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3
​​For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1,\left(\frac{p}{q}\right)^{\frac{p}{q}}=p^{\left(\frac{p}{q}-1\right)}$. Then,$q^{p}=p^{q}$$q^{p}=p^{2 q}...
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4
​Which one of the given options is a possible value of $x$ in the following sequence?\[3,7,15, x, 63,127,255\]$35$$40$$45$$31$
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5
​​​​​On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time $12:05:00$ hours to $12: 55: 00$ ...
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10
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11
​​​​​The smallest positive root of the equation\[x^{5}-5 x^{4}-10 x^{3}+50 x^{2}+9 x-45=0\]lies in the range$0 < x \leq 2$$2 < x \leq 4$$6 \leq x \leq 8$$10 \le...
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15
Concrete of characteristic strength $30 \mathrm{MPa}$ is required. If $40$ specimens of concrete cubes are to be tested, the minimum number of specimens having at least $...
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17
The following figure shows the arrangement of formwork for casting a cantilever $\mathrm{RC}$ beam.The correct sequence of removing the Shores/Props is$\mathrm{S} 1 \righ...
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20
The number of degrees of freedom for a natural open channel flow with a mobile bed is$2$$3$$4$$5$
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25
​​​​​If the number of sides resulting in a closed traverse is increased from three to four, the sum of the interior angles increases by$90^{\circ}$$180^{\circ}$...
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29
The elements that DO NOT increase the strength of structural steel areCarbonManganeseSulphurChlorine
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31
The primary air pollutant(s) is/areSulfur dioxideLeadOzoneSulphuric acid
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35
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36
​​​​​What are the eigenvalues of the matrix $\left[\begin{array}{lll}2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2\end{array}\right]$ ?$1,2,5$$1,3,4$$-5,1,2$$-5,-1,2$
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39
​​​​​The beam shown in the figure is subjected to a uniformly distributed downward load of intensity $q$ between supports $\text{A}$ and $\text{B}$.Considering ...