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$\frac{1}{\log_{2}100} – \frac{1}{\log_{4}100} + \frac{1}{\log_{5}100} – \frac{1}{\log_{10}100} + \frac{1}{\log_{20}100} – \frac{1}{\log_{25}100} + \frac{1}{\log_{50}100}...
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There are two drums, each containing a mixture of paints $\text{A}$ and $\text{B}$. In drum $1, \text{A}$ and $\text{B}$ are in the ratio $18: 7$. The mixtures from drums...
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On a long stretch of east-west road, $\text{A}$ and $\text{B}$ are two points such that $\text{B}$ is $350$ km west of $\text{A}$. One car starts from $\text{A}$ and anot...
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A shopkeeper sells two tables, each procured at cost price $p,$ to Amal and Asim at a profit of $20\%$ and at a loss of $20\%$, respectively. Amal sells his table to Bima...
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John gets Rs $57$ per hour of regular work and Rs $114$ per hour of overtime work. He works altogether $172$ hours and his income from overtime hours is $15\%$ of his inc...
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If $\log _{e}x+\log _{e}(1+x)=0,$ then:$x^{2}+x-1=0$$x^{2}+x+1=0$$x^{2}+x-e=0$$x^{2}+x+e=0$
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In $2010$, a library contained a total of $11500$ books in two categories -fiction and nonfiction. In $2015$, the library contained a total of $12760$ books in these two ...
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The strength of a salt solution is $p\%$ if $100$ ml of the solution contains $p$ grams of salt. Each of three vessels $\text{A, B, C}$ contains $500$ ml of salt solutio...
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What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer?$8$$12$$16$$6$
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In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is e...
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In an examination, the score of $\text{A}$ was $10\%$ less than that of $\text{B}$, the score of $\text{B}$ was $25\%$ more than that of $\text{C}$, and the score of $\te...
1 1 vote
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$5\%$ income of $A$ is equal to $15\%$ income of $B$ and $10\%$ income of $B$ is equal to $20\%$ income of $C$. If income of $C$ is ₹ $2000$, then total income of $A, B$ ...
1 1 vote
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A conical tent is to accommodate $10$ persons. Each person must have $6m^{2}$ space to sit and $30m^{3}$ of air to breath. What will be height of cone?$37.5$ m$150$ m$75$...
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What is the area of a semicircle with a diameter of $16$ inches?$32 \pi$ square inches$64 \pi$ square inches$128 \pi$ square inches$256 \pi$ square inches