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 $\left| z_{1} + z_{2} \right|^{2} = \left| z_{1} \right|^{2} + \left| z_{z} \right|^{2}$ then which of the following is incorrect.Mathematics· Complex Numbers· Easy / Moderate/ Tough· figure
2. 2If a > 0 and the equation $\left| z - a^{2} \right| + |z - 2a| = 3$ represents an ellipse, then complete set of values of a isMathematics· Complex Numbers· Easy
3. 3If $z^{2} + z|z| + \left| z^{2} \right| = 0,$ then the locus of z isMathematics· Complex Numbers· Moderate
4. 4The value of $\frac{tan20^{\circ}}{cot70^{\circ}}$ is equal to.Mathematics· Trigonometry· Easy
5. 5If A + B = $\frac{\pi}{4},$ then (tan⁡A+1)(tan⁡B+1) is equal to.Mathematics· Trigonometry· Easy
6. 6If $4\sin^{4}x + \cos^{4}x = 1,x \neq n\pi\ $then xMathematics· Trigonometry· Moderate
7. 7The period of the function f(x) $= \frac{|sinx| + |cosx|}{|sinx - cosx|}$ is.Mathematics· Functions· Tough
8. 8The modulus and the principal argument of the complex number [IMAGE] are respectivelyMathematics· Complex Numbers· Moderate· figure
9. 9The number of values of x in the interval satisfying the equation 3sin^2x - 7 sin x + 2 = 0 isMathematics· Trigonometry· Easy
10. 10The sum of series $\frac{\ ^{50}C_{0}}{50!50!} + \frac{\ ^{50}C_{1}}{49!51!} + \frac{\ ^{50}C_{2}}{48!52!}$+.........+$\frac{\…Mathematics· Binomial Theorem· Moderate
11. 11If |z_1| = 1, |z_2| =2, |z_3| = 3 and |z_2z_3 + 4z_1z_3 + 9z_1z_2| = 12, then the value of |z_1+ z_2 + z_3| equalsMathematics· Complex Numbers· Moderate· figure
12. 12If numerically greatest term in the expansion of (1- x)^21 has the numerically greatest co-efficient is (x > 0) then complete set of values…Mathematics· Binomial Theorem· Moderate
13. 13Given the relation R = on the set A=. The minimum number of ordered pairs which when added to R make it an equivalence relation isMathematics· Relation· Easy
14. 14If $\ \frac{z - (1 + i)}{z + (1 + i)}$ is purely imaginary then z lies on a circle. Find radius of circleMathematics· Complex Numbers· Moderate· figure
15. 15If $arg(\frac{z - i}{z + i}) = \frac{3\pi}{4}$, and minimum value of |z| is λ then value of is greatest integer function.Mathematics· Complex Numbers· Tough· figure
16. 16If the value of $sin10^{\circ}sin70^{\circ}sin50^{\circ}$ is equal to K then $\frac{1}{K}$ is equal toMathematics· Trigonometry· Moderate
17. 17The values of $\theta$ satisfying $\sin{7\theta} = sin4\theta - sin\theta$ and $0 < \theta < \frac{\pi}{2}\ are\…Mathematics· Trigonometry· Tough
18. 18If |Z - 3i| = 3 and arg [IMAGE], then cot(arg Z) - [IMAGE] is equal toMathematics· Complex Numbers· Moderate· figure
19. 19If the real part of [IMAGE] is equal to the imaginary part of [IMAGE], then the point Z lies on aMathematics· Complex Numbers· Tough· figure
20. 20If z_1 and z_2 are non-zero complex numbers such that |z_1 - z_2| = |z_1| + |z_2|, thenMathematics· Complex Numbers· Easy· figure
21. 21There are 100 families in a society, 40 families buy newspaper A, 30 families buy newspaper B, 30 families buy newspaper C, 10 families buy…Mathematics· Sets· Moderate· figure
22. 22In a given venn-diagram the value of p + q + r is- $\ $(where$\ \left. \ n(A \cup B \cup C) + n(A \cup B \cup C)^{'} = 50 \right)$Mathematics· Sets· Easy· figure
23. 23If $g(x) = \sin^{2}x + \sin^{2}\left( \frac{\pi}{3} + x \right) + cosx \cdot cos\left( x + \frac{\pi}{3} \right)\ and\ f\left( \frac{5}{4}…Mathematics· Functions· Moderate
24. 24Let f(x): (-1, 1) $\rightarrow$ B be a function defined by f(x) $= \tan^{- 1}\left( \frac{2x}{1 - x^{2}} \right)$, if f (x) is bijective,…Mathematics· Functions· Tough