List of top Mathematics Questions asked in JEE Main

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?
The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) – f(c) = f(d) is :
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

Let E1, E2, E3 be three mutually exclusive events such that
\(P(E_1)=\frac{2+3p}{6}, P(E_2)=\frac{2−p}{8} and\ P(E_3)=\frac{1−p}{2}.\)
If the maximum and minimum values of p are p1 and p2, then (p1 + p2) is equal to :

A six faced die is biased such that
3 × P (a prime number) = 6 × P (a composite number) = 2 × P (1).
Let X be a random variable that counts the number of times one gets a perfect square on some
throws of this die. If the die is thrown twice, then the mean of X is :

Let S = {1, 2, 3, …, 2022}. Then the probability that a randomly chosen number n from the set S such that HCF (n, 2022) = 1, is
Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

Let
 \(x = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\) and \(A = \begin{bmatrix} -1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1 \end{bmatrix}\)
For k ∈ N, if X’AkX = 33, then k is equal to ____ .

Let P(a, b) be a point on the parabola y2 = 8x such that the tangent at P passes through the centre of the circle x2 + y2 – 10x – 14y + 65 = 0. Let A be the product of all possible values of a and B be the product of all possible values of b. Then the value of A + B is equal to
The remainder when \(7^{2022}+3^{2022}\) is divided by \(5\) is:
If the equation of the parabola, whose vertex is at \((5, 4)\) and the directrix is \(3x + y – 29 = 0\), is \(x^2 + ay^2 + bxy + cx + dy + k = 0\), then \(a + b + c + d + k\) 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

Let S = {4, 6, 9} and T = {9, 10, 11, …,1000}. If A = {a1 + a2 + … +ak :k∈N, a1, a2, a3, …, ak∈S}, then the sum of all the elements in the set T – A is equal to ____________.
The value of the integral \(\begin{array}{l} \displaystyle\int\limits_0^{\frac{\pi}{2}}60\frac{\sin\left(6x\right)}{\sin x}dx \end{array}\) is equal to ______.
\(\lim_{x\rightarrow \frac{\pi}{4}}\) 8\(\sqrt2\)−(cosx+sinx)\(^{\frac{7}{\sqrt2}}\)−\(\sqrt2\)sin2x is equal to
A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is tan-1(3/4). Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is

Let f be a differential function satisfying
f(x) =\(\frac{ 2}{√3} \)\(∫^{√30} f(\frac{λ2x}{3})dλ,x>0 and f(1) = √3.\)
If y = f(x) passes through the point (α, 6), then α is equal to _____

If \(\begin{array}{l}\int_{0}^{\sqrt{3}}\frac{15x^3}{\sqrt{1+x^2 + \sqrt{(1+x^2)^3}}}dx = \alpha \sqrt{2}+\beta\sqrt{3},\end{array}\)where \(α, β\) are integers, then \(α + β\) is equal to
 
Let \(\vec a\)=\(\hat i\)−\(\hat j\)+2\(\hat k\) and \(\vec b\) be a vector such that 
\(\vec a\)×\(\vec b\)=2\(\hat i\)−\(\hat k\) and \(\vec a\)⋅\(\vec b\)=3. 
Then the projection of  \(\vec b\) on the vector \(\vec a\)−\(\vec b\) is :
\(lim_{n→∞} \frac1{2^n}(\frac1{\sqrt{1-1/2^n}} +\frac1{\sqrt{1-\frac2{2^n}}}+\frac1{\sqrt{1-\frac3{2^n}}}+...+\frac1{\sqrt{1-\frac{2^n-1}{2^n}}})\) is equal to
Let \(\overset{→}a = \hat{i}- \hat{J}+2\hat{K}\) and \(\overset{→}b\) be a vector such that \(\overset{→}a×\overset{→}b=2\hat{i}−\hat{k} \) and \(\overset{→}a⋅\overset{→}b=3\). Then the projection of \(\overset{→}b\) on the vector \(\overset{→}a-\overset{→}b\) is :
If A and B are two events such that \(P(A)=\frac1{3},P(B)=\frac1{5}\)  and \(P(A∪B)=\frac1{2}\) then \(P(\frac{A}{B'}) + P(\frac{B}{A'})\) is equal to

A common tangent T to the curves
\(C_1:\frac{x^2}{4}+\frac{y^2}{9} = 1\)
and
\(C_2:\frac{x^2}{4^2}\frac{-y^2}{143} = 1\)
does not pass through the fourth quadrant. If T touches C1 at (x1, y1) and C2 at (x2, y2), then |2x1 + x2| is equal to ______.

2sin(\(\frac{\pi}{22}\))sin(\(\frac{3\pi}{22}\))sin(\(\frac{5\pi}{22}\))sin(\(\frac{7\pi}{22}\))sin(\(\frac{9\pi}{22}\)) is equal to

The statement 
\((p⇒q)∨(p⇒r) \)
is NOT equivalent to