JEE Main 2006 Mathematics — Questions with Solutions

∫₀^π x f( x) d x is equal to

∫₋₃ π / ₂⁻ⁱ / ² [(x+π)³+ ²(x+3 π) ] d x is equal to

The value of ∫₁^a[x] fⁱme(x) d x, a>1, where [x] denotes the greatest integer not exceeding x is

The value of the integral, ∫₃⁶ √(x)√(9-x)+√(x) d x is

The values of a, for which the points A, B, C with position vectors 2 i-j+k, i-3 j-5 k and a i-3 j+k respectively are t…

If (a × b) × c=a ×(b × c), where a, b and c are any three vectors such that a · b ≠ 0, b · c ≠ 0, then a and c are

A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the an…

A B C is a triangle, right angled at A. The resultant of the forces acting along A B, A C with magnitudes (1)/(A B) and…

The value of ₌₁¹⁰ ( (2 k π)/(11)+i (2 k π)/(11) ) is

If a₁, a₂, …, an are in H.P., then the expression a₁ a₂+a₂ a₃+…+an₋₁ an is equal to