List of top Questions asked in KEAM

If A and B are two events such that P(A)=0.5, P(B)=0.4 and P(A\(\cap\)B)=0.2, then P(A|(A\(\cup\)B)) is equal to
Three fair dice are rolled simultaneously. Let a, b, c be the numbers on the top of the dice. Then the probability that min(a, b, c) =6 is
The angle between the planes x=√3 and z = √2 is equal to
The distance from the point (2, 2, 2) to the plane 2x-y+3z = 5 is equal to
If \(\theta\) is angle between the lines \(\frac{x}{1}=\frac{y+1}{2}=\frac{z-1}{3}\) and \(\frac{x+1}{3}=\frac{y}{2}=\frac{z}{1}\), then \(\cos\theta=\)
The equation of the plane through the point (1, 5, 3) and having a normal vector \(\hat n=2\hat i-2\hat j-\hat k\) is
If the points (1, 0, 0), (0, 3, 0) and (0, 0, 2) lie on a plane, then the unit normal vector \(\hat n\) to the plane is
The equation of the line through the point (1, 1, 1) and parallel to the line joining the points (-2, 2, 0) and (-1, 1, 1) is
The equation of the plane passing through the point (-1,-2,-3) and perpendicular to the x-axis is
If \(|\bar u|=3,|\bar v|=2\ and\ |\bar u\times \bar v|=3\), then the angle between \(\bar u\ and\ \bar v\) is equal to
If \(\bar{a}=2\hat{i}+3\hat{j}-4\hat{k}\) and \(\bar{b}=\hat{i}+3\hat{j}+2\hat{k}\), then a unit vector in the direction of \(\bar a +\bar b\) is
If \(\bar a\ and\ \bar b\) are position vectors of the points (a, 3, 0) and (1, 0, 0) respectively and if the angle between the vectors \(\bar a\ and\ \bar b\ is\ \frac{\pi}{4}\), then the value of a is equal to
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 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