Answers by deepak01

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If \({ }^{n} C_{r-1}=36,{ }^{n} C_{r}=84\) and \({ }^{n} C_{r+1}=126\) then the value of \({ }^{n} C_{8}\) is

answered Dec 20, 2021 in Sets, relations and functions

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If \(\alpha\) and \(\beta\) are roots of \(a x^{2}+b x+c=0\) then the equation whose roots are \(\alpha^{2}\) and \(\beta^{2}\) is

answered Dec 20, 2021 in Sets, relations and functions

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The sum of \(n\) terms of the following series; \(1^{3}+3^{3}+5^{3}+7^{3}+\ldots .\) is

answered Dec 20, 2021 in Sets, relations and functions

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If the matrix \(A=\left(\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 2 & 0 & 2\end{array}\right)\), then \(A^{n}=\left(\begin{array}{lll}a & 0 & 0 \\ 0 & a & 0 \\ b & 0 & a\end{array}\right), n \in N\) where

answered Dec 20, 2021 in Sets, relations and functions

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The letters of the word COCHIN are permuted and all permutation are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

answered Dec 20, 2021 in Sets, relations and functions

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The points of the ellipse \(16 x^{2}+9 y^{2}=400\) at which the ordinate decreases at the same rate at which the abscissa increases is/are given by

answered Dec 20, 2021 in Sets, relations and functions

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General solution of \(y \frac{d y}{d x}+b y^{2}=a \cos x, 0<x<1\) is

answered Dec 20, 2021 in Sets, relations and functions

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For non-zero vectors \(\vec{a}\) and \(\vec{b}\) if \(|\vec{a}+\vec{b}|<|\vec{a}-\vec{b}|\), then \(\vec{a}\) and \(\vec{b}\) are

answered Dec 20, 2021 in Sets, relations and functions

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If \([\mathrm{x}]\) denotes the greatest integer less than or equal to \(\mathrm{x}\), then the value of the integral \(\int_{0}^{2} \mathrm{x}^{2}[\mathrm{x}] \mathrm{dx}\) equals

answered Dec 20, 2021 in Sets, relations and functions

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Standard Deviation of n observations \(\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3} \ldots . \mathrm{a}_{\mathrm{n}}\) is \(\sigma .\) Then the standard deviation of the observations \(\lambda \mathrm{a}_{1}, \lambda \mathrm{a}_{2}, \ldots \lambda \mathrm{a}_{n}\)

answered Dec 20, 2021 in Sets, relations and functions

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If the function \(f: \mathbb{R} \rightarrow R\) is defined by \(f(x)=\left(x^{2}+1\right)^{35} \forall \in \mathbb{R}\), then \(f\) is

answered Dec 20, 2021 in Sets, relations and functions

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If \(A=\left\{5^{n}-4 n-1: n \in N\right\}\) and \(B=\{16(n-1): n \in N\}\), then

answered Dec 20, 2021 in Sets, relations and functions

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Let \(R\) be a relation defined on the set \(Z\) of all integers and \(x R y\) when \(x+2 y\) is divisible by 3 . Then

answered Dec 20, 2021 in Sets, relations and functions

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Let \(Q=\left(\begin{array}{cc}\cos \frac{\pi}{4}-\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right)\) and \(x=\left(\begin{array}{c}\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}}\end{array}\right)\) then \(Q^{3} x\) is equal to

answered Dec 20, 2021 in Sets, relations and functions

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Let \(A\) is a \(3 \times 3\) matrix and \(B\) is its adjoint matrix. If \(|B|=64\), then \(|A|=\)

answered Dec 20, 2021 in Sets, relations and functions

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If \(x, y\) and \(z\) be greater than 1 , then the value of \(\left|\begin{array}{ccc}1 & \log _{x} y & \log _{x} z \\ \log _{y} x & 1 & \log _{y} z \\ \log _{z} x & \log _{z} y & 1\end{array}\right|\) is

answered Dec 20, 2021 in Sets, relations and functions

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\(1+{ }^{n} C_{1} \cos \theta+{ }^{n} C_{2} \cos 2 \theta+\ldots \ldots+{ }^{n} C_{n} \cos n \theta\) equals

answered Dec 20, 2021 in Sets, relations and functions

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In the expansion of \((x-1)(x-2) \ldots .(x-18)\), the coefficient of \(x^{17}\) is

answered Dec 20, 2021 in Sets, relations and functions

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For \(+\) ve integer \(n, n^{3}+2 n\) is always divisible by

answered Dec 20, 2021 in Sets, relations and functions

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If, \(\frac{1}{{ }^{5} C_{t}}+\frac{1}{{ }^{6} C_{r}}=\frac{1}{{ }^{4} C_{t}}\), then the value of r equals to

answered Dec 20, 2021 in Sets, relations and functions

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