List of top Mathematics Questions

Let \( f(x) = \frac{1+x{1-x} \). Find the value of \( f(x) + f(-x) \):}
In a circle of radius 13 cm, a chord is at a distance of 12 cm from the center of the circle. Find the length (in cm) of the chord.
If $ a $ and $ b $ are the roots of the equation $ 4x^2 - 12x + 11 = 0 $, find the value of $ a^2 + b^2 $.
Find the determinant of the matrix: $$ \begin{bmatrix} 3 & 2 \\ 1 & 5 \end{bmatrix} $$
Let \( A(1,2), B(3,4) \) and \( C(k,6) \) be three points such that the area of triangle \( ABC \) is 5 square units. The possible values of \( k \) are:
If \( y = \log \left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^2 \), then show that \( x(x + 1)^2 y_2 + (x + 1)^2 y_1 = 2 \).
The general solution of the differential equation \( x\,dy + \left(y - e^x\right) dx = 0 \) is:
If \( \tan(\theta - \phi) = \frac{3}{4} \) and \( \theta + \phi = \frac{\pi}{2} \), then the value of \[ \tan \left( \frac{\pi}{4} - \theta \right) + \tan \left( \frac{\pi}{4} - \phi \right) \] is:
If the tangent to the curve \( y = ax^2 + bx + c \) at the point \( (1,1) \) is parallel to the x-axis, and the curve passes through the point \( (2,3) \), then find the value of \( a + b + c \):
Let \[ f(x) = x^4 - 4x^3 + 6x^2 + k \] \text{If \(f(x) \geq 0\) for all real \(x\), then the value of \(k\) is:}
Let \( f(\theta) = \begin{vmatrix} 1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1 \end{vmatrix} \). Suppose \( A \) and \( B \) are respectively the maximum and minimum values of \( f(\theta) \). Then \( (A, B) \) is equal to:
A rectangular garden has a length that is 3 meters more than its width. If the area of the garden is 88 square meters, what is the width of the garden?
What is the distance between the points $(3, -2)$ and $(-1, 4)$?
If $A$ is a square matrix of order 3 such that $|A| = 2$, then $|\operatorname{adj}(\operatorname{adj}(A))|$ is:
A pair of linear equations \( a_1 x + b_1 y + c_1 = 0 \) and \( a_2 x + b_2 y + c_2 = 0 \) is such that \( \frac{a_1}{a_2} \neq \frac{b_1}{b_2} \), then they are:
Evaluate the integral: \[ \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx \]
A hemispherical bowl is packed in a cuboidal box. The bowl just fits in the box. Inner radius of the bowl is 10 cm. Outer radius of the bowl is 10.5 cm.
hemispherical bowl is packed in a cuboidal box
A triangular window of a building is shown above. Its diagram represents a \(\triangle ABC\) with \(\angle A = 90^\circ\) and \(AB = AC\). Points P and R trisect AB and \(PQ \parallel RS \parallel AC\).
triangular window of a building
Gurveer and Arushi built a robot that can paint a path as it moves on a graph paper. Some co-ordinate of points are marked on it. It starts from graph paper. Some co-ordinate of points are marked on it. It starts from (0, 0), moves to the points listed in order (in straight lines) and ends at (0, 0).
Gurveer and Arushi built a robot that can paint
Find the sum of first 20 terms of an A.P. whose n\(^{th}\) term is given by \(a_n = 5 + 2n\). Can 52 be a term of this A.P. ?
Find the A.P. whose third term is 16 and seventh term exceeds the fifth term by 12. Also, find the sum of first 29 terms of the A.P.
Evaluate : \(\frac{\cos 45^\circ}{\tan 30^\circ + \sin 60^\circ}\)

The Statue of Unity situated in Gujarat is the world’s largest Statue which stands over a 58 m high base. As part of a project, a student constructed an inclinometer and wishes to find the height of the Statue of Unity using it. He noted the following observations from two places:
Situation – I: The angle of elevation of the top of Statue from Place A, which is $80\sqrt{3}$ m away from the base of the Statue, is found to be $60^\circ$. 
Situation – II: The angle of elevation of the top of the Statue from a Place B, which is 40 m above the ground, is found to be $30^\circ$ and the total height of the statue including the base is given to be 240 m.
Based on the given information, answer the following:

Let a complex number \(z\) satisfy the equation: \[ |z - z_1| = 2 |z - z_2|,\quad \text{where } z_1 = 1 + 2i,\ z_2 = 3i \] Then choose the correct options:

If the domain of the function \( f(x) = \frac{1}{\sqrt{3x + 10 - x^2}} + \frac{1}{\sqrt{x + |x|}} \) is \( (a, b) \), then \( (1 + a)^2 + b^2 \) is equal to: