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 coplanar, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=$
Previous 10 Questions — NIMCET 2021
Nearest first
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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…
Topic: NIMCET 2021
The four geometric means between 2 and 64 are
Topic: NIMCET 2021
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\…
Topic: NIMCET 2021
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…
Topic: NIMCET 2021
If $32\, \tan ^8\theta=2\cos ^2\alpha-3\cos \alpha$ and $3\, \cos \, 2\theta=1$, then the general value of $\alpha$ =
Topic: NIMCET 2021
If $y=\sin ^{-1}(\frac{{x}^2+1}{\sqrt[]{1+3{x}^2+{x}^4}}),\, (x>0),$ then $\frac{dy}{dx}$=
Topic: NIMCET 2021
If $H_1,H_2,\ldots,H_n$ are n harmonic means between a and b $(b\ne a)$;,then $\frac{{{H}}_n+a}{{{H}}_n-a}+\frac{{{H}}_…
Topic: NIMCET 2021
In a triangle, if the sum of two sides is x and their product is y such that (x+z)(x-z)=y, where z is the third side of…
Topic: NIMCET 2021
The value of $\tan 9{^{\circ}}-\tan 27{^{\circ}}-\tan 63{^{\circ}}+\tan 81{^{\circ}}$ is equal to
Topic: NIMCET 2021
If $y={\tan }^{-1}\lgroup{\frac{3x-{x}^3}{1-3{x}^2}}\rgroup\, ,\, \frac{-1}{\sqrt[]{3}}{\lt}x{\lt}\frac{1}{\sqrt[]{3}}$…
Topic: NIMCET 2021
Next 10 Questions — NIMCET 2021
Ascending by ID
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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…
Topic: NIMCET 2021
If the system of equations $3x-y+4z=3$ , $x+2y-3z=-2$ , $6x+5y+λz=-3 $ has atleast one solution, then $λ=$
Topic: NIMCET 2021
If a variable takes values 0, 1, 2,…, 50 with frequencies $1,\, {{50}}_{{{C}}_1},{{50}}_{{{C}}_2},\ldots..,{{50}}_…
Topic: NIMCET 2021
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 n is an integer between 0 to 21, then find a value of n for which the value of $n!(21-n)!$ is minimum
Topic: NIMCET 2021
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…
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The eccentric angle of the extremities of latus-rectum of the ellipse $\frac{{x}^2}{{a}^2}^{}+\frac{{y}^2}{{b}^2}^{}=1$…
Topic: NIMCET 2021
If α≠β and $\alpha^2=5\alpha-3,\beta^2=5\beta-3$, then the equation whose roots are $\frac{\alpha}{\beta}$&nb…
Topic: NIMCET 2021
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…
Topic: NIMCET 2021
Angle between $\vec{a}$ and $\vec{b}$ is $120{^{\circ}}$. If $|\vec{b}|=2|\vec{a}|$ and the vectors , $\vec{a}+x\vec{b…
Topic: NIMCET 2021
