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. 1If a variable tangent to the curve $x^{2}y = c^{3}$ makes intercepts a, b on x and y axis respectively, then the value of $a^{2}b$ isMathematics· Application of derivatives· Tough
  2. 2The number of zeroes at the end of $(101)^{11} - 1$ isMathematics· Binomial Theorem· Tough· figure
  3. 3A and B are two independent events. The probability that both A and B occur simultaneously is $\frac{1}{6}$ and the probability that…Mathematics· Probability· Moderate· figure
  4. 4The line y = mx bisects the area enclosed by the curve y = 1 + 4x - x^2 and the lines x = 0, x = $\frac{3}{2}$ and y = 0.Then the value of…Mathematics· Area under curve· Tough· figure
  5. 5Mr. A lives at origin on the cartesian plane and has his office at (4, 5). His friend lives at (2, 3) on the same plane. Mr. A can go to…Mathematics· Probability· Tough· figure
  6. 6[IMAGE] are three non coplanar vectors. If [IMAGE] is perpendicular to [IMAGE], then minimum value of x^2 + y^2 is. yEcor~ rksa x^2 + y^2…Mathematics· Vectors· Tough· figure
  7. 7Three shots are fired independently at a target in succession. The probabilities of a hit in the first shot is $\frac{1}{2}$, in the second…Mathematics· Probability· Tough
  8. 8The expression in the vector form for the point [IMAGE] of intersection of the plane $\overrightarrow{r}.\overrightarrow{n} = d$ and the…Mathematics· Vectors· Tough· figure
  9. 9There are 6 red balls and 6 green balls in a bag. Five balls are drawn out at random and placed in a red box. The remaining seven balls are…Mathematics· Probability· Easy / Moderate/ Tough
  10. 10Let [IMAGE] and [IMAGE]. The point of intersection of the lines [IMAGE] andMathematics· Vectors· Tough· figure
  11. 11The area of the closed figure bounded by x = - 1, x = 2 and y = $\left\{ \begin{matrix} - x^{2} + 2, & x \leq 1 \\ 2x - 1, & x > 1…Mathematics· Area under curve· Tough· figure
  12. 12A vector [IMAGE] of magnitude $20\sqrt{6}$ parallel to the bisector of the angle between [IMAGE] andMathematics· Vectors· Tough· figure
  13. 13The three vectors [IMAGE] taken two at a time form three planes. The three unit vectors drawn perpendicular to these three planes form a…Mathematics· Vectors· Tough· figure
  14. 14If the line y = mx, bisects the area of the region $\left\{ (x,y):0 \leq x \leq \frac{3}{2},0 \leq y \leq 1 + 4x - \ \ \ \ \ \ \ \ \ \ \ \…Mathematics· Area under curve· Tough· figure
  15. 15Let [IMAGE] and [IMAGE]. If [IMAGE] is a vector such that [IMAGE] and the angle between [IMAGE] and [IMAGE] is 30º, then the magnitude of…Mathematics· Vectors· Tough· figure
  16. 16A mapping is selected at random from all the mappings defined on set A =. If the selected mapping is an injective mapping, then what is the…Mathematics· Probability· Tough
  17. 17In a triangle PQR, S and T are points on QR and PR respectively, such that QS = 3SR and PT = 4TR. Let M be the point of intersection of PS…Mathematics· Vectors· Tough
  18. 18If the shortest distance between the lines$x + 2\lambda = 2y = - 12z,x = y + 4\lambda = 6z - 12\lambda$ is $4\sqrt{2}$units, then a value…Mathematics· Vectors· Tough· figure
  19. 19A line L is perpendicular to the lines having direction ratios (3, 2, 1) and (1, 2, 3).The sum of direction cosines of line L isMathematics· Three dimension· Tough
  20. 20If $\overset{\rightarrow}{a},\overset{\rightarrow}{b}\ and\ \overset{\rightarrow}{c}$are unit vectors, then $|\overset{\rightarrow}{a} -…Mathematics· Vectors· Tough
  21. 21The solution of differential equation$\frac{dy}{dx} = \frac{y}{2y\left( siny^{2} + cosy^{2} \right) - x}\ $is. vody lehdj.k dk gy…Mathematics· Differential equation· Moderate
  22. 22A fair die is tossed. If 2, 3 or 5 occurs, the player wins that number of rupees, but if 1, 4, or 6 occurs, the player loses that number of…Mathematics· Probability· Tough
  23. 23The degree and order of differential equation of the family of all parabolas whose axis is x-axis are respectively. lHkh ftu xMathematics· Differential equation· Moderate
  24. 24The probability that a randomly chosen 3 digit number when divided by 7 leaves remainder 2, is;kn`fPNd pquh xbZ 3 va s 7 ls foHkkftr djus…Mathematics· Probability· Moderate
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