List of top Mathematics Questions

Among the two statements
(S1) : (p ⇒ q)∧(q ∧(~q)) is a contradiction and  
(S2) : (p∧q) v ((~p)∧q) v (p ∧ (~q)) v ((~p) ∧ (~q)) is a tautology 
The number of five-digit numbers, greater than 40000 and divis ible by 5, which can be formed using the digits 0, 1, 3, 5, 7, and 9 without repetition, is equal to:

A parabola with focus (3, 0) and directrix x = –3. Points P and Q lie on the parabola and their ordinates are in the ratio 3 : 1. The point of intersection of tangents drawn at points P and Q lies on the parabola

If the probability that the random variable \( X \) takes values \( x \) is given by \( P(X = x) = k(x + 1) 3^{-x}, x = 0, 1, 2, \dots \), where \( k \) is a constant, then \( P(X \geq 2) \) is equal to:

Let \( R = \{a, b, c, d, e\} \) and \( S = \{1, 2, 3, 4\} \). Total number of onto functions \( f: R \to S \) such that \( f(a) \neq 1 \), is equal to:

Let a die be rolled \( n \) times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is \( \frac{k}{2^{15}} \), then \( k \) is equal to:
\(y=f(x)\) is a quadratic function passing through (–1, 0) and tangent to it at (1, 1) is \(y=x\). Find x intercept by normal at point (𝛂, 𝛂 + 1), (𝛂 > 0)

Let O be the origin and OP and OQ be the tangents to the circle \( x^2 + y^2 - 6x + 4y + 8 = 0 \) at the points P and Q on it. If the circumcircle of the triangle OPQ passes through the point \( \left( \alpha, \frac{1}{2} \right) \), then a value of \( \alpha \) is.

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
Let a and b are roots of \(x^2 – 7x – 1 = 0\). The value of \(\frac{(a_{21} + b_{21} + a_{17} + b_{17})}{(a_{19} + b_{19})}\) is?
The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0,2π] 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?
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?