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 · 2015 · Shift 1

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
2015 · Shift 1
Mathematics

Mathematics · 2015 · Shift 1

20 questions from this JEE Advanced paper

Permutations and Combinations1 questions Trigonometric Functions and Equations1 questions Vector Algebra2 questions Parabola3 questions Application of Derivatives1 questions Differential Equations2 questions Definite Integration1 questions Application of Integration1 questions Probability1 questions 3D Geometry2 questions Properties of Triangle1 questions Matrices and Determinants2 questions Limits Continuity and Differentiability1 questions Functions1 questions

Q21.Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that…
Mathematics · Permutations and Combinations · Numerical
Q22.The number of distinct solutions of the equation $\frac{5}{4} cos^{2} 2 x + cos^{4} x + sin^{4} x + cos^{6} x + sin^{6} x = 2$ in the interval $[0, 2 π]$ is
Mathematics · Trigonometric Functions and Equations · Numerical
Q23.Match the following : Column $I$ (A) In $R^{2},$ If the magnitude of the projection vector of the vector $α i + β j$ on $3 i + j$ and If $α = 2 + 3 β,$ …
Mathematics · Vector Algebra · MCQ
Q24.Let $P$ and $Q$ be distinct points on the parabola $y^{2} = 2 x$ such that a circle with $P Q$ as diameter passes through the vertex $O$ of the parabola. If $P$ lies in the first quadrant and the area of the triangle $Δ O P Q$ is $32,$ …
Mathematics · Parabola · Multiple correct
Q25.If the normals of the parabola $y^{2} = 4 x$ drawn at the end points of its latus rectum are tangents to the circle $(x - 3)^{2} + (y + 2)^{2} = r^{2}$ , then the value of $r^{2}$ is
Mathematics · Parabola · Numerical
Q26.Let the curve $C$ be the mirror image of the parabola $y^{2} = 4 x$ with respect to the line $x + y + 4 = 0$ . If $A$ and $B$ are the points of intersection of $C$ with the line $y = - 5$ , then the distance between $A$ and $B$ is
Mathematics · Parabola · Numerical
Q27.A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of $V m m^{3}$ , has a $2$ mm thick solid wall and is open at the top. The bottom of the container is a solid…
Mathematics · Application of Derivatives · Numerical
Q28.Let $y (x)$ be a solution of the differential equation $(1 + e^{x}) y^{'} + y e^{x} = 1.$ If $y (0) = 2$ , then which of the following statement is (are) true?
Mathematics · Differential Equations · Multiple correct
Q29.Consider the family of all circles whose centres lie on the straight line $y = x,$ If this family of circle is represented by the differential equation $P y^{''} + Q y^{'} + 1 = 0,$ where $x, y$ are functions of $y^{'}$ and $y^{'}$ $(h er e y^{'} = \frac{d y}{d x}, y^{''} = \frac{d ^{2} y}{d x ^{2}})$ …
Mathematics · Differential Equations · Multiple correct
Q30.Let $f : R \to R$ be a function defined by $f (x) = {[x], 0, x \leq 2 x > 2$ where $[x]$ is the greatest integer less than or…
Mathematics · Definite Integration · Numerical
Q31.Let $F (x) = x \int x^{2} + \frac{π}{6} 2 cos^{2} t (d t)$ for all $x \in R$ and $f : [0, \frac{1}{2}] \to [0, \infty]$ be a continuous function. For $a \in [0, \frac{1}{2}],$ …
Mathematics · Application of Integration · Numerical
Q32.The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least $0.96,$ is
Mathematics · Probability · Numerical
Q33.In $R^{3},$ consider the planes $P_{1} : y = 0$ and $P_{2} : x + z = 1.$ Let $P_{3}$ be the plane, different from $P_{1}$ and $P_{2}$ , which passes through the intersection of $P_{1}$ and $P_{2} .$ If the distance of the point $(0, 1, 0)$ from…
Mathematics · 3D Geometry · Multiple correct
Q34.In $R^{3},$ let $L$ be a straight lines passing through the origin. Suppose that all the points on $L$ are at a constant distance from the two planes $P_{1} : x + 2 y - z + 1 = 0$ and $P_{2} : 2 x - y + z - 1 = 0.$ Let $M$ be the locus of the…
Mathematics · 3D Geometry · Multiple correct
Q35.Let $Δ P QR$ be a triangle. Let $a = QR, b = R P$ and $c = P Q .$ If $a = 12, b = 43, b . c = 24,$ …
Mathematics · Vector Algebra · Multiple correct
Q36.Match the following : Includes table
Mathematics · Properties of Triangle · MCQ
Q37.Let X and Y be two arbitrary, 3 $\times$ 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 $\times$ 3, non-zero, symmetric matrix. Then which of the following matrices is(are) skew symmetric?
Mathematics · Matrices and Determinants · Multiple correct
Q38.Which of the following values of $α$ satisfy the equation $(1 - α)^{2} (2 + α)^{2} (3 + α)^{2} (1 + 2 α)^{2} (2 + 2 α)^{2} (3 + 2 α)^{2} (1 + 3 α)^{2} (2 + 3 α)^{2} (3 + 3 α)^{2} = - 648 α$ …
Mathematics · Matrices and Determinants · Multiple correct
Q39.Let $g : R \to R$ be a differentiable function with $g (0) = 0$ , $g^{'} (0) = 0$ and $g^{'} (1) e 0$ . Let $f (x) = {\frac{x}{∣ x ∣} g (x), 0, x e 0 x = 0$ and $h (x) = e^{∣ x ∣}$ …
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q40.Let $f (x) = sin (\frac{π}{6} sin (\frac{π}{2} sin x))$ for all $x \in R$ and g(x) = $\frac{π}{2} sin x$ for all x $\in$ R. Let $(f \circ g) (x)$ denote f(g(x)) and $(g \circ f) (x)$ denote g(f(x)).…
Mathematics · Functions · Multiple correct