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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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Let \(\alpha, \beta\) be the roots of the equation \(x^{2}-6 x-2=0\) with \(\alpha>\beta\). If \(a_{n}=\alpha^{n}-\beta^{n}\) for \(n \geq 1\), then the value of \(\frac{a_{10}-2 a_{8}}{2 a_{9}}\) is

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

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Let \(C\) denote the set of all complex numbers. Define \(A=\{(z, w) \mid z, w \in C\) and \(|z|=|w|\}, B=\left\{(z, w) \mid z, w \in C\right.\) and \(\left.z^{2}=w^{2}\right\}\). Then

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

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Let \(a, b, c\) be real numbers, each greater than 1 , such that \(\frac{2}{3} \log _{b} a+\frac{3}{5} \log _{c} b+\frac{5}{2} \log _{a} c=3\). If the value of \(b\) is 9 , then the value of 'a' must be

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

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Consider the real valued function \(h:\{0,1,2 \ldots . .100\} \rightarrow R\) such that \(h(0)=5, h(100)=20\) and satisfying \(h(p)=\frac{1}{2}\{h(p+1)+h(p-1)\}\) for every \(p=1,2 \ldots . .99\). Then the value of \(h(1)\) is

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

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3 answers

Let \(\vec{\alpha}, \vec{\beta}, \vec{\gamma}\) be three non-zero vectors which are pairwise non-collinear. If \(\vec{\alpha}+3 \vec{\beta}\) is collinear with \(\vec{\gamma}\) and \(\vec{\beta}+2 \vec{\gamma}\) is collinear with \(\vec{\alpha}\), then \(\vec{\alpha}+3 \vec{\beta}+6 \vec{\gamma}\) is

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

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Let \(f: R \rightarrow R\) be given by \(f(x)=\left|x^{2}-1\right|, x \in R\). then

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

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A bulb is placed at the centre of a circular track of radius \(10 \mathrm{~m}\). A vertical wall is erected touching the track at a point P. A man is running along the track with a speed of \(10 \mathrm{~m} / \mathrm{sec}\). Starting from P the speed with which his shadow is running along the wall when he is at an angular distance of \(60^{\circ}\) from \(\mathrm{P}\) is

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

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Two particles \(A\) and \(B\) move from rest along a straight line with constant accelerations \(f\) and f' respectively. If \(A\) takes \(\mathrm{m}\) sec. more than that of \(\mathrm{B}\) and describes \(\mathrm{n}\) units more than that of \(\mathrm{B}\) in acquiring the same velocity, then

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

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If \(x \frac{d y}{d x}+y=\frac{x f(x y)}{f^{\prime}(x y)}\), then \(|f(x y)|\) is equal to

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

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The value of \(\int_{0}^{5} \max \left\{x^{2}, 6 x-8\right\} d x\) is

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

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The straight line through the origin which divides the area formed by the curves \(y=2 x-x^{2}, y=0\) and \(x=1\) into two equal halves is

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

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8 answers

If \(A, B\) are two events such that \(P(A \cup B) \geq \frac{3}{4}\) and \(\frac{1}{8} \leq P(A \cap B) \leq \frac{3}{8}\) then

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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Let \(f: X \rightarrow X\) be such that \(f(f(x))=x\) for all \(x \in X\) and \(X \subseteq R\), then

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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If \(z=\sin \theta-i \cos \theta\) then for any integer \(n\),

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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26 answers

If the equation \(x^{2}+y^{2}-10 x+21=0\) has real roots \(x=a\) and \(y=\beta\) then

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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If \(\varphi(t)=\left\{\begin{array}{l}1, \text { for } 0 \leq t+1 \\ 0 \text { othenwe then }\end{array} \int_{-3000}^{3000}\left(\sum_{r=2014}^{2016} \varphi\left(t-r^{\prime}\right) \varphi(t-2016)\right) d t=\right.\)

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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On the ellipse \(4 x^{2}+9 y^{2}=1\), the points at which the tangents are parallel to the line \(8 x=9 y\) are

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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