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List of top Mathematics Questions

The number of elements in the set $ \left\{ x \in \mathbb{N} : \binom{20 - 2x}{x - 3} \in \mathbb{N} \right\} $ is

Let $ \overline{OA} = 2\overline{i} - 3\overline{j} + \overline{k} $, $ \overline{OB} = \overline{i} - 4\overline{j} - 3\overline{k} $, and $ \overline{OC} = -3\overline{i} + \overline{j} + 2\overline{k} $ be the position vectors of three points A, B, C respectively. If G is the centroid of triangle ABC, then find: \[ BC^2 + CA^2 + AB^2 + 9(OG)^2 \]

If $ f(x) = \begin{cases} x \left( 1 + \frac{1}{2} \sin(\log x^2) \right), & x \neq 0 \\ 0, & x = 0 \end{cases} $, then $ \lim_{x \to 0} \frac{f(x) - f(0)}{x} $

If $ f(x) $ is a differentiable function, $ f'(x) \geq 5 $ for $ x \in [2,6] $, $ f(2) = 4 $ and $ f(3) = 15 $, then a possible value of $ f(6) $ is:

There are 10 points in a plane, of which no three points are colinear expect 4. Then the number of distinct triangles that can be formed by joining any three points of these ten points, such that at least one of the vertices of every triangle formed is from the given 4 colinear points is

If n is a positive integer and f(n) is the coeffcient of xⁿ in the expansion of (1 + x)(1-x)ⁿ, then f(2023) =

lim n→∞ $\frac{1}{n^3}$ $\sum_{k=1}^{n} k^{2} =$

If the solution of the differential equation $\frac{dy}{dx}=\frac{2x+3y}{3x-2y}$ is y = xtan(f(x)) + c then f(x) =

If a line ax + 2y = k forms a triangle of area 3 sq.units with the coordinate axis and is perpendicular to the line 2x - 3y + 7 = 0, then the product of all the possible values of k is

In △ABC, if a : b : c = 4 : 5 : 6, then the ratio of the circumference to its in radius is

If cosθ = $\frac{-3}{5}$- and π < θ < $\frac{3π}{2}$, then tan $\frac{ θ}{2}$ + sin $\frac{ θ}{2}$+ 2cos $\frac{ θ}{2}$ =

If x+√3y = 3 is the tangent to the ellipse 2x² + 3y² = k at a point P then the equation of the normal to this ellipse at P is

If (2,-1,3) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is

If f(x) = e^x, h(x) = (fof) (x), then $\frac{h'(x)}{h'(x)}$ =

Let y = t² - 4t -10 and ax + by + c = 0 be the equation of the normal L. If G.C.D of (a,b,c) is 1, then m(a+b+c) =

If A(1,2,3) B(3,7,-2) and D(-1,0,-1) are points in a plane, then the vector equation of the line passing through the centroids of △ABD and △ACD is

\[\int_{-1}^{1} x|x| \,dx\]

The variance of 50 observations is 7. Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is

Let α,β be the roots of the quadratic equation x²+√6x+3=0. Then $\frac{α^23+β^23 + α ^14 + β ^14 }{α ^15 + β ^15 + α 160 + β ^{10}}$ is equal to

The integral $\int \left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x \log x \, dx$ is equal to:

If the sum of the series $\left(\frac{1}{2}-\frac{1}{3}\right) + \left(\frac{1}{2^2}-\frac{1}{2·3} + \frac{1}{3^2}\right) + \left(\frac{1}{2^2}-\frac{1}{2^2·3} + \frac{1}{2·3^2} - \frac{1}{3^3}\right) + \left(\frac{1}{2^4}-\frac{1}{2^3·3} + \frac{1}{2^2·3^2} - \frac{1}{2·3^3} + \frac{1}{3^4}\right) + ........ $
is $\frac{α}{β}$ , where α and β are co-prime, then α+3β is equal to ________

The set of all values of $a$ for which $\displaystyle\lim _{x \rightarrow a}([x-5]-[2 x+2])=0$,where $[\propto]$ denotes the greatest integer less than or equal to $\propto$ is equal to

If a_a is the greatest term in the sequence $a_n=\frac{n^3}{n^4+147},n=1,2,3,...,$ then a is equal to______________.

In a binomial distribution $B(n, p)$, the sum and the product of the mean and the variance are 5 and 6 respectively, then $6(n+p-q)$ is equal to

Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation R = {((a₁, b₁), (a₂, b₂)) ∈ (A × B, A × B) : a₁ divides b₂ and a₂ divides b₁} is