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The area of the figure bounded by the curves y = cos x and y = sin x and the ordinates x = 0 and x = π/4 is
The sum of the coefficients in the expansion of (1+x3x^{2})^{3148} is
The equation of circle which passes through the points (3,2) and (2,0) and whose centre lies on the line 2xy3=0 is
The equation of a circle which is ortho gonal to circles x^{2}+y^{2}+3x5y+6=0 and 4x^{2}+4y^{2}28x+29=0 and whose centre lies on the line 3x+4y+1=0 is
The differential equation for the family of curves x^{2} + y^{2}  2ay = 0, where a is an arbitrary constant is
From the top of a building of height h metres, the angle of depression of an object on the ground is α. The distance (in metres) of the object from the foot of the building is
The area of the region bounded by the curves y = x2, x = 1, x = 3 and the xaxis is
The product of the perpendicular, drawn from any point on a hyperbola to its asymptotes is
The differential equation (d^{2}y/dx^{2})^{2/3} = (y + (dy/dx))^{1/2} is of
The sum of first 50 terms of the series cot^{⁻1} 3 + cot^{⁻1} 7 + cot^{⁻1} 13 + cot^{⁻1} 21 + ... is
If B is a nonsingular matrix and A is a square matrix, then det (B^{⁻1} AB) is equal to
If in a square matrix A=[a_{ij}], we find that
a_{ij} = a_{ji} ∀ i,j, then A is a
If the function f(x) = 2x^{3}  9ax^{2} + 12a^{2}x + 1, where a > 0, attains its max. and min. at p and q respectively such that p^{2} = q then a equals
If the normal at the point t on a parabola y = 4ax meet it again at t_{1}, then t_{1} =
The locus of the point of intersection of two normals to the parabola x^{2}=8y, which are at right angles to each other,is
Each line represented by equation (x₁yxy₁)^{2}=a^{2}(x^{2}+y^{2}) is at a distance from (x₁,y₁)
The number of words formed from the letters of the word INDEPENDENCE when vowels are together is
A problem in mathematics is given to 3 students whose chances of solving individually are 1/2, 1/3, and 1/4. The probability that the problem will be solved atleast by one is
The numbers of all words formed from the letters of the word CALCUTTA is
No of letter in the given word is 8 No of repeated word is "C" 2 times, "A" 2 times and "T" 2 times. So the equation is
The mean and variance of a Binomial distribution are 6 and 4. The parameter n is
In a ΔABC , A : B : C = 3 : 5 : 4 . Then a + b + c √2 is equal to
If the product of the roots of the equation mx^{2} + 6x + 2m  1 = 0 is 1, then the value of m is
If the sum of n terms of the series 2^{3} + 4^{3} + 6^{3} + ... ∞ is 3528, then n equals
to n terms is S, then S is equal to n(n + 3)/4
If the parametric equation of a curve is given by x=e^{t} cos t, y=e^{t} sin t, then tangent to the curve at the point t=(π/4) makes the angle with the axis of x
The equidistance point from lines 4x+3y+10=0, 5x12y+26=0 and 7x+24y50=0 is
The entercepts of the plane 2x3y+4z=12 on the coordinate axes are given by
The plane which passes through the point (3, 2, 0) and the line (x  3)/1 = (y  6)/5 = (z  4)/4 is
The general solution of the equation tan2θ.tanθ=1 for n∈I is, θ is equal to
In a triangle A B C , s − a Δ = 1 8 , s − b Δ = 1 12 , s − c Δ = 1 24 , then b =
If x tan 45^{o} cos 60^{o}= sin 60^{o} cot 60^{o}, then x is equal to
If a+b+c=0, a=3, b=5, c=7, then the angle between a and b is
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