List of top Mathematics Questions

The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + ... is
\(I(x) = \int \frac{x^2(xsec^2x + tanx)}{(xtanx+1)^2} dx\). If \(I(0)=1\) then \(I(\frac{\pi}{4})\) is equal to
Let the foot of perpendicular from the point A(4, 3, 1) on the plane P : x - y + 2z + 3 = 0 be N. If B(5,α,β) ∈ Z   is a point on plane P such that the area of the triangle ABN in 3√2 . then α2 + β2 + αβ is equal to ____ .
\(5\^{i}+5\hat{j}+2λ\hat{k},\hat{i}+2\hat{j}+3\hat{k},-2\hat{i}+λ\hat{j}+4\hat{k}\) and \(-\hat{i}+5\hat{j}+6\hat{k}.\) Let the set S = {λ∈ \(\mathbb{R}\) : The points A, B, C and D are coplanar}. Then \(\displaystyle\sum_{λ∈S}^{}(λ+2)^2\) is equal to

If the maximum distance of normal to the ellipse \(\frac{x^2}{4}+\frac{y^2}{b^2}=1, b<2\), from the origin is 1 , then the eccentricity of the ellipse is 

Find all the four letter words with two vowels and 2 consonants from the word UNIVERSE?
If area bounded by region \({x, y)| |x^{2}-2| ≤ y ≤ x}\) is A, then 6A + 16\(\sqrt{2}\) is?
For α, β, z ∈ C and λ > 1, if \(\sqrt{λ - 1}\) is the radius of the circle |z - α|2 + |z - β|2 = 2λ, then |α - β| is equal to _____.
Suppose a1, a2, 2, a3, a4 be in an arithmeticogeometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is \(\frac{49}{2}\) , then a4 is equal to ________ .
Let the tangent at any point P on a curve passing through the points (1, 1) and (\(\frac{1}{10}\),100), intersect positive x-axis and y-axis at the points A and B respectively. If PA : PB = 1 : k and y = y(x) is the solution of the differential equation  \(\frac{dy}{e^{dx}}Kx+\frac{K}{2}\) , y(0) = k, then 4y(1) – 5loge3 is equal to ______ .
In the figure, θ1 + θ2 = \(\frac{π}{2}\) and √3 (BE) = 4 (AB). If the area of ΔCAB is 2√3 - 3 unit2 , when \(\frac{θ_2}{θ_1}\) is the largest, then the perimeter (in unit) of ΔCED is equal to ________.
√3 (BE) = 4 (AB). If the area of ΔCAB is √2

Among the statements : 
\((S1)\) \((( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )\)
\((S2)\)\((( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))\)

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)

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to ______.

Three dice are rolled. If the probability of getting different numbers on the three dice is \(\frac{p}{q}\), where \(p\) and \(q\) are co-prime, then \(q - p\) is equal to:
Let the line \(\frac{x}{1}=\frac{6−y}{2}=\frac{z+8}{5}\)  intersect the lines  \(\frac{x-5}{1}=\frac{y-7}{3}=\frac{z+2}{1}\) and \(\frac{x+3}{6}=\frac{3−y}{3}=\frac{z-6}{1}\) at the points A and B respectively. Then the distance of the mid-point of the line segment AB from the plane 2x – 2y + z = 14 is 
Let s={\(z=x+ry:\frac{2z-3i}{4z+2i}\) is a real number}. Then which of the following is not correct?
Let \(\overrightarrow{a}=2\^i+7\^j−\^k ,\overrightarrow{b} =3\^i+5 \^k\) and \(\overrightarrow{c}=\^i=\^j+2\^k\) . Let \(\overrightarrow{d}\) be a vector which is perpendicular to both \(\overrightarrow{a}\) and \(\overrightarrow{b}\) , and \(\overrightarrow{c}.\overrightarrow{d}=12\). Then \((-\^i+\^j=\^k).(\overrightarrow{c}\times\overrightarrow{d})\) is equal to
Let the vectors \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) represent three coterminous edges of a parallelepiped of volume \(V\). Then the volume of the parallelepiped, whose coterminous edges are represented by \(\mathbf{a} + \mathbf{b} + \mathbf{c}\) and \(\mathbf{a} + 2\mathbf{b} + 3\mathbf{c}\), is equal to:
If the line x = y = z intersects the line
xsinA+ysinB+zsinC-18=0=xsin2A+ysin2B+zsin2C-9,
where A, B, C are the angles of a triangle ABC, then 80\(\left( sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2} \right)\) is equal to ________.
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:
Let the line L pass through the point (0, 1, 2), intersect the line  \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and be parallel to the plane 2x + y – 3z = 4. Then the distance of the point P(l, –9, 2) from the line L is 
A plane P contains the line of intersection of the plane  \(\overrightarrow{r} .( \^i+\^j+\^k )=6\) and \(\overrightarrow{r }.( 2\^i+3\^j+4\^k) = − 5\).  If P passes through the point (0, 2, –2), then the square of distance of the point (12, 12, 18) from the plane P is 
Let the plane P contain the line 2x+y-z-3=0=5x-3y+4z+9 and be parallel to the line \(\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}\). Then the distance of the point
A(8, -1, -19) from the plane P measured parallel to the line \(\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}\) 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: