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. 1Which of the following statement is a tautology?Mathematics· Mathematical reasoning· Easy
2. 2If p: 4 is an even prime number q: 6 is a divisor of 12 r: HCF of 4 and 6 is 2, then which one of the following is trueMathematics· Mathematical reasoning· Moderate
3. 3If $\omega$ is an imaginary cube root of unity then the value of $sin\left( \left( \omega^{19} + \omega^{101} \right)\pi - \frac{\pi}{6}…Mathematics· Complex Numbers· Moderate
4. 4Length of tangents from A, B, C to the incircle are in A.P, thenMathematics· Triangles· Tough· figure
5. 5In an equilateral $\Delta$ABC, r, R, r_1, form (where symbols have usual meanings)Mathematics· Triangles· Easy
6. 6Let a triangle is formed by selecting 3 vertices of cuboid having length of edges are 3, 4 and 5. Find the probability that triangle formed…Mathematics· Triangles· Moderate
7. 7In a triangle ABC following usual notations, if r_1 = 12, r_2 = 18, r_3 = 36 then find the length of tangent from vertex A to excircle…Mathematics· Triangles· Tough· figure
8. 8In $\Delta$ABC internal angle bisectors AI, BI and CI are produced to meet opposite sides in C', respectively. Find the maximum value of…Mathematics· Triangles· Tough
9. 9If a polynomial is defined as P(x) = 2x^5 + ax^4 + bx^3 + cx^2 + dx + e such that P (0) = 4, PMathematics· Mathematical induction· Moderate
10. 10Consider the complex number z_1 = 10 + 6i and z_2 = 4 + 2i.(where $i = \sqrt{- 1})$If arg⁡$(\frac{z - z_{1}}{z - z_{2}}) = \frac{\pi}{4}$,…Mathematics· Complex Numbers· Moderate· figure
11. 11Let equation of two sides of a triangle are 4x + 5y = 20 and 3x - 2y + 6 = 0. If orthocenter of triangle is (1, 1) then the equation of…Mathematics· Triangles· Tough
12. 12If the vertices of a variable triangle are (3, 4), $(5cos\theta,5\sin\theta)$ and $(5\sin\theta, - 5\cos\theta)$, then the locus of its…Mathematics· Triangles· Moderate
13. 13If the points A(z), A(-z) and A(z -1) form an equilateral triangle then value of z isMathematics· Complex Numbers· Moderate
14. 14The complex z satisfies$|2z + 10 + 10i| \leq 5\sqrt{3} - 5$, and then the least principal argument of z isMathematics· Complex Numbers· Moderate· figure
15. 15Let p, q, r be three statements, then (p $\rightarrow$ (q $\rightarrow$ r)) $\rightarrow$ ((p $\rightarrow$ q) $\rightarrow$ r), is aMathematics· Mathematical reasoning· Easy
16. 16In a $\Delta$ABC, a, b, A are given and c_1, c_2 are two values of the third side c. The sum of the areas of two triangles with sides a, b,…Mathematics· Triangles· Easy
17. 17Consider the following statements P: Suman is brilliant Q: Suman is rich R: Suman is honest The negation of the statement "Suman is…Mathematics· Mathematical reasoning· Moderate
18. 18If n is even than [IMAGE]Mathematics· Binomial Theorem· Easy· figure
19. 19The contents of urn I and II are as follows, Urn I: 4 white and 5 black balls Urn II: 3 white and 6 black balls One urn is chosen at random…Mathematics· Probability· Tough· figure
20. 20If $\left( C_{0} + C_{1} \right)\left( C_{1} + C_{2} \right)\ldots\left( C_{n} - 1 + C_{n} \right) = mC_{1}C_{2}$......$C_{n - 1}$, then m…Mathematics· Binomial Theorem· Tough
21. 21The number of words from the letters of the word ' BHARAT in which B and H will never come together, isMathematics· Permutations and Combinations· Easy
22. 22If$\ x\ $follows binomial distribution with parameter n = 8 and p = $\frac{1}{2}$ then P $(|x - 4| \leq 2)$ is equal to$\ $Mathematics· Binomial Theorem· Moderate
23. 23$A = \{ 1,2,3,\ldots,9\}.$ If three numbers are selected from set A and are arranged, the probability that three numbers are either in…Mathematics· Probability· Easy· figure
24. 243 different numbers are selected at random from the set $A = \{ 1,2,3,\ldots\ldots.10\}$. Then the probability that the product of two…Mathematics· Permutations and Combinations· Moderate· figure