For an invertible matrix A, which of the following is not always true:

1

If $\sin x=\sin y$ and $\cos x=\cos y$, then the value of x-y is

Topic: NIMCET 2024

2

The value of $\tan \Bigg{(}\frac{\pi}{4}+\theta\Bigg{)}\tan \Bigg{(}\frac{3\pi}{4}+\theta\Bigg{)}$ is

Topic: NIMCET 2024

3

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

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4

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

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5

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

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6

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

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7

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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8

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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9

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

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

1

For what values of $\lambda$ does the equation $6x^2 - xy + \lambda y^2 = 0$ represents two perpendicular lines and two…

Topic: NIMCET 2024

2

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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3

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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4

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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5

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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6

The value of $\sum ^n_{r=1}\frac{{{{}^nP}}_r}{r!}$ is:

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7

Let A and B be two events defined on a sample space $\Omega$. Suppose $A^C$ denotes the complement of A relative to the…

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8

Let Z be the set of all integers, and consider the sets $X=\{(x,y)\colon{x}^2+2{y}^2=3,\, x,y\in Z\}$ and $Y=\{(x,y)\co…

Topic: NIMCET 2024

9

The value of $f(1)$ for $f\Bigg{(}\frac{1-x}{1+x}\Bigg{)}=x+2$ is

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10

Given a set A with median $m_1 = 2$ and set B with median $m_2 = 4$What can we say about the median of the combined set?

Topic: NIMCET 2024