List of top Mathematics Questions

Let r ∈ {p, q, ~p, ~q} be such that the logical statement r ∨ (~p) ⇒ (p ∧ q) ∨ r is a tautology. Then r is equal to :
Let \(p, q, r \)be three logical statements. Consider the compound statements
\(S_1 : ((~p) ∨q) ∨ ((~p) ∨r)\) and
\(S_2 :p→ (q∨r)\)
Then, which of the following is NOT true?
Let \(f :R→R\) be a continuous function such that \(f(3x) – f(x) = x\). If \(f(8) = 7\), then \(f(14\)) is equal to
Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let \(\frac \pi 8\) and \(θ\) be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then \(tan^2θ\) is equal to
Let ABC be a triangle such that \(\vec{BC}\)=\(\vec a\),\(\vec{CA} \)=\(\vec b\),\(\vec AB\)=\(\vec c\),|\(\vec a\)|=6\(\sqrt2\),|\(\vec b\)|=2\(\sqrt3\) and \(\vec b\)⋅\(\vec c\)=12 Consider the statements:
(S1):|(\(\vec a\)×\(\vec b\))+(\(\vec c\)×\(\vec d\))|−|\(\vec c\)|=6(2\(\sqrt2\)−1)
(S2):\(\angle\)ACB=cos−1⁡(\(\sqrt{\frac{2}{3}}\))
Then
The number of solutions of the equation \(cos \bigg(x+\frac{π}{3}\bigg)cos\bigg(\frac{π}{3-x}\bigg)=\frac{1}{4}cos^22x,x ∈ [-3π, 3π]\) is:
Let the points on the plane P be equidistant from the points (–4, 2, 1) and (2, –2, 3). Then the acute angle between the plane P and the plane 2x + y + 3z = 1 is
Let a be an integer such that  \(lim _{x→7} \frac{18−[1−x]}{[x−3a]}\) exists, where [t] is greatest integer \(≤ t\). Then \(a\) is equal to :
If the maximum value of the term independent of t in the expansion of (t2x\(^{\frac{1}{5}}\)+\(\frac{(1−x)^{\frac{1}{10}}}{t}\)),x≥0 is K, then 8 K is equal to__________.
If \(x=∑_{n=0}^∞a^n,y=∑_{n=0}^∞b^n,z=∑_{n=0}^∞c^n\), where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc≠ 0, then :
The line of the shortest distance between the lines \(\frac{x-2}{0}=\frac{y-1}{1}=\frac{z}{1}\) and \(\frac{x-3}{2}=\frac{y-5}{2}=\frac{z-1}{1}\) makes an angle of cos−1⁡\(\sqrt{\frac{2}{27}}\) with the plane P: ax – y – z = 0, (a> 0). If the image of the point (1, 1, –5) in the plane P is (α, β, γ), then α + β – γ is equal to ________.
If the shortest distance between the lines \(\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{λ}\; and\; \frac{x-2}{1 }= \frac{y-4}{4 }= \frac{z-5}{5 }\;is\; \frac{1}{\sqrt3}\), then the sum of all possible values of \(λ\) is :

Let the equation of two diameters of a circle x2 + y2 – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x2 – y2 = 3 passing through the centre of the circle is equal to _______.

Let a1 = b1 = 1, an = an – 1 + 2 and bn = aa + bn – 1 for every natural number n ≥ 2. Then\(\sum_{n=1}^{15}\) \(a_n⋅b_n\) is equal to ______.

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :

 If the numbers appeared on the two throws of a fair six faced die are α and β, then the probability that x2 + αx + β> 0, for all x ∈ R, is :

Consider the following two propositions:
\(P_1 : ~ (p → ~ q)\)
\(P_2: (p ∧ ~q) ∧ ((-~p) ∨ q)\)
If the proposition \(p → ((~p) ∨ q)\) is evaluated as FALSE, then:
Which of the following statements is a tautology?

Let the locus of the centre (α, β), β> 0, of the circle which touches the circle x2 +(y – 1)2 = 1 externally and also touches the x-axis be L. Then the area bounded by L and the line y = 4 is :

If \(\frac {1}{2⋅3^{10}}+\frac {1}{2^2⋅3^9}+⋯+\frac {1}{2^{10}⋅3} = \frac {K}{2^{10}⋅3^{10}}.\) Then the remainder when \(K\) is divided by \(6\) is:
The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 – 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :
The number of distinct real roots of \(x^4 – 4x + 1 = 0\) is :

The acute angle between the pair of tangents drawn to the ellipse 2x2 + 3y2 = 5 from the point (1, 3) is

In the given figure, ABCD is a rectangle. AB is 3m and BC is 2m. It is given that CF is 1m. AF intersects CD at E, and it is known that BE is parallel to HG and GE is perpendicular to AB. Find the length of HG (in m).
ABCD is a rectangle. AB is 3m and BC is 2m.
A work was completed by three persons of equal ability, first one doing \( m \) hours for \( m \) days, second one doing \( n \) hours for \( n \) days (where \( m \) and \( n \) are integers) and third one doing 16 hours for 16 days. The work could have been completed in 29 days by the third person alone with his respective working hours. If all of them do the work together with their respective working hours, then they can complete it in about: