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List of top Mathematics Questions

The circle S = x² + y² − 2x − 4y + 1 = 0 cuts the y-axis at A, B (OA: OB). If the radical axis of S ≡ 0 and S′ = x² + y² − 4x − 2y + 4 = 0 cuts the y-axis at C, then the ratio in which C divides AB is:

If $ A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix} $ and $ \alpha^2 + \beta A = 21 $ for some $ \alpha, \beta \in \mathbb{R} $, then find $ \alpha + \beta $:

If $ \alpha, \beta, \gamma $ are roots of the equation $ x^3 + ax^2 + bx + c = 0 $, then $ \alpha^{-1} + \beta^{-1} + \gamma^{-1} $ is:

The normal drawn at a point $ (2, -4) $ on the parabola $ y^2 = 8x $ cuts again the same parabola at $ (\alpha, \beta) $. Then $ \alpha + \beta $ is:

The locus of the midpoints of the chords of the hyperbola $ x^2 - y^2 = a^2 $ which touch the parabola $ y^2 = 4ax $ is:

If the product of the eccentricities of the ellipse $ \frac{x^2}{16} + \frac{y^2}{b^2} = 1 $ and the hyperbola $ \frac{x^2}{9} - \frac{y^2}{16} = 1 $ is 1, then the value of $ b^2 $ is:

If a real valued function $ f: [a, \infty) \to [b, \infty) $ is defined by $ f(x) = 2x^2 - 3x + 5 $ and is a bijection, then find the value of $ 3a + 2b $:

If the circle S = 0 cuts the circles x² + y² - 2x + 6y = 0, x² + y² - 4x - 2y + 6 = 0, and x² + y² - 12x + 2y + 3 = 0 orthogonally, then the equation of the tangent at (0, 3) on S = 0 is:

If a variable straight line passing through the point of intersection of the lines x - 2y + 3 = 0 and 2x - y - 1 = 0 intersects the X and Y axes at A and B respectively, then the equation of the locus of a point which divides the segment AB in the ratio -2 : 3 is:

$\int_{0}^{\pi}x \sin^4 x \cos^6 x dx = $

If $\int \frac{\log(1+x^4)}{x^3} dx = f(x) \log(\frac{1}{g(x)}) + \tan^{-1}(h(x)) + c$, then $h(x) [f(x) + f(\frac{1}{x})] =$

If $\lim_{n\rightarrow\infty}[(1+\frac{1}{n^{2}})(1+\frac{4}{n^{2}})(1+\frac{9}{n^{2}})\cdots(1+\frac{n^{2}}{n^{2}})]^{\frac{1}{n}}=ae^{b}$, then a+b=

$ \lim_{x \to 3} \frac{x^3 - 27}{x^2 - 9}. $

If $ f(x) $ is given as: $ f(x) = \begin{cases} 3ax - 2b, & x<1 ax + b + 1, & x<1 \end{cases} $ and $ \lim_{x \to 1} f(x) $ exists, then the relation between $ a $ and $ b $ is:

.The function $ f(x) $ is given by: \[ f(x) = \begin{cases} \frac{2}{5 - x}, & x<3 \\ 5 - x, & x \geq 3 \end{cases} \] Which of the following is true

If $$ y = (1 + a + a^2 + \dots)e^{nx} $$ then the relative error in $y$ is:

If the equation of the tangent at (2, 3) on y² = ax³ + b is y = 4x - 5, then the value of a² + b² is:

If Rolle's theorem is applicable for the function $f(x) = x(x+3)e^{-x/2}$ on $[-3, 0]$, then the value of $c$ is:

If $ A(1,2,0), B(2,0,1), C(-3,0,2) $ are the vertices of $ \triangle ABC $, then the length of the internal bisector of $ \angle BAC $ is:

The area (in square units) of the triangle formed by the lines 6x² + 13xy + 6y² = 0 and x + 2y + 3 = 0 is:

The angle subtended by the chord $ x + y - 1 = 0 $ of the circle $ x^2 + y^2 - 2x + 4y + 4 = 0 $ at the origin is:

The real part of $ \frac{\left( \cos a + i \sin a \right)^6}{\left( \sin b + i \cos b \right)^8} $ is:

If $$ f(x) = \min \{ x, x^2 \} $$ Which of the following is true?

If a tangent of slope 2 to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ touches the circle $x^2 + y^2 = 4$, then the maximum value of ab is:

In a triangle ABC, if $ (a-b)(s-c) = (b-c)(s-a) $, then $ r_1 + r_3 = $: