² − 3λx + 4λ = 0, λ ≠ −2, has two positive roots, then the number of possible integral values of...
- Let A = bmatrix 1&2&7 4&-2&8 3&8&-7 bmatrix and det(A−αI)=0, where α is a real number. If the largest possible value of α is p,...
- Let α = 1/4+1/8+1/16+… ∞ and β = 1/3+1/9+1/27+… ∞. Then the value of (0.2)^ _ 5 + (0.04)^ _5 is equal to:
- For 10 observations x₁,…,x₁₀, if _ i=1 ^ 10 (x_i+2)^2=180 and _ i=1 ^ 10 (x_i-1)^2=90, then their standard deviation is:
- In the expansion of (9x - 1 3 x )^ 18 , x > 0, if the term independent of x is (221)k, then k is equal to:
- Let P(3cosα, 2sinα), α≠0, be a point on the ellipse x²/9+y²/4=1, Q be a point on the circle x²+y²−14x−14y+82=0 and R be a point...
- Let H : x²/a² − y²/b² = 1 be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is...
- _ 0 x (16 ( x2 ) ^3 ( x2 ) ) is equal to:
- The shortest distance between the lines r= ( 13 i+2 j+ 83 k )+ (2 i-5 j+6 k) and r= (- 23 i- 13 k )+ ( j- k), λ,μ∈ℝ, is:
- If (2 +1, ^2-3 , -1 2 ) is the image of (α, 2α, 1) in the line x-2 3= y-1 2= z1, then the possible value(s) of α is (are)
- Let û and v̂ be unit vectors inclined at an acute angle such that | u v|= 3 2. If A= u+ v+( u v), then λ is equal to:
- Let A = (a,b,c) : a,b,c are non-negative integers and a+b+2c=22 . Then n(A) is equal to:
- The area of the region bounded by the curves x+3y²=0 and x+4y²=1 is equal to:
- Let y=y(x) be the solution of the differential equation dy dx + ( 6x^2+(3x^2+2x^3+4)e^ -2x (x^3+2)(2+e^ -2x ) )y = 2+e^ -2x ,...
- From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P....