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Mathematics · 2018 · Shift 2

18 questions from this JEE Advanced paper

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JEE Advanced
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2018 · Shift 2
Mathematics

Mathematics · 2018 · Shift 2

18 questions from this JEE Advanced paper

Inverse Trigonometric Functions1 questions Hyperbola2 questions Matrices and Determinants2 questions Ellipse1 questions Complex Numbers1 questions Limits Continuity and Differentiability2 questions Definite Integration1 questions Functions2 questions Differential Equations1 questions Trigonometric Functions and Equations1 questions 3D Geometry2 questions Mathematical Induction and Binomial Theorem1 questions Permutations and Combinations1 questions

Q19.For any positive integer n, define $f_{n} : (0, \infty) \to R$ as $f_{n} = j = 1 \sum n tan^{- 1} (\frac{1}{1 + ( x + j ) ( x + j - 1 )})$ for all x $\in$ (0, $\infty$ ). (Here, the inverse trigonometric…
Mathematics · Inverse Trigonometric Functions · Multiple correct
Q20.Let T be the line passing through the points P( $-$ 2, 7) and Q(2, $-$ 5). Let F1 be the set of al pairs of circles (S1, S2) such that T is tangent to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point,…
Mathematics · Hyperbola · Multiple correct
Q21.Let S be the set of all column matrices $b_{1} b_{2} b_{3}$ such that $b_{1}, b_{2}, b_{3} \in R$ and the system of equations (in real variables) $- x + 2 y + 5 z = b_{1} 2 x - 4 y + 3 z = b_{2} x - 2 y + 2 z = b_{3}$ …
Mathematics · Matrices and Determinants · Multiple correct
Q22.Consider two straight lines, each of which is tangent to both the circle x2 + y2 = (1/2) and the parabola y2 = 4x. Let these lines intersect at the point Q. Consider the ellipse whose centre is at the origin O(0, 0) and whose semi-major…
Mathematics · Ellipse · Multiple correct
Q23.Let s, t, r be non-zero complex numbers and L be the set of solutions $z = x + i y (x, y \in R, i = - 1)$ of the equation $sz + t \overline{z} + r = 0$ where $\overline{z}$ = x $-$ iy. Then, which of the following statement(s) is(are)…
Mathematics · Complex Numbers · Multiple correct
Q24.Let f : (0, $π$ ) $\to$ R be a twice differentiable function such that $t \to x lim \frac{f ( x ) s i n t - f ( t ) s i n x}{t - x} = sin^{2} x$ for all x $\in$ (0, $π$ ). If $f (\frac{π}{6}) = - \frac{π}{12}$ …
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q25.The value of the integral $\int_{0}^{1/2} \frac{1 + 3}{( ( x + 1 ) ^{2} ( 1 - x ) ^{6} ) ^{1/4}} d x$ is ........
Mathematics · Definite Integration · Numerical
Q26.Let P be a matrix of order 3 $\times$ 3 such that all the entries in P are from the set { $-$ 1, 0, 1}. Then, the maximum possible value of the determinant of P is ............ .
Mathematics · Matrices and Determinants · Numerical
Q27.Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If $α$ is the number of one-one functions from X to Y and $β$ is the number of onto functions from Y to X, then the value of $\frac{1}{5 !} (β - α)$ …
Mathematics · Functions · Numerical
Q28.Let f : R $\to$ R be a differentiable function with f(0) = 0. If y = f(x) satisfies the differential equation $\frac{d y}{d x} = (2 + 5 y) (5 y - 2)$ , then the value of $n \to - \infty lim f (x)$ is ...........
Mathematics · Differential Equations · Numerical
Q29.Let f : R $\to$ R be a differentiable function with f(0) = 1 and satisfying the equation f(x + y) = f(x) f'(y) + f'(x) f(y) for all x, y $\in$ R. Then, the value of loge(f(4)) is ...........
Mathematics · Trigonometric Functions and Equations · Numerical
Q30.Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is perpendicular to the plane x + y = 3 and the mid-point of PQ lies in the plane x + y = 3) lies on the Z-axis. Let the distance of P…
Mathematics · 3D Geometry · Numerical
Q31.Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the X-axis, Y-axis and Z-axis, respectively, where O(0, 0, 0) is the origin. Let $S (\frac{1}{2}, \frac{1}{2}, \frac{1}{2})$ be the centre of…
Mathematics · 3D Geometry · Numerical
Q32.Let $X = (^{10} C_{1})^{2} + 2 (^{10} C_{2})^{2} + 3 (^{10} C_{3})^{2} + ... + 10 (^{10} C_{10})^{2}$ , where $^{10} C_{r}$ , r $\in$ {1, 2, ..., 10} denote binomial coefficients. Then, the value of $\frac{1}{1430} X$ is ..........
Mathematics · Mathematical Induction and Binomial Theorem · Numerical
Q33.Let $E_{1} = {x \in R : x \neq = 1 and \frac{x}{x - 1} > 0}$ and $E_{2} = {x \in E_{1} : sin^{- 1} (lo g_{e} (\frac{x}{x - 1})) is a real number}$ (Here, the inverse…
Mathematics · Functions · MCQ
Q34.In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4, G5. (i) Let $α$ 1 be the total number of ways in which the committee can be formed such that the committee has 5… Includes table
Mathematics · Permutations and Combinations · MCQ
Q35.Let $H : \frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ , where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60 $^{\circ}$ at one of its vertices N. Let the area of the $Δ$ LMN be $43$ … Includes table
Mathematics · Hyperbola · MCQ
Q36.Let $f_{1} : R \to R$ , $f_{2} : (- \frac{π}{2}, \frac{π}{2}) \to R$ , $f_{3} : (- 1, e^{π /2} - 2) \to R$ and $f_{4} : R \to R$ be functions defined by (i) $f_{1} (x) = sin (1 - e^{- x^{2}})$ …
Mathematics · Limits Continuity and Differentiability · MCQ