List of top Mathematics Questions asked in JEE Main

Let $P$ be the plane containing the straight line $\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$ and perpendicular to the plane containing the straight lines $\frac{ x }{2}=\frac{ y }{3}=\frac{ z }{5}$ and $\frac{ x }{3}=\frac{ y }{7}=\frac{ z }{8}$ If $d$ is the distance of $P$ from the point $(2,-5,11)$, then $d ^2$ is equal to :
If \(y = m_1x + c_1 \)and \(y = m_2x + c_2\), \(m_1≠m_2\) are two common tangents of circle \(x_2 + y_2 = 2\) and parabola \(y^2 = x\), then the value of \(8|m_1m_2|\) is equal to :
Let \(Q\) be the mirror image of the point \(P(1, 0, 1)\) with respect to the plane \(S\): \(x + y + z = 5\). If a line L passing through \((1, –1, –1)\), parallel to the line \(PQ\) meets the plane \(S\) at \(R\), then \(QR_2\) is equal to :
Let \(x=2t,\ y=\frac {t^2}{3}\) be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then \(\lim\limits_{t \to 1} k\) is equal to
A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α, β). Then, the value of \(7α + 3β\) is equal to ________ .
Let l be a line which is normal to the curve \(y = 2x^2 + x + 2\) at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to _________ .
Let the lines
\(y + 2x = \sqrt {11} + 7\sqrt 7\) and \(2y + x = 2\sqrt {11} + 6\sqrt 7\)
be normal to a circle \(C : (x – h)^2 + (y – k)^2 = r^2\). If the line
\(\sqrt {11}y - 3x =\frac { 5\sqrt {17}}{3} + 11\)
is tangent to the circle C, then the value of \((5h – 8k)^2 + 5r^2\) is equal to _______.
Let $O$ be the origin and $A$ be the point $z _1=1+2 i$. If $B$ is the point $z _2, \operatorname{Re}\left( z _2\right)<0$, such that $OAB$ is a right angled isosceles triangle with $OB$ as hypotenuse, then which of the following is NOT true ?

Let z1 and z2 be two complex numbers such that 

\(z_1=iz_2 \,and \,arg(\frac{z_1}{z_2})=π.\)

If z2 + z + 1 = 0,
\(z ∈ C\), then \(\left| \sum_{n=1}^{15} \left( z_n + (-1)^n \frac{1}{z_n} \right)^2 \right|\)
is equal to ________.

Let \(S = z ∈ C: |z-3| <= 1\) and \(z (4+3i)+z(4-3)≤24.\)
If α + iβ is the point in S which is closest to 4i, then 25(α + β) is equal to ______.

The number of elements in the set { \(z = a + ib ∈ C : a,b ∈ Z\) and \(1 < | z - 3 + 2i | < 4\) } is _______ .

Sum of squares of modulus of all the complex numbers z satisfying 
\(\overline{z}=iz^2+z^2–z \)
is equal to ________.

Let S be the set of (α,β),π<α,β<2π,for which the complex number
\(\frac{1-i\sinα}{1+2i\sinα}\) is purely imaginary and \(\frac{1+i\cosβ}{1-2i\cosβ}\) is purely real,
Let \(Zαβ = \sin2α+i\cos2β, (α,β) ∈ S\). Then
\(\sum_{(\alpha, \beta) \in S} \left(iZ_{\alpha\beta} + \frac{1}{iZ_{\alpha\beta}}\right)\)
is equal to

If z = x + iy satisfies | z | – 2 = 0 and |z – i| – | z + 5i| = 0, then

Let a function ƒ : N →N be defined by
 \(f(n) = \left\{ \begin{array}{ll} 2n & n = 2,4,6,8,\ldots \\ n - 1 &  n = 3,7,11,15,\ldots \\ \frac{n+1}{2} &  n = 1,5,9,13 \end{array} \right.\)
then, ƒ is

Let f: ℝ → ℝ satisfy f(x + y) = 2x f(y) + 4y f(x), ∀ x, y∈ ℝ. If f(2) = 3, then 14. f'(4)/f'(2) is equal to ___.
The number of real solutions of x7 + 5x3 + 3x + 1 = 0 is equal to ______.
The number of real solutions of the equation e4x + 4e3x - 58e2x + 4ex + 1 = 0 is _____.
Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x) = 0 is –1, then the sum of the roots of f(x) = 0 is equal to:

Let f,g : R → R be functions defined by*
\(f(x) = \begin{cases}   [x], &  x < 0 \\   |1 - x|, &  x \geq 0 \end{cases}\)
and \(g(x) = \begin{cases}   e^x - x, &  x < 0 \\   {(x - 1)^2 - 1}, &  x \geq 0 \end{cases}\)
Where [x] denotes the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly:

If 
\(f(x) = \begin{cases}     x + a, & x \leq 0 \\     |x - 4|, &  x > 0 \end{cases}\) and \(g(x) = \begin{cases}     x + 1, & x < 0 \\     (x - 4)^2 + b, &  x \geq 0 \end{cases}\)
 are continuous on R, then (gof) (2) + (fog) (–2) is equal to

Let 
\(f(x) = \begin{cases}     x^3 - x^2 + 10x - 7, & x \leq 1 \\     -2x + \log_2(b^2 - 4), &  x > 1 \end{cases}\)
Then the set of all values of b, for which f(x) has maximum value at x = 1, is

Let a function f: ℝ → ℝ be defined as :
\(\begin{array}{l}f(x) = \left\{\begin{matrix}\int_{0}^{x}(5-|t-3|)dt, & x>4 \\x^2 + bx, & x \le4 \\\end{matrix}\right.\end{array}\)
where b ∈ ℝ. If f is continuous at x = 4 then which of the following statements is NOT true?
Let A and B be two events such that
 \(\begin{array}{l} P\left(B/A\right)\frac{2}{5},\ P\left(A/B\right)=\frac{1}{7}\ \text{and}\ P\left(A\cap B\right)=\frac{1}{9}.\end{array} Consider \begin{array}{l} \left(S1\right)P\left(A’\cup B\right)=\frac{5}{6},\end{array}\)
\(\begin{array}{l} \left(S2\right)P\left(A’\cap B’\right)=\frac{1}{18}.\end{array}\)Then