Recent questions in Sets, relations and functions

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The locus of the centre of the circles which touch both the circles \(x^{2}+y^{2}=a^{2}\) and \(x^{2}+y^{2}=4 a x\) externally is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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The equation \(r \cos \left(\theta-\frac{\pi}{3}\right)=2\) represents

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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The differential equation of the family of curves \(y=e^{x}(A \cos x+B \sin x)\) where \(A, B\) are arbitrary constants is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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\(\cos (2 x+7)=a(2-\sin x)\) can have a real solution for

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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A rifleman is firing at a distant target and has only \(10 \%\) chance of hitting it. The least number of rounds he must fire to have more than \(50 \%\) chance of hitting it at least once, is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Four persons A, B, C and D throw an unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the probability that A wins if A begins ?

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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The unit vector in ZOX plane, making angles \(45^{\circ}\) and \(60^{\circ}\) respectively with \(\vec{\alpha}=2 \hat{i}+2 \hat{j}-\hat{k}\) and \(\vec{\beta}=\hat{j}-\hat{k}\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let the relation \(\rho\) be defined on \(\mathbb{R}\) by a \(\rho b\) holds if and only if \(a-b\) is zero or irrational, then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(f: S \rightarrow \mathbb{R}\) where \(S\) is the set of all non-singular matrices of order 2 over \(\mathbb{R}\) and \(f\left[\begin{array}{ll}\left(\begin{array}{ll}0 & b \\ c & d\end{array}\right)\end{array}\right]=a d-b c\), then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(\left|\begin{array}{ccc}a^{2} & b c & c^{2}+a c \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right|=k a^{2} b^{2} c^{2}\), then \(k=\)

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)\) be a \(2 \times 2\) real matrix with \(\operatorname{det} A=1\). If the equation \(\operatorname{det}\left(A-\lambda I_{2}\right)=0\) has imaginary roots \(\left(I_{2}\right.\) be the Identity matrix of order 2), then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(A=\left(\begin{array}{ccc}12 & 24 & 5 \\ x & 6 & 2 \\ -1 & -2 & 3\end{array}\right) .\) The value of \(x\) for which the matrix \(A\) is not invertible is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(A=\left(\begin{array}{ccc}3-t & 1 & 0 \\ -1 & 3-t & 1 \\ 0 & -1 & 0\end{array}\right)\) and \(\operatorname{det} A=5\), then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(c_{0}, c_{1}, c_{2}, \ldots \ldots c_{15}\) are the Binomial co-efficients in the expansion of \((1+x)^{15}\), then the value of \(\frac{c_{1}}{c_{0}}+2 \frac{c_{2}}{c_{1}}+3 \frac{c_{3}}{c_{2}}+\cdots \cdots+15 \frac{c_{15}}{c_{14}}\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(\mathrm{I}(\mathrm{n})=\mathrm{n}^{\mathrm{n}}, \mathrm{J}(\mathrm{n})=1.3 .5 \ldots \ldots(2 \mathrm{n}-1)\) for all \((\mathrm{n}>1), \mathrm{n} \in \mathrm{N}\), then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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If the total number of m-element subsets of the set \(A=\left\{a_{1}, a_{2}, \ldots . a_{n}\right\}\) is \(k\) times the number of \(m\) element subsets containing \(a_{4}\), then \(n\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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In a 12 storied building, 3 persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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The expression \(a x^{2}+b x+c(a, b\) and \(c\) are real \()\) has the same sign as that of a for all \(x\) if

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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The equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) represents a circle of radius

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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The number of complex numbers \(p\) such that \(|p|=1\) and imaginary part of \(p^{4}\) is 0 , is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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