jee-advanced

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2025
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2024
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2023
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2022
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2020
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2019
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2017
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2016
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2015
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2013
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2012
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2011
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2010
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2009
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2008
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2007
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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
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2003 screening

17 maths questions

Q6 Matrices Matrix Power Computation and Application View
6. If
$$A = \left[ \begin{array} { l l } \alpha & 0 \\ 1 & 1 \end{array} \right] \text { and } B = \left[ \begin{array} { l l } 1 & 0 \\ 5 & 1 \end{array} \right] ,$$
then value of $a$ for which $A ^ { 2 } = B$, is:
(a) 1
(b) - 1
(c) 4
(d) no real values
Q7 Vectors 3D & Lines MCQ: Identify Correct Equation or Representation View
7. The value of $k$ such that $( x - 4 ) / 1 = ( y - 2 ) / 1 = ( z - k ) / 2$ lies in the plane $2 x - 4 y + z = 7$, is:
(a) 7
(b) - 7
(c) no real value
(d) 4
Q8 Sine and Cosine Rules Find a side or angle using the sine rule View
8. If the angles of a triangle are in the ratio $4 : 1 : 1$, then the ratio of the longest side to the perimeter is:
(a) $\sqrt { } 3 : ( 2 + \sqrt { } 3 )$
(b) $1 : 6$
(c) $1 : 2 + \sqrt { } 3$
(d) $2 : 3$
Q9 Chain Rule Limit Evaluation Involving Composition or Substitution View
9. If $\lim _ { ( x \rightarrow 0 ) } ( ( ( a - n ) n x - \tan x ) \sin n x ) / x ^ { 2 } = 0$, where $n$ is non zero real number, then $a$ is equal to:
(a) 0
(b) $( n + 1 ) / n$
(c) $n$
(d) $n + 1 / n$
Q10 Probability Definitions Finite Equally-Likely Probability Computation View
10. Two numbers are selected randomly from the set $S = \{ 1,2,3,4,5,6 \}$ without replacement one by one. The probability that minimum of the two numbers is less than 4 is :
(a) $[ 1 / 15 ]$
(b) $[ 14 / 15 ]$
(c) $[ 1 / 5 ]$
(d) $[ 4 / 5 ]$
Q11 Conic sections Eccentricity or Asymptote Computation View
11. For hyperbola $x ^ { 2 } / \left( \cos ^ { 2 } a \right) - y ^ { 2 } / \left( \sin ^ { 2 } a \right) = 1$ which of the following remains constant with change in ' a ' :
(a) abscissae of vertices
(b) abscissa of foci
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(c) eccentricity
(d) directrix
Q12 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
12. Range of the function $f ( x ) = \left( x ^ { 2 } + x + 2 \right) / \left( x ^ { 2 } + x + 1 \right) ; x \hat { I } R$ is:
(a) $( 1 , ¥ )$
(b) $( 1,11 / 7 )$
(c) $( 1,7 / 3 )$
(d) $( 1,7 / 5 )$
Q13 Differentiation from First Principles Limit Involving Derivative Definition of Composed Functions View
13. $\lim _ { ( h \rightarrow 0 ) } \left( \mathrm { f } \left( 2 \mathrm {~h} + 2 + \mathrm { h } ^ { 2 } \right) - \mathrm { f } ( 2 ) \right) / \left( \mathrm { f } \left( \mathrm { h } - \mathrm { h } ^ { 2 } + 1 \right) - \mathrm { f } ( 1 ) \right)$, given that $f ^ { \prime } ( 2 ) = 6$ and $f ^ { \prime } ( 1 ) = 4$ :
(a) does not exists
(b) is equal to $- 3 / 2$
(c) is equal to $3 / 2$
(d) is equal to 3
Q14 Discriminant and conditions for roots Parameter range for specific root conditions (location/count) View
14. If $f ( x ) = x ^ { 2 } + 2 b x + 2 c ^ { 2 }$ and $g ( x ) = - x ^ { 2 } - 2 c x + b ^ { 2 }$ such that min $f ( x ) > \max g ( x )$, then the relation between $b$ and $c$, is :
(a) no real value of $b$ and $c$
(b) $0 <$ c $<$ b $\sqrt { } 2$
(c) $| \mathrm { c } | < | \mathrm { b } | \sqrt { } 2$
(d) $| c | > | b | \sqrt { } 2$
Q15 Circles Inscribed/Circumscribed Circle Computations View
15. The centre of circle inscribed in square formed by the lines $x ^ { 2 } - 8 x + 12 = 0$ and $y ^ { 2 } - 14 y + 45 = 0$, is:
(a) $( 4,7 )$
(b) $( 7,4 )$
(c) $( 9,4 )$
(d) $( 4,9 )$
Q16 Circles Tangent Lines and Tangent Lengths View
16. The focal chord to $y ^ { 2 } = 16 x$ is tangent to $( x - 6 ) ^ { 2 } + y ^ { 2 } = 2$, then the possible values of the slope of this chord, are :
(a) $\{ - 1,1 \}$
(b) $\{ - 2,2 \}$
(c) $\{ - 2,1 / 2 \}$
(d) $\{ 2,1 / 2 \}$
Q17 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
17. Domain of definition of the function $f ( x ) = \sqrt { } \left( \sin ^ { - 1 } ( 2 x ) + \pi / 6 \right)$ for real valued $x$, is :
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(a) $\left[ - \frac { 1 } { 4 } , \frac { 1 } { 2 } \right]$
(b) $\left[ - \frac { 4 } { 2 } , \frac { 2 } { 2 } \right]$
(c) $\left( - \frac { 1 } { 2 } , \frac { 1 } { 9 } \right)$
(d) $\left( - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right)$
Q18 Complex Numbers Argand & Loci Identifying Real/Imaginary Parts or Components View
18. If $1 / 2 z 1 / 2 = 1$ and $\omega = z - 1 / z + 1$ (where $z \neq - 1$ ), then $\operatorname { Re } ( w )$ is:
(a) 0
(b) $\quad 1 / | z + 1 | ^ { 2 }$
(c) $\quad ( | 1 / ( z + 1 ) | ) \left( 1 / [ z + 1 ] ^ { 2 } \right)$
(d) $\quad \sqrt { } 2 / | z + 1 | ^ { 2 }$
Q19 Inequalities Identify Always-True Inequality from Options View
19. If $a \hat { I } ( 0 , \Pi / 2 )$ then $\sqrt { } \left( x ^ { 2 } + x \right)$ is always greater than or equal to :
(a) $2 \tan a$
(b) 1
(c) 2
(d) $\quad \sec ^ { 2 } a$
Q20 Integration by Substitution Reduction Formula or Recurrence via Integration by Parts View
20. If $I ( m , n ) = \int _ { 0 } { } ^ { 1 } t ^ { m } ( 1 + t ) ^ { n } \mathrm { dt }$, then the expression for $I ( m , n )$ in terms of $I ( m + 1 , n$ 1) is:
(a) $\left. \left. 2 ^ { n } / m + 1 \right) - n / m + 1 \right) * I ( m + 1 , n - 1 )$
(b) $n / m + 1 ) * \mid ( m + 1 , n - 1 )$
(c) $\quad 2 ^ { n } / ( m + 1 ) + n / ( m + 1 ) * I ( m + 1 , n - 1 )$
(b) $\quad m / ( m + 1 ) * I ( m + 1 , n - 1 )$
Q21 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions View
21. If $f ( x ) = \int _ { x } { } ^ { 2 ( x 2 + 1 ) } e ^ { - t 2 } d t$, then $f ( x )$ increases in:
(a) $\quad ( 2,2 )$
(b) no value of $x$
(c) $\quad ( 0 , ¥ )$
(d) $( - ¥ , 0 )$
Q22 Areas by integration View
22. The area of bounded by the curves $y = \sqrt { } x , 2 y + 3 = x$ and $x$-axis in the $1 ^ { \text {st } }$ quadrant is :
(a) 9
(b) $27 / 4$
(c) 36
(d) 18
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  1. Coefficient of $t ^ { 24 }$ in $\left( 1 + t ^ { 2 } \right) ^ { 12 } \left( 1 + t ^ { 12 } \right) \left( 1 + t ^ { 24 } \right)$ is:
    (a) $\quad { } ^ { 12 } \mathrm { C } _ { 6 } + 3$
    (b) $\quad { } ^ { 12 } \mathrm { C } _ { 6 } + 1$
    (c) $\quad { } ^ { 12 } \mathrm { C } _ { 6 }$
    (d) $\quad { } ^ { 12 } \mathrm { C } _ { 6 } + 2$
  2. The value of ' $a$ ' so that the volume of parallelepiped formed by $\hat { i } + a \hat { j } + k , \hat { j } + a k$ and aî $+ k$ because minimum is:
    (a) $\quad - 3$
    (b) 3
    (c) $1 / \sqrt { } 3$
    (d) $\sqrt { } 3$
  3. If the system of equations $x + a y = 0 , a z + y = 0$ and $a x + z = 0$ has infinite solutions, then the value of $a$ is
    (a) $\quad - 1$
    (b) 1
    (c) 0
    (d) no real values
  4. If $y ( t )$ is a solution of $( 1 + t ) d y / d t - t y = 1$ and $y ( 0 ) = - 1$, then $y ( 1 )$ is equal to:
    (a) $\quad - 1 / 2$
    (b) $\mathrm { e } + \frac { 1 } { 2 }$
    (c) $\mathrm { e } - \frac { 1 } { 2 }$
    (d) $\quad 1 / 2$
  5. Tangent is drawn to ellipse $x ^ { 2 } / 27 + y ^ { 2 } = 1$ at $( 3 \sqrt { } 3 \cos \theta , \sin \theta )$ (where $\theta \hat { \mathrm { I } } ( 0$, $\Pi / 2$ ). Then the value of $\theta$ such that sum of intercepts on axes made by this tangent is minimum, is
    (a) $\mathrm { p } / 3$
    (b) $\quad p / 6$
    (c) $\mathrm { p } / 8$
    (d) $\mathrm { p } / 4$
  6. Orthocentre of triangle with vertices $( 0,0 ) , ( 3,4 )$ and $( 4,0 )$ is:
    (a) $\quad ( 3,4 / 5 )$
    (b) $( 3,12 )$
    (c) $( 3,3 / 4 )$
    (d) $( 3,9 )$