List of top Mathematics Questions

Let (a+bx+cx²)10 = $ \sum_{i=0}^{20} $ pixi, a,b,c∈N. If p1=20 and P₂ = 210, then 2(a+b+c) is equal to

Let \(λ ≠ 0\) be a real number. Let α, β be the roots of the equation \(14x^2 – 31x + 3λ = 0\) and α, γ be the roots of the equation \(35x^2 – 53x + 4λ = 0\). Then \(\frac{3\alpha}{\beta}\) and \(\frac{4\alpha}{\lambda}\) are the roots of the equation
Let the plane P : 4x – y + z = 10 be rotated by an angle \(\frac{π}{2}\) about its line of intersection with the plane x + y – z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α is
If a plane passes through the points $(-1, k, 0),(2, k,-1),(1,1,2)$ and is parallel to the line $\frac{x-1}{1}=\frac{2 y+1}{2}=\frac{z+1}{-1}$, then the value of $\frac{k^2+1}{(k-1)(k-2)}$ is
Let\( |\vec{a}|=2, |\vec{b}|=3\) and the angle between the vectors \(\vec{a}\) and \(\vec{b}\) be \(\frac{π}{4}\). Then \(|(\vec{a}+2\vec{b})×(2\vec{a}-3\vec{b})|^2\) is equal to
Let C be the circle in the complex plane with centre z0 =\(\frac{1}{2}\) (1+3i) and radius r = 1. Let z1 = 1+ i and the complex number z2 be outside the circle C such that |z1 – z0| |z2 – z0| = 1. If z0, z1 and z2 are collinear, then the smaller value of |z2|2 is equal to
Let \(f(x)=x+\frac{a}{\pi^2-4} sinx+\frac{b}{\pi^2-4} cos x\), \(x∈R\) be a function which satisfies \(f(x)=x+∫_0^{\frac{\pi}{2}} sin(x+y) f(y)dy\). Then (a+b) equal to
The statement (p∧ (-q)) v ((~ p) ∧ q) v ((~q)) is equivalent to
Let be a sequence such that a1 + a2 +....+ an=\(\frac{n^2+3n}{(n+1) (n+2)}\) If  \(28 ∑^{10}_{k=1} \frac{1}{a_k} =  P _1 P_ 2 P _3 . . . P_ m\) , where p1, p2, …..pm are the first m prime numbers, then m is equal to
The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is
Let \(\Delta\) be the area of the region \(\{(x,y)∈R^2:x^2+y^2≤21,y^2≤4x,x≥1\}\). Then \(\frac{1}{2}(\Delta-21\text{ sin}^{-1} (\frac{2}{\sqrt7}))\) is equal to
Let \(𝑦=𝑦(𝑥)\) be the solution of the differential equation \(𝑥\;𝑙𝑜𝑔_𝑒⁡𝑥\frac{𝑑𝑦}{ 𝑑𝑥} +𝑦=𝑥^2𝑙𝑜𝑔_𝑒⁡𝑥,(𝑥>1)\).  If \(𝑦(2)=2\), then \(𝑦(𝑒)\) is equal to 
Let s={\(z=x+ry:\frac{2z-3i}{4z+2i}\) is a real number}. Then which of the following is not correct?
If the coefficient of x7 in (\(ax^2 +\frac{ 1}{2bx}^{11}\)) and x-7 in (\(ax - \frac{1}{3bx^2}^{11}\)), are euual then
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 
If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three non-zero vectors and \(\hat{\mathbf{n}}\) is a unit vector perpendicular to \(\mathbf{c}\) such that: \(\mathbf{a} = \alpha \mathbf{b} - \hat{\mathbf{n}}, \, (\alpha \neq 0)\) and \( \mathbf{b} \cdot \mathbf{c} = 12 \), then \( \mathbf{c} \times (\mathbf{a} \times \mathbf{b}) \) is equal to:
All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is

\(\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)\)is equal to

The statement ~[p v (~(p ∧ q))] is equivalent to
Let x = x(y) be the solution of the differential equation 2(y+2) loge (y+2)dx+(x+4-2loge(y+2))dy = 0, y >-1 with x (e4-2)=1. Then x(e9-2) is equal to

The value of $\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x$ is equal to

Let $y=y(x)$ be the solution of the differential equation $\left(3 y^2-5 x^2\right) y d x+2 x\left(x^2-y^2\right) d y=0$ such that $y(1)=1$ Then $\left|(y(2))^3-12 y(2)\right|$ is equal to :

The set of all values of $a^2$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P \left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x^2+2 y^2-(1+a) x-(1-a) y=0$, is equal to :
If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are three non-zero vectors and \(\hat{n}\) is a unit vector perpendicular to \(\vec{c}\) such that \(\vec{a}\)=\(\alpha \vec{b}\)-\(\hat{n}\), \(\alpha \neq 0\) and \(\vec{b}\) .\( \vec{c}\)=12, then |\(\vec{c} \times(\vec{a} \times \vec{b})\)| is equal to:
The minimum value of the function $f(x)=\int\limits_0^2 e^{|x-t|} d t$ is :