Recent questions in JEEMAIN PAST PAPERS

If the two circles $(x-1)^2 + (y-3)^2 = r^2$ and $x^2 + y^2 - 8x + 2y + 8 =0$ intersect in two distinct points, then :

asked Dec 11, 2018 by pady_1

0 answers

A square of side $a$ lies above the $x$-axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha ( 0 < \alpha < \frac{\pi}{4})$ with the positive direction of $x$-axis. The equation of its diagonal not passing through the origin is :

asked Dec 11, 2018 by pady_1

1 answer

If the pair of straight line $x^2 -2pxy - y^2 = 0$ and $x^2 - 2qxy - y^2 = 0$ be such that each pair bisects the angle between the other pair, then :

asked Dec 11, 2018 by pady_1

0 answers

Locus of centroid of the triangle whose vertices are $( a \cos t, \; a \sin t), \; (b \sin t, -b \cos t)$ and $(1, 0)$ where $t$ is a parameter, is :

asked Dec 11, 2018 by pady_1

0 answers

If the equation of the locus of a point equidistant from the points $(a_1, b_1)$ and $(a_2, b_2)$ is $(a_1 - a_2) x + (b_1 - b_2) y + c = 0$, then the value of $'C'$ is :

asked Dec 11, 2018 by pady_1

0 answers

The solution of the differential equation $(1+y^2) + (x - e^{\tan^{-1} y} )\frac{dy}{dx} = 0 $ is :

asked Dec 11, 2018 by pady_1

0 answers

The degree and order of the differential equation of the family of all parabolas whose axis is $x$-axis, are respectively :

asked Dec 11, 2018 by pady_1

0 answers

Let $f(x)$ be a function satisfying $f'(x) = f(x)$ with $f(0) = 1$ and $g(x)$ be a function that satisfies $f(x) + g(x) = x^2$. Then the value of the integral $\begin{align} \int_0^1 f(x) \; g(x) \;dx \end{align} $ is :

asked Dec 11, 2018 by pady_1

0 answers

The area of the region bounded by the curves $y = |x-1| $ and $y=3 - |x|$ is :

asked Dec 11, 2018 by pady_1

0 answers

Let $\begin{align}\frac{d}{dx} F(x) =(\frac{e^{\sin x}}{x}), \; x > 0 \end{align}$ If $\begin{align} \int_1^4 \frac{3}{x} e^{\sin x^3} dx = F(k) - F(1) \end{align}$, then one of the possible values of $k$, is

asked Dec 11, 2018 by pady_1

0 answers

$\displaystyle\lim_{n \to \infty} \frac{1 + 2^4 + 3^4 + ...+ n^4}{n^5} - \displaystyle\lim_{n \to \infty} \frac{1+2^3 + 3^3 + ....+ n^3}{n^5}$ is :

asked Dec 11, 2018 by pady_1

0 answers

The value of the integral $\begin{align}I = \int_0^1 x(1-x)^n dx \end{align}$ is :

asked Dec 11, 2018 by pady_1

0 answers

The value of $\displaystyle\lim_{x \to 0} \frac{ \int_0^{x^2} \sec^2t \; dt}{x \sin x}$ is :

asked Dec 11, 2018 by pady_1

0 answers

If $f(a + b - x) = f(x) $, then $\int_a^b x f(x) dx$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $f(y) = e^y,\; g(y) = y; \; y>0$ and $F(t) = \int^t_0 f(t-y) \;g(y) \;dy$, then :

asked Dec 11, 2018 by pady_1

0 answers

If the function $f(x) = 2x^3 - 9 ax^2 + 12 a^2x + 1$, where $a>0$, attains its maximum and minimum at $p$ and $q$ respectively such that $p^2 = q$, then $a$ equals :

asked Dec 11, 2018 by pady_1

0 answers

If $ f(x) = \begin{cases} xe^{-\begin{bmatrix}\frac{1}{|x|} - \frac{1}{x}\end{bmatrix}}, & \quad \text{$x$ $\neq$ 0} \text{ then $f(x)$ is :}\\ \; \; \; 0 & \quad \text{$x=0$} \end{cases}$

asked Dec 11, 2018 by pady_1

0 answers

The function $f(x) = \log (x +\sqrt{x^2+1})$, is :

asked Dec 11, 2018 by pady_1

0 answers

If $f^n(a),g^n(a)$ exist and are not equal for some $n$. Further is $f(a) = g(a) =k$ and $\displaystyle\lim_{x \to a} \frac{f(a)g(x) - f(a) - g(a) f(x) + g(a) }{g(x) - f(x)} = 4$, then the value of $k$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $\displaystyle\lim_{x \to 0} \frac{\log(3+x) - \log(3-x)}{x} = k$, the value of $k$ is :

asked Dec 11, 2018 by pady_1

0 answers

$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{[1- \tan(\frac{x}{2})][1 - \sin x]}{[1+\tan(\frac{x}{2})][\pi - 2x]^3}$ is :

asked Dec 11, 2018 by pady_1

0 answers

Domain of definition of the function $f(x) = \frac{3}{4-x^2} + \log_{10} (x^3 - x)$, is :

asked Dec 11, 2018 by pady_1

0 answers

If $f(x) = x^n$, then the value of $f(1) - \frac{f'(1)}{1!} + \frac{f''(1)}{2!} - \frac{f'''(1)}{3!} + ....+\frac{(-1)^nf^n(1)}{n!} $ is :

asked Dec 11, 2018 by pady_1

0 answers

If $f : R \to R$ satisfies $f(x+y) = f(x) + f(y)$, for all $x, \; y \in R$ and $f(1) = 7$, then $\displaystyle\sum_{r=1}^{n} f(r)$ is :

asked Dec 11, 2018 by pady_1

0 answers

The real number $x$ when added to its inverse gives the minimum value of the sum at $x$ equals to :

asked Dec 11, 2018 by pady_1

0 answers

The upper $3/4th$ portion of a vertical pole subtends an angle $\tan^{-1} 3/5$ at a point in the horizontal plane through its foot and a distance $40\;m$ from the foot. A possible height of the vertical pole is :

asked Dec 11, 2018 by pady_1

0 answers

The trigonometric equation $\sin^{-1}x = 2 \sin^{-1} a$, has a solution for :

asked Dec 11, 2018 by pady_1

0 answers

In a triangle ABC, medians AD and BE are drawn. If $AD=4$, $\angle{DAB} = \frac{\pi}{6}$ and $\angle{ABE} = \frac{\pi}{3}$, then the area of the $\Delta ABC$ is :

asked Dec 11, 2018 by pady_1

0 answers

If in a triangle $ABC$ $a \cos^2(\frac{C}{2} ) + c \cos^2(\frac{A}{2} ) = \frac{3b}{2}$, then the sides $a,\;b$ and $c$ :

asked Dec 11, 2018 by pady_1

0 answers

The sum of the radii of inscribed and circumscribed circles for an $n$ sided regular polygon of side $a$ is :

asked Dec 11, 2018 by pady_1

0 answers

If $x_1, \; x_2, \; x_3$ and $y_1, \; y_2, \; y_3$ are both in GP with the same common ratio, then the points $(x_1, y_1), \; (x_2, \; y_2)$ and $(x_3, y_3)$:

asked Dec 11, 2018 by pady_1

0 answers

Let $f(x)$ be a polynomial function of second degree. If $f(1) = f(-1)$ and $a, \; b, \; c$ are in AP, then $f'(a), \; f'(b)$ and $f'(c)$ are in :

asked Dec 11, 2018 by pady_1

0 answers

The sum of the series $\frac{1}{1.2} - \frac{1}{2.3} + \frac{1}{3.4} - ...$ upto $\infty$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $x$ is positive, the first negative term in the expansion of $(1+x)^{27/5}$ is :

asked Dec 11, 2018 by pady_1

0 answers

The number of integral terms in the expansion of $(\sqrt{3} + 8\sqrt{5})^{256}$ is :

asked Dec 11, 2018 by pady_1

0 answers

If $^nC_r$ denotes the number of combinations of $n$ things taken $r$ at a time, then the expression $^nC_{r+1} + ^nC_{r-1} + 2 \times ^nC_r$ equals :

asked Dec 11, 2018 by pady_1

0 answers

If $1, \omega, \omega^2$ are the cube roots of unity, then : $\Delta = \begin{vmatrix} 1 & \omega^n & \omega^{2n} \\ \omega^n & \omega^{2n} & 1 \\ \omega^{2n} & 1& \omega^n \end{vmatrix}$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by :

asked Dec 11, 2018 by pady_1

0 answers

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is :

asked Dec 11, 2018 by pady_1

0 answers

If $A = \begin{bmatrix} a & b \\ b & a \end{bmatrix}$ and $A^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix}$, then :

asked Dec 11, 2018 by pady_1

0 answers

The value of 'a' for which one root of the quadratic equation $(a^2 -5a +3) x^2 + (3a - 1)x+2 =0$ is twice as large as the other, is :

asked Dec 11, 2018 by pady_1

0 answers

The number of the real solutions of the equation $x^2 - 3|x| + 2 =0$ is :

asked Dec 11, 2018 by pady_1

0 answers

If the sum of the roots of the quadratic equation $ax^2 + bx + c =0$ is equal to the sum of the square of their reciprocals, then $\frac{a}{c}, \frac{b}{a}$ and $\frac{c}{b}$ are in :

asked Dec 11, 2018 by pady_1

0 answers

If the system of linear equations $\; \; \; \; x +2 ay + az = 0 $ $\; \; \; \; x + 3by + bz=0$ $\; \; \; \; x +4cy +cz = 0$ has a non-zero solution, then $a, \; b,\; c$:

asked Dec 11, 2018 by pady_1

0 answers

If $\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0$ and vectors $(1, a, a^2), \; (1, b, b^2)$ and $(1, c, c^2)$ are non-coplanar, then the product $abc$ equals :

asked Dec 11, 2018 by pady_1

0 answers

If $\begin{pmatrix} \frac{1+i}{1-i} \end{pmatrix}^x=1$, then:

asked Dec 11, 2018 by pady_1

0 answers

If $z$ and $\omega$ are two non-zero complex numbers such that $|z \; \omega| = 1$, and $arg (z) - arg(\omega) = \frac{\pi}{2}$, then $\overline{z} \omega$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

Let $z_1$ and $z_2$ be two roots of the equation $z^2 + az + b = 0 , \; z$ being complex. Further, assume that the origin, $z_1$ and $z_2$ form an equilateral triangle. Then :

asked Dec 11, 2018 by pady_1

0 answers

A function $ f$ from the set of natural numbers of integers defined by $ f(n) = \begin{cases} \frac{n-1}{2}, & \quad \text{when } n \text{ is odd}\\ -\frac{n}{2 } & \quad \text{when } n \text{ is even} \end{cases} $ is :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following could act as a propellant for rockets ?

asked Dec 11, 2018 by pady_1

0 answers

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