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Locus of the point, the sum of squares of whose distances from the points (a,0) and (a,0) is equal to 2c^{2} is
If T₂/T₃ in the expansion of (a+b)^{n} and T₃/T₄ in the expansion of (a+b)^{(n+3)} are equal, then n=
The locus of mid point of the chords of the circle x^{2}+y^{2}2x6y10=0 passing through the origin 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
AOB is the positive quadrant of the ellipse , where OA = a, OB = b. The area between the arc AB and the chord AB of the ellipse is
If y=a cos (log x) + b sin (log x) where a,b are parametres, then x^{2}y+xy'
Correct Answer : b
Explanation : y = acos(logx) + bsin(logx)
dy/dx = asin(logx)/x + bsin(logx)/x
xdy/dx = asin(logx) + bsin(logx)
xd^{2}y/dx^{2} + dy/dx = acos(logx)/x  bsin(logx)/x
x^{2}d^{2}y/dx^{2} + xdy/dx = acos(logx)  bsin(logx)
x^{2}d^{2}y/dx^{2} + xdy/dx = y
The function f(x)=x^{3}3x^{2}24x+5 is increasing in the interval
1/(1.2.3.4) + 4/(3.4.5.6) + 9/(5.6.7.8) + 16/(7.8.9.10) + ....... ∞ =
The angle of elevation of the top of a tower from the top and bottom of a building of height 'a' are 30^{o} and 45^{o} respectively. If the tower and the building stand at the same level, the height of the tower is
The curve represented by x = a (cosh θ + sinh θ), y = b (cosh θ − sinh θ) is
The parabolas y^{2} = 4x and x^{2} = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ is
The area of the region bounded by the curves y = x1 and y = 3x is
If cos^{1}p + cos^{1}q+cos^{1}r = π, then p^{2} + q^{2} + r^{2} + 2pqr is equal to
Let cos^{1} p = α, cos^{1} q = β and cos^{1} r = γ
⇒ cosα = p, cosβ = q and cosγ = r
From question, α + β + γ = π
∴ cos (α + β) = cos (π  γ)
or, cosα cosβ  sinα sinβ =  cosγ
or pq  1 − p 2 1 − q 2 = − r
or, pq + r = 1 − p 2 1 − q 2
Squaring, we get p^{2}q^{2} + r^{2} + 2pqr = 1  p^{2}  q^{2} + p^{2}q^{2}
or, p^{2} + q^{2} + r^{2} + 2pqr = 1
The value of α for which the function f(x)=1+αx, α≠0 is the inverse of itself, is
x₁+2x₂+3x₃ = 2x₁+3x₂+x₃ = 3x₁+x₂+2x₃ = 0. This system of equation has
If the traces of the matrices A and B are 20 and 8, then the trace of (A + B)=
A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same capacity is
On the parabola y^{2} = 8 x if one extremity of a focal chord is (1 ∕ 2, − 2) then its other extremity is
How many words can be formed from the letters of the word COMMITTEE?
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
Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is
Three identical dice are rolled. The probability that the same number will appear on each of them is
Total number of ways = 6 × 6 × 6 = 6^{3} Number of favourable ways = 6 ∴ probability of the required event
If two angles of a Δ A B C are 45^{o} and 60^{0}then the ratio of the smallest and the greatest sides are
In a triangle the line joining circumcentre and incentre is parallel to BC, then cosB+cosC=
The value of p for which the difference between the roots of the equation x^{2}+px+8 = 0 is 2, are
If a, b, c be in G.P. and p, q be respectively A.M., between a, b and b, c then
The sum of first n terms of the series (3/1^{2}) + (5/(1^{2} + 2^{2})) + (7/(1^{2} + 2^{2} + 3^{2})) + ... is
If lines 3y+4x=1, y=x+5 and 5y+bx=3 are concurrent, then the value of b is
The length of the sub normal to the parabola y^{2}=4ax at any point is equal to
The smallest radius of the sphere passing thro'(1,0,0),(0,1,0) and (0,0,1) is
Let the sphere be
x^{2} + y^{2} + z^{2} + 2ux + 2vy + 2wz + d' = 0 ...(i)
It passes through the points (1, 0, 0), (0, 1, 0), (0, 0, 1)
∴ 1 + 2y + d' = 0...(ii)
1 + 2v + d' = 0 ...(iii)
1 + 2w + d' = 0 ...(iv)
The d.r. of normal to the plane through (1,0,0), (0,1,0) which makes an angle π/4 with plane x + y = 3 are
The general solution of the equation tan2θ.tanθ=1 for n∈I is, θ is equal to
The position vector of a point which divides the segment joining 2a3b and 3a2b in the ratio 2:3 internally is
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