List of top Questions asked in JEE Main

If [t] denotes the greatest integer ≤ t, then the number of points, at which the function
$f(x) = 4|2x + 3| + 9\lfloor x + \frac{1}{2} \rfloor - 12\lfloor x + 20 \rfloor$
is not differentiable in the open interval (–20, 20), is ____ .

Let $S_1=\left\{z_1 \in C:\left|z_1-3\right|=\frac{1}{2}\right\}$ and $S _2=\left\{ z _2 \in C :\left| z _2-\right| z _2+1||=\left| z _2+\right| z _2-1||\right\}$ Then, for $z_1 \in S_1$ and $z_2 \in S_2$, the least value of $\left|z_2-z_1\right|$ is :

A Carnot engine has efficiency of $50 \%$ .If the temperature of sink is reduced by $40^{\circ} C$, its efficiency increases by $30 \%$ .The temperature of the source will be :

A uniform metal chain of mass m and length ‘$L$’ passes over a massless and frictionless pully. It is released from rest with a part of its length ‘$l$’ is hanging on one side and rest of its length '$L – l$' is hanging on the other side of the pully. At a certain point of time, when $l = L/x$, the acceleration of the chain is $g/2$. The value of $x$ is ______.

If the system of linear equations
2x + 3y – z = –2
x + y + z = 4
x – y + |λ|z = 4λ – 4
where λ ∈ R, has no solution, then

If the initial velocity in horizontal direction of a projectile is unit vector $\hat i$ and the equation of trajectory is $y = 5x(1 – x)$. The y component vector of the initial velocity is ______ $\hat j$.
(Take $g=10\ m/s^2$)

Let f(x)=$\left\{\begin{matrix} |4x^2-8x+5|, & if\,8x^2-6x+1\geq0 \\ |4x^2-8x+5|, & if\,8x^2-6x+1<0 \end{matrix}\right.$ where [α] denotes the greatest integer less than or equal to α.Then the number of points in R where f is not differentiable 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?

When a certain amount of solid A is dissolved in 100 g of water at 25°C to make a dilute solution, the vapour pressure of the solution is reduced to one-half of that of pure water. The vapour pressure of pure water is 23.76 mmHg. The number of moles of solute A added is _________. (Nearest Integer).

A √(34) m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If F_f and F_w are the reaction forces of the floor and the wall, then ratio of F_w/F_f will be:
(Use g = 10 m/s²)

Let the function
$f(x)$=$\begin{cases} \frac{\log_e(1+5x) - \log_e(1+\alpha x)}{x}, & \text{if } x ∈ 0 \\ \space 10 & \text;{if } x = 0 \\ \end{cases}$
be continuous at x = 0. Then α is equal to

Let A be a $2×2$ matrix with $det (A) = –1$ and $det((A + I) (Adj (A) + I)) = 4$. Then the sum of the diagonal elements of A can be

A plane of electromagnetic waves travels in a medium with a relative permeability of 1.61 and relative permittivity of 6.44. If the magnitude of magnetic intensity is 4.5 × 10^–2 Am^–1at a point, what will be the approximate magnitude of electric field intensity?(Given: Permeability of free space μ₀ = 4π × 10^–7 NA^–2, speed of light in vacuum c = 3 × 10⁸ ms^–1)

SO₂Cl₂ in reaction with an excess water results in the acidic mixture
SO₂CL₂+2H₂O$\rightarrow$H₂SO₄+2HCL
16 moles of NaOH is required for the complete neutralization of the resultant acidic mixture. The number of moles of SO₂Cl₂ used is

Let A=$\begin{pmatrix} 2 &-1 &-1 \\ 1&0 &-1 \\ 1&-1 &0 \end{pmatrix}$ and B=A–I. If ω=$\frac{\sqrt3 i-1}{2}$, then the number of elements in the set {n∈{1,2,⋯,100}:$A^n+(ωB)^n$=A+B} is equal to _______.

$\sum_{r=1}^{20}$(r²+1)(r!) is equal to

A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100 °C, then the internal energy for vaporization in kJ mol^–1 is ________. [nearest integer]
[Assume steam to be an ideal gas. Given Δ_vapH^Θ for water at 373 K and 1 bar is 41.1 kJ mol^–1; R = 8.31 J K^–1 mol^–1]

If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for the coefficient of viscosity is

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
$A = \begin{pmatrix} 1+i & 1 \\ -i & 0 \end{pmatrix}$ where $i=\sqrt{−1}.$
Then, the number of elements in the set
$\left\{n∈\left\{1,2,…,100\right\}:A^n=A\right\}$
is ________.

$\int_{0}^{2} \left( |2x^2 - 3x| + \left[x - \frac{1}{2}\right] \right) \, dx,$
where [t] is the greatest integer function, is equal to

Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be 98/25. Then the sum of the first 21 terms of an AP, whose first term is 10ar, n^th term is a_n and the common difference is 10ar², is equal to

Let A = {1, a₁, a₂…a₁₈, 77} be a set of integers with 1 <a₁<a₂<….<a₁₈< 77. Let the set A + A = {x + y :x, y∈A} contain exactly 39 elements. Then, the value of a₁ + a₂ +…+a₁₈ is equal to _____.

If the system of linear equations.
$8x + y + 4z = –2$
$x + y + z = 0$
$λx–3y=μ$
has infinitely many solutions, then the distance of the point $(λ, μ, -1/2)$ from the plane $8x + y + 4z + 2 = 0$ is

Let α, β(α > β) be the roots of the quadratic equation x² – x – 4 = 0.
If $P_n=α^n–β^n, n∈N$ then $\frac{P_{15}P_{16}–P_{14}P_{16}–P_{15}^2+P_{14}P_{15}}{P_{13}P_{14}}$
is equal to _______.