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
paper1 20 paper2 20
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
2001 screening

28 maths questions

Q8 Composite & Inverse Functions Find or Apply an Inverse Function Formula View
8. If $f : [ 1 , \infty )$ is given by $f ( x ) = x + 1 / x$ then $f - 1 ( x )$ equals :
(A) $( x + \sqrt { } ( x 2 - 4 ) ) / 2$
(B) $x / 1 + x 2$
(C) $( x - \sqrt { } ( x 2 - 4 ) ) / 2$
(D) $1 + \sqrt { } ( \times 2 - 4 )$
Q9 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
9. The domain of definition of $f ( x ) = ( \log 2 ( x + 3 ) ) / ( x 2 + 3 x + 2 )$ is:
(A) $\mathrm { R } \backslash \{ - 1 , - 2 \}$
B) $( - 2 , \infty )$
(C) $\mathrm { R } / \{ - 1 , - 2 , - 3 \}$
(D) $( - 3 , \infty ) \backslash \{ - 1 , - 2 \}$
Q10 Circles Tangent Lines and Tangent Lengths View
10. The equation of the common tangent touching the circle $( x - 3 ) 2 + y 2 = 9$ and the parabola $y 2 = 4 x$ above the $x$-axis is :
(A) $\sqrt { } 3 y = 3 x + 1$
(B) $\sqrt { } 3 y = - ( x + 3 )$
(C) $\sqrt { } 3 y = x + 3$
(D) $\sqrt { } 3 y = - ( 3 x + 1 )$
Q11 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View
11. The value of $\int - ח ( \cos 2 x / 1 + a x ) d x , a > 0$, is
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(A) $\sqcap$
(B) ап
(C) $\pi / 2$
(D) $2 \sqcap$
Q12 Circles Circle-Related Locus Problems View
12. Let $A B$ be a chord of the circle $x 2 + y 2 = r 2$ subtending a right angle at the centre. Then the locus of the centroid of the triangle PAB as P moves on the circle is:
(A) A parabola
(B) A circle
(C) An ellipse
(D) A pair of straight lines
Q13 Simultaneous equations Line Equation and Parametric Representation View
13. The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3 x + 4 y = 9$ and $y = m x + 1$ is also an integer, is :
(A) 2
(B) 0
(C) 4
(D) 1
Q14 Circles Circle Identification and Classification View
14. The equation of the directrix of the parabola $y 2 + 4 y + 4 x + 2 = 0$ is:
(A) $x = - 1$
(B) $x = 1$
(C) $x = - 3 / 2$
(D) $x = 3 / 2$
Q15 Geometric Sequences and Series Arithmetic-Geometric Sequence Interplay View
15. Let $a$ and $\beta$ be the roots of $x 2 - x + p = 0$ and $y$ and $\delta$ be the roots of $x 2 - 4 x + q = 0$. if $\mathrm { a } , \beta , \mathrm { Y } , \delta$ are in G.P. then the integral values of P and q respectively, are:
(A) $- 2 , - 32$
(B) $- 2,3$
(C) $- 6,3$
(D) $- 6 , - 32$
Q16 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
16. In the binomial expansion of ( $\mathrm { a } - \mathrm { b } ) \mathrm { n } , \mathrm { n } \geq 5$, the sum of the 5 th and 6 th terms is zero. Then a/b equals:
(A) $( n - 5 ) / 6$
(B) $( n - 4 ) / 5$
(C) $5 / ( n - 4 )$
(D) $6 / ( n - 5 )$
Q17 Completing the square and sketching Vertex and parameter conditions for a quadratic graph View
17. Let $f ( x ) = ( 1 + b 2 ) x 2 + 2 b x + 1$ and let $m ( b )$ be the minimum value of $f ( x )$. As $b$ varies, the range of $m ( b )$ is:
(A) $[ 0,1 ]$
(B) $[ 0,1 / 2 ]$
(C) $[ 1 / 2,1 ]$
(D) $[ 0,1 ]$
Q18 3x3 Matrices Determinant of Parametric or Structured Matrix View
18. The number of distinct roots of $\left| \begin{array} { l } \sin x \cos x \cos x \\ \cos x \sin x \cos x \\ \cos x \cos x \sin x \end{array} \right| = 0$ in the interval $- \frac { \pi } { 4 } \leq x \leq \frac { \pi } { 4 }$ is:
(A) 0
(B) 2
(C) 1
(D) 3
Q19 Combinations & Selection Counting Functions with Constraints View
19. Let $E = \{ 1,2,3,4 \}$ and $F = \{ 1,2 \}$. Then the number of onto functions from $E$ to $F$ is:
(A) 14
(B) 16
(C) 12
(D) 8
Q20 Combinations & Selection Geometric Combinatorics View
20. Let T\_n denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T n + 1$ - $T n = 21$, then $n$ equals:
(A) 5
(B) 7
(C) 6
(D) 4
Q21 Complex Numbers Argand & Loci Geometric Interpretation and Triangle/Shape Properties View
21. The complex numbers $\mathrm { z } 1 , \mathrm { z } 2$, and z 3 ,satisfying ( $\mathrm { z } 1 - \mathrm { z } 3$ )/ ( $\mathrm { z } 2 - \mathrm { z } 3$ ) $= ( 1 - \mathrm { i } \sqrt { } 3 ) / 2$ are the vertices of a triangle which is :
(A) Of area zero
(B) Right-angled isosceles
(C) Equilateral
(D) Obtuse-angled isosceles
Q22 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
22. If the sum of the first $2 n$ terms of the A.P. $2,5,8 , \ldots \ldots \ldots \ldots \ldots$, is equal to the sum of the first $n$ terms of the A.P. $57,59,61 , \ldots .$. ,then $n$ equals:
(A) 10
(B) 12
(C) 11
(D) 13
Q23 Complex Numbers Argand & Loci Roots of Unity and Cyclotomic Expressions View
23. Let z 1 and z 2 be nth roots of unity which subtend a right angle at the origin. Then n must be of the form:
(A) $4 \mathrm { k } + 1$
(B) $4 \mathrm { k } + 2$
(C) $4 \mathrm { k } + 3$
(D) 4 k
Q24 Arithmetic Sequences and Series Properties of AP Terms under Transformation View
24. Let the positive numbers $\mathrm { a } , \mathrm { b } , \mathrm { c } , \mathrm { d }$ be in A.P. Then $\mathrm { abc } , \mathrm { abd } , \mathrm { acd } , \mathrm { bcd }$ are:
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(A) NOT in A.P./G.P/H.P.
(B) In A.P
(C) In G.P
(D) In H.P
Q25 Composite & Inverse Functions Recover a Function from a Composition or Functional Equation View
25. Let $f ( x ) = a x / ( x + 1 ) , x \neq - 1$. Then for what value of $a$ is $f [ f ( x ) ] = x$ :
(A) $\sqrt { } 2$
(B) $- \sqrt { } 2$
(C) 1
(D) - 1
Q26 Vectors Introduction & 2D Inequality or Proof Involving Vectors View
26. If If $\vec { a } , \vec { b }$, and $\vec { c }$ are unit vectors, then
$$| \vec { a } - \vec { b } | ^ { 2 } + | \vec { b } - \vec { c } | ^ { 2 } + | \vec { c } - \vec { a } | ^ { 2 }$$
does not exceed :
(A) 4
(B) 9
(C) 8
(D) 6
Q27 Chain Rule Piecewise Function Differentiability Analysis View
27. Which of the following functions is differentiable at $x = 0$ :
(A) $\cos ( | x | ) + | x |$
(B) $\cos ( | x | ) - | x |$
(C) $\sin ( | x | ) + | x |$
(D) $\sin ( | x | ) - | x |$
Q28 Laws of Logarithms Solve a Logarithmic Equation View
28. The number of solutions of $\log 4 ( x - 1 ) = \log 2 ( x - 3 )$ is :
(A) 3
(B) 1
(C) 2
(D) 0
Q29 Vectors 3D & Lines Vector Properties and Identities (Conceptual) View
29. Let $\vec { a } = \vec { \imath } - \vec { k } , \vec { b } = x \vec { \imath } + \vec { \jmath } + ( 1 - x ) \vec { k }$ and $\vec { c } = y \vec { \imath } + x \vec { \jmath } + ( 1 + x - y ) \vec { k }$. Then $[ \vec { a } , \vec { b } , \vec { c } ]$ depends on :
(A) Only x
(B) Only $y$
(C) Neither $x$ nor $y$
(D) Both $x$ and $y$
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Q30 Straight Lines & Coordinate Geometry Area Computation in Coordinate Geometry View
30. Area of the parallelogram formed by the lines $y = m x , y = m x + 1 , y = n x$ and $y = n x + 1$ equals:
(A) $| m + n | / ( m - n ) ^ { 2 }$
(B) $2 / | m + n |$
(C) $1 / | m + n |$
(D) $1 / | m - n |$
Q31 Standard trigonometric equations Tangent Lines and Tangent Lengths View
31. Let $P Q$ and $R S$ be tangents at the extremities of the diameter $P R$ of a circle of radius $r$. If PS and RQ intersect at a point X on the circumference of the circle, then 2 r equals :
(A) $\sqrt { } ( \mathrm { PQ } . \mathrm { RS } )$
(B) $( P Q + R S ) / 2$
(C) $( 2 \mathrm { PQ } \cdot \mathrm { RS } ) / ( \mathrm { PQ } + \mathrm { RS } )$
(D) $\sqrt { } ( ( P Q 2 + R S 2 ) / 2 )$
Q32 Addition & Double Angle Formulae Horizontal Launch or Dropped Object Problems View
32. A man from the top of a 100 metres high tower sees a car moving towards the tower at an angle of depression of 300 . After some time, the angle of depression becomes 600. The distance (in metres) travelled by the car during this time is :
(A) $100 \sqrt { 3 }$
(B) $( 200 \sqrt { } 3 ) / 3$
(C) $( 100 \sqrt { } 3 ) / 3$
(D) $200 \sqrt { } 3$
Q33 Geometric Sequences and Series Addition/Subtraction Formula Evaluation View
33. If $a + \beta = \pi / 2$ and $\beta + \gamma = a$, then tan $a$ equals:
(A) $2 ( \tan \beta + \tan \gamma )$
(B) $\tan \beta + \tan \gamma$
(C) $\tan \beta + 2 \tan \gamma$
(D) $2 \tan \beta + \tan \gamma$
Q34 Stationary points and optimisation Inverse trigonometric equation View
34. $\sin - 1 ( x - x 2 / 2 + x 3 / 4 - \ldots ) + \cos - 1 ( x 2 - x 4 / 2 + x 6 / 4 - \ldots ) = n / 2$ for $0 < | x | < \sqrt { } ( 2$, ) then $x$ equals :
(A) $\frac { 1 } { 2 }$
(B) 1
(C) $- 1 / 2$
(D) - 1
Q35 Circles Find absolute extrema on a closed interval or domain View
35. The maximum value of $( \cos a 1 ) \cdot ( \cos a 2 ) \cdot \ldots \cdot \cdot ( \cos a n )$, under the restrictions $0 \leq \mathrm { a } 1 , \mathrm { a } 2 , \ldots \ldots , \mathrm { an } \leq \pi / 2$ and $( \cot \mathrm { a } 1 )$. ( $\cot \mathrm { a } 2$ ). ..... ( $\cot \mathrm { an } ) = 1$ is:
(A) $1 / 2 n / 2$
(B) $1 / 2 n$
(C) $1 / 2 n$
(D) 1