Recent questions in JEE

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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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2 answers

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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2 answers

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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1 answer

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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1 answer

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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2 answers

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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1 answer

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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1 answer

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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1 answer

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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3 answers

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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2 answers

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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3 answers

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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3 answers

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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1 answer

if \(f(x)\) is a function such that \(f^{\prime}(x)=(x-1)^{2}(4-x)\), then

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

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6 answers

If the parabola \(x^{2}=\) ay makes an intercept of length \(\sqrt{40}\) unit on the line \(y-2 x=1\) then a is equal to

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

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3 answers

The coordinates of a point on the line \(x+y+1=0\) which is at a distance \(\frac{1}{5}\) unit from the line \(3 x+4 y+2=0\) are

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

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