Questions by deepak01

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In a group 14 males and 6 females, 8 and 3 of the males and females respectively are aged above 40 years. The probability that a person selected at random from the group is aged above 40 years, given that the selected person is female, is

asked Dec 8, 2021 in Sets, relations and functions

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1 answer

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

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

If \(\omega\) is an imaginary cube root of unity, then the value of \((2-\omega)\left(2-\omega^{2}\right)+2(3-\omega)\left(3-\omega^{2}\right)+\ldots . .+(n-1)(n-\omega)\left(n-\omega^{2}\right)\) is

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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1 answer

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

asked Dec 8, 2021 in Sets, relations and functions

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2 answers

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 \(\lambda \mathrm{a}_{1}, \lambda \mathrm{a}_{2}, \ldots \lambda \mathrm{a}_{n}\)

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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2 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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3 answers

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

asked Dec 8, 2021 in Sets, relations and functions

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1 answer

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

asked Dec 8, 2021 in Sets, relations and functions

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2 answers

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

asked Dec 8, 2021 in Sets, relations and functions

0 votes

1 answer

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

asked Dec 8, 2021 in Sets, relations and functions

0 votes

1 answer

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

asked Dec 8, 2021 in Sets, relations and functions

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