New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Mathematics · 2011 · Shift 2

20 questions from this JEE Advanced paper

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Advanced
Papers
2011 · Shift 2
Mathematics

Mathematics · 2011 · Shift 2

20 questions from this JEE Advanced paper

Quadratic Equation and Inequalities2 questions Complex Numbers1 questions Circle2 questions Parabola2 questions Hyperbola1 questions Application of Integration1 questions Probability1 questions Vector Algebra2 questions Differential Equations1 questions Limits Continuity and Differentiability2 questions Functions3 questions Matrices and Determinants2 questions

Q21.The number of distinct real roots of $x^{4} - 4 x^{3} + 12 x^{2} + x - 1 = 0$
Mathematics · Quadratic Equation and Inequalities · Numerical
Q22.Let $ω = e^{\frac{iπ}{3}}$ , and a, b, c, x, y, z be non-zero complex numbers such that $a + b + c = x a + bω + c ω^{2} = y a + b ω^{2} + c ω = z$ Then the value of $\frac{∣ x ∣ ^{2} + ∣ y ∣ ^{2} + ∣ z ∣ ^{2}}{∣ a ∣ ^{2} + ∣ b ∣ ^{2} + ∣ c ∣ ^{2}}$ …
Mathematics · Complex Numbers · Numerical
Q23.A value of $b$ for which the equations $x^{2} + b x - 1 = 0 x^{2} + x + b = 0$ have one root in common is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q24.The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point.
Mathematics · Circle · MCQ
Q25.The straight line 2x - 3y = 1 divides the circular region $x^{2} + y^{2} \leq 6$ into two parts. If $S = {(2, \frac{3}{4}), (\frac{5}{2}, \frac{3}{4}), (\frac{1}{4} - \frac{1}{4}), (\frac{1}{8}, \frac{1}{4})}$ …
Mathematics · Circle · Numerical
Q26.Let $(x, y)$ be any point on the parabola $y^{2} = 4 x$ . Let $P$ be the point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $1 : 3$ . Then the locus of $P$ is
Mathematics · Parabola · MCQ
Q27.Let $P (6, 3)$ be a point on the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ . If the normal at the point $P$ intersects the $x$ -axis at $(9, 0)$ , then the eccentricity of the hyperbola is
Mathematics · Hyperbola · MCQ
Q28.Let f $:$ $[- 1, 2] \to [0, \infty]$ be a continuous function such that $f (x) = f (1 - x)$ for all $x \in [- 1, 2]$ Let $R_{1} = - 1 \int 2 x f (x) d x,$ …
Mathematics · Application of Integration · MCQ
Q29.Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$ . If $P (T)$ denotes the probability of occurrence of…
Mathematics · Probability · Multiple correct
Q30.Match the statements given in Column - $I$ with the values given in Column- $I I .$ Column- $I$ (A) If $a = j + 3 k, b = - j + 3 k$ …
Mathematics · Vector Algebra · MCQ
Q31.Let $a = - i - k, b = - i + j$ and $c = i + 2 j + 3 k$ be three given vectors. If $r$ is a vector such that $r \times b = c \times b$ …
Mathematics · Vector Algebra · Numerical
Q32.Let $y^{'} (x) + y (x) g^{'} (x) = g (x), g^{'} (x), y (0) = 0, x \in R,$ where $f^{'} (x)$ denotes $\frac{df ( x )}{d x}$ and $g (x)$ is a given non-constant…
Mathematics · Differential Equations · Numerical
Q33.If $x \to 0 lim [1 + x ln (1 + b^{2})]^{1/ x} = 2 b sin^{2} θ$ , $b > 0$ and $θ \in (- π, π]$ , then the value of $θ$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q34.Let f(x) = x2 and g(x) = sin x for all x $\in$ R. Then the set of all x satisfying $(f \circ g \circ g \circ f) (x) = (g \circ g \circ f) (x)$ , where $(f \circ g) (x) = f (g (x))$ , is
Mathematics · Functions · MCQ
Q35.Let $ω e$ 1 be a cube root of unity and S be the set of all non-singular matrices of the form $1 ω ω^{2} a 1 ω b c 1$ ,…
Mathematics · Matrices and Determinants · MCQ
Q36.If $f (x) = {- x - \frac{π}{2}, - cos x x \leq - \frac{π}{2} - \frac{π}{2} 1$ , then
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q37.Let $f : (0, 1) \to R$ be defined by $f (x) = \frac{b - x}{1 - b x}$ , where b is a constant such that $0 < b < 1$ . Then
Mathematics · Functions · Multiple correct
Q38.Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by
Mathematics · Parabola · Multiple correct
Q39.Let M be a 3 $\times$ 3 matrix satisfying $M 010 = - 1 23$ , $M 1 - 1 0 = 11 - 1$ …
Mathematics · Matrices and Determinants · Numerical
Q40.Match the statements given in Column I with the intervals/union of intervals given in Column II : Includes diagram
Mathematics · Functions · MCQ