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. 1In $\Delta$ABC, if (a + b + c) (a - b + c) = 3ac, thenMathematics· Moderate
  2. 2Length of two sides of a triangle are 2 and $\sqrt{3}$ and angle between the sides is $\frac{\pi}{6}$, then circumradius of the triangle isMathematics· Moderate
  3. 3In a $\Delta$ABC, b = 12 units, c = 5 units and $\Delta$ = 30 square units. If d is the distance between vertex A and incenter of the…Mathematics· Tough
  4. 4In $\Delta$ABC, if r = 1, R = 3 and S = 5, then the value of a^2 + b^2 + c^2 isMathematics· Moderate
  5. 5The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60º. If the area of the quadrilateral is…Mathematics· Tough· figure
  6. 6The sides of the $\Delta$ABC satisfy the relations a + b - c = 2 and 2ab - c^2 = 4, x is the area of $\Delta$ then the value of x^6 isMathematics· Moderate
  7. 7If in a$\ \Delta ABC,\sqrt{3}$ sinC = 2secA - tanA and $\angle C = \lambda^{\circ}$, then $\frac{\lambda}{18}$ is equal toMathematics· Tough
  8. 8In a triangle ABC, if a: b: c = 3: 7: 8, then $\frac{R}{r}$ is equal toMathematics· Moderate
  9. 9In a $\Delta$ABC, $\frac{a}{b} = 2 + \sqrt{3}$ and $\angle$C = 60°. Then the ordered pair $(\angle A,\angle B)$ is equal toMathematics· Moderate
  10. 10The sides of a triangle are 3x +2, 2x +1 and 2x. If the cosine of greatest angle of the triangle is $- \frac{3}{7}$, then x is equal toMathematics· Moderate
  11. 11In given figure, area of shaded region is (in square units)Mathematics· Tough· figure
  12. 12If G is centroid of $\Delta$ABC, then (GA^2 + GB^2 + GC^2): (AB^2 + BC^2 + CA^2) is equal toMathematics· Easy
  13. 13If in a △ABC, the altitudes from the vertices A,B,C on opposite sides are in H.P., then sinA, sinB, sinC are inMathematics· Moderate
  14. 14In a $\Delta$ABC, if 2a^2 + 4b^2 + c^2 = 4ab + 2ac, then the triangle isMathematics· Easy
  15. 15In a triangle ABC, if a = 2, bc = 9, then the value of 2R$\Delta$ isMathematics· Moderate
  16. 16In an obtuse angle triangle ABC, a = $\sqrt{3} + 1,B = \frac{\pi}{3}$ and R = $\sqrt{2}$, then angle C isMathematics· Easy
  17. 17The point $P(\alpha,\alpha + 1)$ will lie inside the triangle with vertices $A(0,3),B( - 2,0)$ and $C(6,1)$ if fcUnq $P(\alpha,\alpha + 1)$…Mathematics· Straight Lines· Tough· figure
  18. 18The straight lines x + y = 0, 3x + y = 4 and x + 3y = 4 form a triangle which isMathematics· Straight Lines· Easy
  19. 19The equation of circle with origin as the centre and passing through vertices of an equilateral triangle whose median is of length 3a, is…Mathematics· Circles· Moderate· figure
  20. 20A variable circle passes through fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is,d pj o`Ùk…Mathematics· Circles· Tough· figure
  21. 21The vertices of a triangle are $A( - 1, - 7),B(5,1)\ and\ C(1,4)$. The equation of bisector of $\angle ABC$ is f=Hkqt A(-1, -7), B(5, 1)…Mathematics· Straight Lines· Moderate· figure
  22. 22Let $x^{2} + y^{2} - 4x - 2y - 11 = 0$ be a circle. A pair of tangents from the point (4, 5) with a pair of radii form a quadrilateral of…Mathematics· Circles· Moderate· figure
  23. 23Locus of the points which are at equal distance from 3x + 4y - 11 = 0 and 12x + 5y + 2 = 0 and which is nearer to origin is fcUnqvksa dk…Mathematics· Straight Lines· Tough
  24. 24The equation of the circle, which is the mirror image of the circle, $x^{2} + y^{2} - 2x = 0$, in the line, y = 3-x is ml o`Ùk dk lehdj.k]…Mathematics· Circles· Tough
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