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For the following questions answer them individually
The term independent of $$x$$ in the expansion of is $$\left(3x^{3} - \frac{1}{2x^{4}}\right)^{7}$$
A square matrix A is called an orthogonal matrix if A satisfies
A is a $$3\times3$$ matrix and B is its adjoint matrix. If the determinant of B is 64, then the
determinant of A is
$$\lim_{x \rightarrow \infty} (\sqrt{x^{2} + x + 1} - \sqrt{x^{2} + 1}) = $$
If $$3x^{2} + 2xy + y^{2} = 6$$, then $$\frac{dy}{dx}$$ at (-1, 2) is
A right angled triangle is to be constructed such that the sum of lengths of perpendicular sides can't be greater than 24cm and the area is to be maximum. Then the length of hypotenuse (in cm) is
The diagonals of a trapezium PQRS interect at the point A. If the ratio PA : PR is 3 : 7, then the ratio of lengths of its parallel sides is
Two circles have radii 13cm and 29cm, and the distance between their centres is 15 cm, then the number of common tangents that can be drawn to the two circles is
If the points A(3, 2) ; B(-3, 2) and C(0, h) form the verticies of an equilateral triangle, then one value of h is
The distance of point $$(a, b)$$ to the line $$\alpha x + \beta y + \gamma = 0$$ is
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