Recent questions in JEEMAIN PAST PAPERS

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $60^{\circ}$ and when he retires $40$ meter away from the tree the angle of elevation becomes $30^{\circ}$. The breadth of the river is

asked Nov 5, 2018 by pady_1

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The sides of the triangle are $\sin \alpha, \cos \alpha$ and $\sqrt{1 + \sin \alpha \cos \alpha}$ for some $0 < \alpha < \frac{\pi}{2}$. Then the greatest angle of the triangle is

asked Nov 5, 2018 by pady_1

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If $u = \sqrt{a^2 \cos^2 \theta +b^2 \sin^2 \theta} + \sqrt{a^2 \sin^2 \theta + b^2 \cos^2 \theta}$, then the difference between the maximum and minimum values of $u^2$ is given by

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Let $\alpha, \beta$ be such that $\pi - \alpha - \beta < 3 \pi$. If $\sin \alpha + \sin \beta = -\frac{21}{65}$ and $\cos \alpha + \cos \beta = -\frac{27}{65}$, then the value of $\cos \frac{\alpha - \beta}{2}$ is

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The sum of series $\frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!}+... $ is

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The sum of the first n terms of the series $1^2 + 2.2^2 + 3^2 + 2.4^2 + 5^2 + 2.6^2+...$ is $\frac{n(n+1)^2}{2}$ when $n$ is even. When $n$ is odd the sum is

asked Nov 5, 2018 by pady_1

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Let $T_f$ be the $r^{th}$ term of an A.P whose first term is a and common difference is $d$. If for some positive integers $m, \;n, \;m \neq n, \;T_m = \frac{1}{n}$ and $T_n = \frac{1}{m}$, then $a-d$ equals

asked Nov 5, 2018 by pady_1

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If $S_n =\displaystyle\sum_{r=0}^{n} \frac{1}{^nC_r}$ and $t_n= \displaystyle\sum_{r=0}^{n} \frac{r}{^nC_r}$, then $\frac{t_n}{S_n}$ is equal to

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The coefficient of $x^n$ in expansion of $(1+x)(1-x)^n$ is

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The coefficient of the middle term in the binomial expansion in powers of $(1 + \alpha x)^4$ and of $(1- \alpha x)^6$ is the same if $\alpha$ equals

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The one root of the equation $x^2 + px + 12 = 0$ is 4, while the equation $x^2+px+q=0$ has equal roots, then the value of 'q' is

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The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

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Hoe many ways are there to arrange the letters in the worf GARDEN with the vowels in alphabetical order ?

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Let $S(K) = 1 + 3 + 5 + ....+ (2K-1) = 3 + K^2$. Then which of the following is true ?

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If $(1-p)$ is a root of quadratic equation $x^2 + px + (1-p) =0$, then its roots are

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Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation-

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If $a_1, a_2, a_3, ....,a_n,....$ are in G.P., then the value of the determinant $\begin{vmatrix} \log a_n & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8} \end{vmatrix}$, is

asked Nov 5, 2018 by pady_1

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Let $A =\begin{pmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{pmatrix} \; (10) B = \begin{pmatrix} 4 &2 &2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{pmatrix} $. If $B$ is the inverse of matrix $A$, then $\alpha$ is

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Let $A = \begin{pmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{pmatrix}$. The only correct statement about the matrix $A$ is

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If $|z^2-1| = |z|^2 + 1 $, then $z$ lies on

asked Nov 5, 2018 by pady_1

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If $z = x -i y$ and $z^{\frac{1}{3}} = p + i q$, then $\frac{(\frac{x}{p} + \frac{y}{q})}{(p^2+q^2)}$ is equal to

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Let $z$, $w$ be complex numbers such that $\overline{z} +i \overline{w} =0$ and $arg \; zw = \pi$. Then $arg\; z$ equals

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The range of the function $f(x) = ^{7-x}P_{x-3}$ is

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Let $R = \{ (1,3), (4,2), (2,4), (2,3), (3,1) \}$ be a relation on the set $A = \{1, 2, 3, 4\}$. The relation R is

asked Nov 5, 2018 by pady_1

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