Let a = i + 2j -2k and b = 2i - j - 2k be two vectors. If the orthogonal projection vector of a on b is x and orthogonal projection vector of b on a is y then |x - y| =
The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is
If Xn = cos \(\frac{ π}{2^n}\) + i sin\(\frac{ π}{2^n}\) , then
There are 10 points in a plane, of which no three points are colinear expect 4. Then the number of distinct triangles that can be formed by joining any three points of these ten points, such that at least one of the vertices of every triangle formed is from the given 4 colinear points is
If the angle between the asymptotes of a hyperbola is 30° then its eccentricity is
If x = log (y +√y2 + 1 ) then y =
If the roots of the equation z2 - i = 0 are α and β, then | Arg β - Arg α | =
If the points of intersection of the parabola y2 = 5x and x2 = 5y lie on the line L, then the area of the triangle formed by the directrix of one parabola, latus rectum of another parabola and the line L is
A student is asked to answer 10 out of 13 questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is
A bag contains four balls. Two balls are drawn randomly and found them to be white. The probability that all the balls in the bag are white is
If
then an integer root of 3x2-4x+2= \(\frac{3k}{5}\) is
Let X= {[a b c d] / a,b,c,d ∈ R}. If f:X → R is defined by f(A) = det (A) ⦡ A ∈ X, then f is:
If R -(α,β) is the range of \(\frac{x+3}{(x-1)(x+2)}\) then the sum of the intercepts of the line ax + βy + 1 = 0 on the coordinate axes is:
If x+√3y = 3 is the tangent to the ellipse 2x2 + 3y2 = k at a point P then the equation of the normal to this ellipse at P is
In a triangle BC, if the mid points of sides AB, BC, CA are (3,0,0), (0,4,0),(0,0,5) respectively, then AB2 + BC2 + CA2 =
The quadratic equation whose roots are
\(l = \lim_{\theta\to0} \frac{3sin\theta - 4sin^3\theta}{\theta}\)
m = \(\lim_{\theta\to0} \frac{2tan\theta}{\theta(1-tan^2\theta)}\) is
The variance of 50 observations is 7. Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is
If (2,-1,3) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is
If y = \(\frac{3}{4} + \frac{3.5}{4.8}+\frac{5.5.7}{4.8.12}+ \).... to ∞, then
If A(1,2,3) B(3,7,-2) and D(-1,0,-1) are points in a plane, then the vector equation of the line passing through the centroids of △ABD and △ACD is
If a point P moves so that the distance from (0,2) to P is \(\frac{1}{√2 }\) times the distance of P from (-1,0), then the locus of the point P is
If x2 + 2px - 2p + 8 > 0 for all real values of x, then the set of all possible values of p is
Let y = t2 - 4t -10 and ax + by + c = 0 be the equation of the normal L. If G.C.D of (a,b,c) is 1, then m(a+b+c) =
If f(x) is a function such that f(x+y) = f(x)+ f(y) and f(1) = 7 then \( \sum_{r=1}^{n}\) f(r) =
If the radical center of the given three circles x2 + y2 = 1, x2 + y2 -2x - 3 =0 and x2 + y2 -2y - 3 = 0 is C(α,β) and r is the sum of the radii of the given circles, then the circle with C(α,β) as center and r as radius is