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The equation of circle of radius \(\sqrt{17}\) unit, with centre on the positive side of \(x\)-axis and through the point \((0,1)\) is

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

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Area in the first quadrant between the ellipses \(x^{2}+2 y^{2}=a^{2}\) and \(2 x^{2}+y^{2}=a^{2}\) is

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

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A straight line through the origin \(O\) meets the parallel lines \(4 x+2 y=9\) and \(2 x+y+6=0\) at \(P\) and \(Q\) respectively. The point \(\mathrm{O}\) divides the segment \(\mathrm{PQ}\) in the ratio

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

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Let each of the equations \(x^{2}+2 x y+a y^{2}=0 \& a x^{2}+2 x y+y^{2}=0\) represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by

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

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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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