Choose the correct answer. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is.

Choose the correct answer. The number of parallelograms that can …

The equation of $2{x^2} + 3{y^2} - 8x - 18y + 35 = k$ represents

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The length of the latus-rectum of the parabola $4 y^2+2 x-20 y+17=0$ is

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If $4\text{x}+3<6\text{x}+7$ then x belongs to the interval:

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If the tangent on the point $(2\sec \phi ,\;3\tan \phi )$ of the hyperbola $\frac{{{x^2}}}{4} - \frac{{{y^2}}}{9} = 1$ is parallel to $3x - y + 4 = 0$, then the value of $\phi$ is ............ $^o$

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If $\alpha=\lim _{x \rightarrow \pi / 4} \frac{\tan ^{3} x-\tan x}{\cos \left(x+\frac{\pi}{4}\right)}$ and $\beta=\lim _{x \rightarrow 0}(\cos x)^{\operatorname{cotx}}$ are the roots of the equation, $a x^{2}+b x-4=0$, then the ordered pair $(\mathrm{a}, \mathrm{b})$ is :

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The equation of the circle which passes through the origin and cuts off intercepts of $2$ units length from negative coordinate axes, is

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If $x$ be real, the least value of ${x^2} - 6x + 10$ is

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If $^n{C_{r - 1}} = 36,{\;^n}{C_r} = 84$ and $^n{C_{r + 1}} = 126$, then the value of $r$ is

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The sum of the series 1² + 2² + 3² + ……….. n² is:

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A straight line $L$ through the point $(3, - 2)$ is inclined at an angle of $60^o$ to the line $\sqrt 3 x + y = 1$ . If $L$ also intersects the $x-$ axis, then the equation of $L$ is

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