A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing at right angle to the ground. Top of the pillar subtends angles $tan^{–1}$ 3 and $tan^{–1} 2$ at A and B respectively. Which of the following choice represents the height of the pillar?
Previous 10 Questions — NIMCET 2023
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A real valued function f is defined as $f(x)=\begin{cases}{-1} & {-2\leq x\leq0} \\ {x-1} & {0\leq x\leq2}\end{…
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Which of the following number is the coefficient of $x^{100}$ in the expansion of $\log _e\Bigg{(}\frac{1+x}{1+{x}^2}\B…
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The range of values of θ in the interval (0, π) such that the points (3,5) and
(sinθ, cosθ) lie on the same side of t…
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If $| x - 6|= | x - 4x | -| x^2- 5x +6 |$ , where x is a real variable
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Let R be reflexive relation on the finite set a having 10 elements and if m is the number of ordered pair in R, then
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$\theta={\cos }^{-1}\Bigg{(}\frac{3}{\sqrt[]{10}}\Bigg{)}$ is the angle between $\vec{a}=\hat{i}-2x\hat{j}+2y\hat{k}$ &…
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Let a, b, c, d be no zero numbers. If the point of intersection of the line 4ax + 2ay + c = 0 & 5bx + 2by + d=0 lie…
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If $\int x\, \sin x\, sec^3x\, dx=\frac{1}{2}\Bigg{[}f(x){se}c^2x+g(x)\Bigg{(}\frac{\tan x}{x}\Bigg{)}\Bigg{]}+C$, then…
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A point P in the first quadrant, lies on $y^2 = 4ax$, a > 0, and keeps a distance of 5a units from its focus. Which …
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The negation of $\sim S\vee(\sim R\wedge S)$ is equivalent to
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Next 10 Questions — NIMCET 2023
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If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the…
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Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ballsis trans…
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Let $f(x)=\frac{x^2-1}{|x|-1}$. Then the value of $lim_{x\to-1} f(x)$ is
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If yellow is called white, white is called black, black is called green, green is called pink, pink is called blue and …
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P, Q, R, S, T, U, V, W are sitting around a round table in the same order, for group discussion at equal distances. The…
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Find a number from the given options which best completes the series:39, 416, 525,…......................., 749, 864
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In the half yearly exam only 60% of the students were passed. Out of these (passed in half-yearly) only 70% students ar…
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Fill the blanks with the most appropriate combination of options.Further, to augment bond market liquidity, corporates …
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Statements:Most teachers are boys.Some boys are students.Conclusion:I. Some students are boys.II. Some teachers are stu…
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