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Mathematics

Algebra

Easy

Question

If x, y, z real and $4 x squared plus 9 y squared plus 16 z squared minus 6 x y minus 12 y z minus 8 z x equals 0$ , then x, y, z are in

A.P.
G.P.
H.P.
none of these

The correct answer is: H.P.

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If x,2y,3z are in A.P. where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is

If x,2y,3z are in A.P. where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is

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If $a squared plus b squared comma a b plus b c$ and $b squared plus c squared$ are in G.P., then a, b, c in

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Let $a subscript 1 comma a subscript 2 comma a subscript 3 comma horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis$ be terms of an A.P. If $fraction numerator a subscript 1 plus a subscript 2 plus horizontal ellipsis horizontal ellipsis a subscript p over denominator a subscript 1 plus a subscript 2 plus horizontal ellipsis horizontal ellipsis a subscript 9 end fraction equals p squared over q squared comma p not equal to q$ then $a subscript 6 over a subscript 21$ equals

Let $a subscript 1 comma a subscript 2 comma a subscript 3 comma horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis$ be terms of an A.P. If $fraction numerator a subscript 1 plus a subscript 2 plus horizontal ellipsis horizontal ellipsis a subscript p over denominator a subscript 1 plus a subscript 2 plus horizontal ellipsis horizontal ellipsis a subscript 9 end fraction equals p squared over q squared comma p not equal to q$ then $a subscript 6 over a subscript 21$ equals

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If the sum and product of the first three terms in AP are 33 and 1155, respectively, then a value of its 11^th term is

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Let the sum of the first n terms of a non- constant AP $a subscript 1 comma a subscript 2 comma a subscript 3 horizontal ellipsis horizontal ellipsis$ be $50 n plus fraction numerator n left parenthesis n minus 7 right parenthesis over denominator 2 end fraction A comma$ where A is a constant, If d is the common difference of this AP, then the ordered pair $open parentheses d comma a subscript 50 close parentheses$ is equal to

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$text If end text a subscript 1 comma a subscript 2 comma a subscript 3 comma horizontal ellipsis.. text are in A.P. such that end text a subscript 1 plus a subscript 7 plus a subscript 16 equals 40 comma text then the sum of the first end text 15 text terms of this end text A text .P. is : end text$

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$text If end text a subscript 1 comma a subscript 2 comma a subscript 3 comma horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis a subscript n text are in A.P. and end text a subscript 1 plus a subscript 4 plus a subscript 7 plus horizontal ellipsis horizontal ellipsis horizontal ellipsis.. plus a subscript 16 equals 114 comma text then end text a subscript 1 plus a subscript 6 plus a subscript 11 plus a subscript 16 text is equal to : end text$

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$T h e space s u m stack space space sum with k equals 1 below and 20 on top k 1 over 2 to the power of k space i s space e q u a l space t o$

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$I f space t h e space s u m space a n d space p r o d u c t space o f space t h e space f i r s t space t h r e e space t e r m s space i n space a n space A. P. space a r e space 33 space a n d space 1155 comma space r e s p e c t i v e l y comma space t h e n space a space v a l u e space o f space i t s space 11 t h space t e r m space i s space colon$

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$text Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, end text text the second row consists of two balls and so on. If 99 more identical balls are added to the total number of end text text balls used in forming the equilateral triangle, then all these balls can be arranged in a square whose each side end text text contains exactly end text 2 text balls less than the number of balls each side of the triangle contains. Then the number of end text text balls used to form the equilateral triangle is: end text$

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Suppose a, b, c, d and 2ac=b+d. Consider the quadratic equations $x squared plus 2 a x plus b equals 0$ and $x squared plus 2 c x plus d equals 0$ .Then

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