List of practice Questions

If \(\bar{a}\times\bar{b}=7\hat{i}+9\hat{j}+10\hat{k}\) and \(\bar{a}\cdot\bar{b}=-20\), then \(|\bar{a}|^{2}|\bar{b}|^{2}=\)
The eccentricity of the hyperbola \(\frac{(x-3)^2}{9}+\frac{4(y-1)^2}{45}=1\) is equal to
If (-1, 0) and (3, 0) are foci of an ellipse and the length of the major axis is 6, then the length of the minor axis is
The centre of the ellipse x2+7y2-14x+28y+49=0 is
If the line 2x-3y+c=0 passes through the focus of the parabola x2 = -8y, then the value of c is equal to
If the radius of the circle x2+y2+ax+by+3=0 is 2, then the point (a, b) lies on the circle
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
\(\begin{vmatrix} \sin\alpha & \cos(\alpha+\theta) & \cos\alpha \\ \sin\beta & \cos(\beta+\theta) & \cos\beta \\ \sin\gamma & \cos(\gamma+\theta) & \cos\gamma\end{vmatrix}=\)