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

1

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

Topic: NIMCET 2024

2

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

3

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

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4

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

5

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

6

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

7

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 card…

Topic: NIMCET 2024

8

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

9

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

10

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