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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 f(x) = a log | x | + bx2 + x has extreme values at x = -1 and at x = 2, then find a+2b.Mathematics· figure
  2. 2If 683 + 883 is divided by 49, then the remainder isMathematics· figure
  3. 3Through the vertex A of the parabola [IMAGE], where z = x + iy (i =[IMAGE] ) two chords AP and AQ are drawn and the circles on AP and AQ as…Mathematics· figure
  4. 4If the number of positive integral solutions of v + u + w = n be denoted by p_n, then the absolute value of determinantMathematics· figure
  5. 5If letters of the word 'KUBER' are written in all possible orders and arranged as in a dictionary, then rank of the word 'KUBER' will beMathematics
  6. 6The locus represented by the equation | z -1 | = |z - i| isMathematics
  7. 7Equation of the line passing through centre and bisecting the chord 7x + y = 20 of the ellipse [IMAGE], isMathematics· figure
  8. 8The locus of the middle points of the focal chords of parabola, y2 = 8x is another parabola whose length of latus rectum isMathematics· figure
  9. 9The value of the integral[IMAGE] isMathematics· figure
  10. 10The function f(x) is defined for all real x, if [IMAGE] and [IMAGE], then f(2011) isMathematics· figure
  11. 11JM-M-02-Q8Mathematics· figure
  12. 12JM-M-02-Q9Mathematics· figure
  13. 13x^2 + ax + 1 = 0 x^2 - x - a = 0 aMathematics· Quadratic Equations· Moderate
  14. 14ar, ar^2, ar^3,.......... ar^10 18 6Mathematics· Sequences and Series· Moderate· figure
  15. 15The first term of an infinitely decreasing G.P. is unity and its sum is S. The sum of the squares of the terms of the progression isMathematics
  16. 16If [IMAGE]Mathematics· figure
  17. 17,, [IMAGE] -.Mathematics· Trigonometry· Moderate· figure
  18. 18x ∈ (0, 1) x = 1 - x + x^2 - x^3 + x^4 - x^5 +....∞ xMathematics· Trigonometry· Moderate· figure
  19. 19[IMAGE] is not divisible byMathematics· figure
  20. 20[IMAGE] x x - (1) 0 (2) -2 (3) 4 (4) 1Mathematics· Binomial Theorem· Easy· figure
  21. 21 2z_1 - 3z_2 -z_3 = 0 rc z_1, z_2, z_3Mathematics· Complex Numbers· Moderate· figure
  22. 22[IMAGE] ? ω - [IMAGE] (4)Mathematics· Complex Numbers· Moderate· figure
  23. 23, x^3 + ax^2 + bx + c = 0 [IMAGE] - (1) 3 (2) 4 (3) 5 (4) 6Mathematics· Quadratic Equations· Moderate· figure
  24. 24If λ is real and (λ^2 + λ - 2)x^2 + (λ +2) x < 1 for all real x, then set of all values of λ isMathematics· Quadratic Equations· Moderate· figure
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