The 10th term of the expansion of (x1)^{11} (in decreasing powers of x) is
The term independent of x in the expansion of ((x^{2})  (1/3x))^{9} is equal to
x=7 touches the circle x^{2} + y^{2}  4x  6y  12 = 0, then the coordinates of the point of contact are
If in the expansion of ((x^{4})  (1/x^{3}))^{15}, x^{17} occurs in the rth term, then
x^{2} + y^{2} + 2(2K+3)x  2Ky +(2K+3)^{2} + K^{2}  r^{2} = 0 represents the family of circles with centres on the line
The solution of the equation (1+x^{2})(1+y)dy+(1+x)(1+y^{2})dx=0 is
The differential equation of family of curves y=a cos(x+b) is
If z 1 and z 2 are two nonzero complex numbers such that z_{1} + z_{2} = z_{1} + z_{2} , then Arg z_{1 } − Arg z_{2} is
The differential of sin⁻^{1}[(1x)/(1+x)] w.r.t. √x is equal to
Let u = sin^{1}(1 – x)/(1 + x)
v = √x
Differentiate w.r.t.x
du/dx = [1/√(1 – (1 – x)^{2}/(1 + x)^{2} ][d/dx (1 – x)/(1 + x)]
= (1+ x)/√((1 + x)^{2} – (1 – x)^{2}) [ (1 + x) ×1 – (1x)]/(1 + x)^{2}
= (1/√4x)×[ 1 – x – 1 + x]/(1 + x)
= 2/√(4x)(1 + x)
= 1/√x(1 + x)
dv/dx = 1/2√x
du/dv = (du/dx)/(dv/dx)
= 2/(1 + x)
The function f(x)=x is defined on [1,1]. It does not satisfy the Rolle's theorem because
In an ellipse the distance between the foci is 6 and it's minor axis is 8. Then its eccentricity is
If S′ and S are the foci of the ellipse (x^{2}/a^{2})+(y^{2}/b^{2})=1 and P(x,y) be a point on it, then the value of SP + S′P is
If e and e ′ are the eccentricities of the hyperbola x^{2} ∕ a^{2} − y^{2} ∕ b^{2} = 1 and its conjugate hyperbola, the value of 1 ∕ e^{2} + 1 ∕ e′^{2} is
Sin (sin⁻^{1}1/2 + cos⁻^{1}1/2) equals
The equation of circle which passes through (4,5) and whose centre is (2,2) is
If the function f (x) = increases for all x, then
Since the function f(x) increases for all x, therefore,
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 A is a square matrix such that A^{2} = I, then A⁻^{1} is equal to
If the parabola y^{2}=4ax passes thro' the point (1,2), then the tangent at this point is
Since the parabola y2=4ax passes through the point (1,−2),
∴(−2)2=4a(I)⇒a=1
Equation of tangent to the parabola at (1,−2)
yy1=2a(x+x1) or
y(−2)=2(1)(x+1) or x+y+1=0
The line xy+2=0 touches the parabola y^{2}=8x at the point
The number of 7 digit numbers which can be formed using the digits 1, 2, 3, 2, 3, 3, 4 is
There are 7 digits 1, 2, 3, 2, 3, 3, 4 in which 2 occurs 2 times and 3 occurs 3 times
Number of 7 digit numbers
How many words are formed from the letters of the word EAMCET so that two vowels are never together?
Reqd ways =
The probability of getting a total of 10 in a single throw of two dice is
A fair dice is tossed repeatedly until six shows up 3 times. The probability that exactly 5 tosses are needed is
The probability that a radar will detect an object is p. The probability that it will be detected in n cycles is
In an equilateral triangle, (circumradius) : (inradius) : (exradius) is equal to
The exradius =
If the side of a triangle are 13, 14, 15, then the radius of the incircle is
Let α, β be the roots of the quadratic equation x^{2} + px + p^{3} = 0. If (α, β) is a pt. on the parabola y^{2} = x, then the roots of the qudratic equation are
The absiccae of the points of the curve y = x^{3} in the interval [2, 2], when the slope of the tangent can be obtained by mean value theorem for the interval [2, 2] are
Given that equation of curve y = x^{3} = f (x)
If a, b, c are distinct +ve real numbers and a^{2} + b^{2} + c^{2} = 1 then ab + bc + ca is
If the roots of the equation x^{3}  12x^{2} + 39x  28 = 0 are in A.P., then their common difference will be
The function f (x) = log ((1 + x)/(1  x)) satisfies the equation
If A = [(x,y) : x^{2} + y^{2} = 25] and B = [(x,y) : x^{2} + 9y^{2} = 144] and A ∩ B contains
The equation of bisectors between the lines 3x+4y7=0 and 12x+5y+17=0 are
The roots of the equation x^{4}  4x^{3 } + 9x^{2} − 12x + 18 = 0 are____
The sides AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices is
If the curves intersect each other at right angles, then
Let the algebraic sum of the perpendicular distances from (3, 0), (0, 3) and (2, 2) to a variable line is zero, then the line passes through a fixed point whose coordinates are
Let d_{1} , d_{2} , d_{3} , … …, d_{k} be all the divisors of a positive integer n including 1 and n.
Suppose d_{1} , d_{2} , d_{3} + … … + d_{k} = 72 , then the
value of is
The equation f(x) = 0 has eight distinct real solution f also satisfy f(4+x) = f(4x). The sum of all the eight solution of f(x) = 0 is
In a triangle X Y Z , ∠ Z = are the roots of the equation ax^{2} + bx + c = 0, a ≠ 0 then
If , then
In triangle ABC, line joining circumcentre and incentre is parallel to side AC, then cos A + cos C is equal to
The system of confocal conics
being an arbitary constant
Two mutually perpendicular tangents of the parabola y^{2} = 4ax meet the axis in P_{1} and P_{2}. If S is the focus then equals
If a line segment AM = 'a' moves in the plane XOY remaining parallel to OX so that the left end point A slides along the circle x^{2} + y^{2} = a^{2}, the locus of M is
Let P (a secθ , b tan θ) and Q (a sec φ , b tan φ) where θ + φ = π/2 , be two points on the hyperbola x^{2} ∕ a^{2} − y^{2} ∕ b^{2} = 1 . If (h, k) is the point of intersection of normals at P and Q, then k is equal to
Let g x = ;0 < x < 2, m and n are integers, m ≠0, n > 0 and let p be the left hand derivative of  x  1  at x = 1. then
The locus of the orthocentre of the triangle formed by the lines
(1 + p)x  py + p(1 + p) = 0,
(1 + q)x  qy + q(1 + q) = 0,
and y = 0, where p ≠ q , is
Let x be a positive real number not equal to 1. In each of the following diagrams, the shaded region does not include its boundary. Which of these regions represents the set {x,y log_{x} log_{x}y^{2} > 0} ?
The set of discontinuities of the function f (x) = ( 1/2 − cos2x) contains the set
The value of is
In a triangle ABC, tan C < 0. Then
Two functions f and g have first and second derivatives at x = 0 and satisfy the relations,
The differential equation
Let x_{0} = 2007 and let Then
If z_{1} = a + ib and z_{2} = c + id are complex number such that z_{1} = z_{2} = 1 and Re = 0, then the pair of complex numbers w_{1} = a + ic and w_{2} = b + id satisfies :
Let A and B be two square matrices of same order that satisfy A + B = 2B^{⊤} and 3A + 2B = l then which of the following statements is true?
There exist a triangle ABC satisfying the conditions,
If P is any point lying on the ellipse whose foci are S and S'. Let ∠ PSS ′ = α and ∠ PS′S = β , then:
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