List of top Mathematics Questions

The distance between the point \( (1,2) \) and the point of intersection of the lines \( 2x + y = 2 \) and \( x + 2y = 2 \) is

If a straight line is perpendicular to \( 2x + 8y = 10 \) and meets the x-axis at \( (5,0) \), then it meets the y-axis at

Let \( A(0,0) \) and \( B(8,0) \) be two vertices of a right angled triangle whose hypotenuse is \( BC \). If the circumcentre is \( (4,2) \), then the point \( C \) is:

If coordinates of the circumcentre and the orthocentre of a triangle are respectively \( (5,5) \) and \( (2,2) \), then the coordinates of the centroid are:

If the points \( A(3,4) \), \( B(x_1,y_1) \) and \( C(x_2,y_2) \) are such that both \( 3,x_1,x_2 \) and \( 4,y_1,y_2 \) are in A.P., then

If \( \cos^{-1}x > \sin^{-1}x \), then \(x\) lies in the interval

If \( \sin(\theta+\phi) = n \sin(\theta-\phi), \; n \neq 1 \), then the value of \( \frac{\tan\theta}{\tan\phi} \) is

If \( 0 \le x \le 2\pi \), then the number of solutions of the equation \( \sin^8 x + \cos^8 x = 1 \) is

\( 2\tan^{-1}\left(\frac{1}{3}\right) + \tan^{-1\left(\frac{1}{4}\right) = \)}

If \( \cos^{-1}x + \cos^{-1}y = \frac{2\pi}{7} \), then the value of \( \sin^{-1}x + \sin^{-1}y \) is equal to

If \( x = 5 + 2\sec \theta \) and \( y = 5 + 2\tan \theta \), then \( (x-5)^2 - (y-5)^2 \) is equal to

Consider the two statements \(P\): He is intelligent and \(Q\): He is strong. Then the symbolic form of the statement “It is not true that he is either intelligent or strong” is

The value of \( \tan 15^\circ + \tan 75^\circ \) is equal to

Let \(p, q, r\) be three statements. Then \( \sim (p \vee (q \wedge r)) \) is equal to

The period of the function \( f(x) = \cos 4x + \tan 3x \) is

If \( \tan \frac{\theta}{2} = \frac{1}{2} \), then the value of \( \sin \theta \) is

The area and perimeter of a rectangle are \(A\) and \(P\) respectively. Then \(P\) and \(A\) satisfy the inequality

For any two statements \(p\) and \(q\), the statement \( \sim(p \vee q) \vee (\sim p \wedge q) \) is equivalent to

If \( A = \begin{pmatrix} x & x-1 \\ 2x & 1 \end{pmatrix} \) and if \( \det A = -9 \), then the values of \(x\) are

The value of the determinant \[ \begin{vmatrix} \cos^2 54^\circ & \cos^2 36^\circ & \cot 135^\circ \\ \sin^2 53^\circ & \cot 135^\circ & \sin^2 37^\circ \\ \cot 135^\circ & \cos^2 25^\circ & \cos^2 65^\circ \end{vmatrix} \] is equal to

If \( A \) and \( B \) are square matrices of same order and \( A = A^T, B = B^T \), then \( (ABA)^T = \)

If \( |x-3| < 2x+9 \), then \(x\) lies in the interval

If \( m_1 \) and \( m_2 \) satisfy the relation \( {}^{m+5}P_{m+1} = \frac{11}{2}(m-1)({}^{m+3}P_m) \), then \( m_1 + m_2 \) is

If \( \Delta = \begin{vmatrix}1& 2& 3 \\ 2& 3& 5 \\ 3& 6& 12\end{vmatrix} \) and \( \Delta' = \begin{vmatrix}4& 8& 15 \\ 3& 6& 12 \\ 2& 3& 5\end{vmatrix} \), then

The roots of the equation \[ \begin{vmatrix} 1+x & 3 & 5 \\ 2 & 2+x & 5 \\ 2 & 3 & x+4 \end{vmatrix} = 0 \] are