Practice/Question bank/JEE Main

JEE Main practice questions

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

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  1. 1Number of positive integral values of x satisfying the inequality $\frac{(x - 4)^{2017} \cdot (x + 8)^{2016}(x + 1)}{x^{2016}(x - 2)^{3}…Mathematics· Inequalities and absolute value· Moderate· figure
  2. 2Which of the following is a null set?Mathematics· Sets· Easy· figure
  3. 3If $\log_{a}(ab) = x$ then $\log_{b}(ab)$ is equal toMathematics· Logarithm and its applications· Easy
  4. 4Number of elements in set $A = \left\{ p:p = \frac{\left( 2n^{5} + 3n^{4} + 4n^{3} + 5n^{2} + 6 \right)(n + 2)}{n^{2} + 2n};n,p \in Z^{+}…Mathematics· Sets· Easy
  5. 5A class has 175 students. The following data shows the number of students obtaining one or more subjects: Mathematics 100, Physics 70,…Mathematics· sets· Moderate· figure
  6. 6The highest composite number satisfying the rational inequality $1 < \frac{3x^{2} - 7x + 8}{x^{2} + 1} \leq 2$ isMathematics· Inequalities and absolute value· Moderate· figure
  7. 7The product of integral solution of the equation $|||x - 1| - 2| - 1| = 2$ is $- \lambda$ then find the value of $\lambda$.Mathematics· Inequalities and absolute value· Tough
  8. 8If the value of $\left( \frac{1}{49} \right)^{1 + \log_{7}2} + 5^{- \log_{1/5}7}$ is $a + \frac{1}{b}(where\ a,b \in N)$ then find the…Mathematics· Logarithm and its applications· Tough
  9. 9If a set has 2 elements then the difference between the subsets of its powers set and number of its subset isMathematics· Sets· Moderate
  10. 10If A and B be two sets such that n(A) = 15, n(B) = 25, then number of possible values of $n(A\Delta B)$ (symmetric difference of A and B) isMathematics· Sets· Tough
  11. 11In a certain town, 25 of the families own a phone and 15 own a car; 65 families own neither a phone nor a car and 2,000 families own both a…Mathematics· Sets· Moderate· figure
  12. 12The number of integers satisfying the inequality $\frac{(x - 1)(x - 2)(x - 3)}{(x + 1)(x + 2)(x + 3)} \leq 0$ isMathematics· Inequalities and absolute value· Easy· figure
  13. 13The number of positive integral values of x satisfying the inequality $\frac{\left( 3^{x} - 5^{x} \right)(x - 2)}{\left( x^{2} + 5x + 2…Mathematics· Inequalities and absolute value· Tough
  14. 14The number of negative integers satisfying the equation $|2x - 4| - 2\left| x^{2} + x - 3 \right| + 2|(x - 1)(x + 1)| = 0$ isMathematics· Inequalities and absolute value· Moderate
  15. 15The complete solution set of $\left| \frac{2x - 1}{x - 1} \right| > 2$ isMathematics· Inequalities and absolute value· Easy
  16. 16For the equation 3x^2 + px + 3 = 0, p > 0 if one of the roots is square of the other, then p is equal toMathematics· Theory of Equations· Moderate
  17. 17If the equations k (6x^2 + 3) + rx + 2x^2 - 1 = 0 and 6k (2x^2 + 1) + px + 4x^2 - 2 = 0 have both roots common, then the value of (2r - p)…Mathematics· Theory of Equations· Tough
  18. 18If a, b, p, q are non-zero real numbers, then two equations 2a^2 x^2 - 2 ab x + b^2 = 0 and p^2 x^2 + 2 pq x + q^2 = 0 haveMathematics· Theory of Equations· Easy
  19. 19The graphs of y = x^4 - 2x^2 + 5 isMathematics· Theory of Equations· Moderate
  20. 20The first term of an A.P. of consecutive integer is p^2 + 1. The sum of (2p + 1) terms of this series can be expressed asMathematics· Theory of Equations· Moderate
  21. 21Let 6 Arithmetic means $A_{1},A_{2},A_{3},A_{4},A_{5},A_{6}$ are inserted between two consecutive natural number a and (a > b). If…Mathematics· Series and progressions· Easy
  22. 22If S is the sum to infinity of a G.P. whose first term is then the sum of the first n terms isMathematics· Series and progressions· Tough
  23. 23For a sequence $\{ a_{n}\},a_{1} = 2$ and $\frac{a_{n + 1}}{a_{n}} = \frac{1}{3}$. Then [IMAGE] isMathematics· Series and progressions· Moderate· figure
  24. 24If a, b, c are in H.P. then the value of $\frac{b + a}{b - a} + \frac{b + c}{b - c}$ isMathematics· Series and progressions· Easy
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