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From a point \((d, 0)\) three normals are drawn to the parabola \(y^{2}=x\) then

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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Two tangents to the circle \(x^{2}+y^{2}=4\) at the points \(A\) and \(B\) meet at \(M(-4,0)\). The area of the quadrilateral \(M A O B\), where \(\mathrm{O}\) is the origin is

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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A ray of light along \(x+\sqrt{3 y}=\sqrt{3}\) gets reflected upon reaching \(x\)-axis, the equation of the reflected ray is

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(a>0, b>0\) then the maximum area of the parallelogram whose three vertices are \(O(0,0) . A(a \cos \theta, b \sin \theta)\) and \(\mathrm{B}(\mathrm{a} \cos \theta,-\mathrm{b} \sin \theta)\) is

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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A moving line intersects the lines \(x+y=0\) and \(x-y=0\) at the points \(A, B\) respectively such that the area of the triangle with vertices \((0,0), A \& B\) has a constant area \(C\). The locus of the mid-point \(A B\) is given by the equation

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(A\) be the point \((0,4)\) and \(B\) be a moving point on \(x\)-axis. Let \(M\) be the midpoint of \(A B\) and let the perpendicular bisector of \(A B\) meets the \(y\)-axis at \(R\). The locus of the midpoint \(P\) of \(M R\) is

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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3 answers

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 \(\mathrm{A}\) wins the game if A begins?

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(S_{n}=\cot ^{-1} 2+\cot ^{-1} 8+\cot ^{-1} 18+\cot ^{-1} 32+\ldots \ldots .\) to \(n^{\text {th }}\) term. Then \(\lim _{n \rightarrow \infty} S_{n}\) is

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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1 answer

The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of exactly two succsses is

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(a_{n}(>0)\) be the \(n^{\text {th }}\) term of a G.P. then \(\left|\begin{array}{ccc}\log a_{n} & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8}\end{array}\right|\) is equal to

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(T \& U\) be the set of all orthogonal matrices of order 3 over \(R \&\) the set of all non-singular matrices of order 3 over R respectively Let \(A=\{-1,0,1\}\), then

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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2 answers

Let \(A, B, C\) be three non-void subsets of set \(S\). Let \((A \cap C) \cup\left(B \cap C^{\prime}\right)=\phi\) where \(C^{\prime}\) denote the complement of set \(C\) in S. Then

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(M\) is a \(3 \times 3\) matrix such that \((012) M=(100),(345) M=(010)\), then \((678) M\) is equal to

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(A\) and \(B\) be two non-singular skew symmetric matrices such that \(A B=B A\), then \(A^{2} B^{2}\left(A^{\top} B\right)^{-1}\left(A B^{-1}\right)^{\top}\) is equal to

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \text { cost } & \sin t \\ 0 & -\sin t & \cos t\end{array}\right)\) et \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) be the roots of \(\operatorname{det}\left(A-\lambda I_{3}\right)=0\), where \(I_{3}\) denotes the identity matrix. If \(\lambda_{1}+\lambda_{2}+\lambda_{3}=\sqrt{2}+1\), then the set f possible values of \(t,-\pi \leq t<\pi\) is

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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For \(x \in R, x \neq-1\), if \((1+x)^{2016}+x(1+x)^{2015}+x^{2}(1+x)^{2014}+\ldots \ldots+x^{2016}=\sum_{i=0}^{2016} a_{i} \cdot x^{i}\), then \(a_{17}\) is equal to

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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The digit in the unit's place of the number \(1 !+2 !+3 !+\ldots \ldots . .+99 !\) is

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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What is the number of ways in which an examiner can assign 10 marks to 4 questions, giving not less than 2 marks to any questions?

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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Five letter words, having distinct letters, are to be constructed using the letters of the word 'EQUATION' so that each word contains exactly three vowels and two consonants. How many of them have all the vowels together?

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(|z|=1\) and \(z \neq \pm 1\), then all the points representing \(\frac{z}{1-z^{2}}\) lie on;

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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