List of top Questions asked in KEAM

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 end points of the major axis of an ellipse are (2, 4) and (2,-8). If the distance between foci of this ellipse is 4, then the equation of the ellipse 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 three vertices of a triangle are (0, 0), (3, 1) and (1, 3). If this triangle is inscribed in a circle, then the equation of the circle is

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

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

If the solution set of the inequality \(|a+3x|\leq6\ is\ [\frac{-8}{3},\frac{4}{3}]\), then the value of a is