Practice/Question bank/JEE Main

JEE Main practice questions

NTA-style Physics, Chemistry and Maths MCQs with solutions. 2,688 questions in the bank.

1. 1If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$,then k is equal toMathematics· Special functions· Tough
2. 2Let $\alpha$ and $\beta$ be two roots of the equation x^2 + 2x + 2 = 0, then $\alpha^{15}\ + \beta^{15}$ is equal toMathematics· Quadratic Equations· Tough
3. 3The coefficient of t^4 in the expansion of $\left( \frac{1 - t^{6}}{1 - t} \right)^{3}$ isMathematics· Binomial Theorem· Moderate
4. 4The area of the region A = in square units, isMathematics· Integration· Tough· figure
5. 5If the eccentricity of the hyperbola $x^{2} - y^{2}\sec^{2}\alpha = 5\ is\ \sqrt{3}$ times the eccentricity of the ellipse x^2 sec^2α + y^2…Mathematics· Conic Sections· Moderate
6. 6Let A is a non - zero matrix of order such that A + adj A = A^-1 then determinant of (2A^-1) is equal toMathematics· Matrix and determinants· Moderate
7. 7Unit vectors [IMAGE] and [IMAGE] is coplanar; unit vector [IMAGE] is perpendicular to them. If [IMAGE] and angle between [IMAGE] and…Mathematics· Vectors· Tough· figure
8. 8Let (1 + x)^n = 1 + a_1x + a_2x^2 +...+ a_nx^n. If a_1, a_2 and a_3 are in AP, then the value of n isMathematics· Sequences and Series· Tough· figure
9. 9Function f(x) is defined such that [IMAGE] then identify the INCORRECT option ?Mathematics· Continuity and differentiability· Moderate· figure
10. 10A game is played with a special fair cubic die which has one red side, two blue sides, and three green sides. The result is the colour of…Mathematics· Probability· Moderate· figure
11. 11The lengths of sides of a triangle are three consecutive natural numbers and its largest angle is twice the smaller one. Perimeter of the…Mathematics· Properties of triangle· Tough
12. 12Let PQ be the common tangent to circles x^2 + y^2 + 2x = 0 and x^2 + y^2 - 6x = 0 as shown in figure, then find the area of the shaded…Mathematics· Circles· Moderate· figure
13. 13$\int_{0}^{\infty}\mspace{2mu}\frac{\mathcal{l}n2x}{1 + x^{2}}$ dx is equal toMathematics· Definite Integration· Easy
14. 14The center of set of circles, each of radius 3, lies on the circles x^2 + y^2 = 25. The locus of any point in the set isMathematics· Circles· Tough
15. 15Number of integral values of m for which the inequality $\frac{x^{2} - mx - 2}{x^{2} - 3x + 4} > - 1$ is satisfied by all real values of x.Mathematics· Inequalities· Easy
16. 16Number of ways in which AAA B B B can be placed in the squares of the figure as shown, so that no row remains empty, isMathematics· Permutations and Combinations· Moderate· figure
17. 17If $\alpha,\beta,\gamma,\delta$ are the solutions of the equation $\tan\left( \theta + \frac{\pi}{4} \right) = 3tan3\theta$ (where no two…Mathematics· Trigonometry· Moderate
18. 18The statement $(p \Rightarrow q) \Leftrightarrow ( \sim p \land q)$ is equivalentMathematics· Logical reasoning· Easy
19. 19Find the number of positive integral ordered pairs of (x, y) so that 8, x, y are in harmonic progression.Mathematics· Sequences and Series· Easy
20. 20In $\bigtriangleup$ABC,$\angle C = 2\angle$A and AC = 2BC. Then the value of $\frac{2\left( a^{2} + b^{2} + c^{2} \right)}{R^{2}}$ (where R…Mathematics· Easy
21. 21The point (x, y) lies on the line 2x + 3y = 6. The smallest value of the quantity $\sqrt{x^{2} + y^{2}}$ is m. Then the value of 26m^2 / 5…Mathematics· Straight Lines· Tough
22. 22Let S = $\sum_{n = 1}^{9999}\mspace{2mu}\frac{1}{(\sqrt{n} + \sqrt{n + 1})(\sqrt[4]{n} + \sqrt[4]{n + 1})}$, then 2S equalsMathematics· Sequences and Series· Moderate
23. 23Let is a square matrix of order 2 where a_ij$\in$ then number of matrices A such that A^-1 exists is $\lambda$ then $\lambda$- 300 is…Mathematics· Matrix and determinants· Tough· figure
24. 24The set of value of if the equation x^3 - 3x^2 + 2 = k has only 1 real root is equal to $( - \infty,a) \cup (b,\infty)$. Find value of…Mathematics· Theory of Equations· Moderate· figure