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. 1The sum of infinite series $\frac{1.3}{2} + \frac{3.5}{2^{2}} + \frac{5.7}{2^{3}} + \frac{7.9}{2^{4}} + \ldots...\infty$Mathematics· Series and progressions· Tough
2. 2If A, G, H are respectively the A.M., G.M. & H.M. of three positive numbers a, b, & c then the equation whose roots are a, b, & c is given…Mathematics· Series and progressions· Moderate
3. 3If $\alpha,\ \beta,$ and $\gamma$ are the roots of the equation x^3 - x - 1 = 0 then, $\frac{1 + \alpha}{1 - \alpha} + \frac{1 + \beta}{1 -…Mathematics· Theory of Equations· Tough
4. 4Find the value of the expression $2x^{3} + 2x^{2} - 7x + 72$ when $x = \frac{3 + 5\sqrt{- 1}}{2}$Mathematics· Theory of Equations· Moderate
5. 5The value of $\sum_{r = 1}^{n}{\frac{1}{\sqrt{a + r}x + \sqrt{a + (r - 1)x}}\ }$isMathematics· Series and progressions· Moderate
6. 6If $ax^{2} + bx + c = 0\ and\ bx^{2} + cx + a = 0$ have a common root and a, b, c are non-zero real numbers, then find value of…Mathematics· Theory of Equations· Easy
7. 7Find the least prime integral value of such that the roots $\alpha,\beta$ of the equation $2x^{2} + 6x + a = 0$ satisfy the inequality…Mathematics· Theory of Equations· Moderate
8. 8Find the sum of first 35 terms of the series whose p^th term is $\frac{p}{7} + 2$.Mathematics· Theory of Equations· Tough
9. 9$10^{2} + 13^{2} + 16^{2} + \ldots$ upto 10 termsMathematics· Series and progressions· Moderate
10. 10If two roots of the equation x^3- px^2 + qx - r = 0, $(r \neq 0)$ are equal in magnitude but opposite in sign, thenMathematics· Theory of Equations· Easy
11. 11If one roots of equation $x^{2} - \sqrt{3}x + \lambda = 0,\lambda \in R\ is\ \sqrt{3} + 2$ then other root isMathematics· Theory of Equations· Easy
12. 12Let a and b be real numbers such that 4a + 2b + c = 0 and ab > 0. Then the equation ax^2 + bx + c = 0 hasMathematics· Theory of Equations· Moderate
13. 13If f(x) = x^2 + 2bx + 2c^2 and g(x) = - x^2 - 2cx + b^2 are such that min f(x) > max g(x), then the relation between b and c, isMathematics· Theory of Equations· Tough
14. 14The expression y = ax^2 + bx + c has always the same sign as of ifMathematics· Theory of Equations· Easy· figure
15. 15If $\alpha,\beta$ are the roots of the quadratic equation x^2 - 2p(x - 4) -15 = 0, then the set of values of for which one root is less…Mathematics· Theory of Equations· Moderate· figure
16. 16Set of real values of k if the equation x^2 - (k-1)x + k^2 = 0 has at least one root in (1,2) isMathematics· Theory of Equations· Tough
17. 17The complex number z = x + iy which satisfy the equation $\left| \frac{z - 5i}{z + 5i} \right| = 1$ lies onMathematics· Complex Numbers· Moderate
18. 18Match List I with List II and select the correct answer using the code given below the lists: List - I List - II (P) If arg (z + 3) $=…Mathematics· Complex Numbers· Tough
19. 19In a triangle ABC, let D be the midpoint of BC. If angle ADB is 45º and angle ACD is 30º then angle BAD will be equal to?Mathematics· Triangles· Easy
20. 20Let $z_{1},\ z_{2},\ z_{3},\ z,\ \omega$ be complex numbers such that$\left| z_{1} \right| = 1,\left| z_{2} \right| = 2,\left| z_{3}…Mathematics· Complex Numbers· Tough
21. 21In a triangle ABC if the equation of medians AD and BE are 2x + 3y = 6 and 3x - 2y = 10 respectively. If AD = 6, BE = 11. Then the area of…Mathematics· Triangles· Easy· figure
22. 22Let area of $\Delta$ABC be 8 square units. Then the value of the expression E = b^2sin2C + c^2 sin 2B is equal to.Mathematics· Triangles· Moderate
23. 23In ∆ ABC with usual notation, let $\angle A\ = \ 36{^\circ},\ \ B\ = \ 54{^\circ}$ and $\angle\ C\ = \ 90{^\circ}$. If r is the inradius…Mathematics· Triangles· Easy
24. 24In $\Delta$ABC (with usual notations); a = 2b and $|A - B| = \frac{\pi}{3}$ then which of the following doesn't hold good?Mathematics· Triangles· Moderate