List of practice Questions

The co-ordinates of the points P and Q are (2, 6, 4) and (8, -3, 1) respectively. If the point R lies on the line segment PQ such that \(2|\overrightarrow{PR}|=|\overrightarrow{RQ}|\), then the co-ordinates of R are
The foci of a hyperbola are (8, 3) and (0, 3) and eccentricity is \(\frac{4}{3}\). Then the length of the transverse axis is
The eccentricity of the ellipse \(\frac{x^2}{36}+\frac{y^2}{16}=1\) is
The equation of the parabola with focus (3, 0) and directrix x + 3 = 0 is
One of the vertices of the major axis of an ellipse is (1, 1) and one of the vertices of its minor axis is (-2, -1). If the centre of the ellipse is (-2, 1), then the equation of the ellipse is
The equation of the parabola with vertex (-6,2), passing through (-3, 5) and having axis parallel to x-axis is
The two diameters of a circle are segments of the straight lines x - y = 5 and 2x + y = 4. If the radius of the circle is 5, then the equation of the circle is
The end-points of a diameter of a circle are (-1, 4) and (5, 4). Then the equation of the circle is
The equation of the circle is 3x2+3y2+6x-4y-1=0. Then its radius is
A straight line makes an angle a with the positive direction of x-axis, where \(\cos a=\frac{\sqrt3}{2}\). If it passes through (0,-2), then its equation is
If x-intercept of the straight line ax+2ay=30 is 10, then the y-intercept is
The equation of the line which is parallel to \(x+\frac{1}{2}y=\frac{3}{2}\) and passing through (1,3) is
The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0,-4) is
The y-intercept of the line passing through (2, 5) with slope \(\frac{1}{2}\) is equal to
If ay=x+b is the equation of the line passing through the points (-5,-2) and (4, 7), then the value of 2a + b is equal to
If $sin\alpha +sin \beta = \frac{\sqrt6}2$ and $cos \alpha + cos\beta = \frac{\sqrt2}2$ then $coas(\alpha - \beta)$ is equa; to
The values of x in the interval $[0,\pi]$ such that $sin 2x = \frac{\sqrt3}2$
$tan(2tan^{-1}(\frac{2}5))$ is equal to
$cos^4 \frac{\pi}{12} - sin^4 \frac{\pi}{12}$ is equal to
The value of $sin^2(cos^{-1}(\frac{3}5))$ is equal to
If 0 < θ < $\frac{π}2 $ and tanθ = $\frac{\sqrt5}2$, then cosθ is equal to
The value of $tan^{-1} (\frac{7}4) - tan^{-1} (\frac{3}{11})$ is equal to 
If cosecθ + cotθ = 5, then the value of tanθ is equal to
The value of θ in the range 0 ≤ θ ≤ π/2 which satisfies the equation sin (θ + π/6) = cosθ is equal to
Let X be the set {1, π, {42, √2}, {1,3}}. Which of the following statement(s) is/are true? Ρ : π ∈X , Q :{1,3} ⊆ X , R : {1,7} ⊆ X