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. 1A line makes equal angles with the diagonals of a cube. What is the sine of that angle?,d js[kk ?ku ds fod.kZ ds lkFk cjkcj dks.k cukrhMathematics· Three dimension· Tough· figure
2. 2A person throws dice, one the common cube and the other regular terahedron, the number on the lowest face being taken in the case of a…Mathematics· Probability· Tough
3. 3The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, centre at the origin and…Mathematics· Differential equation· Moderate
4. 45 students of a class have an average height 150 cm and variance 18 cm^2. A new student, whose height is 156 cm, joined them. the variance…Mathematics· Statistics· Tough· figure
5. 5Let the equations of two sides of a triangle be 3x - 2y + 6 = 0 and 4x + 5y - 20 = 0. If the orthocentre of this triangle is at (1, 1),…Mathematics· Tough
6. 6Let f be a differentiable function from R to R such that $|f(x) - f(y)| \leq 2|x - y|^{3/2}$, for all x, y $\in$ R. If f(0) = 1 then…Mathematics· Continuity and differentiability· Tough
7. 7Let A(4, -4) and B(9, 6) be points on the parabola, y^2 = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such…Mathematics· Parabola· Tough· figure
8. 8A point P moves on the line 2x - 3y +4 = 0. If Q(1, 4) and R(3, -2) are fixed points, then the locus of the centroid of $\Delta$PQR is a…Mathematics· Straight Lines· Tough
9. 9If [IMAGE] then k equalsMathematics· Binomial Theorem· Easy / Moderate/ Tough· figure
10. 10Let n ≥ 2 be a natural number and $0 < \theta < \pi/2.$ Then $\int\frac{\left( \sin^{n}\theta - sin\theta…Mathematics· Integration· Tough
11. 11Let $f(x) = \left\{ \begin{matrix} \max\left\{ |x|,x^{2} \right\}, & |x| \leq 2 \\ 8 - 2|x|, & 2 < |x| \leq 4 \end{matrix} \right.\ $ Let S…Mathematics· Sets· Moderate· figure
12. 12If 5, 5r, 5r^2 are the lengths of the sides of a triangle, then r cannot be equal toMathematics· Tough
13. 13Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m. A vertical lamp post at the mid point D of AC subtends an angle…Mathematics· Moderate· figure
14. 14Let $I = \int_{a}^{b}\mspace{2mu}\left( x^{4} - 2x^{2} \right)dx.$ If 1 is minimum then the ordered pair (a,b) isMathematics· Integration· Tough· figure
15. 15Equation of a common tangent to the circle, x^2 + y^2 - 6x = 0 and the parabola, y^2 = 4x, isMathematics· Circle and parabola· Tough
16. 16If the third term in the binomial expansion of $\left( 1 + x^{\log_{2}x} \right)^{5}$ equals 2560, then a possible value of x isMathematics· Binomial Theorem· Moderate
17. 17Suppose [IMAGE] holds for some positive integer n. Then [IMAGE] equals.Mathematics· Binomial Theorem· Tough· figure
18. 18Let [IMAGE] and $\overrightarrow{b} = \imath + 2j + k$be two vectors. Consider a vector [IMAGE] R. If the projection of [IMAGE] on the…Mathematics· Vectors· Tough· figure
19. 19Let |X| denote the number of elements in a set X. Let S = be a sample space, where each element is equally likely to occur. If A and B are…Mathematics· Probability· Tough· figure
20. 20The value of $\sec^{- 1}\left( \frac{1}{4}\sum_{k = 0}^{10}\mspace{2mu} sec\left( \frac{7\pi}{12} + \frac{k\pi}{2} \right)sec\left(…Mathematics· Inverse Trigonometric functions· Tough
21. 21Five persons A,B,C,D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and…Mathematics· Permutations and Combinations· Tough
22. 22Let $A = \left\{ \theta \in \left( - \frac{\pi}{2},\pi \right):\frac{3 + 2isin\theta}{1 - 2isin\theta}\ ispurely\ imaginary\ \right\}.$…Mathematics· Complex Numbers· Tough· figure
23. 23If $A = \begin{bmatrix} cos\theta & - sin\theta \\ sin\theta & cos\theta \end{bmatrix}$, then the matrix $A^{- 50}when\ \theta =…Mathematics· Matrix· Tough
24. 24$\lim_{y \rightarrow 0}\mspace{2mu}\frac{\sqrt{1 + \sqrt{1 + y^{4}}} - \sqrt{2}}{y^{4}}$Mathematics· Limits· Tough