Practice questions
88551 published questions with worked solutions.
- A data consists of n observations: x_1, x_2, , x_n. If _ i=1 ^n(x_i + 1)^2 = 9n and _ i=1 ^n(x_i - 1)^2 = 5n, then the standard...
- If 0 x < 2, then the number of values of x for which sin x − sin 2x + sin 3x = 0, is:Not in JEE Main syllabus
- If the lines x = ay + b, z = cy + d and x = a′z + b′, y = c′z + d′ are perpendicular then:
- The equation of the plane containing the straight line x2 = y3 = z4 and perpendicular to the plane containing the straight lines...
- Let f be a differentiable function from R to R such that |f(x) - f(y)| 2|x - y|^ 3/2 , for all x, y ∈ R. If f(0) = 1 then _0^1...
- Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on...
- The area of the region A = (x, y) : 0 y x|x| + 1 and -1 x 1 in sq. units, is:
- If the circles x^2 + y^2 - 16x - 20y + 164 = r^2 and (x - 4)^2 + (y - 7)^2 = 36 intersect at two distinct points, then:
- An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is...
- If A = bmatrix e^t & e^ -t t & e^ -t t e^t & -e^ -t t - e^ -t t & -e^ -t t + e^ -t t e^t & 2e^ -t t & -2e^ -t t bmatrix then A is:
- The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits...
- If _0^ /3 2k d = 1 - 1 2 , (k > 0), then the value of k is:
- The number of all possible positive integral values of α for which the roots of the quadratic equation, 6x^2 - 11x + = 0 are...
- If the system of linear equations x − 4y + 7z = g, 3y − 5z = h, −2x + 5y − 9z = k is consistent, then:
- If both the roots of the quadratic equation x^2 - mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m...
- If x = ^ -1 ( 10) and y = ^ -1 ( 10), then y − x is equal to:
- Let A = x ∈ R : x is not a positive integer . Define a function f: A → R as f(x) = 2x x - 1 , then f is:
- For each x ∈ R, let [x] be the greatest integer less than or equal to x. Then _ x 0^- x([x] + |x|) [x] |x| is equal to:
- Let A(4, −4) and B(9, 6) be points on the parabola, y^2 = 4x. Let C be chosen on the arc AOB of the parabola, where O is the...
- A mixture of 2 moles of helium gas (atomic mass = 4u), and 1 mole of argon gas (atomic mass = 40u) is kept at 300 K in a...