List of top Questions asked in JEE Main

The series of positive multiples of 3 is divided into sets: {3}, {6, 9, 12}, {15, 18, 21, 24, 27},…… Then the sum of the elements in the 11^th set is equal to ________.

Let the system of linear equations
x + y + az = 2
3x + y + z = 4
x + 2z = 1
have a unique solution (x*, y*, z*). If (α, x*), (y*, α) and (x*, –y*) are collinear points, then the sum of absolute values of all possible values of α is

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is $\frac1{n}$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 is:

Two inclined planes are placed as shown in figure. A block is projected from the point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top point B at a height 10 m. After reaching the point B the block sides down on inclined plane BC. Time it takes to reach to the point C from point A is t(√2 + 1) s. The value of t is ______.
(Use g = 10 m/s²)

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2Mg force. In this situation, tension in the string is x/5 Mg for x=__________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.
(Given g= acceleration due to gravity)

Let $(a_n)^∞_{n=0}$ be a sequence such that a₀=a₁=0 and $a_{n+2}=2a_{n+1}−a_n+1$ for all n⩾0. Then, $∑^∞_{n=2} \frac{a_n}{7^n}$ is equal to

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60 \%$ candidates qualify it The number of females qualifying the exam is twice the number of males qualifying it A candidate is randomly chosen from the qualified candidates The probability, that the chosen candidate is a female, is :

The odd natural number a, such that the area of the region bounded by $y = 1, y = 3, x = 0, x = y^a$ is $\frac {364}{3}$, is equal to

A light ray is incident at an incident angle θ₁on the system of two plane mirrors M₁ and M₂ having an inclination angle 75° between them (as shown in figure).
After reflecting from mirror M₁ it gets reflected back by the mirror M₂ with an angle of reflection 30°. The total deviation of the ray will be ________ degree.

A light ray is incident, at an incident angle θ1

The sum 1 + 2 ⋅ 3 + 3 ⋅ 3² + …. + 10 ⋅ 3⁹ is equal to

Let S = {1, 2, 3, 4}.Then the number of elements in the set {f : S × S → S : f is onto and f(a,b)=f(b,a) ≥ a ∀ (a, b)∈ S × S is _____.

If the line y = 4 + kx, k > 0, is the tangent to the parabola y = x – x² at the point P and V is the vertex of the parabola, then the slope of the line through P and V is:

The value of $cos⁡(\frac{2π}{7})+cos⁡(\frac{4π}{7})+cos⁡(\frac{6π}{7})$ is equal to:

Let $S=\left\{θ∈[0,2π]:8^{2sin^2⁡θ}+8^{2cos^2⁡θ}=16\right\}$ .
Then$n(S) + \sum_{\theta \in S}\left( \sec\left(\frac{\pi}{4} + 2\theta\right)\cosec\left(\frac{\pi}{4} + 2\theta\right)\right)$is equal to :

A zener of breakdown voltage V_Z = 8 V and maximum Zener current, I_ZM = 10 mA is subjected to an input voltage V_i = 10 V with series resistance R = 100 Ω. In the given circuit R_L represents the variable load resistance. The ratio of maximum and minimum value of R_L is __________.

The number of elements in the set S= {x∈R : 2cos⁡$(\frac{x_2+x}{6})$=$4^x+4^{-x}$}

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over a frictionless pulley as shown below.
The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of the block is (Given g = 10 ms^–2)

A person moved from A to B on a circular path as shown in figure If the distance travelled by him is 60 m, then the magnitude of displacement would be Given ( Cos 135° = -0.7)

Let

$S=\left\{x∈[-6,3]-\left\{-2,2 \right\} :\frac{|x+3|-1}{|x|-2}>=0 \right\} \space and \space \left\{T={x∈Z:x^2-7|x|+9<=0}\right\}$

Then the number of elements in S ⋂ T is

Haemoglobin contains $0.34\%$ of iron by mass. The number of Fe atoms in $3.3$ g of haemoglobin is(Given: Atomic mass of Fe is $56$ u, $N_A$ = $6.022 × 1023$ $mol^{–1}$)

Let $\frac{dy}{dx} = \frac{ax-by+a}{bx+cy+a}$, where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is

Let p and p + 2 be prime numbers and let
$Δ=\begin{vmatrix} p! & (p+1)! & (p+2)! \\ (p+1)! & (p+2)! & (p+3)! \\ (p+2)! & (p+3)! & (p+4)! \\ \end{vmatrix}$
Then the sum of the maximum values of α and β, such that p^α and (p + 2)^β divide Δ, is _______.

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

If for p ≠ q ≠ 0, the function
$f(x) = \frac{{^{\sqrt[7]{p(729 + x)-3}}}}{{^{\sqrt[3]{729 + qx} - 9}}}$
is continuous at x = 0, then

Sum of oxidation state (magnitude) and coordination number of cobalt in $Na[Co(bpy)Cl_4]$ is____ .
(Given : bpy =

)