Let C denote the set of all tuples (x,y) which satisfy $x^2 -2^y=0$ where x and y are natural numbers. What is the cardinality of C?

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If the perpendicular bisector of the line segment joining p(1,4) and q(k,3) has yintercept -4, then the possible values…

Topic: NIMCET 2024

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There are 9 bottle labelled 1, 2, 3, ... , 9 and 9 boxes labelled 1, 2, 3,....9. The number of ways one can put these b…

Topic: NIMCET 2024

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The number of distinct real values of $\lambda$ for which the vectors ${\lambda}^2\hat{i}+\hat{j}+\hat{k},\, \hat{i}+{\…

Topic: NIMCET 2024

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The value of m for which volume of the parallelepiped is 4 cubic units whose three edges are represented by a = mi + j …

Topic: NIMCET 2024

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The value of the limit $$\lim _{{x}\rightarrow0}\Bigg{(}\frac{{1}^x+{2}^x+{3}^x+{4}^x}{4}{\Bigg{)}}^{1/x}$$ is

Topic: NIMCET 2024

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The number of one - one functions f: {1,2,3} → {a,b,c,d,e} is

Topic: NIMCET 2024

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If (4, 3) and (12, 5) are the two foci of an ellipse passing through the origin, then the eccentricity of the ellipse is

Topic: NIMCET 2024

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If $x=1+\sqrt[{6}]{2}+\sqrt[{6}]{4}+\sqrt[{6}]{8}+\sqrt[{6}]{16}+\sqrt[{6}]{32}$ then ${\Bigg{(}1+\frac{1}{x}\Bigg…

Topic: NIMCET 2024

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The number of solutions of ${5}^{1+|\sin x|+|\sin x{|}^2+\ldots}=25$ for $x\in(-\mathrm{\pi},\mathrm{\pi})$ is

Topic: NIMCET 2024

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The system of equations $x+2y+2z=5$, $x+2y+3z=6$, $x+2y+\lambda z=\mu$ has infinitely many solutions if 

Topic: NIMCET 2024

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Which of the following is TRUE?A. If $f$ is continuous on $[a,b]$, then $\int ^b_axf(x)\mathrm{d}x=x\int ^b_af(x)\mathr…

Topic: NIMCET 2024

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If F|= 40N (Newtons), |D| = 3m, and $\theta={60^{\circ}}$, then the work done by F actingfrom P to Q is

Topic: NIMCET 2024

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A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either se…

Topic: NIMCET 2024

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Find the cardinality of the set C which is defined as $C={\{x|\, \sin 4x=\frac{1}{2}\, forx\in(-9\pi,3\pi)}\}$.

Topic: NIMCET 2024

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At how many points the following curves intersect $\frac{{y}^2}{9}-\frac{{x}^2}{16}=1$ and $\frac{{x}^2}{4}+\…

Topic: NIMCET 2024

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If for non-zero x, $cf(x)+df\Bigg{(}\frac{1}{x}\Bigg{)}=|\log |x||+3,$ where $c\ne 0$, then $\int ^e_1f(x)dx=$

Topic: NIMCET 2024

10

A critical orthopedic surgery is performed on 3 patients. The probability of recovering a patient is 0.6. Then the prob…

Topic: NIMCET 2024