List of top Mathematics Questions

Using integration, find the area of the ellipse: \[ \frac{x^2}{16} + \frac{y^2}{4} = 1, \] included between the lines \(x = -2\) and \(x = 2\).
Solve the following differential equation: \[ (\tan^{-1}y - x) \, dy = (1 + y^2) \, dx. \]
Find the equation of a line \( l_2 \) which is the mirror image of the line \( l_1 \) with respect to line \( l : \frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3} \), given that line \( l_1 \) passes through the point \( P(1, 6, 3) \) and is parallel to line \( l \).
Find: \[ \int \frac{x^2}{(x^2 + 4)(x^2 + 9)} \, dx. \]
If \( \sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y) \), prove that \( \frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{\sqrt{1 - x^2}} \).
A relation \( R \) on set \( A = \{1, 2, 3, 4, 5\} \) is defined as \[ R = \{(x, y) : |x^2 - y^2| <8\}. \] Check whether the relation \( R \) is reflexive, symmetric, and transitive.
E and F are two independent events such that \( P(\overline{E}) = 0.6 \) and \( P(E \cup F) = 0.6 \). Find \( P(F) \) and \( P(\overline{E} \cup \overline{F}) \).
Evaluate: \[ \int_0^{\frac{\pi^2}{4}} \frac{\sin\sqrt{x}}{\sqrt{x}} \, dx \]
Find: \[ \int x \sqrt{1 + 2x} \, dx \]
If \( P(A|B) = P(A'|B) \), then which of the following statements is true?
A linear programming problem deals with the optimization of a/an:
If the direction cosines of a line are \( \sqrt{3}k, \sqrt{3}k, \sqrt{3}k \), then the value of \( k \) is:
If \( f(x) \) is an odd function, then: \[ \int_{-\pi/2}^{\pi/2} f(x) \cos^3 x \, dx \, \text{equals:} \]
Let \( f(x) \) be a continuous function on \([a, b]\) and differentiable on \((a, b)\). Then, this function \( f(x) \) is strictly increasing in \((a, b)\) if:
Let \( \theta \) be the angle between two unit vectors \( \hat{a} \) and \( \hat{b} \) such that \( \sin \theta = \frac{3}{5} \). Then, \( \hat{a} \cdot \hat{b} \) is equal to:
The number of corner points of the feasible region determined by constraints \( x \geq 0, y \geq 0, x + y \geq 4 \) is:
The distance of point \( P(a, b, c) \) from the y-axis is:
Replace * in each of the following by the correct number : 
  1. \(\frac{2}{7} = \frac{8}{*}\)
  2. \(\frac{5}{8} =\frac{10}{*}\)
  3. \(\frac{3}{5} =\frac{*}{20}\)
  4. \(\frac{45}{ 60}= \frac{15}{*}\)
  5. \(\frac{18}{24} =\frac{*}{4}\)
For the data:
Xi13579
fi42428𝞪8
If the mean of data is 5 and mean deviation about mean is M and variance is 𝝈2 , then 3𝞪/M+𝝈2 is?
Give three examples of shapes with no line of symmetry.
Three different views of a dice are shown in the figure below.
\includegraphics[width=0.5\linewidth]{91.png}
The piece of paper that can be folded to make this dice is:
Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make?
Person 1 and Person 2 invest in three mutual funds A, B, and C. The amounts they invest in each of these mutual funds are given in the table.
\includegraphics[width=0.5\linewidth]{8a.png}
At the end of one year, the total amount that Person 1 gets is ₹500 more than Person 2. The annual rate of return for the mutual funds B and C is 15\% each. What is the annual rate of return for the mutual fund A?
Factorise 
  1.  \(4p^ 2 - 9q ^2\) 
  2.  \(63a^ 2 - 112b ^2\) 
  3.  \(49x^ 2 - 36\) 
  4.  \(16x^ 5 - 144x^ 3\)
  5.  \((l + m)^ 2 - (l - m) ^2\) 
  6.  \(9x^ 2 y^ 2 - 16 \)
  7.  \((x^ 2 - 2xy + y^ 2 ) - z^ 2\) 
  8.  \(25a ^2 - 4b^ 2 + 28bc - 49c ^2\)
Convert each part of the ratio to percentage: 
  1.  3:1 
  2.  2:3:5 
  3.  1:4 
  4.  1:2:5