List of top Mathematics Questions

Let a circle of radius 4 be concentric to the ellipse \( 15x^2 + 19y^2 = 285 \). Then the common tangents are inclined to the minor axis of the ellipse at the angle:
Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways in which they can be transported is:

The coefficient of x7 in (1 – 2x + x3)10 is?

Find the number of integral values of x which satisfy the inequality x2–10x+19<6. 
 
From a square of side 30 cm the squares of side x cm is cut off to make a cuboid of maximum volume. The surface area of cuboid with open top is?

The negation of \( (p \land (\sim q)) \lor (\sim p) \) is equivalent to:

3, 8, 13, ......,373 are in arithmetic series. The sum of numbers not divisible by three is

Mean of first 15 numbers is 12 and variance is 14. Mean of next 15 numbers is 14 and variance is a. If variance of all 30 numbers is 13, then a is equal to

If (21)18 + 20·(21)17 + (20)2 · (21)16 + ……….. (20)18 = k (2119 – 2019) then k =

A has 5 elements and B has 2 elements. The number of subsets of A × B such that the number of elements in subset is more than or equal to 3 and less than 6, is?

A rectangle is drawn by lines x=0, x=2, y=0 and y=5. Points A and B lie on coordinate axes. If line AB divides the area of rectangle in 4:1, then the locus of mid-point of AB is?
Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?
The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0, 2π] is
The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0,2π] is
Let a and b are roots of x2 – 7x – 1 = 0. The value of \(\frac{a^{21} + b^{21} + a^{17} + b^{17}}{a^{19} + b^{19}}\) is?
Given A, B, C represents angles of a  ⃤ AB and cosA + 2 cosB + cosC = 2 and AB = 3 and BC = 7 then cosA – cosC is?

The mean of coefficients of x, x2, ....., x7 in the binomial expansion of (2 + x)9 is?

The number of rational terms in the expansion of (33/4 + 53/2)60?

Maximum value n such that (66)! is divisible by 3n

Three dice are thrown. Then the probability that no outcomes is similar is p/q then q – p is (where p and q are co-prime)

Matrix A is 2×2 matrix and A2=I, no elements of the matrix are zero, let the sum of diagonal elements is a and det(A)=b, then the value of 3a2+b2 is?

The number of points of non-differentiability of the function f(x) = [4 + 13sinx] in (0, 2𝜋) is ____.

Let \((\alpha, \beta, \gamma)\) \(\text{ be the image of the point }\) \(P(3, 3, 5) \text{ in the plane } 2x + y - 3z = 6\). \(\text{ Then } \alpha + \beta + \gamma \text{ is equal to:}\)

Consider two sets A and B. Set A has 5 elements whose mean & variance are 5 and 8 respectively. Set B has also 5 elements whose mean & variance are 12 & 20 respectively. A new set C is formed by subtracting 3 from each element of set A and by adding 2 to each element of set B. The sum of mean & variance of the set C is

The mean of coefficients of \(x, x^2, ....., x^7\) in the binomial expansion of \((2 + x)^9\) is?