jee-advanced

Papers (53)
2025
paper1 16 paper2 16
2024
paper1 17 paper2 17
2023
paper1 17 paper2 17
2022
paper1 18 paper2 18
2021
paper1 23 paper2 19
2020
paper1 18 paper2 18
2019
paper1 18 paper2 18
2018
paper1 18 paper2 18
2017
paper1 18 paper2 18
2016
paper1 18 paper2 18
2015
paper1 20 paper2 20
2014
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2013
paper1 20 paper2 20
2012
paper1 1 paper2 2
2011
paper1 6 paper2 9
2010
paper1 28 paper2 19
2009
paper1 19 paper2 17
2008
paper1 23 paper2 22
2007
paper1 27 paper2 5
2006
jee-advanced_2006.pdf 26
2005
mains 10 screening 16
2004
mains 18 screening 17
2003
mains 20 screening 17
2002
mains 4 screening 27
2001
mains 12 screening 28
2000
mains 5 screening 30
1999
jee-advanced_1999.pdf 33
1998
jee-advanced_1998.pdf 25
2000 screening

30 maths questions

Q6 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
6. The domain of definition of the function $y ( x )$ is given by the equation $2 x + 2 y = 2$ is :
(A) $0 < x \leq 1$
(B) $0 \leq x \leq 1$
(C) $- \infty < x \leq 0$
(D) $- \infty < x < 1$
Q7 Differentiating Transcendental Functions Second derivative via implicit differentiation View
7. If $x 2 + y 2 = 1$, then :
(A) yy'" - 2(y ' )2+1=0
(B) $y y ^ { \prime \prime } + \left( y ^ { \prime } \right) 2 + 1 = 0$
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(C) $y y \prime \prime = \left( y ^ { \prime } \right) 2 - 1 = 0$
(D) $y y ^ { \prime \prime } + 2 \left( y ^ { \prime } \right) 2 + 1 = 0$
Q8 Inequalities Optimization Subject to an Algebraic Constraint View
8. If $\mathrm { a } , \mathrm { b } , \mathrm { c } , \mathrm { d }$ are positive real numbers such that $\mathrm { a } + \mathrm { b } + \mathrm { c } + \mathrm { d } = 2$, then $\mathrm { M } = ( \mathrm { a } + \mathrm { b } ) ( \mathrm { c } +$ d) satisfies the relation :
(A) $0 \leq M \leq 1$
(B) $1 \leq \mathrm { M } \leq 2$
(C) $2 \leq M \leq 3$
(D) $3 \leq M \leq 4$
Q9 Circles Circle Identification and Classification View
9. If the system of equations $x - k y - z = 0 , k x - y - z = 0 , x + y - z = 0$ has a non-zero solution, then possible values of $k$ are :
(A) $- 1,2$
(B) 1,2
(C) 0,1
(D) $- 1,1$
Q10 Sine and Cosine Rules Find a side or angle using the sine rule View
10. The triangle $P Q R$ is inscribed in the circle $x 2 + y 2 = 25$. If $Q$ and $R$ have coordinates ( 3 , $4 )$ and $( - 4,3 )$ respectively, then $\angle P Q R$ is equal to:
(A) $\pi / 2$
(B) $\pi / 3$
(C) $\pi / 4$
(D) $\pi / 6$
Q11 Exponential Functions MCQ on Function Properties View
11. In a triangle $A B C , 2 a c \sin 1 / 2 ( A - B + C ) =$
(A) $a 2 + b 2 - c 2$
(B) $c 2 + a 2 - b 2$
(C) $b 2 - c 2 - a 2$
(D) $c 2 - a 2 - b 2$
Q12 Geometric Sequences and Series Determine the Limit of a Sequence via Geometric Series View
12. For $x \in R$, $\operatorname { limn } \rightarrow \infty ( ( x - 3 ) / ( x + 2 ) ) x =$
(A) e
(B) $e - 1$
(C) $e - 5$
(D) e 5
Q13 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
13. Consider an infinite geometric series with first term and common ratio $r$. If its sum is 4 and the second term is $3 / 4$, then :
(A) $a = 4 / 7 , r = 3 / 7$
(B) $\mathrm { a } = 2 , \mathrm { r } = 3 / 8$
(C) $\mathrm { a } = 3 / 2 , \mathrm { r } = 1 / 2$
(D) $\mathrm { a } = 3 , \mathrm { r } = 1 / 4$
Q14 Sine and Cosine Rules Integral Inequalities and Limit of Integral Sequences View
14. Let $\mathrm { g } ( \mathrm { x } ) = \int 0 \mathrm { x } f ( t ) \mathrm { dt }$, where f is such that $1 / 2 \leq f ( t ) \leq 1$ for $\mathrm { t } \in [ 0,1 ]$ and $0 \leq f ( t ) \leq 1 / 2$ for $\mathrm { t } \in [ 1,2 ]$. Then $\mathrm { g } ( 2 )$ satisfies the inequality:
(A) $- 3 / 2 \leq g ( 2 ) < 1 / 2$
(B) $0 \leq g ( 2 ) < 2$
(C) $3 / 2 < g ( 2 ) \leq 5 / 2$
(D) $2 < g ( 2 ) < 4$
Q15 Permutations & Arrangements Circumradius or incircle radius computation View
15. In a triangle $A B C$, Let $\angle C = n / 2$. If $r$ is the inradius and $R$ is the circum-radius of the triangle, then $2 ( r + R )$ is equal to :
(A) $a + b$
(B) $b + c$
(C) $c + a$
(D) $a + b + c$
Q16 Permutations & Arrangements Counting Arrangements with Run or Pattern Constraints View
16. How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even position :
(A) 16
(B) 36
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(C) 60
(D) 180
Q17 Complex Numbers Argand & Loci Line Equation and Parametric Representation View
17. If $\arg ( \mathrm { z } ) < 0$, then $\arg ( - \mathrm { z } ) - \arg ( \mathrm { z } ) =$
(A) п
(B) - п
(C) $- \pi / 2$
(D) $\pi / 2$
Q18 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
18. Let $P S$ be the median of the triangle with vertices $P ( 2,2 ) , Q ( 6 - 1 )$ and $R ( 7,3 )$. The equation of the line passing through $( 1 , - 1 )$ and parallel to PS is:
(A) $2 x - 9 y - 7 = 0$
(B) $2 x - 9 y - 11 = 0$
(C) $2 x + 9 y - 11 = 0$
(D) $2 x - 9 y - 11 = 0$
Q19 Indefinite & Definite Integrals Inscribed/Circumscribed Circle Computations View
19. A pole stands vertically inside a triangular park $\triangle A B C$. If the angle of elevation of the top of the pole from each corner of the park is same, then in $\triangle \mathrm { ABC }$ the foot of the pole is at the :
(A) centroid
(B) circumcentre
(C) incentre
(D) orthocenter.
Q20 Circles Piecewise/Periodic Function Integration View
20. If $f ( x ) = \left\{ \begin{array} { c c } e ^ { \cos x } \sin x & \text { for } | x | \leq 2 , \\ 2 & \text { otherwise, } \end{array} \right.$ then $\int _ { - 2 } ^ { 3 } f ( x ) d x =$
(A) 0
(B) 1
(C) 2
(D) 3
Q21 Trig Graphs & Exact Values Inscribed/Circumscribed Circle Computations View
21. The incentre of the triangle with vertices $( 1 , \sqrt { 3 } ) , ( 0,0 )$ and $( 2,0 )$ is :
(A) $( 1 , \sqrt { } 3 / 2 )$
(B) $( 2 / 3,1 / \sqrt { } 3 )$
(C) $( 2 / 3 , \sqrt { } 3 / 2 )$
(D) $( 1,1 / \sqrt { } 3 )$
Q22 Stationary points and optimisation Variation Table and Monotonicity from Sign of Derivative View
22. Consider the following statements in S and R : $S$ : Both $\sin x$ and $\cos x$ are decreasing functions in the interval $( \sqcap / 2 , \sqcap )$ R : If a differentiable function decreases in an interval ( $\mathrm { a } , \mathrm { b }$ ), then its derivative also decreases in (a, b). Which of the following is true :
(A) Both S and R are wrong
(B) Both S and R are correct, but R is not the correct explanation of S .
(C) S is correct and R is correct explanation for S .
(D) S is correct and R is wrong.
Q23 Circles Determine intervals of increase/decrease or monotonicity conditions View
23. Let $f ( x ) = \int \operatorname { ex } ( x - 1 ) ( x - 2 ) d x$. Then $f$ decreases in the interval :
(A) $( \infty , - 2 )$
(B) $( - 2 , - 1 )$
(C) $( 1,2 )$
(D) $( 2 , + \infty )$
Q24 Vectors Introduction & 2D Intersection of Circles or Circle with Conic View
24. If the circles $x 2 + y 2 + 2 x + 2 k y + 6 = 0$ and $x 2 + y 2 + 2 k y + k = 0$ intersect orthogonally, then $k$ is :
(A) 2 or $- 3 / 2$
(B) - 2 or $3 / 2$
(C) 2 or $3 / 2$
(D) $( 2 , + \infty )$
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Q25 Tangents, normals and gradients True/False or Multiple-Statement Verification View
25. If the vectors $\vec { a } , \vec { b }$ and $\vec { c }$ form the sides $B C , C A$ and $A B$ respectively of $a$ triangle ABC , then:
(A) $\vec { a } , \vec { b } + \vec { b } , \vec { c } + \vec { c } , \vec { a } = 0$
(B) $\vec { a } \times \vec { b } = \vec { b } \times \vec { c } = \vec { c } \times \vec { a }$
(C) $\vec { a } , \vec { b } = \vec { b } , \vec { c } = \vec { c } , \vec { a }$
(D) $\vec { a } \times \vec { b } + \vec { b } \times \vec { c } + \vec { c } \times \vec { a } = 0$
Q26 Tangents, normals and gradients Normal or perpendicular line problems View
26. If the normal to the curve $y = f ( x )$ at the point ( 3,4 ) makes an angle $3 p / 4$ with the positive $x$-axis then $\mathrm { f } ^ { \prime } ( 3 ) =$
(A) - 1
(B) $- 3 / 4$
(C) $4 / 3$
(D) 1
Q27 Vectors: Cross Product & Distances View
27. Let the vectors $a , b , c$ and $d$ be such that $( a \times b ) \times ( c \times d ) = 0$. Let P1 and P2be planes determined by the pairs of vectors $a , b$ and $c , d$ respectively, then the angle between $P 1$ and P 2 is :
(A) 0
(B) $\mathrm { p } / 4$
(C) $\mathrm { p } / 3$
(D) $\mathrm { p } / 2$
Q28 Stationary points and optimisation Composite or piecewise function extremum analysis View
28. Let $f ( x ) = \left\{ \begin{array} { c l l } | x | & \text { for } 0 < | x | \leq 2 \\ 1 & \text { for } & x = 0 . \end{array} \right.$
Then at $\mathrm { x } = 0 , \mathrm { f }$ has :
(A) A local maximum
(B) no local maximum
(C) a local minimum
(D) no extremum
Q29 Solving quadratics and applications Vector Properties and Identities (Conceptual) View
29. If $\vec { a } , \vec { b }$ and $\vec { c }$ are unit coplanar vectors, then the scalar triple product
$$[ 2 \vec { a } - \vec { b } , 2 \vec { b } - \vec { c } , 2 \vec { c } - \vec { a } ] =$$
(A) 0
(B) 1
(C) $- \sqrt { } 3$
(D) $\sqrt { } 3$
Q30 Complex Numbers Arithmetic Counting solutions or configurations satisfying a quadratic system View
30. If $\mathrm { b } > \mathrm { a }$, then the equation $( \mathrm { x } - \mathrm { a } ) ( \mathrm { x } - \mathrm { b } ) - 1 = 0$ has:
(A) both roots in (a, b)
(B) both roots in ( $- ¥$, a)
(C) both roots in $( b , + ¥ )$
(D) one root in ( $- ¥$, a) and the other in ( $b , + \neq$ )
Q31 Complex Numbers Arithmetic Modulus Computation View
31. If $\mathrm { z } 1 , \mathrm { z } 2$ and z 3 are complex numbers such that $| z 1 | | z 2 | = | z 3 | = | 1 / z 1 + 1 / z 2 + 1 / z 3 | = 1$, then $| z 1 + z 2 + z 3 |$ is :
(A) equal to 1
(B) less than1
(C) greater than 3
(D) equal to 3
Q32 Solving quadratics and applications Quadratic equation with parametric or self-referential conditions View
32. For the equation $3 \times 2 + p x + 3 = 0 , p > 0$, if one of the root is square of the other, then $p$ is equal to :
(A) $1 / 3$
(B) 1
(C) 3
(D) $2 / 3$
Q33 Exponential Functions Parameter Determination from Conditions View
33. If the line $x - 1 = 0$ is the directrix of the parabola $y 2 - k x + 8 = 0$ then one of the values of ... Powered By IITians k is :
(A) $1 / 8$
(B) 8
(C) 4
(D) $1 / 4$
Q34 Indefinite & Definite Integrals Integral Inequalities and Limit of Integral Sequences View
34. For all $\in ( 0,1 )$ :
(A) $e x < 1 + x$
(B) loge $( 1 + x ) < x$
(C) $\sin x > x$
(D) loge $x > x$.
Q35 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View
35. The value of the integral $\int \mathrm { e } - 1 \mathrm { e } 2 | \log \mathrm { x } / \mathrm { x } | \mathrm { dx }$ is :
(A) $3 / 2$
(B) $5 / 2$
(C) 3
(D) 5