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The area (in square units) of the region enclosed by the curves y = x^{2} and y = x^{3} is
In the expansion of (y^{1/6 } y^{1/3})^{9} the term independent of y is :
Equation of the diameter of the circle x^{2} + y^{2}  6x + 2y = 0 which passes thro' the origin is
If the two circles 2x^{2} + 2y^{2} 3x + 6y + k = 0 and x^{2} + y^{2}  4x + 10y + 16 = 0 cut orthogonally, then the value of k is
The order and degree of differential equation √(dy/dx)  4 (dy/ dx)  7x = 0 are
√(dy/ dx) 4 (dy/dx) 7x = 0
or √(dy/ dx) = 4 (dy/dx) + 7x
Squaring both side
dy/ dx = [4 (dy/dx ) + 7x]^{2}
or dy dx = 16 ( dy/dx )^{2} + 49x^{2} + 56 dy/ dx x
∴ order = 1
degree = 2
If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (3) is equal to
The length of the shadow of a rod inclined at 10^{o} to the vertical towards the sun is 2.05 metres when the elevation of the sun is 38^{o}.The length of the rod is
The area of the region bounded by the curve y = x  x^{2} between x = 0 and x = 1 is
The product of the perpendicular, drawn from any point on a hyperbola to its asymptotes is
The sum of first 50 terms of the series cot^{⁻1}3 + cot^{⁻1} 7 + cot^{⁻1} 13 + cot^{⁻1} 21 + ... is
The area bounded by the curve x = at^{2}, y = 2at and the Xaxis is 1 ≤ t ≤ 3 is
If A and B are two matrices such that AB = B and BA = A, then A^{2} + B^{2} is equal to
if A is a 3 x 3 matrix and B is its adjoint matrix. If ∣B∣ = 64, then ∣A∣ =
The strength of a beam varies as the product of its breadth b and square of its depth d. A beam cut out of a circular log of radius r would be strong when
The pole of the line lx+my+n=0 w.r.t. the parabloa y^{2} =4ax
Equation x^{2}+7xy+3y^{2}+8x+14y+λ=0 represents a pair of straight lines, value of λ is
y^{2} = 5x + 4y + 1
or y^{2}  4y = 5x + 1
or y^{2}  2.2.y + (2)^{2}  (2)^{2} = 5x + 1
or (y  2)^{2} = 5x + 5
or (y  2)^{2} = 5(x + 1)
Length of the latus rectum = 5
How many total words can be formed from the letters of the word INSURANCE in which vowels are always together?
A committee consists of 9 experts from three institutions A, B and C, of which 2 are from A, 3 from B and 4 from C. If three experts resign, then the probability that they belong to different institutions is
A single letter is selected at random from the word "PROBABILITY". The probability that it is a vowel is
If the area of a Δ A B C be λ then a^{2} sin 2B + b^{2} sin 2A is equal to
In a Δ A B C , a = 1 and the perimeter is six times the AM of the sines of the angles. The measure of ∠ A is
If α, β are the roots of the equation x^{2} 2x + 2 = 0, then the value of α^{2} + β^{2} is
The sum of an infinite G.P. is 3. The sum of the series formed by squaring its terms is also 3. The series is
The 5th term of a G.P. is 2, then the product of its first 9 term is
If f : R → R is given as f (x) = x and A = {x ∈ R : x > o}, then f^{⁻1}(A) =
If f (x) = {2x  3, x ≤ 2} {x, x > 2} then f (1) is equal to
The equation line passing through the point P(1,2) whose portion cut by axes is bisected at P, is
The equation of the common tangent to the curves y^{2}=8x and xy=1 is :
The radius of the circle in which the sphere x^{2} + y^{2} + z^{2} + 2x  2y  4z  19 = 0 is cut by the plane x + 2y + 2z + 7 = 0, is
The acute angle between the planes 2xy+z=6 and x+y+2z=3 is
If 0≤x≤π and 81^{sin2x} + 81 ^{cos2x} = 30, then x is equal to
If 1 + sin x + sin ^{2} x + … ∞ = 4 + 2 √ 3 , 0 < x < π , x ≠ π/2 then x =
The value of b such that the scalar product of the vector î+ĵ+k̂ with the unit vector parallel to the sum of the vectors 2î + 4ĵ  5k̂ and bî+ 2ĵ + 3k̂ is one is
Parallel vector =(2+b)i+6j−2k
Unit vector = (2+b)i+6j−2k / (b^{2}+4b+44)^{1/2}
According to the question,
1 = (2+b)+6−2/b^{2}+4b+44
⇒b^{2}+4b+44=b^{2}+12b+36
⇒8b=8⇒b=1
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