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| = 4, |b| = 5, |a - b| = 3 and θ is the angle between the vectors a and b, then cot2 θ =
In △ABC, if a : b : c = 4 : 5 : 6, then the ratio of the circumference to its in radius is
The locus of z such that \(\frac{|z-i|}{|z+i|}\)= 2, where z = x+iy. is
If x = log (y +√y2 + 1 ) then y =
If sin 2θ and cos 2θ are solutions of x2 + ax - c = 0, then
If cosθ = \(\frac{-3}{5}\)- and π < θ < \(\frac{3π}{2}\), then tan \(\frac{ θ}{2}\) + sin \(\frac{ θ}{2}\)+ 2cos \(\frac{ θ}{2}\) =
If \(\frac{3x+2}{(x+1)(2x^2+3)} = \frac{A}{x+1}+ \frac{Bx+C}{2x^2+3}\), then A - B + C=
If y = \(\frac{3}{4} + \frac{3.5}{4.8}+\frac{5.5.7}{4.8.12}+ \).... to ∞, then
If (-c, c) is the set of all values of x for which the expansion is (7 - 5x)-2/3 is valid, then 5c + 7 =
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
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
The number of diagonals of a polygon is 35. If A, B are two distinct vertices of this polygon, then the number of all those triangles formed by joining three vertices of the polygon having AB as one of its sides is:
The roots of the equation x4 + x3 - 4x2 + x + 1 = 0 are diminished by h so that the transformed equation does not contain x2 term. If the values of such h are α and β, then 12(α - β)2 =
The quadratic equation whose roots are sin218° and cos2 36° is
If x2 + 2px - 2p + 8 > 0 for all real values of x, then the set of all possible values of p 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 Xn = cos \(\frac{ π}{2^n}\) + i sin\(\frac{ π}{2^n}\) , then
If A = \(\begin{bmatrix} 0 & 3\\ 0 & 0 \end{bmatrix}\)and f(x) = x+x2+x3+.....+x2023, then f(A)+I =
If A is a square matrix of order 3, then |Adj(Adj A2)| =
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) =
The perimeter of a △ABC is 6 times the arithmetic mean of the values of the sine of its angles. If the side BC is of the unit length, then ∠A =