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Mathematics · 2016 · Shift 1

18 questions from this JEE Advanced paper

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JEE Advanced
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2016 · Shift 1
Mathematics

Mathematics · 2016 · Shift 1

18 questions from this JEE Advanced paper

Trigonometric Functions and Equations1 questions 3D Geometry1 questions Probability1 questions Definite Integration1 questions Differential Equations2 questions Application of Derivatives1 questions Properties of Triangle1 questions Differentiation1 questions Parabola1 questions Circle1 questions Mathematical Induction and Binomial Theorem1 questions Permutations and Combinations1 questions Quadratic Equation and Inequalities1 questions Matrices and Determinants3 questions Limits Continuity and Differentiability1 questions

Q19.Let $S = {x \in (- π, π) : x e 0, \pm \frac{π}{2}} .$ The sum of all distinct solutions of the equation $3 sec x + csc x + 2 (tan x - cot x) = 0$ in the set S is equal to
Mathematics · Trigonometric Functions and Equations · MCQ
Q20.Consider a pyramid $O P QR S$ located in the first octant $(x \geq 0, y \geq 0, z \geq 0)$ with $O$ as origin, and $O P$ and $O R$ along the $x$ -axis and the $y$ -axis, respectively. The base $O P QR$ of the pyramid is a square with $O P = 3.$ …
Mathematics · 3D Geometry · Multiple correct
Q21.A computer producing factory has only two plants $T_{1}$ and $T_{2} .$ Plant $T_{1}$ produces $20$ % and plant $T_{2}$ produces $80$ % of the total computers produced. $7$ % of computers produced in the factory turn out to be defective. It is…
Mathematics · Probability · MCQ
Q22.The total number of distinct $x \in [0, 1]$ for which $0 \int x \frac{t ^{2}}{1 + t ^{4}} d t = 2 x - 1$
Mathematics · Definite Integration · Numerical
Q23.A solution curve of the differential equation $(x^{2} + x y + 4 x + 2 y + 4) \frac{d y}{d x} - y^{2} = 0,$ $x > 0,$ passes through the point $(1, 3)$ . Then the solution curve
Mathematics · Differential Equations · Multiple correct
Q24.The least value of a $4 a x^{2} + \frac{1}{x} \geq 1,$ for which $4 a x^{2} + \frac{1}{x} \geq 1,$ , for all $x > 0$ . is
Mathematics · Application of Derivatives · MCQ
Q25.In a triangle $Δ X Y Z$ , let $x, y, z$ be the lengths of sides opposite to the angles $X, Y, Z$ respectively, and $2 s = x + y + z$ . If $\frac{s - x}{4} = \frac{s - y}{3} = \frac{s - z}{2}$ and area of incircle of the triangle $X Y Z$ …
Mathematics · Properties of Triangle · Multiple correct
Q26.Let $f : R \to R, g : R \to R$ and $h : R \to R$ be differentiable functions such that $f (x) = x^{3} + 3 x + 2, g (f (x)) = x$ and $h (g (g (x))) = x$ …
Mathematics · Differentiation · Multiple correct
Q27.The circle $C_{1} : x^{2} + y^{2} = 3,$ with centre at $O$ , intersects the parabola $x^{2} = 2 y$ at the point $P$ in the first quadrant, Let the tangent to the circle $C_{1}$ , at $P$ touches other two circles $C_{2}$ and $C_{3}$ at $R_{2}$ …
Mathematics · Parabola · Multiple correct
Q28.Let RS be the diameter of the circle $x^{2} + y^{2} = 1$ , where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at…
Mathematics · Circle · Multiple correct
Q29.Let $m$ be the smallest positive integer such that the coefficient of $x^{2}$ in the expansion of $(1 + x)^{2} + (1 + x)^{3} + ........ + (1 + x)^{49} + (1 + m x)^{50}$ …
Mathematics · Mathematical Induction and Binomial Theorem · Numerical
Q30.A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection of a captain (from among these 4 members ) for the team. If the team has to include at most one boy, then the number…
Mathematics · Permutations and Combinations · MCQ
Q31.Let $- \frac{π}{6} < θ < - \frac{π}{12} .$ Suppose $α_{1}$ and $β_{1}$ are the roots of the equation $x^{2} - 2 x sec θ + 1 = 0$ and $α_{2}$ and $β_{2}$ are the roots of the equation $x^{2} + 2 x tan θ - 1 = 0. I f α_{1} > β_{1}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q32.Let $f : (0, \infty) \to R$ be a differentiable function such that $f^{'} (x) = 2 - \frac{f ( x )}{x}$ for all $x \in (0, \infty)$ and $f (1) e 1$ . Then
Mathematics · Differential Equations · Multiple correct
Q33.Let $P = 323 - 1 0 - 5 - 2 α 0$ , where $α \in$ R. Suppose $Q = [q_{ij}]$ is a matrix such that PQ = kl, where k $\in$ R, k $e$ …
Mathematics · Matrices and Determinants · Multiple correct
Q34.The total number of distinct x $\in$ R for which $x 2 x 3 x x^{2} 4 x^{2} 9 x^{2} 1 + x^{3} 1 + 8 x^{3} 1 + 27 x^{3} = 10$ is …
Mathematics · Matrices and Determinants · Numerical
Q35.Let $z = \frac{- 1 + 3 i}{2}$ , where $i = - 1$ , and r, s $\in$ {1, 2, 3}. Let $P = [(- z)^{r} z^{2 s} z^{2 s} z^{r}]$ and I be the identity…
Mathematics · Matrices and Determinants · Numerical
Q36.Let $α$ , $β \in$ R be such that $x \to 0 lim \frac{x ^{2} s i n ( β x )}{α x - s i n x} = 1$ . Then 6( $α$ + $β$ ) equals .
Mathematics · Limits Continuity and Differentiability · Numerical