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Mathematics · 2013 · Shift 1

20 questions from this JEE Advanced paper

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JEE Advanced
Papers
2013 · Shift 1
Mathematics

Mathematics · 2013 · Shift 1

20 questions from this JEE Advanced paper

Trigonometric Functions and Equations2 questions Sequences and Series2 questions Complex Numbers1 questions Mathematical Induction and Binomial Theorem1 questions Permutations and Combinations1 questions 3D Geometry2 questions Straight Lines and Pair of Straight Lines1 questions Ellipse1 questions Inverse Trigonometric Functions1 questions Application of Derivatives1 questions Matrices and Determinants1 questions Application of Integration1 questions Definite Integration1 questions Differential Equations1 questions Probability2 questions Vector Algebra1 questions

Q21.Let $f (x) = x sin π x, x > 0.$ Then for all natural numbers $n, f^{'} (x)$ vanishes at
Mathematics · Trigonometric Functions and Equations · Multiple correct
Q22.A pack contains $n$ cards numbered from $1$ to $n .$ Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is $1224.$ If the smaller of the numbers on the removed cards is $k,$ then $k - 20 =$ …
Mathematics · Sequences and Series · Numerical
Q23.Let complex numbers $α an d \frac{1}{α}$ lie on circles $(x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}$ and $(x - x_{0})^{2} + (y - y_{0})^{2} = 4 r^{2}$ …
Mathematics · Complex Numbers · MCQ
Q24.The number of points in $(- \infty \infty),$ for which $x^{2} - x sin x - cos x = 0,$ is
Mathematics · Trigonometric Functions and Equations · MCQ
Q25.The coefficient of three consecutive terms of $(1 + x)^{n + 5}$ are in the ratio $5 : 10 : 14.$ Then $n$ =
Mathematics · Mathematical Induction and Binomial Theorem · Numerical
Q26.Consider the set of eight vectors $V = {a \hat{i} + b \hat{j} + c \hat{k} : a, b, c \in {- 1, 1}}$ . Three non-coplanar vectors can be chosen from v in $2^{p}$ ways. Then p is
Mathematics · Permutations and Combinations · Numerical
Q27.Let $S_{n} = k = 1 \sum 4 n (- 1)^{\frac{k ( k + 1 )}{2}} k^{2} .$ Then $S_{n}$ can take value(s)
Mathematics · Sequences and Series · Multiple correct
Q28.Perpendiculars are drawn from points on the line $\frac{x + 2}{2} = \frac{y + 1}{- 1} = \frac{z}{3}$ to the plane $x + y + z = 3$ . The foot of perpendiculars lie on the line
Mathematics · 3D Geometry · MCQ
Q29.For $a > b > c > 0,$ the distance between $(1, 1)$ and the point of intersection of the lines $a x + b y + c = 0$ and $b x + a y + c = 0$ is less than $(22)$ . Then
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q30.A vertical line passing through the point $(h, 0)$ intersects the ellipse $\frac{x ^{2}}{4} + \frac{y ^{2}}{3} = 1$ at the points $P$ and $Q$ . Let the tangents to the ellipse at $P$ and $Q$ meet at the point $R$ . If $Δ (h)$ …
Mathematics · Ellipse · Numerical
Q31.The value of $cot (n = 1 \sum 23 cot^{- 1} (1 + k = 1 \sum n 2 k))$ is
Mathematics · Inverse Trigonometric Functions · MCQ
Q32.A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8 : 15$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed…
Mathematics · Application of Derivatives · Multiple correct
Q33.For 3 × 3 matrices M and N, which of the following statement(s) is(are) NOT correct?
Mathematics · Matrices and Determinants · Multiple correct
Q34.The area enclosed by the curves $y = sin x + cosx o l imi t s$ and $y = ∣ cos x - sin x ∣$ over the interval $[0, \frac{π}{2}]$ is
Mathematics · Application of Integration · MCQ
Q35.Let $f$ $: [\frac{1}{2}, 1] \to R$ (the set of all real number) be a positive, non-constant and differentiable function such that $f^{'} (x) < 2 f (x)$ and $f (\frac{1}{2}) = 1.$ …
Mathematics · Definite Integration · MCQ
Q36.A curve passes through the point $(1, \frac{π}{6})$ . Let the slope of the curve at each point $(x, y)$ be $\frac{y}{x} + sec (\frac{y}{x}), x > 0.$ Then the equation of the curve is
Mathematics · Differential Equations · MCQ
Q37.Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8} .$ Then the probability that the problem is solved correctly by at least one of them is
Mathematics · Probability · MCQ
Q38.Of the three independent events $E_{1}, E_{2}$ and $E_{3},$ the probability that only $E_{1}$ occurs is $α,$ only $E_{2}$ occurs is $β$ and only $E_{3}$ occurs is $γ .$ Let the probability $p$ that none of events…
Mathematics · Probability · Numerical
Q39.A line $l$ passing through the origin is perpendicular to the lines $l_{1} : (3 + t) i + (- 1 + 2 t) j + (4 + 2 t) k, - \infty < t < \infty l_{2} : (3 + 2 s) i + (3 + 2 s) j + (2 + s) k, - \infty < s < \infty$ …
Mathematics · 3D Geometry · Multiple correct
Q40.Let $PR = 3 \hat{i} + \hat{j} - 2 \hat{k}$ and $SQ = \hat{i} - 3 \hat{j} - 4 \hat{k}$ determine diagonals of a parallelogram $P QR S$ and $PT = \hat{i} + 2 \hat{j} + 3 \hat{k}$ …
Mathematics · Vector Algebra · MCQ