List of top Mathematics Questions asked in JEE Main

Let the solution curve y = y(x) of the differential equation
$[ \frac{x}{\sqrt{x² -y²}} + e^\frac{y}{x} ] x \frac{dy}{dx} = x + [ \frac{x}{\sqrt{x² -y²}} + e^\frac{y}{x} ]y$
pass through the points (1, 0) and (2α, α), α> 0. Then α is equal to

If y = y (x) is the solution of the differential equation
$(1 + e^{2x})\frac{dy}{dx} + 2(1 + y^2)e^x = 0$
and y(0) = 0, then
$6 \left( y'(0) + \left( \log_e\left(\sqrt{3}\right) \right)^2 \right)$
is equal to

Let
$\vec{a}=\hat{i} - 2\hat{j} + 3\hat{k}, \vec{b}=\hat{i} - \hat{j} + \hat{k} $ and $\vec{c}$
be a vector such that
$\vec{a} + (\vec{b}×\vec{c}) = \vec{0}$ and $\vec{b}.\vec{c} = 5.$
Then the value of 3($\vec{c}.\vec{a}$) is equal to

For $\alpha \in N$, consider a relation $R$ on $N$ given by $R=\{(x, y): 3 x+\alpha y$ is a multiple of 7$\}$ The relation $R$ is an equivalence relation if and only if :

The area of the region enclosed between the parabolas y² = 2x – 1 and y² = 4x – 3 is

If the sum of the first ten terms of the series
$\frac{1}{5} + \frac{2}{65} + \frac{3}{325} + \frac{4}{1025} + \frac{5}{2501}$+… is $\frac{m}{n}$,
where m and n are co-prime numbers, then m + n is equal to __________.

Let the mirror image of the point (a, b, c) with respect to the plane 3x – 4y + 12z + 19 = 0 be (a – 6, β, γ). If a + b + c = 5, then 7β – 9γ is equal to __________.

Let E₁, E₂, E₃be 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 :

If $∫\frac{1}{x}$ $√{\frac{1-x}{1+x}}$ dx = $g(x) + c,g(1) = 0$ , then g $(\frac{1}{2})$
is equal to

Choose the correct answer :

1. The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :

The number of ways to distribute 30 identical candies among four children C₁, C₂, C₃ and C₄ so that C₂ receives atleast 4 and atmost 7 candies, C₃ receives atleast 2 and atmost 6 candies, is equal to:

g :R→R be two real valued functions defined as
$f(x) = \begin{cases} -|x + 3| & x < 0 \\ e^x, & x \geq 0 \end{cases}$
and
$g(x) = \begin{cases} x^2 + k_1x ,& x < 0 \\ 4x + k_2 ,& x \geq 0 \end{cases}$
where k₁ and k₂ are real constants. If (goƒ) is differentiable at x = 0, then (goƒ) (–4) + (goƒ) (4) is
equal to:

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle, Then the area of ΔPQR is

Let the mean and the variance of 5 observations x₁, x₂, x₃, x₄, x₅ be $\frac{24}{5} $ and $\frac{194}{25}$, respectively. If the mean and variance of the first 4 observations are $\frac{7}{2}$ and a, respectively, then (4a + x₅) is equal to

$\lim_{{x \to \frac{1}{\sqrt{2}}}} \frac{\sin(\cos^{-1}(x)) - x}{1 - \tan(\cos^{-1}(x))}$
is equal to :

The normal to the hyperbola
$\frac{x²}{a²} - \frac{y²}{9} = 1$
at the point (8, 3√3) on it passes through the point:

Let $\hat a$ and $\hat b$ be two unit vectors such that the angle between them is $\frac{\pi}{4}$. If θ is the angle between the vectors ($\hat a$+$\hat b$) and ($\hat a$+2$\hat b$+2($\hat a$×$\hat b$)), then the value of 164 cos²θ is equal to :

If the inverse trigonometric functions take principal values, then
$cos^{-1} ( \frac{3}{10} cos (tan^{-1} (\frac{4}{3})) + \frac{2}{5} sin (tan^{-1} (\frac{4}{3})))$
is equal to :

Let X be a binomially distributed random variable with mean 4 and variance 4/3. Then, 54 P(X≤ 2) is equal to

The integral $\int_0^{\frac{\pi}{2}} \frac{1}{3 + 2\sin x + \cos x} \, dx$ is equal to

Let z₁ and z₂ be two complex numbers such that

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

If the foot of the perpendicular from the point $A(–1, 4, 3)$ on the plane $P : 2x + my + nz = 4$, is $\left(-2, \frac{7}{2}, \frac{3}{2}\right)$, then the distance of the point A from the plane P, measured parallel to a line with direction ratios $3, –1, –4$, is equal to

The ordered pair (a, b), for which the system of linear equations
3x – 2y + z = b
5x – 8y + 9z = 3
2x + y + az = –1
has no solution, is :

Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x – 3y + 5z = 8. If the mirror image of the point
$(2,−\frac{1}{2},2) $
in the rotated plane is B( a, b, c),then

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is