If m, n are any two odd positive integer with n < m, then the largest positive integers which divides all the numbers of the type m^2 – n^2 is:

If m, n are any two odd positive integer with n < m, then the lar…

Let $b_1, b_2,......, b_n$ be a geometric sequence such that $b_1 + b_2 = 1$ and $\sum\limits_{k = 1}^\infty {{b_k} = 2} $ Given that $b_2 < 0$ , then the value of $b_1$ is

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If the equation $\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0$ has real solutions for $\theta,$ then $\lambda$ lies in the interval

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The equation of a straight line passing through $(3,2)$ and cutting an intercept of $2\,units$ between the lines $3x + 4y = 11$ and $3x + 4y = 1$ is :-

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The equation of the circle passing through the point $( - 1,\; - 3)$ and touching the line $4x + 3y - 12 = 0$ at the point $(3, 0)$ is

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Choose the correct answer. A plane is parallel to yz-plane so it is perpendicular to:

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If $(-3,2)$ lies on the circle $x^2+y^2+2 g x+2 f y+c=0$ which is concentric with the circle $x^2+y^2+6 x+8 y-5=0$, then $\mathrm{c}=$

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For positive integers ${n_1},{n_2}$the value of the expression ${(1 + i)^{{n_1}}} + {(1 + {i^3})^{{n_1}}} + {(1 + {i^5})^{{n_2}}} + {(1 + {i^7})^{{n_2}}}$where $i = \sqrt { - 1} $ is a real number if and only if

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The number of triangles that can be formed by choosing the vertices from a set of $12$ points, seven of which lie on the same straight line, is

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A parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed is

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Let $\alpha $ and $\beta $ be two roots of the equation $x^2 + 2x + 2 = 0$ , then is equal to ${\alpha ^{15}} + {\beta ^{15}}$ is equal to

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