List of practice Questions

The points of intersection of the line y=x+2 and the circle (x-2)2 + y2 = 16 are
If the lines 2x-3y+5=0, 9x-5y+14=0 and 3x-7y+λ=0 are concurrent, then the value of λ is equal to
Let A(-1, 2), B(1, 3) and C(a, b) be collinear. If B divides AC such that BC=8AB, then the coordinates of C are
If the line y = mx + c is perpendicular to y=1+x and passes through the point (1, 2), then the value of c is equal to
The intercepts of a line with coordinate axes are equal. If the line passes through (2, 3), then its equation is
The equation of the straight line parallel to y=-3x and passing through the point (3,-2) is
\(\cos \left( \sin^{-1}(\frac{\sqrt{3}}{200})+\cos^{-1}(\frac{\sqrt{3}}{200}) \right)=\)
The value of \(\tan(\sin^{-1}(\frac{7}{25}))\) is equal to
The value of \(\cos^{-1}(\cos(\frac{7\pi}{6}))\) is equal to
The solutions of the equation \(cos\theta=2-3sin(\frac{\theta}{2})\ in\ the\ interval\ 0\leq\theta\leq\pi\ are\)
If \(\theta \isin(-\pi,0)\ and\ cos\theta=\frac{-12}{13}, then\ \sin(\frac{\theta}{2})=\)
The period of the function \(g(x)=5\cot(\frac{\pi}{3}x+\frac{\pi}{6})+2\) is equal to
The range of the function f(x) = 2sin(3x) +1 is equal to
If \( \alpha \) and \( \beta \) are two acute angles of a right triangle, then \[ (\sin \alpha + \sin \beta)^2 + (\cos \alpha + \cos \beta)^2 = \] 
If \(\cos\theta=\frac{5}{11}\) and \(\tan\theta\lt0\), then the value of \(\sin\theta\) is equal to
Consider the following statements:
(i) For every positive real number X, x-10 is positive.
(ii) Let n be a natural number. If n2 is even, then n is even.
(iii) If a natural number is odd, then its square is also odd.
Then
The set of all x satisfying the inequality |3x+4| ≤ 7 is
The solution set of the inequality \(-2\leq\frac{3x+2}{2}\lt7\) is
\(\begin{vmatrix} \sin\alpha & \cos(\alpha+\theta) & \cos\alpha \\ \sin\beta & \cos(\beta+\theta) & \cos\beta \\ \sin\gamma & \cos(\gamma+\theta) & \cos\gamma\end{vmatrix}=\)
If A is non-singular matrix and if \(A^{-1}=\frac{1}{2}\begin{bmatrix} -10&-4\\2&1\end{bmatrix}\), then adj(A)=
If A=[2 0 6] and \(B=\begin{bmatrix} 3&\ \ 5\\7&-2\\6&\ \ 6 \end{bmatrix}\), then AB=
The value of x satisfying the equation \(\begin{vmatrix} x&\ \ 4&\ \ 0\\2&-2&-x\\1&\ \ 1&\ \ 1 \end{vmatrix}=0\) are
Let \(\begin{vmatrix} 2&1&-2\\1&1&-1\\1&0&\ \ 3 \end{vmatrix}\)and let B=|A|adj(A). Then |B|=
Let \(A= \begin{bmatrix} 3&4\\ 1&-2 \end{bmatrix}\) and let \(AB= \begin{bmatrix} -5&41\\ 5&-13 \end{bmatrix}\). Then |BT| =
If nC5 + nC6 = 51C6, then the value of n is equal to