Mathematics questions
18011 published questions with worked solutions.
- If the lines r = ( i - j + k ) + (3 j - k ) and r = ( i - j ) + (2 j - 3 k ) are co-planar, then the distance of the plane...
- Let a = i + j + 2 k , b = 2 i - 3 j + k and c = i - j + k be three given vectors. Let v be a vector in the plane of a and b whose...
- The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was...
- 16 sin(20°) sin(40°) sin(80°) is equal to :
- If the inverse trigonometric functions take principal values, then ^ -1 ( 3 10 ( ^ -1 43 ) + 25 ( ^ -1 43 ) ) is equal to :
- Let r p, q, ~p, ~q be such that the logical statement r (~p) (p q) r is a tautology. Then r is equal to :Not in JEE syllabus
- If z^ 2 + z + 1 = 0, z ℂ, then | _ n=1 ^ 15 (z^n + (-1)^n 1 z^n )^2 | is equal to _____.
- If ^ 40 C_ 0 + ^ 41 C_ 1 + ^ 42 C_ 2 + …. + ^ 60 C_ 20 = (m/n) ^ 60 C_ 20 , m and n are coprime, then m + n is equal to _____.
- If a_ 1 (> 0), a_ 2 , a_ 3 , a_ 4 , a_ 5 are in a G.P., a_ 2 + a_ 4 = 2a_ 3 + 1 and 3a_ 2 + a_ 3 = 2a_ 4 , then a_ 2 + a_ 4 + 2a_...
- The integral 24 _0^ 2 (2 - x^2)dx (2 + x^2) 4 + x^4 is equal to _____.
- Let a line L_ 1 be tangent to the hyperbola x^ 2 /16 - y^ 2 /4 = 1 and let L_ 2 be the line passing through the origin and...
- Let f(x) = x-1 x+1 , x ℝ − 0, −1, 1 . If f^ n+1 (x) = f(f^ n (x)) for all n ℕ, then f^ 6 (6) + f^ 7 (7) is equal to
- Let A = z C : | z+1 z-1 | < 1 and B = z C : ( z-1 z+1 ) = 2 3 . Then A B is :
- Let A be a 3 3 invertible matrix. If |adj(24A)| = |adj(3 adj(2A))|, then |A|^ 2 is equal to :
- The ordered pair (a, b), for which the system of linear equations 3x − 2y + z = b, 5x − 8y + 9z = 3, 2x + y + az = −1 has no...
- The remainder when (2021)^ 2023 is divided by 7 is :
- _ x 1 2 ( ^ -1 x) - x 1 - ( ^ -1 x) is equal to :
- f, g : ℝ ℝ be two real valued functions defined as f(x) = −|x + 3| for x < 0 and e^ x for x 0, and g(x) = x^ 2 + k_ 1 x for x < 0...
- The sum of the absolute minimum and the absolute maximum values of the function f(x) = |3x − x^ 2 + 2| − x in the interval [−1,...
- Let S be the set of all natural numbers, for which the line x/a + y/b = 2 is a tangent to the curve (x/a)^ n + (y/b)^ n = 2 at...