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The area bounded by the curve y = x^{3}, the xaxis and the ordiantes at x = 2 and x = 1 is
If the sum of the coefficients in the expansion of (α^{2}x^{2}  2αx + 1)^{51} vanishes, then α is equal to
The angle between the tangents from the origin to the circle (x7)^{2} + (y+1)^{2} = 25 is
The limiting point of the system of coaxial circles x^{2}+y^{2}6x6y+4=0, x^{2}+y^{2}2x4y+3=0 is
If [(1 + i√3)/(1 + i√3)]^{n} is an integer ,then n is equal to
Presuming the question actually means
[ ( 1 + √3i ) / ( 1  √3i ) ]ⁿ
i.e. the whole thing raised to the power of n, not just the denominator.
Let w = ( 1 + √3i ) / ( 1  √3i )
Multiplying numerator and denominator by ( 1 + √3i ) gives
w = ( 1 + √3i )² / [ ( 1  √3i ) ( 1 + √3i ) ]
= ( 1  3 + 2√3i ) / ( 1 + 3 )
= ( 2 + 2√3i ) / 4
= ( 1 + √3i) / 2.
So w is a primitive cubed root of unity. (*) ... see note below
So wⁿ is an integer
<=> wⁿ = 1
<=> n is a multiple of 3.
The differential equation for the family of curves x^{2} + y^{2}  2ay = 0, where a is an arbitrary constant is
The number of points at which the function f(x)=x0.5+x1+tanx is not differentiable in (0,2) is
Sum of the infinite series 1 + 3/2! + 6/3! + 10/4! + ...... is
If a flag staff of 6 mt high placed on the top of a tower throws a shadow of 2 √3 mt along the ground then the angle that the sun makes with the ground is
A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1:2 is
The general solution of the differential equation (dy/dx) = (x^{2}/y^{2}) is
The area bounded by the curve y^{2} = 9x and the lines x = 1, x = 4 and y = 0 in the first quadrant is
Let f(x + y) = f(x)f(y) for all x and y. Suppose that f(3) = 3 and f′(0) = 11 then f′(3) is given by
If A and B are square matrices and A^{⁻1} and B^{⁻1} of same order exists, then (AB)^{⁻1} is equal to
The curved surface of the cone inscribed in a given sphere is maximum if h=
If z is a complex number, then  3z − 1  = 3  z − 2  represents
If x+y+1=0 tocuhes the parabola y^{2}=λx,then λ is equal to
How many words are formed from the letters of the word EAMCET so that two vowels are never together?
Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, is
The mean and variance of a Binomial distribution are 6 and 4. The parameter n is
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is
Out of 5 horses only 1 is the winning horse
The probability that Mr A selected the losing horse = 4/5 x 3/4
∴ The probability that Mr A selected the winning horse = 1  4/5 x 3/4 = 2/5
If the sum of the roots of the quadratic equation ax^{2}+bx+c = 0, is equal to the sum of the squares of their reciprocals, then (a/c), (b/a), (c/b) are in
The coordinates of midpoint of portion of line cut by coordinate axis are (3,2), the equation of the line is
A tetrahedron has vertices at O (0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C (1, 1, 2). Then the angle between the faces OAB and ABC will be
The angle between the curves y^{2} = x, x^{2} = y at (1,1) is
The direction ratios of the diagonals of a cube which joins the origin to the opposite corner are (when the 3 concurrent edges of the cube are coordinate axes)
In any right angled triangle hypotenuse is equal to 2√2 times the perpendicular drawn from the opposite vertex on it, then other angles are
If sin 2x=n sin 2y, then the value of tan (x+y)/tan(xy) is
The moment of the couple formed by the forces a n d acting at the points (9,−1,2) and (3,−2,1) respectively is
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