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
2002 screening

27 maths questions

Q2 Complex Numbers Argand & Loci Modulus Computation View
2. For all complex numbers $z _ { 1 } , z _ { 2 }$ satisfying $\left| z _ { 1 } \right| = 12$ and $\left| z _ { 2 } - 3 - 4 i \right| = 5$, the minimum value of $\left| z _ { 1 } - z _ { 2 } \right|$ is:
(A) 0
(B) 2
(C) 7
(D) 17
Q3 Arithmetic Sequences and Series Geometric or applied optimisation problem View
3. If $\mathrm { a } _ { 1 } \mathrm { a } _ { 2 } , \ldots , \mathrm { a } _ { \mathrm { n } }$ are positive real numbers whose product is a fixed number c , then the minimum value of $a _ { 1 } + a _ { 2 } + \ldots + a _ { n - 1 } + 2 a _ { n }$ is
(A) $\quad n ( 2 c ) ^ { 1 / n }$
(B) $\quad ( n + 1 ) c ^ { 1 / n }$
(C) $\quad 2 \mathrm { nc } ^ { 1 / \mathrm { n } }$
(D) $\quad ( n + 1 ) ( 2 c ) ^ { 1 / n }$
Q4 Geometric Sequences and Series Arithmetic-Geometric Hybrid Problem View
4. Suppose $a , b , c$ are I A.P. and $a ^ { 2 } , b ^ { 2 } , c ^ { 2 }$ are in G.P. If $\mathrm { a } < \mathrm { b } < \mathrm { c }$ and $a + b + c = 3 / 2$, then the value of $a$ is
(A) $\quad 1 / 2 \sqrt { } 2$
(B) $1 / 2 \sqrt { } 3$
(C) $\quad 1 / 2 - 1 / \sqrt { } 3$
(D) $\quad 1 / 2 - 1 / \sqrt { } 3$
Q5 Permutations & Arrangements Word Permutations with Repeated Letters View
5. The number of arrangements of the letters of the word BANANA in which the two N' s do not appear adjacently is
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(A) 40
(B) 60
(C) 80
(D) 100
Q6 Binomial Theorem (positive integer n) Evaluate a Summation Involving Binomial Coefficients View
6. The sum
$$\sum _ { i = 0 } ^ { m } \binom { 10 } { i } \binom { 20 } { m - i } \text {, Where } \binom { p } { q } = 0$$
if $p > q$ is maximum when $m$ is
(A) 5
(B) 10
(C) 15
(D) 20
Q7 Simultaneous equations View
7. The number of values of k for which the system of equations $( \mathrm { k } + 1 ) \mathrm { x } + 8 \mathrm { y } = 4 \mathrm { k }$ $\mathrm { kx } + ( \mathrm { k } + 3 ) \mathrm { y } = 3 \mathrm { k } - 1$ has infinitely many solution is
(A) 0
(B) 1
(C) 2
(D) Infinite
Q8 Inequalities Absolute Value Inequality View
8. The set of all real numbers $x$ for which $x ^ { 2 } - | x + 2 | + x > 0$ is
(A) $( - \infty , - 2 ) \cup ( 2 , \infty )$
(B) $( - \infty , - \sqrt { } 2 ) \cup ( \sqrt { } 2 , \infty )$
(C) $( - \infty , - 1 ) \cup ( 1 , \infty )$
(D) $( \sqrt { } 2 , \infty )$
Q9 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions View
9. The length of a longest interval in which the function $3 \sin x - 4 \sin ^ { 3 } x$ is increasing, is
(A) $\pi / 3$
(B) $\pi / 2$
(C) $3 \sqcap / 3$
(D) $\Pi$
Q10 Sine and Cosine Rules Ambiguous case and triangle existence/uniqueness View
10. Which of the following pieces of data does NOT uniquely determine an acute-angled triangle $A B C$ ( $R$ being the radius of the circumcircle)?
(A) $a \sin A , \sin B$
(B) $a , b , c$
(C) $a , \sin B , R$
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(D) $a , \sin A , R$
Q11 Standard trigonometric equations Solve trigonometric equation for solutions in an interval View
11. The number of integral values of $k$ for which the equation $7 \cos x + 5 \sin x = 2 k +$ 1 has a solution is
(A) 4
(B) 8
(C) 10
(D) 12
Q12 Function Transformations View
12. Let $0 < a < \Pi / 2$ be a fixed angle. If $P = ( \cos \theta , \sin \theta )$ and $Q = ( \cos ( a - \theta ) , \sin ( a - \theta ) )$ then Q is obtained from P by
(A) Clockwise rotation around origin through an angle a
(B) Anticlockwise rotation around origin through an angle a
(C) Reflection in the line through origin with slope tan a
(D) Reflection in the line through origin with slope $\tan \mathrm { a } / 2$
Q13 Straight Lines & Coordinate Geometry Slope and Angle Between Lines View
13. Let $P = ( - 1,0 ) Q = ( 0,0 ) R = ( 3,3 \sqrt { } 3 )$ be three points. Then the equation of the bisector of the bisector of the angle PQR is
(A) $\sqrt { } 3 / 2 x + y = 0$
(B) $x + \sqrt { } 3 y = 0$
(C) $\sqrt { } 3 x + y = 0$
(D) $x + \sqrt { } 3 / 2 y = 0$
Q14 Straight Lines & Coordinate Geometry Section Ratio and Division of Segments View
14. A straight line through the origin $O$ meets the parallel lines $4 x + 2 y = 9$ and $2 x + y + 6 = 0$ at points $P$ and $Q$ respectively. Then the point $O$ divides the segment $P Q$ in the ratio
(A) $1 : 2$
(B) $\quad 3 : 4$
(C) $\quad 2 : 1$
(D) $4 : 3$
Q15 Circles Tangent Lines and Tangent Lengths View
15. If the tangent at the point $P$ on the circle $x ^ { 2 } + y ^ { 2 } + 6 x + 6 y = 2$ meets the straight line $5 x + 2 y = 6$ at a point $Q$ on the $y$-axis, then the length of $P Q$ is
(A) 4
(B) $2 \sqrt { } 5$
(C) 5
(D) $3 \sqrt { 5 }$
Q16 Circles Tangent Lines and Tangent Lengths View
16. If $a > 2 b > 0$ then the positive value of $m$ for which $y = m x - b \sqrt { } \left( 1 + m ^ { 2 } \right)$ is $a$ common tangent to $x ^ { 2 } + y ^ { 2 } = b ^ { 2 }$ and $( x - a ) ^ { 2 } + y ^ { 2 } = b ^ { 2 }$ is
(A) $2 b / \sqrt { } \left( a ^ { 2 } - 4 b ^ { 2 } \right)$
(B) $\quad \sqrt { } \left( a ^ { 2 } - 4 b ^ { 2 } \right) / 2 b$
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(C) $2 \mathrm {~b} / ( \mathrm { a } - 2 \mathrm {~b} )$
(D) $\mathrm { b } / ( \mathrm { a } - 2 \mathrm {~b} )$
Q17 Conic sections Locus and Trajectory Derivation View
17. The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $y ^ { 2 } = 4 a x$ is another parabola with directrix
(A) $\mathrm { x } = - \mathrm { a }$
(B) $x = - a / 2$
(C) $\quad x = 0$
(D) $\quad x = a / 2$
Q18 Areas by integration View
18. The area bounded by the curves $y = | x | - 1$ and $y = - | x | + 1$ is
(A) 1
(B) 2
(C) $\quad 2 \sqrt { } 2$
(D) 4
Q19 Composite & Inverse Functions Graphical Interpretation of Inverse or Composition View
19. Suppose $f ( x ) = ( x + 1 ) ^ { 2 }$ for $x \geq - 1$ If $g ( x )$ is the function whose graph is reflection of the graph of $f ( x )$ with respect to the line $y = x$ then $g ( x )$ equals
(A) $\quad - \sqrt { } x - 1 , x \geq 0$
(B) $\quad 1 / ( x + 1 ) ^ { 2 } , x > - 1$
(C) $\quad \sqrt { } ( x + 1 ) , x \geq - 1$
(D) $\quad \sqrt { } \mathrm { x } - 1 , \mathrm { x } \geq 0$
Q20 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification View
20. Let function $f : R \rightarrow R$ be defined by $f ( x ) = 2 x + \sin x$ for $x \in R$ Then $f$ is
(A) One-to-one and onto
(B) One-to-one but NOT onto
(C) Onto but NOT one-to-one
(D) Neither one-to-one nor onto
Q21 Differentiation from First Principles View
21. The domain of the derivative of the function
$$f ( x ) = \left\{ \begin{array} { c } \tan ^ { - 1 } x , \text { if } | x | \leq 1 \\ \frac { 1 } { 2 } ( | x | - 1 ) , \text { if } | x | > 1 \end{array} \right\} \text { is }$$
(A) $\mathrm { R } - \{ 0 \}$
(B) $\mathrm { R } - \{ 1 \}$
(C) $\mathrm { R } - \{ - 1 \}$
(D) $\mathrm { R } - \{ - 1,1 \}$
Q22 Chain Rule Limit Evaluation Involving Composition or Substitution View
22. The integer $n$ for which $\lim _ { x \rightarrow 0 } ( \cos x - 1 ) \left( \cos x - e ^ { x } \right) / x ^ { n }$ is a finite non-zero number is
(A) 1
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(B) 2
(C) 3
(D) 4
Q23 Chain Rule Limit Involving Derivative Definition of Composed Functions View
23. Let $f : R \rightarrow R$ be such that $f ( 1 ) = 3$, and $f ^ { \prime } ( 1 ) = 6$ Then $\lim _ { x \rightarrow 0 } ( f ( 1 + x ) / f ( 1 ) ) ^ { 1 / x }$ equals
(A) 1
(B) $\quad \mathrm { e } ^ { 1 / 2 }$
(C) $\quad \mathrm { e } ^ { 2 }$
(D) $\quad \mathrm { e } ^ { 3 }$
Q24 Tangents, normals and gradients Find tangent line with a specified slope or from an external point View
24. The point (s) on the curve $y ^ { 3 } + 3 x ^ { 2 } = 12 y$ where the tangent is vertical, is (are)
(A) $\quad ( \pm 4 / \sqrt { } 3 , - 2 )$
(B) $\quad ( \pm \sqrt { } 11 / 3 , - 0 )$
(C) $( 0,0 )$
(D) $\quad ( \pm 4 / \sqrt { } 3,2 )$
Q25 Tangents, normals and gradients Common tangent line to two curves View
25. The equation of the common tangents to the curves $y ^ { 2 } = 8 x$ and $x y = - 1$ is
(A) $\quad 3 y = 9 x + 2$
(B) $\quad y = 2 x + 1$
(C) $\quad 2 y = x + 8$
(D) $\quad y = x + 2$
Q26 Standard Integrals and Reverse Chain Rule Integral Equation to Determine a Function Value View
26. Let $f ( x ) = \int ^ { x } { } _ { 1 } \sqrt { } \left( 2 - t ^ { 2 } \right)$ The real roots of the equation $x ^ { 2 } - f ^ { \prime } ( x ) = 0$ are
(A) $\quad \pm 1$
(B) $\pm 1 / \sqrt { } 2$
(C) $\quad \pm 1 / 2$
(D) 0 and 1
Q27 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View
27. Let $\mathrm { T } > 0$ be a fixed real number. Suppose f is a continuous function such that for all $x \varepsilon R . f ( x + T )$ If $I = \int _ { T 0 } f ( x ) . d x$ then the value of $\int _ { 3 } { } ^ { 3 + 3 T }$ is
(A) $( 3 / 2 ) \mathrm { I }$
(B) I
(C) 3 I
(D) 6 I
Q28 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View
28. The integral $\int _ { 1 / 2 - 1 / 2 } ( [ x ] + \ln ( 1 + x / 1 + x ) ) d x$ equals
(A) $- 1 / 2$
(B) 0
(C) 1
(D) $2 \ln ( 1 / 2 )$
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  1. If vector $a$ and bare two vectors such that $a \rightarrow + 2 b \rightarrow$ and $5 a \rightarrow - 4 b \rightarrow$ are perpendicular to each other then the angle between vector $a$ and $b$ is
    (A) $\quad 45 ^ { \circ }$
    (B) $\quad 60 ^ { 0 }$
    (C) $\quad \cos ^ { - 1 } 1 / 3$
    (D) $\quad \cos ^ { - 1 } 2 / 7$
  2. Let vector $\mathrm { V } = 2 \mathrm { i } ^ { \rightarrow } + \mathrm { j } ^ { \rightarrow } - \mathrm { k } ^ { \rightarrow }$ and $\mathrm { W } ^ { \rightarrow } = \mathrm { i } ^ { \rightarrow } + 3 \mathrm { k } ^ { \rightarrow }$. If vector U is a unit vector, then the maximum value of the scalar triple product $\left[ \mathrm { U } ^ { \rightarrow } \mathrm { V } ^ { \rightarrow } \mathrm { W } ^ { \rightarrow } \right]$ is
    (A) - 1
    (B) $\quad \sqrt { } 10 + \sqrt { } 6$
    (C) $\sqrt { } 59$
    (D) $\sqrt { } 60$