List of top Mathematics Questions

Let the system of equations \(x+2y+3z = 5\), \(2x+3y+z = 9\), \(4x+3y+λz = μ\) have an infinite number of solutions. Then \(λ + 2μ\) is equal to
The number of solution of the equation \(4sin^2 x-4cos^3 x+9-4cos x = 0\), \(x ∈ [-2\pi, 2\pi]\)
If \(n-1C_r= (k^2-8)^nC_r+1\) Find \(k\).
If \(f(x) = (x - 2)^2 (x - 3)^3\) and \(x ∈ [1, 4]\) and If \(M\) and \(m\) denotes maximum and minimum values respectively, then \(M - m\) is
A = {1, 2, 3, 4} , R = {(1, 2), (2, 3), (2, 4)} R ⊆ S and S is an equivalence relation then the minimum number of elements to be added to R is n, then the value of n is?
An equation of a plane parallel to the plane \(x-2y+2z-5=0\) and at a unit distance from the origin is?
Given data \(60, 60, 44, 58, 68, α, β, 56\) has mean \(58\), variance = \(66.2\), then find \(α^2 + β^2\).
The value of integral \(∫_0^{\frac \pi4} \frac {xdx}{cos^42x+sin^42x}\).
\(3, 7, 1,......., 404\) and \(4, 7, 10,......, 403\). Find sum of common terms.
Number of ways of arranging 5 officers in 4 rooms.
If : \(|z + 1| = αz + ß(i + 1)\) and \(z = \frac 12 - 2i\), find \(α + ß\).
Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$ Then $12 A$ is equal to _____
Let \(𝑎_1=𝑏_1=1\)and \(𝑎_𝑛=𝑎_{𝑛−1}+(𝑛−1)\), \(𝑏_𝑛=𝑏_{𝑛−1}+𝑎_{𝑛−1}\), \(∀𝑛≥2\). If \(𝑆= \displaystyle\sum_{ 𝑛=1}^{10}\frac {𝑏_𝑛}{2^𝑛}\) and \(𝑇= \displaystyle\sum_{𝑛=1}^{8} \frac {𝑛}{2^{𝑛−1}}\), then \(2^7(2𝑆−𝑇)\)  is equal to ____ .
Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____

7 boys and 5 girls are to be seated around a circular table such that no two girls sit together is?

Let B =\(\begin{bmatrix} 1 & 3 & α \\ 1 & 2& 3 \\ α & α & 4 \end{bmatrix}\) , α>2 be the adjoint of a matrix A and |A| = 2, then [α - 2α α] B\(\begin{bmatrix} α \\ -2α  \\ α \end{bmatrix}\)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 $\alpha>0$, be the smallest number such that the expansion of $\left(x^{\frac{2}{3}}+\frac{2}{x^3}\right)^{30}$ has a term $\beta x^{-a}, \beta \in N$.
Then \(α\) is equal to _________. 

If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r
Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is
The domain of the real valued function \(f(x)=\dfrac{√(x2−7x+6)}{√(​x2−4​+1)}\)  is
If f : R \(\rightarrow\) R be a continuous function satisfying \(\int^{\frac{\pi}{2}}_0f(sin2x)sinxdx+\alpha\int^{\frac{\pi}{4}}_0f(cos2x)cosxdx=0\), then the value of \(\alpha\) is
Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$ If $S =\left\{\alpha \in R : y ^2=1- x \right\}$, then $\displaystyle\sum_{\alpha \in S } 16 \alpha^3$ is equal to ______

Let $f: R -\{2,6\} \rightarrow R$ be real valued function defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}$ Then range of $f$ is

Let A and B be orthogonal and det A+det B=0. Then