If the equations x2 + bx−1 = 0 and x2 + x + b = 0 have a common root different from −1, then $$\left|b\right|$$ is equal to :

The sum of all real values of $$x$$ satisfying the equation $${\left(x^2-5x+5\right)}^{x^2+4x-60}=1$$ is :

The eccentricity of the hyperbola whose length of the latus rectum is equal to $$8$$ and the length of its conjugate axis is equal to half of the distance between its foci, is :

Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation 9e2 − 18e + 5 = 0. If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of this hyperbola, then a2 − b2 is equal to :

A hyperbola whose transverse axis is along the major axis of the conic, {{{x^2}} \over 3} + {{{y^2}} \over 4} = 4 and has vertices at the foci of this conic. If the eccentricity of the hyperbola is {3 \over 2}, then which of the following points does NOT lie on it?

If the line, {{x - 3} \over 2} = {{y + 2} \over { - 1}} = {{z + 4} \over 3}\, lies in the planes, $$lx+my-z=9,$$ then $$l^2+m^2$$ is equal to :

The distance of the point $$(1,-5,9)$$ from the plane $$x-y+z=5$$ measured along the line $$x=y=z$$ is :

The number of distinct real values of $$\lambda$$ for which the lines {{x - 1} \over 1} = {{y - 2} \over 2} = {{z + 3} \over {{\lambda ^2}}} and {{x - 3} \over 1} = {{y - 2} \over {{\lambda ^2}}} = {{z - 1} \over 2} are coplanar is :

ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C($$\lambda$$, 5, $$\mu$$). If the median through A is equally inclined to the coordinate axes, then the value of ($$\lambda$$3 + $$\mu$$3 + 5) is :

The distance of the point (1, − 2, 4) from the plane passing through the point (1, 2, 2) and perpendicular to the planes x − y + 2z = 3 and 2x − 2y + z + 12 = 0, is :

The shortest distance between the lines {x \over 2} = {y \over 2} = {z \over 1} and {{x + 2} \over { - 1}} = {{y - 4} \over 8} = {{z - 5} \over 4} lies in the interval :

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean deviation from the mean of the data is :

If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :

If the $$2^{nd},5^{th}and{9}^{th}$$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :

If the sum of the first ten terms of the series {\left( {1{3 \over 5}} \right)^2} + {\left( {2{2 \over 5}} \right)^2} + {\left( {3{1 \over 5}} \right)^2} + {4^2} + {\left( {4{4 \over 5}} \right)^2} + .......is\,{{16} \over 5}m, then m is equal to :

If A > 0, B > 0 and A + B = {\pi \over 6}, then the minimum value of tanA + tanB is :

Let a1, a2, a3, . . . . . . . , an, . . . . . be in A.P. If a3 + a7 + a11 + a15 = 72, then the sum of its first 17 terms is equal to :

Let z = 1 + ai be a complex number, a > 0, such that z3 is a real number. Then the sum 1 + z + z2 + . . . . .+ z11 is equal to :

Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5 = (0.1) (600)3. Then x3 + y3 + z3is equal to :