List of top Questions asked in KEAM- 2015

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

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 \( \sin(\theta+\phi) = n \sin(\theta-\phi), \; n \neq 1 \), 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

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

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

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

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

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

Let \(p, q, r\) be three statements. Then \( \sim (p \vee (q \wedge r)) \) 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 \( A = \begin{pmatrix} x & x-1 \\ 2x & 1 \end{pmatrix} \) 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

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

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

If \[ \begin{vmatrix} 0 & 3 & 2b \\ 2 & 0 & 1 \\ 4 & -1 & 6 \end{vmatrix} \] is singular, then the value of \(b\) 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

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

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

If \( a, b, c \) are in A.P. and their squares in same order form a G.P., then \( (a+c)^4 = \)

The number of 5-digit numbers (no digit is repeated) that can be formed by using the digits \(0,1,2,\ldots,7\) is