Practice questions
88551 published questions with worked solutions.
- If ^ 20 C_1 + (2^2) , ^ 20 C_2 + (3^2) , ^ 20 C_3 + + (20^2) , ^ 20 C_ 20 = A(2^ ), then the ordered pair (A, β) is equal to:
- The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines r = ( i + j) + ( i + 2 j - k)...
- A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point:
- Let α ∈ R and the three vectors a = i + j + 3 k, b = 2 i + j - k and c = i - 2 j + 3 k. Then the set S = α : a, b and c are...
- The tangents to the curve y = (x - 2)^2 - 1 at its points of intersection with the line x − y = 3, intersect at the point:
- If [x] denotes the greatest integer ≤ x, then the system of linear equations [sin θ]x + [−cos θ]y = 0, [cot θ]x + y = 0
- A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be...
- An ellipse, with foci at (0, 2) and (0, −2) and minor axis of length 4, passes through which of the following points?
- For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the...
- A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular...
- A value of α such that _ ^ +1 dx (x + )(x + + 1) = _e ( 98 ) is:
- _ x 0 x + 2 x x^2 + 2 x + 1 - ^2x - x + 1 is:
- The derivative of ^ -1 ( x - x x + x ), with respect to x2, where x (0, 2 ) is:
- Let S be the set of all α ∈ R such that the equation, cos 2x + α sin x = 2α − 7 has a solution. Then S is equal to:Not in JEE Main syllabus
- Let z ∈ C with Im(z) = 10 and it satisfies 2z - n 2z + n = 2i - 1 for some natural number n. Then:
- Let f(x) = 5 − |x − 2| and g(x) = |x + 1|, x ∈ R. If f(x) attains maximum value at α and g(x) attains minimum value at β, then _...
- The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be 45º from a point A on the...Not in JEE syllabus
- A value of (0, 3 ), for which vmatrix 1 + ^2 & ^2 & 4 6 ^2 & 1 + ^2 & 4 6 ^2 & ^2 & 1 + 4 6 vmatrix = 0, is:Not in JEE Main syllabus
- If a_1, a_2, a_3, are in A.P. such that a_1 + a_7 + a_ 16 = 40, then the sum of the first 15 terms of this A.P. is:
- The term independent of x in the expansion of ( 1 60 - x^8 81 ) (2x^2 - 3 x^2 )^6 is equal to: