The term independent of x in the expansion of [(√(x/3))+(√3/x^{2})]^{10} is
The coefficient of x^{3} in ((√x^{5}) + (3/√x^{3}))^{6} is
If a < 0 < b then
The centre and radius of the circle with the segment of the line x+y=1 cut of by the coordinate axes as diameter are
If (a+ib)(c+id)(e+if)(g+ih) = A+iB, then (a^{2}+b^{2})(c^{2}+d^{2})(c^{2}+f^{2})(g^{2}+h^{2}) =
The area bounded by two curves y^{2}=4ax and x^{2}=4ay is
If a, b, c are different and then x =
The solution of the differential equation x{y d^{2}y/dx^{2} + (dy/dx)^{2}}=y dy/dx is :
The orthogonal trajectories of the family y^{2}=4ax+4a^{2} is the family :
If siny=x sin (a+y), (dy/dx)=
The differential of sin⁻^{1}[(1x)/(1+x)] w.r.t. √x is equal to
The eccentricity of ellipse 4x^{2} + 9y^{2} = 36 is
The major axis of an ellipse is three times the minor axis, then the eccentricity is
The parametric equations of the hyperbola x^{2}/a^{2}  y^{2}/b^{2} = 1 are
The eccentricity of the conic 9x^{2}  16y^{2} = 144 is
Let f(x) = tan^{1} {φ(x)}, where φ(x)is monotonically increasing for 0 < x < π/2. Then f(x) is
being monotonically increasing
tan⁻^{1}(1/4) + tan⁻^{1}(2/9) is equal to
If A and B are two matrices such that AB = B and BA = A, then A^{2} + B^{2} =
A function f(x) is defined as f (x) = [1 − x^{2}] , − 1 ≤ x ≤ 1 , where [x] denotes the greatest integer not exceeding x. The function f(x) is discontinuous at x = 0 because
A square tank of capacity 250 cubic m has to be dug out. The cost of land is Rs 50 per sq.m. The cost of digging increases with the depth and for the whole tank is 400 (depth)^{2} rupees. The dimensions of the tank for the least total cost are
The slope of the normal at the point (at^{2},2at) of the parabola y^{2}=4ax is
The normals to the parabola y^{2}=4ax from the point (5a,2a) are
If α, β are the roots of the equation x^{2}+ 2x + 4 = 0, then (1/α^{3}) + (1/β^{3}) is equal to
In ΔABC , If a^{2} + b^{2} + c^{2} = 8R^{2} , then the triangle is
In ΔABC , if x = tan then x + y + z in terms of x , y , z only is
The equation 3sin^{2}x + 10cosx  6 = 0 is satisfied, if
If f ″ (x) < 0∀x ∈ (a , b), then f'(x) = 0
Suppose, there are two points x_{1} and x_{2} in (a,b) such that f'(x_{1}) = f'(x_{2}) = 0. By Rolle's theorem applied to f' on [x_{1} , x_{2}], there must then be a c ∈ (x_{1}, x_{2} ) such that f''(c) = 0. This contradicts the given condition f ″ (x) < 0∀x ∈ (a , b) Hence, our assumption is wrong. Therefore, there can be at most one point in (a,b) at which f'(x) is zero.
((1)/(1 x 2)) + ((1/2) x (3)) + ((1/3) x (4)) + ... + ((1)/(n(n + 1))) equals
Sin⁻^{1}(3/5) + tan⁻^{1}(1/7) is equal to
The set A [x:x ∈ R, x^{2}=16 and 2x=6] equals
Points (0,0), (2,1) and (9,2) are vertices of a triangle, then cosB =
Given,
Vertices of a ΔABC are (0,0), (2,1) and (9,2) are vertices of a triangle, then cosB =
From figure,
The roots of the equation x^{3} − 2x^{2 } − 4x + 8 = 0 are
If 2cos^{2}x+3sinx3=0, 0≤x≤180º, then x=
From a fixed point A on the circumference of a circle of radius a, the perpendicular AC is drawn to the tangent at B(a variable point). The maximum area of ΔABC is
(where [.] is the greatest integer function and {.} is the fractional part function)
where [.] denotes the greatest integer function, is equal to
Let R be the real line. Consider the following subsets of the plane RxR.
S={(X,Y):y=x+1 and 0<x<2}, T={(X,Y):xy is an integer}. Which one of the following is true?
If two events A and B are such that P(A^{c}) = 0.3, P(B) = 0.4 and P A ∩ B c = 0.5, then is equal to
Let then the sum is equal to
If l is the length of the intercept made by a common tangent to the circle x^{2} + y^{2} = 16 and the ellipse x^{2}/25 + y^{2}/4 = 1, on the coordinate axes, then 81l^{2} + 3 is equal to
{x} and [x] represent fractional and integral part of x, then is equal to
Consider the equation The parameter 'a' so that the given equation has a solution which satisfies
A bag contains some white and some black balls, all combinations of balls being equally likely. The total number of balls in the bag is 10. If three balls are drawn at random without replacement and all of them are found to be black, the probability that the bag contains 1 white and 9 black balls is
A nonzero vector is parallel to the line of intersection of the plane determined by the vectors and the plane determined by the vectors
A line is drawn from A( − 2, 0) to intersect the curve y^{2} = 4x in P and Q in the first quadrant such that then slope of the line is always
is
The equation b cos x − cos 2x = 2b − 7 possess a solution if
If a = cos 2α + i sin 2α , b = cos 2β + i sin 2β ,
c = cos 2γ + i sin 2γ and d = cos 2δ + i sin 2δ , then
The equation of the tangents drawn from the origin to the circle x^{2} + y^{2} − 2rx − 2hy + h^{2} = 0 , are
If dx can be found in terms of known functions of x then u can be
The number of ways in which we can choose 2 distinct integers from 1 to 100 such that difference between them is at most 10 is
If the chord y = mx + 1 of the circle x^{2} + y^{2} = 1 subtends an angle of measure 45º at the major segment of the circle then the value of m is:
The set of discontinuities of the function f (x) = ( 1/2 − cos2x ) contains the set
In the set R of real numbers the function is defined such that is
is equal to
sin mx is an identify in x , then
The interval to which a may belong so that the function increasing ∀× ∈ R
In a triangle ABC, 3sinA + 4cosB = 6 and 4sinB + 3cosA = 1
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