Mathematics questions
18011 published questions with worked solutions.
- Let λ, μ ∈ ℝ. If the system of equations 3x + 5y + λz = 3, 7x + 11y − 9z = 2, 97x + 155y − 189z = μ has infinitely many...
- The coefficient of x⁷⁰ in x²(1 + x)⁹⁸ + x³(1 + x)⁹⁷ + x⁴(1 + x)⁹⁶ + .... + x⁵⁴(1 + x)⁴⁶ is ⁹⁹C_p − ⁴⁶C_q. Then a possible value...
- Let 2 - x 3 + x dx = 12( x + _e| x + x|) + C, where C is the constant of integration. Then + is equal to
- A variable line L passes through the point (3, 5) and intersects the positive coordinate axes at the points A and B. The minimum...
- Let |cos θ cos(60° − θ) cos(60° + θ)| ≤ 1/8, θ ∈ [0, 2π]. Then the sum of all θ ∈ [0, 2π], where cos 3θ attains its maximum...Not in JEE Main syllabus
- Let OA = 2 a, OB = 6 a + 5 b and OC = 3 b, where O is the origin. If the area of the parallelogram with adjacent sides OA and OC...
- If the domain of the function f(x) = ^ -1 ( x-1 2x+3 ) is ℝ − (α, β] then 12αβ is equal to
- If the sum of series 1 1 (1+d) + 1 (1+d)(1+2d) + + 1 (1+9d)(1+10d) is equal to 5, then 50d is equal to
- Let a circle passing through (2, 0) have its centre at the point (h, k). Let (x_c, y_c) be the point of intersection of the lines...
- The shortest distance between the line x-3 4 = y+7 -11 = z-1 5 and x-5 3 = y-9 -6 = z+2 1 is
- The frequency distribution of the age of students in a class of 40 students is given below. | Age | 15 | 16 | 17 | 18 | 19 | 20 |...
- The solution of the differential equation (x² + y²)dx − 5xy dy = 0, y(1) = 0 is :
- Let three vectors a⃗ = αî + 4ĵ + 2k̂, b⃗ = 5î + 3ĵ + 4k̂, c⃗ = xî + yĵ + zk̂ form a triangle such that c⃗ = a⃗ − b⃗ and the area...
- Let α, β be the roots of the equation x² + 2√2x − 1 = 0. The quadratic equation, whose roots are α⁴ + β⁴ and (1/10)(α⁶ + β⁶), is
- Let f(x) = x² + 9, g(x) = x/(x − 9) and a = fog(10), b = gof(3). If e and ℓ denote the eccentricity and the length of the latus...
- Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1, 2, 3, 4....
- The sum of the square of the modulus of the elements in the set z = a + ib; a, b ∈ ℤ, z ∈ ℂ, |z − 1| ≤ 1, |z − 5| ≤ |z − 5i| is...
- Let the set of all positive values of λ, for which the point of local minimum of the function (1 + x(λ² − x²)) satisfies x^2 + x...
- Let _ n ( n n^4+1 - 2n (n^2+1) n^4+1 + n n^4+16 - 8n (n^2+4) n^4+16 + + n n^4+n^4 - 2n n^2 (n^2+n^2) n^4+n^4 ) be π/k, using only...
- The remainder when 428²⁰²⁴ is divided by 21 is .........