If for non-zero x, $cf(x)+df\Bigg{(}\frac{1}{x}\Bigg{)}=|\log |x||+3,$ where $c\ne 0$, then $\int ^e_1f(x)dx=$
Previous 10 Questions — 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
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
A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either se…
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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
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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
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
The number of solutions of ${5}^{1+|\sin x|+|\sin x{|}^2+\ldots}=25$ for $x\in(-\mathrm{\pi},\mathrm{\pi})$ is
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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
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…
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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…
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Next 10 Questions — NIMCET 2024
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A critical orthopedic surgery is performed on 3 patients. The probability of recovering
a patient is 0.6. Then the prob…
Topic: NIMCET 2024
The value of $\tan \Bigg{(}\frac{\pi}{4}+\theta\Bigg{)}\tan \Bigg{(}\frac{3\pi}{4}+\theta\Bigg{)}$ is
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If $\sin x=\sin y$ and $\cos x=\cos y$, then the value of x-y is
Topic: NIMCET 2024
For an invertible matrix A, which of the following is not always true:
Topic: NIMCET 2024
For what values of $\lambda$ does the equation $6x^2 - xy + \lambda y^2 = 0$ represents
two perpendicular lines and two…
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A speaks truth in 40% and B in 50% of the cases. The probability that they contradict
each other while narrating some i…
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The two parabolas $y^2 = 4a(x + c)$ and $y^2 = 4bx, a > b > 0$ cannot
have a common normal unless
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A man starts at the origin O and walks a distance of 3 units in the north-
east direction and then walks a distance of …
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Among the given numbers below, the smallest number which will be divided by 9, 10,
15 and 20, leaves the remainders 4, …
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The value of $\sum ^n_{r=1}\frac{{{{}^nP}}_r}{r!}$ is:
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