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Mathematics · 2016 · Shift 2

18 questions from this JEE Advanced paper

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JEE Advanced
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2016 · Shift 2
Mathematics

Mathematics · 2016 · Shift 2

18 questions from this JEE Advanced paper

Complex Numbers1 questions Trigonometric Functions and Equations1 questions Vector Algebra1 questions 3D Geometry1 questions Probability2 questions Definite Integration2 questions Application of Integration1 questions Application of Derivatives1 questions Ellipse2 questions Parabola1 questions Matrices and Determinants2 questions Sequences and Series1 questions Limits Continuity and Differentiability2 questions

Q19.Let $a, b \in R an d a^{2} + b^{2} e 0$ . Suppose $S = {Z \in C : Z = \frac{1}{a + ib t}, + \in R, t e 0}$ , where $i = - 1$ . Ifz = x + iy and z $\in$ S, then (x, y) lies on
Mathematics · Complex Numbers · Multiple correct
Q20.The value of $k = 1 \sum 13 \frac{1}{s i n ( \frac{π}{4} + \frac{( k - 1 ) π}{6} ) s i n ( \frac{π}{4} + \frac{k π}{6} )}$ is equal to
Mathematics · Trigonometric Functions and Equations · MCQ
Q21.Let $u = u_{1} i + u_{2} j + u_{3} k$ be a unit vector in $R^{3}$ and $w = \frac{1}{6} (i + j + 2 k) .$ Given that there exists a vector $v$ …
Mathematics · Vector Algebra · Multiple correct
Q22.Let $P$ be the image of the point $(3, 1, 7)$ with respect to the plane $x - y + z = 3.$ Then the equation of the plane passing through $P$ and containing the straight line $\frac{x}{1} = \frac{y}{2} = \frac{z}{1}$ is
Mathematics · 3D Geometry · MCQ
Q23.Football teams $T_{1}$ and $T_{2}$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_{1}$ winning, drawing and losing a game against $T_{2}$ are $\frac{1}{2}, \frac{1}{6}$ …
Mathematics · Probability · MCQ
Q24.Football teams $T_{1}$ and $T_{2}$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_{1}$ winning, drawing and losing a game against $T_{2}$ are $\frac{1}{2}, \frac{1}{6}$ …
Mathematics · Probability · MCQ
Q25.Let $f (x) = n \to \infty lim (\frac{n ^{n} ( x + n ) ( x + \frac{n}{2} ) ... ( x + \frac{n}{n} )}{n ! ( x ^{2} + n ^{2} ) ( x ^{2} + \frac{n ^{2}}{4} ) .... ( x ^{2} + \frac{n ^{2}}{n ^{2}} )})^{\frac{x}{n}},$ …
Mathematics · Definite Integration · Multiple correct
Q26.Area of the region ${(x, y) \in R^{2} : y \geq ∣ x + 3 ∣, 5 y \leq x + 9 \leq 15}$ is equal to
Mathematics · Application of Integration · MCQ
Q27.The value of $- \frac{π}{2} \int \frac{π}{2} \frac{x ^{2} c o s x}{1 + e ^{x}} d x$ is equal to
Mathematics · Definite Integration · MCQ
Q28.Let f: R $\to (0, \infty)$ and g : R $\to$ R be twice differentiable functions such that f'' and g'' are continuous functions on R. Suppose f' $(2) =$ g $(2) = 0$ , f'' $(2) e 0$ and g' $(2) e 0$ . If $x \to 2 lim \frac{f ( x ) g ( x )}{f ^{'} ( x ) g ^{'} ( x )} = 1,$ …
Mathematics · Application of Derivatives · Multiple correct
Q29.Let $F_{1} (x_{1}, 0)$ and $F_{2} (x_{2}, 0)$ for $x_{1} < 0$ and $x_{2} > 0$ , be the foci of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{8} = 1$ . Suppose a parabola having vertex at the origin and…
Mathematics · Ellipse · MCQ
Q30.Let $F_{1} (x_{1}, 0)$ and $F_{2} (x_{2}, 0)$ for $x_{1} < 0$ and $x_{2} > 0$ , be the foci of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{8} = 1$ . Suppose a parabola having vertex at the origin and…
Mathematics · Ellipse · MCQ
Q31.Let $P$ be the point on the parabola $y^{2} = 4 x$ which is at the shortest distance from the center $S$ of the circle $x^{2} + y^{2} - 4 x - 16 y + 64 = 0$ . Let $Q$ be the point on the circle dividing the line segment $S P$ internally. Then
Mathematics · Parabola · Multiple correct
Q32.Let $P = 1416014001$ and I be the identity matrix of order 3. If $Q = [q_{ij}]$ is a matrix such that $P^{50} - Q = I$ and $\frac{q _{31} + q _{32}}{q _{21}}$ …
Mathematics · Matrices and Determinants · MCQ
Q33.Let bi > 1 for I = 1, 2, ......, 101. Suppose logeb1, logeb2, ......., logeb101 are in Arithmetic Progression (A.P.) with the common difference loge2. Suppose a1, a2, ......, a101 are in A.P. such that a1 = b1 and a51 = b51. If t = b1 +…
Mathematics · Sequences and Series · MCQ
Q34.Let a, b $\in$ R and f : R $\to$ R be defined by $f (x) = a cos (∣ x^{3} - x ∣) + b ∣ x ∣ sin (∣ x^{3} + x ∣)$ . Then f is
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q35.Let a, $λ$ , m $\in$ R. Consider the system of linear equations ax + 2y = $λ$ 3x $-$ 2y = $μ$ Which of the following statements is(are) correct?
Mathematics · Matrices and Determinants · Multiple correct
Q36.Let $f : [- \frac{1}{2}, 2] \to R$ and $g : [- \frac{1}{2}, 2] \to R$ be function defined by $f (x) = [x^{2} - 3]$ and $g (x) = ∣ x ∣ f (x) + ∣4 x - 7∣ f (x)$ , where [y] denotes the greatest integer less than or equal…
Mathematics · Limits Continuity and Differentiability · Multiple correct