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List of top Mathematics Questions

For all x ∈ [0, 2024] assume that f (x) is differentiable. f (0) = −2 and f ′(x) ≥ 5. Then the least possible value of f (2024) is:

The point (a, b) is the foot of the perpendicular drawn from the point (3, 1) to the line x + 3y + 4 = 0. If (p, q) is the image of (a, b) with respect to the line 3x - 4y + 11 = 0, then $\frac{p}{a} + \frac{q}{b} = $

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

A bag contains 2 white, 3 green, and 5 red balls. If three balls are drawn one after the other without replacement, then the probability that the last ball drawn was red 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:

Let f(x) = $\int \frac{x}{(x^2+1)(x^2+3)} dx$. If f(3) = $\frac{1}{4} \log(\frac{5}{6})$, then f(0) =

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

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:

A ray of light passing through the point (2, 3) reflects on the Y-axis at a point P. If the reflected ray passes through the point (3, 2) and P = (a, b), then 5b = ?

$ \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:

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:

In a consignment of 15 articles, it is found that 3 are defective. If a sample of 5 articles is chosen at random from it, then the probability of having 2 defective articles is:

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

The perpendicular distance from the point $ (-1,1,0) $ to the line joining the points $ (0,2,4) $ and $ (3,0,1) $ is:

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:

If the area of the circum-circle of the triangle formed by the line 2x + 5y + a = 0 and the positive coordinate axes is $\frac{29\pi}{4}$ sq. units, then |a| =

If set $ A $ contains 8 elements, then the number of subsets of $ A $ which contain at least 6 elements is: