List of top Mathematics Questions

Find the value of 'n' so that \( \frac{a^{n+1} + b^{n+1}}{a^n + b^n} \) may be the geometric mean between a and b.

Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse: \[ \frac{x^2}{36} + \frac{y^2}{16} = 1 \]

Solve the given inequalities and represent the solution graphically on the number line: \[ 2(x - 1)<x + 5, \quad 3(x + 2)>2 - x \]

Express the given complex number in the form of \( a + ib \): \( \left( \frac{1}{3} + 3i \right)^3 \)

Find the multiplicative inverse of \( \sqrt{5} + 3i \)

Using Binomial Theorem, Evaluate: \( (102)^5 \)

Solve the given inequality for real \( x \): \[ \frac{3(x - 2)}{5} \leq \frac{5(2 - x)}{3} \]

Evaluate \( \left( \sqrt{3} + \sqrt{2} \right)^6 - \left( \sqrt{3} - \sqrt{2} \right)^6 \)

If \( \frac{2}{11} \) is the probability of an event, what is the probability of the event 'not A'?

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Verify that (0,7,10), (-1,6,6) and (-4,9,6) are the vertices of a right angled triangle.

Show that the points (-2, 3, 5), (1, 2, 3), and (7, 0, -1) are collinear OR verify that the points (0,7,10), (-1,6,6) and (-4,9,6) are the vertices of a right angled triangle.

The 4th term of a G.P. is square of its second term, and the 1st term is -3. Determine its 7th term.

For some constants \( a \) and \( b \), find the derivative of \( \frac{x - a}{x - b} \)

Prove that \( \frac{\sin x - \sin y}{\cos x + \cos y} = \tan \frac{x - y}{2} \).

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

If \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \), \( A = \{2, 4, 6, 8\} \), and \( B = \{2, 3, 5, 7\} \), verify that \( (A \cup B)' = A' \cap B' \).

A collection of most dangerous animals of the world is:

Assertion (A): The derivative of the function \( f(x) = x^2 \) with respect to \( x \) is \( 2x \).
Reason (R): The derivative of a power function \( x^n \) is given by the formula \( \frac{d}{dx}(x^n) = nx^{n-1} \).

Assertion (A): The radius of a circle in which a central angle of 60 degrees intercepts an arc length of 37.4 cm (using \( \pi = \frac{22}{7} \))
Reason (R): The formula to calculate the length of an arc is \( l = Q \times r \), where \( l \) is the arc length, \( Q \) is the central angle in radians, and \( r \) is the radius of the circle.

Assertion (A): When a die is thrown, the event of getting a number greater than 7 is an impossible event. Reason (R): A standard die has six faces, numbered from 1 to 6.

If \( n = 5 \) and \( r = 3 \), then the value of \( ^nP_r \) is:

Complex conjugate of \( 3i - 4 \) is:

A person has two parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.

The radian measure of 520° is: