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Mathematics · 2013 · Shift 2

20 questions from this JEE Advanced paper

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JEE Advanced
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2013 · Shift 2
Mathematics

Mathematics · 2013 · Shift 2

20 questions from this JEE Advanced paper

Vector Algebra1 questions Complex Numbers3 questions 3D Geometry2 questions Probability2 questions Application of Derivatives3 questions Inverse Trigonometric Functions1 questions Properties of Triangle1 questions Parabola3 questions Circle1 questions Quadratic Equation and Inequalities1 questions Limits Continuity and Differentiability1 questions Matrices and Determinants1 questions

Q21.match List $I$ with List $I I$ and select the correct answer using the code given below the lists: List $I$ (P.) Volume of parallelopiped determined by vectors $a, b$ and…
Mathematics · Vector Algebra · MCQ
Q22.Let $ω = \frac{3 + i}{2}$ and $P = {ω^{n} : n = 1, 2, 3, \dots}$ . Further $H_{1} = {z \in C : Re z < \frac{1}{2}}$ and $H_{2} = {z \in C : Re z < \frac{- 1}{2}}$ …
Mathematics · Complex Numbers · Multiple correct
Q23.Consider the lines $L_{1} : \frac{x - 1}{2} = \frac{y}{- 1} = \frac{z + 3}{1}, L_{2} : \frac{x - 4}{1} = \frac{y + 3}{1} = \frac{z + 3}{2}$ and the planes $P_{1} : 7 x + y + 2 z = 3, P_{2} = 3 x + 5 y - 6 z = 4.$ Let $a x + b y + cz = d$ be…
Mathematics · 3D Geometry · MCQ
Q24.Two lines $L_{1} : x = 5, \frac{y}{3 - α} = \frac{z}{- 2}$ and $L_{2} : x = α, \frac{y}{- 1} = \frac{z}{2 - α}$ are coplanar. Then $α$ can take value(s)
Mathematics · 3D Geometry · Multiple correct
Q25.A box $B_{1}$ contains $1$ white ball, $3$ red balls and $2$ black balls. Another box $B_{2}$ contains $2$ white balls, $3$ red balls and $4$ black balls. A third box $B_{3}$ contains $3$ white balls, $4$ red balls and $5$ black balls. If $1$ …
Mathematics · Probability · MCQ
Q26.A box $B_{1}$ contains $1$ white ball, $3$ red balls and $2$ black balls. Another box $B_{2}$ contains $2$ white balls, $3$ red balls and $4$ black balls. A third box $B_{3}$ contains $3$ white balls, $4$ red balls and $5$ black balls. If $2$ …
Mathematics · Probability · MCQ
Q27.Let $f : [0, 1] \to R$ (the set of all real numbers) be a function. Suppose the function $f$ is twice differentiable, $f (0) = f (1) = 0$ and satisfies $f^{''} (x) - 2 f^{'} (x) + f (x) \geq . e^{x}, x \in [0, 1]$ …
Mathematics · Application of Derivatives · MCQ
Q28.Let $f : [0, 1] \to R$ (the set of all real numbers) be a function. Suppose the function $f$ is twice differentiable, $f (0) = f (1) = 0$ and satisfies $f^{''} (x) - 2 f^{'} (x) + f (x) \geq . e^{x}, x \in [0, 1]$ …
Mathematics · Application of Derivatives · MCQ
Q29.Match List $I$ with List $I I$ and select the correct answer using the code given below the lists: List $I P .$ $(\frac{1}{y ^{2}} (\frac{c o s ( t a n ^{- 1} y ) + y s i n ( t a n ^{- 1} y )}{c o t ( s i n ^{- 1} y ) + t a n ( s i n ^{- 1} y )})^{2} + y^{4})^{1/2}$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q30.In a triangle $P QR$ , $P$ is the largest angle and $cos P = \frac{1}{3}$ . Further the incircle of the triangle touches the sides $P Q$ , $QR$ and $R P$ at $M$ and $M$ respectively, such that the lengths of $P N, Q L$ and $R M$ are consecutive…
Mathematics · Properties of Triangle · Multiple correct
Q31.Let $P Q$ be a focal chord of the parabola $y^{2} = 4 a x$ . The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y = 2 x + a$ , $a > 0$ . If chord $P Q$ subtends an angle $θ$ at the vertex of $y^{2} = 4 a x$ , then tan $θ =$ …
Mathematics · Parabola · MCQ
Q32.Let $P Q$ be a focal chord of the parabola $y^{2} = 4 a x$ . The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y = 2 x + a$ , $a > 0$ . Length of chord $P Q$ is
Mathematics · Parabola · MCQ
Q33.A line $L : y = m x + 3$ meets $y$ -axis at R $(0, 3)$ and the arc of the parabola $y^{2} = 16 x, 0 \leq y \leq 6$ at the point $F (x_{0}, y_{0})$ . The tangent to the parabola at $F (x_{0}, y_{0})$ intersects the $y$ -axis…
Mathematics · Parabola · MCQ
Q34.Circle (s) touching x-axis at a distance 3 from the origin and having an intercept of length $27$ on y-axis is (are)
Mathematics · Circle · Multiple correct
Q35.If $3^{x} = 4^{x - 1},$ then $x =$
Mathematics · Quadratic Equation and Inequalities · Multiple correct
Q36.Let $S = S_{1} \cap S_{2} \cap S_{3}$ , where $S_{1} = {z \in C : ∣ z ∣ < 4}, S_{2} = {z \in C : Im o l imi t s [\frac{z - 1 + 3 i}{1 - 3 i}] > 0}$ and $S_{3} = {z \in C : Re o l imi t s z > 0}$ …
Mathematics · Complex Numbers · MCQ
Q37.Let $S = S_{1} \cap S_{2} \cap S_{3}$ , where $S_{1} = {z \in C : ∣ z ∣ < 4}, S_{2} = {z \in C : Im [\frac{z - 1 + 3 i}{1 - 3 i}] > 0}$ and $S_{3} = {z \in C : Re (z) > 0}$ …
Mathematics · Complex Numbers · MCQ
Q38. $a \in R$ (the set of all real numbers), a $e -$ 1, $n \to \infty lim \frac{( 1 ^{a} + 2 ^{a} + ... + n ^{a} )}{( n + 1 ) ^{a - 1} [( na + 1 ) + ( na + 2 ) + ... + ( na + n )]} = \frac{1}{60}$ , Then a = ?
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q39.Let $ω$ be a complex cube root of unity with $ω e$ 1 and P = [pij] be a n $\times$ n matrix with pij = $ω$ i + j. Then P2 $e$ 0, when n = ?
Mathematics · Matrices and Determinants · Multiple correct
Q40.The function $f (x) = 2 ∣ x ∣ + ∣ x + 2 ∣ - ∣ ∣ x + 2 ∣ - 2 ∣ x ∣ ∣$ has a local minimum or a local maximum at x =
Mathematics · Application of Derivatives · Multiple correct