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In the expansion of [7^{ 1 3 } + 11^{ 1 9 }]^{6561}, the number of terms free from radicals is
The approx value of (7.995)^{1}∕^{3}correct to four decimal places is
Two circles x^{2} + y^{2}  2x + 6y + 6 = 0 and x^{2} + y^{2}  5x + 6y + 15 = 0
If z₁ + z₂ = z₁  z₂, then the difference of arguments of z₁ and z₂ is
(1 − ω + ω ^{2 }) (1 − ω^{ 2} + ω^{ 4} ) (1 − ω ^{4} + ω^{ }8 ) (1 − ω ^{8} + ω ^{16}) =
The singular solution of the differential equation y=px+p^{3}, (p=dy/dx) is :
The radius of the circle passing through the foci of the ellipse ((x^{2}/16) + (^{y}2/9) = 1), and having its centre (0,3) is
The equation of the ellipse in the form of ((x^{2}/a^{2}) + (^{y}2/b2) = 1), given the eccentricity to be 2/3 and latus rectum 2/3, is
The tangents to the hyperbola x^{2}  y^{2} = 3 are parallel to the st. line 2x + y + 8 = 0 at the following points
The st. line lx + my + n = 0 touches the hyperbola x^{2}/a^{2} y2/_{b}^{2} = 1 if
If A and B are two square matrices such that B = A⁻^{1} BA, then (A + B)^{2} =
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 number of straight lines that can be formed by joining 20 points of which 4 points are collinear is
If b,c and sinB are given such that ∠B is acute and b<c sinB, then
If k be the perimeter of the Δ A B C then b cos^{2} C/ 2 + c cos^{2} B /2 is equal to
If x^{2}+ax+10 = 0 and x^{2+}bx10=0 have a common rooot,then a^{2}b^{2} is equal to
The range of values of a so that the equation x^{3}  3x + a = 0 has three real and distinct roots is
If (1 p) is a root of quadratic equation x^{2} + px + (1 p) = 0 then its roots are
If a, b, c are in A.P., , mb, c are in G.P.then a, m^{2}b, c are in
Consider the equation 3 . The parameter 'a' so that the given equation has a solution which satisfies
Let f x be an odd function in the interval with a period T, then
Let α , β be any two positive values of x for which 2 cos x ,  cos x  and 1 − 3 cos 2 x are in G.P., then the minimum value of  α − β  is
The range of value of β such that (0, β ) lie on or inside the triangle formed by the lines y + 3x + 2 = 0, 3y − 2x − 5 = 0, 4x + x − 14 = 0 is:
If the line x cos θ + y sin θ = 2 is the equation of a transverse common tangent to the circles
If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C , then :
Let P(3, 2, 6) be a point in space and Q be a point on the line
Then the value of μ for which the vector is parallel to the plane x  4y+3z = 1 is
If a ‸ , b ‸ and c ‸ are three unit vectors, such that a ‸ + b ‸ + c ‸ is also a unit vector and θ 1 , θ 2 and θ 3 are angles between the vectors a ‸ , b ‸ ; b ‸ , c ‸ and c ‸ , a ‸ respectively then among θ 1 , θ 2 and θ 3
The value of the expression
, where ω is an imaginary cube roots of unity, is:
The set of all value of a ∈ R for which the equation 2x^{2} − 2(2a+1)x + a(a1) = 0 has roots α and β satisfying α < a < β is
The tangents drawn from (0, 0) to x^{2} + y^{2} + 2fy + 2gx + c = 0 are perpendicular if (where c = g^{2})
About the equation which of the following statements is correct?
If P is any point lying on the ellipse , whose foci are S and S'. Let ∠ P S S ′ = α and ∠ P S ′ S = β , then:
If in a triangle ABC, CD is the angular bisector of the angle ACB then CD is equal to
Z _{1} , Z _{2} , Z_{ 3}
correspond to the vertices of an equilateral triangle and  Z 1 − 1  =  Z 2 − 1  =  Z 3 − 1  . Then
If the equation cx^{2} + bx  2a = 0 has no roots and then,
If y = tan x tan 2 x tan 3 x then dy /dx has the value equal to
3 videos10 docs54 tests

3 videos10 docs54 tests
