List of top Mathematics Questions

In $\triangle ABC$, the midpoints of the sides $AB$, $BC$, and $CA$ are respectively $(1, 0, 0)$, $(0, m, 0)$, and $(0, 0, n)$. Then, $$ \frac{AB^2 + BC^2 + CA^2}{1^2 + m^2 + n^2} \text{ is equal to:} $$ 

Evaluate: \[ \tan (\cos^{-1} \frac{4}{5}) + \tan^{-1} \frac{2}{3} \]

The minimum value of the function \[ y = x^4 - 2x^2 + 1 \] in the interval \( \left[\frac{1}{2}, 2 \right] \) is:

If \[ \frac{a^n + b^n}{a^{n-1} + b^{n-1}} \] is the arithmetic mean (A.M.) between \( a \) and \( b \), then the value of \( n \) is:

Negation of the Boolean expression \[ p \Leftrightarrow (q \Rightarrow p) \] is:

If \[ R = \{ (x, y) : x \text{ is exactly } 7\text{cm taller than } y \} \] then \( R \) is:

The number of distinct real roots of the equation: \[ x^7 - 7x - 2 = 0 \] is:

Minimise $z = 3x + 8y$ subject to: \[ 3x + 4y \geq 8, 5x + 2y \geq 11, x \geq 0,\; y \geq 0. \]

Let f(z) = u + iv be an analytic function, where u = x³-3xy² +3x² -3y², then the imaginary part v of f(z) is

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A): If volumes of two spheres are in the ratio 125:64, then their surface areas will be in the ratio 25:16.
Reason (R): If volumes of two spheres are V1, V2 and their respective surface areas are S1, S2, then
\(\frac{S_1}{S_2} =(\frac{V_1}{V_2})^\frac{2}{3}\)
In the light of the above statements, choose the most appropriate answer from the options given below:

Given the following sets:
𝐴 = {2, 4, 6, 8, 10, 12}
𝐵 = {8, 10, 12, 14, 16, 18}
𝐶 = {7, 8, 9, 10 11, 12, 13}
(𝐴 ∩ 𝐵) ∪ (𝐵 ∩ 𝐶) is

The order of differential equation $\frac{𝑑^3𝑦}{dx^3} + 2 \frac{𝑑^2𝑦}{dx^2} − 3 \frac{𝑑𝑦}{dx} + 6𝑥^4𝑦$ = 0 is _______.

The value of $\lim_{𝑥→−3}\frac{(2𝑥+6)}{(𝑥+3)}$ is

Given data consists of distinct values of $𝑥_𝑖$ occurring with frequencies $𝑓_𝑖.$ The mean value for the data is _____. (rounded off to one decimal place)

$X_i$	5	6	8	10
$F_i$	8	10	10	12

Let {𝑎_𝑛 }_𝑛≥1 be a sequence such that 𝑎₁=1 and 4𝑎_𝑛+1=\(\sqrt{45 + 16𝑎_𝑛} ,𝑛\)=1, 2, 3, … . Then, which one of the following statements is TRUE?

Let the series 𝑆 and 𝑇 be defined by
\(∑^∞_{n-0}\frac{ 2 ⋅ 5 ⋅ 8 ⋯ (3𝑛 + 2) }{1 ⋅ 5 ⋅ 9 ⋯ (4𝑛 + 1)}\) and \(∑^∞ _{n=1}(1 + \frac{1 }{𝑛} ) ^{−𝑛^2}\)
respectively. Then, which one of the following statements is TRUE?

The volume of the region 𝑅={(𝑥, 𝑦, 𝑧) ∈ ℝ × ℝ × ℝ ∶ 𝑥 ² + 𝑦 ² ≤ 4, 0 ≤ 𝑧 ≤ 4 − 𝑦} is

For real constants 𝛼 and 𝛽, suppose that the system of linear equations
𝑥+2𝑦+3𝑧=6; x+ 𝑦 +𝛼𝑧 = 3; 2𝑦+𝑧=𝛽, 
has infinitely many solutions. Then, the value of 4𝛼 + 3𝛽 equals

Let M= \(\begin{pmatrix} 1 & -1 & 0\\ -a & 2 & -1 \\0&-1&1\end{pmatrix}\)If a non-zero vector 𝑋=(𝑥, 𝑦, 𝑧)^T∈ℝ³ satisfies 𝑀⁶𝑋=𝑋, then a subspace of ℝ3 that contains the vector 𝑋 is

Let 𝑀=𝑀₁𝑀₂, where 𝑀₁ and 𝑀₂ are two 3×3 distinct matrices. Consider the following two statements:
(I) The rows of 𝑀 are linear combinations of rows of 𝑀₂. 
(II) The columns of 𝑀 are linear combinations of columns of 𝑀₁. 
Then,