Mathematics questions
18011 published questions with worked solutions.
- Let the image of the point P(1, 6, a) in the line L: x1= y-1 2= z-a+1 b, b>0, be ( a3, 0, a+c ). If S(α, β, γ), α>0, is the point...
- Let a line L be perpendicular to both the lines L_1: x+1 3= y+3 5= z+5 7 and L_2: x-2 1= y-4 4= z-6 7. If θ is the acute angle...
- The value of _ x 0 ( x^2 ^2x x^2- ^2x ) is:
- The value of the integral _ - /4 ^ /4 ( 32 ^4x 1+e^ x )dx is:
- The area of the region (x,y) : 0≤y≤6−x, y²≥4x−3, x≥0 is:
- Let A= bmatrix -1&1&-1 1&0&1 0&0&1 bmatrix satisfy A²+α(adj(adj(A)))+β(adj(A))(adj(adj(A))) = bmatrix 2&-2&2 -2&0&-1 0&0&-1...
- Let the centre of the circle x²+y²+2gx+2fy+25=0 be in the first quadrant and lie on the line 2x−y=4. Let the area of an...
- If a= i+ j+ k, b= j- k and c are three vectors such that a c= b and a c=3, then c ( a-2 b) is equal to _______.
- For the functions f(θ)=α tan²θ+β cot²θ and g(θ)=α sin²θ+β cos²θ, α>β>0, let _ 0< < /2 f( )= _ 0< < g( ). If the first term of a...
- Let y=y(x) be the solution of the differential equation (x^2-x x^2-1 )dy+(y(x- x^2-1 )-x)dx=0, x≥1. If y(1)=1, then the greatest...
- Consider the relation R on the set −2, −1, 0, 1, 2 defined by (a, b) ∈ R if and only if 1 + ab > 0. Then, among the statements:...
- The number of values of z ∈ ℂ, satisfying the equations |z − (4 + 8i)| = √10 and |z − (3 + 5i)| + |z − (5 + 11i)| = 4√5, is:
- If the system of linear equations: x + y + z = 6, x + 2y + 5z = 10, 2x + 3y + λz = μ has infinitely many solutions, then the...
- Let A= bmatrix &1&2 2&3&0 0&4&5 bmatrix and B= bmatrix 1&0&0 0&-5 &0 0&4 &-2 bmatrix + adj (A). If det(B) = 66, then det(adj(A))...
- Let α = 3 + 4 + 8 + 9 + 13 + 14 + … upto 40 terms. If ( )^ 1020 is a root of the equation x² + x − 2 = 0, β ∈ (0, π/2), then...
- A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation...
- A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the...
- If 26 ( 2^3 3 12 2+ 2^5 5 12 4+ 2^7 7 12 6+ + 2^ 13 13 12 12 )=3^ 13 - , then α is equal to:
- A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so...
- If a straight line drawn through the point of intersection of the lines 4x + 3y − 1 = 0 and 3x + 4y − 1 = 0, meets the...