If n is an integer between 0 to 21, then find a value of n for which the value of $n!(21-n)!$ is minimum
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If A={1,2,3,4} and B={3,4,5}, then the number of elements in (A∪B)×(A∩B)×(AΔB)
Topic: NIMCET 2021
If a variable takes values 0, 1, 2,…, 50 with frequencies $1,\, {{50}}_{{{C}}_1},{{50}}_{{{C}}_2},\ldots..,{{50}}_…
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If the system of equations $3x-y+4z=3$ , $x+2y-3z=-2$ , $6x+5y+λz=-3 $ has atleast one solution, then $λ=$
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Let $\vec{a}=\hat{i}+\hat{j}$ and $\vec{b}=2\hat{i}-\hat{k}$, the point of intersection of the lines $\vec{r}\times\ve…
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If the vectors $a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k},\hat{i}+\hat{j}+c\hat{k}$ , $(a,b,c\ne1)$ are coplana…
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The lines $px+qy=1$ and $qx+py=1$ are respectively the sides AB, AC of the triangle ABC and the bas…
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The four geometric means between 2 and 64 are
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If θ is acute angle between the pair of lines $x^2-7xy+12y^2=0$, then $\frac{2\cos \theta+3\sin \theta}{4\sin \theta+5\…
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In a triangle ABC, $a\cos ^2\frac{C}{2}+\, c\, \, {\cos }^2\frac{A}{2}=\frac{3b}{2}$ then the sides of the triangle are…
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If $32\, \tan ^8\theta=2\cos ^2\alpha-3\cos \alpha$ and $3\, \cos \, 2\theta=1$, then the general value of $\alpha$ =
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Next 10 Questions — NIMCET 2021
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Suppose $A_1,A_2,\ldots,A_{30}$ are 30 sets each with five elements and $B_1,B_2,B_3,\ldots,B_n$ ar…
Topic: NIMCET 2021
The eccentric angle of the extremities of latus-rectum of the ellipse $\frac{{x}^2}{{a}^2}^{}+\frac{{y}^2}{{b}^2}^{}=1$…
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If α≠β and $\alpha^2=5\alpha-3,\beta^2=5\beta-3$, then the equation whose roots are $\frac{\alpha}{\beta}$&nb…
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The probability that a man who is x years old will die in a year is p. Then, amongst n persons $A_1,A_2,\ldots A_n…
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Angle between $\vec{a}$ and $\vec{b}$ is $120{^{\circ}}$. If $|\vec{b}|=2|\vec{a}|$ and the vectors , $\vec{a}+x\vec{b…
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If a number x is selected at random from natural numbers 1,2,…,100, then the probability for $x+\frac{100}{x}{\gt}…
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If X and Y are two sets, then X∩Y ' ∩ (X∪Y) ' is
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$\int {e}^x(\sinh x+\cosh x)dx$
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If $\vec{e_1}=(1,1,1)$ and $\vec{e_2}=(1,1,-1)$ and $\vec{a}$ and $\vec{b}$ an…
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If P(1,2), Q(4,6), R(5,7) and S(a,b) are the vertices of a parallelogram PQRS, then
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