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The abcissa of the points of the curve y = x(x  2)(x  4) where tangents are parallel to xaxis is obtained as
AOB is the positive quadrant of the ellipse x^{2} ∕ a^{2} + y^{2} ∕ b^{2} = 1, where OA = a, OB = b. The area between the arc AB and the chord AB of the ellipse is
Let z₁ and z₂ be two roots of the equation z^{2} + az + b = 0, z being complex further, assume that the origin, z₁ and z₂ form an equilateral triangle, then
The value of f(0) so that f x = sin x/x is continuous at x = 0 is
The general solution of the differential equation is given by
If y=x^{2}(x2)^{2}, then the values of x for which y is increasing, are
If S is the set of all real x such that 2x  1/2x^{3} + 3x^{2} + x is positive, then S contains
Out of 15 points in a plane, no three are in a straight line except 8 points which are collinear. How many triangles can be formed by joining them?
Solution : No. of Δs = 15C3  8C3
= 15!/(3!*12!)  (8!/(3!*5!)
= 455  56 = 399
Let A and B be two events such that P(A) = 0.3, P(A∪B) = 0.8, if A and B are independent events, then P(B) is equal to
The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target at least three times is
In two events P(A∪B) = 5/6, P(A) = 5/6, P(B) = 2/3 then A and B are
A group of 10 items has mean 6. If the mean of 4 of these items is 7.5, then the mean of the remaining items is
From (1), x must be greater than 1 (taking + ve sign.)
∴ 1 < x < 2
If the roots of the equation x^{2}+2mx+m^{2}2m+6=0 are equal, then the value of m is
If a line makes angles α,β,γ with the +ve direction of x,y and z axis respectively, then cos^{2}α+cos^{2}β+cos^{2}γ
If the direction cosines of a line are < (1/c), (1/c), (1/c) >, then
The general value of θ which satisfies the equations sinθ=(1/2) and tanθ=(1/√3) is
If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates are
The equation of the circle having its centre on the line x + 2y  3 = 0 and passing through the points of intersection of the circles x^{2}+ y^{2}  2x  4y + 1 = 0 and x^{2} + y^{2}  4x  2y + 4 = 0 is
If a=i+jk, b=i+2j+k and c=i+2jk, the unit vector perpendicular to a+b and b+c is
Let p=(x+4y)a+(2x+y+1)b and q=(y2x+2)a+(2x3y1)b, where a and b are noncoplanar vectors. If 3p=2q, then the value of x and y are
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