List of top Questions asked in JEE Main- 2022

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
Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z – 1) – arg(z + 1) = π/4 intersect

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

The area of the region 
\(\begin{array}{l} \left\{\left(x,y\right);\left|x-1\right|\leq y \leq \sqrt{5-x^2} \right\}\end{array}\)
is equal to
If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum 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
\(\begin{array}{l}(p \land r )\Leftrightarrow ( p \land (\sim q))\end{array}\)is equivalent to (~ p) when r is
Let f be a differentiable function in \((0, \frac{π}{2})\). If \(∫_{cosx} ^1 t^2f(t)dt=sin^3x+cosx\), then \(\frac{1}{\sqrt3}f'(\frac{1}{\sqrt3})\) is equal to

The area bounded by the curves y = |x2 – 1| and y = 1 is

The area of the region
\(\left\{(x,y) : y² ≤ 8x, y ≥ \sqrt2x, x ≥ 1 \right\}\)
is

Let the solution curve \(y = y(x)\) of the differential equation \((1 + e^{2x})\left(\frac{dy}{dx} + y\right) = 1\) pass through the point \((0, \frac{\pi}{2})\). Then, \(\lim_{{x \to \infty}} e^x y(x)\) is equal to

Match List-I with List-II :
 

List-IList-II
(A) Negatively charged sol(I) Fe2O3.xH2O
(B) Macromolecular colloid(II) CdS sol
(C) Positively charged sol(III) Starch
(D) Cheese(IV) a gel


Choose the correct answer from the options given below:

Consider the above reaction, the compound ‘A’ is :

Fig.
Which of the following oxoacids of sulphur contains \(S\) in two different oxidation states?
In neutral or faintly alkaline medium, KMnO4 being a powerful oxidant can oxidize, thiosulphate almost quantitatively, to sulphate. In this reaction overall change in oxidation state of manganese will be
Statement-I: An alloy of lithium and magnesium is used to make aircraft plates. 
Statement-II: The magnesium ions are important for cell-membrane integrity. 
In the light of the above statements, choose the correct answer from the options given below:
Which statement is not true with respect to nitrate ion test?
Time period of a simple pendulum in a stationary lift is ‘T’. If the lift accelerates with \(\frac{g}{6}\) vertically upwards then the time period will be (Where g = acceleration due to gravity)
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 block of mass 40 kg slides over a surface
One end of a massless spring of spring constant k and natural length \(l_0\) is fixed while the other end is connected to a small object of mass \(m\) lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(ω\) about an axis passing through fixed end, then the elongation of the spring will be :
A beam of light travelling along X-axis is described by the electric field Ey = 900sin ω(t – x/c). The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of 3 × 107 ms–1 will be :
(Given speed of light = 3 × 108 ms–1)
For a transistor to act as a switch, it must be operated in
A block of mass M placed inside a box descends vertically with acceleration ‘a’.The block exerts a force equal to one-fourth of its weight on the floor of the box.
The value of ‘a’ will be
An npn transistor with current gain \(β = 100\) in common emitter configuration is shown in the figure. The output voltage of the amplifier will be
npn transistor with current gain
A potentiometer wire of length 10 m and resistance 20 Ω is connected in series with a 25 V battery and an external resistance 30 Ω. A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The value of E (in volt) is \(\frac {x}{10}\). The value of \(x\) is ______.