| 2023-07-03 | Sides of a triangle \( A B C ; a, b, c \) are in G.P. If \( r \) be the common ratio of this o... |
| 2023-07-03 | Let \( r_{1}, r_{2}, r_{3}, r_{4} \) be the roots of the equation, \( x^{4}-9 x^{3}+a x^{2} \) \... |
| 2023-07-03 | If \( a, b, c, d \in R^{+} \)and \( a, b, c, d \) are in H.P., then
(a) \( a+db+c \)
(b) \( a+bc... |
| 2023-07-03 | If \( a_{1} a_{2} a_{3} \ldots a_{n} \) are in H. P. then \( a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4}... |
| 2023-07-03 | Let \( t_{r}=2^{r / 2}+2^{-r / 2} \). Then \( \sum_{r=1}^{10} t_{r}^{2} \) is equal to
(a) \( \f... |
| 2023-07-03 | If \( 1^{2}+2^{2}+3^{2}+\ldots+2003^{2}=(2003) \) (4007) (334) and (1)
\( (2003)+(2)(2002)+(3)(2... |
| 2023-07-03 | If \( x_{1}, x_{2}, \ldots . x_{20} \) are in H.P. and \( x_{1}, 2, x_{20} \) are in G.P.. then ... |
| 2023-07-03 | In the given square, a diagonal is drawn and parallel line segments joining points on the adjace... |
| 2023-07-03 | The sum of the series \( \frac{x}{1-x^{2}}+\frac{x^{2}}{1-x^{4}}+\frac{x^{4}}{1-x^{8}}+\cdots \)... |
| 2023-07-03 | If \( \sum_{r=1}^{n} r^{4}=I(n) \) then \( \sum_{r=1}^{n}(2 r-1)^{4} \) is equal to
- (a) \( I(2... |
| 2023-07-03 | Greatest integer by which \( 1+\sum_{r=1}^{30} r \times r \) ! is divisible is
(a) Composite num... |
| 2023-07-03 | If the ratio of A.M. between two positive real numbers \( a \) and \( b \) to their H.M. is \( m... |
| 2023-07-03 | If \( A_{1}, A_{2} ; G_{1}, G_{2} \) and \( H_{1}, H_{2} \) be two A.M.s, G.M.s and H.M.s betwee... |
| 2023-07-03 | - (a) 1 (b) -1 - (c) 0 (d) None of these |
| 2023-07-03 | If the sum of first \( p \) terms, first \( q \) terms and first \( r \) terms of an A.P. be \( ... |
| 2023-07-03 | If \( a, b, c \) are in A.P. and \( |a|,|b|,|c|1 \), and
\[
\begin{array}{l}
x=1+a+a^{2}+\ldots ... |
| 2023-07-03 | if the sum of first p,q,r terms of an AP are \( a, b, c \) respectively then \( \frac{a}{p}(q-r)... |
| 2023-07-03 | If \( x, y, z \) are positive then the minimum value of \( x^{\log y-\log z}+y^{\log z-\log x}+z... |
| 2023-07-03 | If \( H \) be the \( H . M \). between \( a \& b \), then
(a) \( (H-2 a)(H-2 b)=H^{2} \)
(b) \( ... |
| 2023-07-03 | If \( a, b, c \) are in A.P. and \( x, y, z \) are in G.P., then find the value of \( x^{b-c} \c... |
| 2023-07-03 | The sum of the series \( 1 \cdot 2 \cdot 3+2 \cdot 3 \cdot 4+3 \cdot 4 \cdot 5+\ldots . \). to \... |
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