The sum of the first ten terms of an \( A P \) is four times the
sum of the first five terms, th.... VIDEO
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\( P \)
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\begin{array}{l}
S=1+\frac{1}{(1+3)}(1+2)^{2}+\frac{1}{(1+3+5)}(1+2+3.... 2024-01-22 Suppose, \( \alpha, \beta \) are roots of \( a x^{2}+b x+c=0 \) and \( \gamma, \delta \) are roo.... 2024-01-22 The \( G M \) of two positive number is 6 . Their \( A M \) is \( A \) and \( H M \) is \( H \) .... 2024-01-22 The minimum value of the quantity
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\( (x-3) \ldots .(x-n) \), i.... 2024-01-22 \begin{tabular}{|l|l|l|l|}
\hline & Column \( \mathbf{I} \) & & Column - II \\
\hline I. & \begi.... 2024-01-22 The sixth term of an \( A P \) is equal to 2 . The value of the
common difference of the \( A P .... 2024-01-22 If \( a, b, c \) and \( d \) are four positive real numbers such that
\( a b c d=1 \), the minim.... 2024-01-22 The sum of the first ten terms of an \( A P \) is four times the
sum of the first five terms, th.... 2024-01-22 If the arithmetic progression whose common difference is non-zero, the sum of first \( 3 n \) te.... 2024-01-22 If \( a_{1}, a_{2}, a_{3}, \ldots \) are in \( G P \) with first term \( a \) and common
ratio \.... 2024-01-22 If \( a, b, c \) are in \( A P \) and \( (a+2 b-c)(2 b+c-a)(c+a- \)
b) \( =\lambda a b c \), the.... 2024-01-22 Let \( a_{n} \) be the nth term of an \( A P \). If \( \sum_{r=1}^{100} a_{2 r}=\alpha \) and
\(.... 2024-01-22 If \( a_{1}, a_{2}, a_{3}, a_{4}, a_{5} \) are in HP, then \( a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4.... 2024-01-22 Consider the pattern shown below:
\begin{tabular}{lllll} Row & 1 & 1 & & \\
Row & 2 & 3 & 5 & \\.... 2024-01-22 For any real \( x \), the expression \( 2(k-x)\left[x+\sqrt{x^{2}+k^{2}}\right] \)
can exceed
W).... 2024-01-22 \begin{tabular}{|l|l|l|l|}
\hline & Column -I & & Column - II \\
\hline I. & \begin{tabular}{l} .... 2024-01-22 Number of real solutions of the equation
\( 5+\left|2^{x}-1\right|=2^{x}\left(2^{x}-2\right) \) .... 2024-01-22 If the sides of a right angled triangle from an \( A P \), the
sines of the acute angles are....
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