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 x + y = 0, 4x + 5y = 0, 2x + y = 8 are the sides of triangle ABC, then the line x-2y = 0 passes throughMathematics· Straight Lines· Tough
  2. 2Chord of the curve $4x^{2} + y^{2} - x + 4y = 0$which subtend a right angle at the origin pass through a fixed point whose co-ordinate are…Mathematics· Circles· Moderate
  3. 3Equation of straight line $ax + by + c = 0$ where $3a + 4b + c = 0$ which is at maximum distance from (1,-2), is -2)Mathematics· Straight Lines· Moderate
  4. 4If the three distinct points $\left( t_{i},2{at}_{i} + {at}_{i}^{3} \right)$for i=1, 2, 3 are collinear then the sum of the abscissae of…Mathematics· Straight Lines· Easy
  5. 5If the point (p, 5) lies on the line parallel to the y-axis and passing through the intersection of the lines $2\left( a^{2} + 1 \right)x +…Mathematics· Straight Lines· Moderate
  6. 6Let $A \equiv (0,0),B \equiv (4,4)$ and $C \equiv (8,2)$ be the vertices of a $\mathrm{\Delta}ABC$. If straight lines through the points B…Mathematics· Straight Lines· Tough· figure
  7. 7What will be the equation of circle whose centre is (3,-1) and which intercept chord of 6 unit length on straight line $2x - 5y + 18 = 0$…Mathematics· Circles· Moderate· figure
  8. 8If the equation $2x^{2} + 2hxy + 6y^{2} - 4x + 5y - 6 = 0$represents a pair of straight lines then find the length of intercept on the x…Mathematics· Straight Lines· Moderate
  9. 9Find the number of integer values of k for which the equation $x^{2} + y^{2} + (k - 1)x - ky + 5 = 0$ represents a circle whose radius…Mathematics· Circles· Moderate
  10. 10If circles $x^{2} + y^{2} + 2gx + 2y + 2 = 0$ and $x^{2} + y^{2} + 2x + 2fy + 4 = 0$ intersect in two distinct points P and Q. and equation…Mathematics· Circles· Moderate
  11. 11Find the number of the values of k for which the lines $kx + 2y + 2 = 0,2x + ky + 3 = 0,3x + 3y + k = 0$ are concurrent k dk eku Kkr dhft,…Mathematics· Straight Lines· Easy
  12. 12The lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangent to the same circle. Find the radius of this circle js[kk,saMathematics· Circles· Moderate
  13. 13If ratio of slopes of lines in $kx^{2} + 4xy + 3y^{2} = 0$ is 2, then the value of;fn lehdj.k $kx^{2} + 4xy + 3y^{2} = 0$ izo.krkvksa dk…Mathematics· Straight Lines· Easy
  14. 14Let H be the orthocenter of $\mathrm{\Delta}ABC$ where $A \equiv (0,0),B \equiv (8,0)$ and $C \equiv (4,4\sqrt{3})$. If…Mathematics· Straight Lines· Tough· figure
  15. 15Equation of circle touching the line x + y = 4 at (1,3) and intersecting the circle $x^{2} + y^{2} = 4$ orthogonally, isMathematics· Circles· Moderate
  16. 16If the tangent at point $P$ on circle $x^{2} + y^{2} + 6x + 6y = 2$meets straight line $5x - 2y + 6 = 0$ at point Q on y-axis then find…Mathematics· Circles· Moderate· figure
  17. 17The new position of the point (1, 2) under rotation through an angle of 90º about the origin in anticlockwise direction is fcUnq (1, 2)…Mathematics· Straight Lines· Moderate
  18. 18Equation of a circle of radius 2 and touching the circles $x^{2} + y^{2} - 4|x| = 0$ is f=T;k 2 ds o`Ùk dk lehdj.k gksxk tks o`Ùkksa $x^{2}…Mathematics· Circles· Moderate· figure
  19. 19Let (a, b) and (c, d) are two points in a plane. Any point on the line joining these points has coordinates $(k \in R)$ okyh js[kk ij dksbZ…Mathematics· Straight Lines· Easy
  20. 20If tangents are drawn from any point on the line x + y = 3 to the circle $x^{2} + y^{2} = 9$ then the chord of contact passes through the…Mathematics· Circles· Easy
  21. 21The orthocentre of triangle with vertices (0,0),(3,4) and (4,0) is f=Hkqt ftl (0,0),(3,4)Mathematics· Straight Lines· Moderate· figure
  22. 22If the chord y = mx + 1 of circle $x^{2} + y^{2} = 1$ subtends an angle of measure 45º at the major segment of the circle, then the value…Mathematics· Circles· Moderate· figure
  23. 23If pair of lines y^2 + 2hxy - 9x^2 = 0 and another pair of lines given by ay^2 + 10xy + x^2 = 0 have exactly one line common and other…Mathematics· Straight Lines· Moderate· figure
  24. 24Let PQ be the common tangent to circles x^2 + y^2 + 2x = 0 and x^2 + y^2 - 6x = 0 as shown in figure, then find the area of the shaded…Mathematics· Circles· Tough· figure
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