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Recent questions tagged goclasses2024_wq1
4
votes
3
answers
1
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 8
Let $k$ be some integer and it is given that $a \equiv b(\bmod n)$ then which of the following(s) is/are ALWAYS true? More than one option can be true. $a \equiv b-3 n(\bmod n)$ $a \equiv b+k(\bmod n)$ $a+k \equiv b+k(\bmod n)$ $a+5 n \equiv b-3 n(\bmod n)$
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3
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2
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2
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 9
Which of the following(s) ALWAYS hold given that $a \equiv b(\bmod n)$ is true for some integers $a, b$ and $n.$ More than one option can be true. $a \bmod n=b \bmod n$ $n \mid(a-b)$ $n \mid a$ $n \mid b$
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1
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2
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3
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 10
Which of the following options is/are TRUE? $43 \equiv-2(\bmod 5)$ $5 \equiv-7(\bmod 3)$ $-10 \equiv-25(\bmod 7)$ $8 \equiv-8(\bmod 5)$
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8
votes
5
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4
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 1
Let $\text{S} =\displaystyle \sum_{i=1}^n f(x_i), \text{A}=\displaystyle\sum_{i=1}^{a} f(x_i)$ and $\text{B}=\displaystyle \sum_{i=a}^n f(x_i)$ ... $\text{S}=\displaystyle \sum_{i=1}^{a-1} f(x_i)+ \text{B}$ $\text{S = A + B}-f(x_a)$
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6
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2
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5
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 2
Evaluate: $1+(1+b)r+(1+b+b^2)r^2+\dots$ to infinite terms for $|br|< 1$. $\frac{1}{(1-br)(1-r)}$ $\frac{1}{(1-r)(1-b)}$ $\frac{1}{(1-b)(b-r)}$ None of these
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5
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1
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6
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 3
Evaluate $1+2x+3x^2+4x^3+\dots$ upto infinity, where $|x|<1$. $\frac{1}{(1-x)^2}$ $\frac{x}{(1-x)^2}$ $\frac{x^2}{(1-x)^2}$ $1-\frac{1}{(1-x)^2}$
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4
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2
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7
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 4
Find the sum of first $24$ terms of the $\text{A.P.}\;a_1,\;a_2,\;a_3,\;\dots$ if it is known that $a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225$
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7
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1
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8
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 5
If $\text{S}$ is the sum to infinity of a $\text{G.P.}$ whose first term is $'a'$, then the sum of the first $n$ terms is $\text{S}\left(1-\dfrac{a}{\text{S}}\right)^n$ ... $\text{S}\left[1-\left(1-\dfrac{\text{S}}{a}\right)^n\right]$
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9
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2
answers
9
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 7
If the sum of $p$ terms of an $\text{A.P.}$ is $q$ and the sum of $q$ terms is $p$, then the sum of $p+q$ terms is _________. $0$ $p-q$ $p+q$ $-(p+q)$
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5
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2
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10
GO Classes Weekly Quiz 1 | Fundamental Course | Question: 6
If the sum of an infinitely decreasing $\text{GP}$ is $3,$ and the sum of the squares of its terms is $9/2,$ the sum of the cubes of the terms is _________ $\frac{105}{13}$ $\frac{108}{13}$ $\frac{729}{8}$ None of these
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