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Mathematics · 2012 · Shift 1

20 questions from this JEE Advanced paper

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JEE Advanced
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2012 · Shift 1
Mathematics

Mathematics · 2012 · Shift 1

20 questions from this JEE Advanced paper

Trigonometric Functions and Equations1 questions Complex Numbers1 questions Vector Algebra1 questions Probability1 questions Permutations and Combinations1 questions Circle1 questions Ellipse1 questions Hyperbola1 questions Parabola1 questions Application of Derivatives2 questions Indefinite Integrals1 questions Application of Integration1 questions Differential Equations1 questions 3D Geometry1 questions Limits Continuity and Differentiability2 questions Matrices and Determinants1 questions Functions1 questions Quadratic Equation and Inequalities1 questions

Q21.Let $θ, φ \in [0, 2 π]$ be such that $2 cos θ (1 - sin φ) = sin^{2} θ (tan \frac{θ}{2} + cot \frac{θ}{2}) cos φ - 1, tan (2 π - θ) > 0$ …
Mathematics · Trigonometric Functions and Equations · Multiple correct
Q22.Let z be a complex number such that the imaginary part of z is non-zero and $a = z^{2} + z + 1$ is real. Then a cannot take the value
Mathematics · Complex Numbers · MCQ
Q23.If $a, b$ and $c$ are unit vectors satisfying $a - b^{2} + b - c^{2} + c - a^{2} = 9,$ …
Mathematics · Vector Algebra · Numerical
Q24.A ship is fitted with three engines $E_{1}, E_{2}$ and $E_{3}$ . The engines function independently of each other with respective probabilities $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{4}$ . For the ship to be operational at least two of its…
Mathematics · Probability · Multiple correct
Q25.The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is
Mathematics · Permutations and Combinations · MCQ
Q26.The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20 to the circle $x^{2} + y^{2} = 9$ is
Mathematics · Circle · MCQ
Q27.The ellipse $E_{1} : \frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_{2}$ passing through the point $(0, 4)$ circumscribes the rectangle $R$ . The…
Mathematics · Ellipse · MCQ
Q28.Tangents are drawn to the hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1,$ parallel to the straight line $2 x - y = 1,$ The points of contact of the tangents on the hyperbola are
Mathematics · Hyperbola · Multiple correct
Q29.Let $S$ be the focus of the parabola $y^{2} = 8 x$ and let $P Q$ be the common chord of the circle $x^{2} + y^{2} - 2 x - 4 y = 0$ and the given parabola. The area of the triangle $P QS$ is
Mathematics · Parabola · Numerical
Q30.Let $f : I R \to I R$ be defined as $f (x) = ∣ x ∣ + x^{2} - 1 .$ The total number of points at which $f$ attains either a local maximum or a local minimum is
Mathematics · Application of Derivatives · Numerical
Q31.Let $p (x)$ be a real polynomial of least degree which has a local maximum at $x = 1$ and a local minimum at $x = 3$ . If $p (1) = 6$ and $p (3) = 2$ , then $p^{'} (0)$ is
Mathematics · Application of Derivatives · Numerical
Q32.The integral $\int \frac{s e c ^{2} x}{( s e c x + t a n x ) ^{9/2}} d x$ equals (for some arbitrary constant $K$ )
Mathematics · Indefinite Integrals · MCQ
Q33.Let $S$ be the area of the region enclosed by $y = e^{- x^{2}}$ , $y = 0$ , $x = 0$ , and $x = 1$ ; then
Mathematics · Application of Integration · Multiple correct
Q34.If $y (x)$ satisfies the differential equation $y^{'} - y t an x = 2 x sec x$ and $y (0) = 0,$ then
Mathematics · Differential Equations · Multiple correct
Q35.The point $P$ is the intersection of the straight line joining the points $Q (2, 3, 5)$ and $R (1, - 1, 4)$ with the plane $5 x - 4 y - z = 1.$ If $S$ is the foot of the perpendicular drawn from the point $T (2, 1, 4)$ to $QR,$ then the length of the…
Mathematics · 3D Geometry · MCQ
Q36.If $x \to \infty lim (\frac{x ^{2} + x + 1}{x + 1} - a x - b) = 4$ , then
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.Let $P = [a_{ij}]$ be a 3 $\times$ 3 matrix and let $Q = [b_{ij}]$ , where $b_{ij} = 2^{i + j} a_{ij}$ for $1 \leq i, j \leq 3$ . If the determinant of P is 2, then the determinant of the matrix Q is
Mathematics · Matrices and Determinants · MCQ
Q38.Let $f (x) = {x^{2} cos \frac{π}{x}, 0, x e 0 x = 0$ x $\in$ R, then f is
Mathematics · Limits Continuity and Differentiability · MCQ
Q39.The function $f : [0, 3] \to [1, 29]$ , defined by $f (x) = 2 x^{3} - 15 x^{2} + 36 x + 1$ , is
Mathematics · Functions · MCQ
Q40.The value of $6 + lo g_{3/2} (\frac{1}{3 2} 4 - \frac{1}{3 2} 4 - \frac{1}{3 2} 4 - \frac{1}{3 2} ...)$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical