List of practice Questions

If \(\bar{a}=\hat{i}-3\hat{j}+3\hat{k}\) and \(\bar{b}=2\hat{i}+\hat{j}-3\hat{k}\), then the value of \((\bar a\times\bar b)\cdot\bar b\) is equal to

If \(|\bar a|=10\ and\ |\bar b|=5\), then the value of \((\bar a+2\bar b)\cdot(\bar a-2\bar b)\) is equal to

If \(|\bar{a}|=\sqrt{14},|\bar{b}|=\sqrt{10},|\bar{a}-\bar{b}|=\sqrt{24}\ and\ \theta\) is angle between \(\bar{a}\ and\ \bar{b}\), then \(\cos\theta=\)

Let \(\bar{a}=\hat{i}+2\hat{j}-3\hat{k}\) and \(\bar{a}+\bar{b}=4\hat{i}-2\hat{j}+\lambda\hat{k}\). If \(\bar{a}\cdot\bar{b}=4\), then the value of \(\lambda\) is equal to

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

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