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List of top Mathematics Questions

Let S be the set of all values of λ, for which the shortest distance between the lines x-λ/0 =y-3/4 = z+6/1 and x+λ/3 = y/-4 = z-6/0 is 13. Then 8 | $ \sum_{ λ∈S} λ| is $

If gcd $ (m, n) = 1 $ and \[ 1^2 - 2^2 + 3^2 - 4^2 + \cdots + (2022)^2 - (2023)^2 = 1012 \, m^2 n \] then $ m^2 - n^2 $ is equal to:

Let S be the set of all (λ, μ) for which the vectors $ λ {i}ˆ-jˆ+kˆ, iˆ +2jˆ+µkˆ and 3iˆ -4jˆ +5kˆ, where λ-μ = 5, are coplanar, then $$ \sum_{(λ, μ) εs}80(λ^2, μ^2) $ is equal to

$lim _{n→∞}{(2^½-2^½)(2^½-2^½)….(2^½-^2{\frac{1}{2n+1}})}$ is equal to

Let the foot of perpendicular of the point P(3, -2, -9) on the plane passing through the points (-1, -2, -3), (9, 3, 4), (9, -2, 1) be Q(α, β, γ). Then the distance of Q from the origin is

Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ Then $S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$ :

If (a, β) is the orthocenter of the triangle ABC with vertices A(3, -7), B(-1, 2), and C(4, 5), then 9α-6β+60 is equal to

Let a differentiable function $f$ satisfy $f(x)+\int\limits_3^x \frac{f(t)}{t} d t=\sqrt{x+1}, x \geq 3$ Then $12 f(8)$ is equal to :

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is:

Let x = x(y) be the solution of the differential equation 2(y+2) log_e (y+2)dx+(x+4-2log_e(y+2))dy = 0, y >-1 with x (e⁴-2)=1. Then x(e⁹-2) is equal to

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

Among the statements:

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

The system of the equations
$x + y + z = 6$
$x + 2y + \alpha z = 5 $
$x + 2y + 6z = $$ \beta$ has

If the coefficients of $ x $ and $ x^2 $ in $ (1 + x)^p(1 - x)^q $ are 4 and -5 respectively, then $ 2p + 3q $ is equal to:

If $a ≠ ±b$ and are purely real, z ϵ complex number, $Re(az^{2}+bz)=a$ and $Re(bz^{2}+az)=b$ then number of value of z possible is

Let [x] denote the greatest integer function and f(x) = max{1+x+[x], 2+x, x+2[x]}, 0 ≤ x ≤2. Let m be the number of points in [0, 2], where f is not continuous and n be the number of points in (0, 2), where f is not differentiable. Then (m+n)² + 2 is equal to 2

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is a and the number of persons who speak only Hindi is b, then the eccentricity of the ellipse 25(β2 x² + α² y2) = α² β² is

Let A₁ and A₂ be two arithmetic means and G₁, G₂, G₃ be three geometric means of two distinct positive numbers. Then $ G_{1}^{4} + G_{2}^{4}+ G_{3}^{4} +G_{1}^{2}G_{3}^{2} $ is equal to

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

The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1,3,5,8, if repetition of digits is allowed, is

Let the determinant of a square matrix A of order $ m $ be $ m - n $, where $ m $ and $ n $ satisfy $ 4m + n = 22 $ and $ 17m + 4n = 93 $. If $ \text{det} (n \, \text{adj}(\text{adj}(mA))) = 3^a 5^b 6^c $, then $ a + b + c $ is equal to:

If the set $\left( Re \left( \frac{z-\bar{z}+z\bar{z}}{2-3z+5\bar{z}}\right) : z ∈ C, Re(z)=3 \right)$ is equal to the interval (α,β), then 24(β-α) is equal to

For all $z \in C$ on the curve $C_1:|z|=4$, let the locus of the point $z+\frac{1}{z}$ be the curve $C_2$ Then:

Let [α] denote the greatest integer ≤ α. Then $[\sqrt1] + [ \sqrt 2 ] + [ \sqrt3 ] + . . . + [ \sqrt120 ] [\sqrt1 ] + [ \sqrt2 ] + [ \sqrt3 ] + . . . + [ 120 ]$ is equal to