List of top Mathematics Questions asked in JEE Main

The value of
$\lim_{{x \to 1}} \frac{{(x^2 - 1) \sin^2(\pi x)}}{{x^4 - 2x^3 + 2x - 1}}$
is equal to

A plane P is parallel to two lines whose direction rations are –2, 1, –3 and –1, 2, –2 and it contains the point (2, 2, –2). Let P intersect the co-ordinate axes at the points A, B, C making the intercepts α, β, γ. If V is the volume of the tetrahedron OABC, where O is the origin and p = α + β + γ, then the ordered pair (V, p) is equal to :

Let S be the set of all a∈ R for which the angle between the vectors$ \begin{array}{l} \overrightarrow{u}=a\left(\text{log}_e b\right)\hat{i}-6\hat{j}+3\hat{k}\end{array}$ and $\begin{array}{l} \overrightarrow{v}=\left(\text{log}_e b\right)\hat{i}+2\hat{j}+2a\left(\text{log}_e b\right)\hat{k},\left(b>1\right)\end{array}$ is acute. Then S is equal to

If
$\frac{dy}{dx}+2y \tan⁡x=\sin⁡x, 0<x<\frac{π}{2} and\ y(\frac{π}{3})=0 $
then the maximum value of y(x) is:

Different A.P.’s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.’s having at least 3 terms and at most 33 terms is ______.

Let for some real numbers $α$ and $β$, $a = α – iβ$. If the system of equations $4ix + (1 + i) y = 0$ and $8\bigg(cosx\frac{2π}{3}+i\;sin\frac{2π}{3}\bigg)x+\bar ay=0 $has more than one solution, then $\frac{α}{β}$ is equal to

Let $S = \{θ ∈ (0, 2π) : 7 cos^2θ – 3 sin^2θ – 2 cos^22θ = 2\}$.
Then, the sum of roots of all the equations $x^2 – 2 (tan^2θ + cot^2θ) x + 6 sin^2θ = 0, θ ∈ S$, is _______.

Let R₁ and R₂ be two relations defined on ℝ by a R₁b ⇔ ab ≥ 0 and aR₂b ⇔ a ≥ b. Then,

Let
f,g:N = {1} → N be functions defined by
f(a) = α, where α is the maximum of the powers of those primes p such that p^α divides a, and g(a) = a + 1, for all a ∈ N – {1}. Then, the function f + g is

Let S be the sample space of all five digit numbers. It p is the probability that a randomly selected number from S, is multiple of 7 but not divisible by 5, then 9p is equal to

For $t \in(0,2 \pi)$, if $ABC$ is an equilateral triangle with vertices$A ( \sin t, -{\cos t}), B ( \cos t, \sin t )$ and $C ( a , b )$ such that its orthocentre lies on a circle with centre $\left(1, \frac{1}{3}\right)$, then $\left(a^2-b^2\right)$ is equal to :

Let $\begin{array}{l} S=\left[-\pi, \frac{\pi}{2}\right)-\left[-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3\pi}{4},\frac{\pi}{4}\right].\end{array}$Then the number of elements in the set $\begin{array}{l} A=\left\{\theta\in S:\tan\theta\left(1+\sqrt{5}\tan\left(2\theta\right)\right)=\sqrt{5}-\tan\left(2\theta\right) \right\} \end{array}$is ________.

The sum of the absolute minimum and the absolute maximum values of the function ƒ(x) = |3x – x² + 2| – x in the interval [–1, 2] is

Let
$S = \left\{z∈C : z^2+\overline{z} = 0 \right\}$. Then $∑_{z∈S}(Re(z)+Im(z))$
is equal to____.

Let α→ = $2\^{i}-\^{j}+5\^{k} and b→= α\^{i}+β\^{j}+2\^{k}. If ((α→×b→)×\^{i}).\^{k} $=$\frac{ 23}{2}$,then $|b→×2\^{j}\| $is equal to

Let ℝ → ℝ be function defined as
f(x) = αsin($(\frac{π[x]}{2})$+[2-x],α∈R
where [t] is the greatest integer less than or equal to t.
If lim x→1 f(x) exists, then the value of$∫_0^4$ f(x)dx
is equal to

If the coefficients of x and x² in the expansion of (1 + x)^p (1 – x)^q, p, q≤15, are – 3 and – 5 respectively, then coefficient of x³ is equal to ______.

Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2….., 10} and nAⁿ + mB^m = I} is _______.