List of top Mathematics Questions

If the cost price of an article is 500 and it is sold at a profit of $10%$, what is the selling price?
The equation \(x^2 - Ky^2 - 4x + 6y - 5 = 0\) represents a pair of straight lines. Find the point of intersection.
(3, −4) and (4, −a) lie on line. Find a?

Identify the total number of surfaces in the given 3D object. 

Let \(x\) and \(y\) be real numbers such that} \[ 50\left(\frac{2x}{1+3i} - \frac{y}{1-2i}\right) = 31 + 17i, \qquad i = \sqrt{-1}. \] Then the value of \(10(x-3y)\) is:
Let \( R=\{(x,y)\in \mathbb{N}\times\mathbb{N}:\log_e(x+y)\le2\} \). Then the minimum number of elements required to be added in \(R\) to make it a transitive relation is ________.
The locus of the mid-point of a chord of the circle \( x^2 + y^2 = 4 \), which subtends a right angle at the origin is
In the given figure, \(AB \parallel DE\) and \(AC \parallel DF\). Show that \(\triangle ABC \sim \triangle DEF\). If \(BC = 10\) cm, \(EB = CF = 5\) cm and \(AB = 7\) cm, then find the length DE.
If \(y = f\left(\frac{3 + 2x}{3 - 2x}\right)\), where \(f(x) = \tan(\log x)\), and \(\frac{dy}{dx} = \frac{A}{B + Cx^2} \cdot \sec^2\left(\log \frac{3 + 2x}{3 - 2x}\right)\), then find \(A, B, C\).
A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use \(\pi = 3.14\))
Consider the following logical statements:
R: If \(p \rightarrow q\) is false, then \(p \vee q\) is false.
S: If \(p \leftrightarrow q\) is false, then \(p \vee q\) is false.
Evaluate the truth values of R and S.
What is the probability of an impossible event?
Solve the equation: \[ \frac{(3x - 4)^2}{9} - \frac{(4x - 3)^2}{8} = 1 \quad \text{(length of the latus rectum)} \]
If $\frac{dy}{dx} = y + 5$ and $y(0) = 4$, then $y(\log 2)$ is equal to
The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0, -4) is
Given: \( P(B) = 0.8 \) and \( P(A \cup B) = 0.8 \), find \( P(A' \cup B') \).
The end-points of a diameter of a circle are \( (-1, 4) \) and \( (5, 4) \). Then the equation of the circle is
A 3-digit number greater than 500 is to be made with the numbers 3, 4, 5, and 7. Find the number of possible ways.
Find the number of combinations of 3-lettered numbers that can be created by 3, 4, 5, and 7 with repeating. The three digits cannot be equal to zero.
The 1st and 20th term of a GP are 512 and \( \frac{1}{1024} \), respectively. Find the common ratio.
Given that \( |AB| = 21 \) and \( |A^{-1}| = 7 \), find \( |B| \).
Evaluate the integral: \[ \int 16x^3 \log_e x \, dx \]
If \( ay = x + b \) is the equation of the line passing through the points (-5, -2) and (4, 7), then the value of \( 2a + b \) is equal to:
Evaluate the integral: \[ \int_0^1 \frac{t}{(t + 1)^3} \, dt \]
Evaluate the integral: \[ \int \left( 27x^3 (1 - x^3)^{\frac{1}{3}} \right) dx \]