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Mathematics · 2008 · Shift 1

23 questions from this JEE Advanced paper

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JEE Advanced
Papers
2008 · Shift 1
Mathematics

Mathematics · 2008 · Shift 1

23 questions from this JEE Advanced paper

Complex Numbers3 questions 3D Geometry1 questions Vector Algebra1 questions Probability1 questions Definite Integration1 questions Application of Integration1 questions Differentiation2 questions Limits Continuity and Differentiability2 questions Inverse Trigonometric Functions1 questions Ellipse2 questions Sequences and Series1 questions Straight Lines and Pair of Straight Lines2 questions Circle3 questions Application of Derivatives1 questions Matrices and Determinants1 questions

Q24.Let A, B, C be three sets of complex numbers as defined below : $A = {z : Im o l imi t s z \geq 1} B = {z : ∣ z - 2 - i ∣ = 3} C = {z : Re o l imi t s (1 - i) z) = 2}$ …
Mathematics · Complex Numbers · MCQ
Q25.Let A, B, C be three sets of complex numbers as defined below : $A = {z : Im o l imi t s z \geq 1} B = {z : ∣ z - 2 - i ∣ = 3} C = {z : Re o l imi t s (1 - i) z) = 2}$ …
Mathematics · Complex Numbers · MCQ
Q26.Consider three planes $P_{1} : x - y + z = 1 P_{2} : x + y - z = 1 P_{3} : x - 3 y + 3 z = 2$ Let $L_{1}, L_{2}, L_{3}$ be the lines of intersection of the planes $P_{2}$ and $P_{3}, P_{3}$ and $P_{1}, P_{1}$ and $P_{2},$ respectively. STATEMENT - 1Z:…
Mathematics · 3D Geometry · MCQ
Q27.The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors $a, b, c$ such that $a . b = b . c = c . a = \frac{1}{2} .$ …
Mathematics · Vector Algebra · MCQ
Q28.Consider the system of equations $a x + b y = 0; c x + d y = 0,$ where $a, b, c, d$ $\in {0, 1}$ STATEMENT - 1 : The probability that the system of equations has a unique solution is $\frac{3}{8} .$ and STATEMENT - 2 : The probability…
Mathematics · Probability · MCQ
Q29.Consider the functions defined implicitly by the equation $y^{3} - 3 y + x = 0$ on various intervals in the real line. If $x \in (- \infty, - 2) \cup (2, \infty)$ , the equation implicitly defines a unique real valued differentiable function $y = f (x)$ . If $x \in (- 2, 2)$ …
Mathematics · Definite Integration · MCQ
Q30.Consider the functions defined implicitly by the equation $y^{3} - 3 y + x = 0$ on various intervals in the real line. If $x \in (- \infty, - 2) \cup (2, \infty)$ , the equation implicitly defines a unique real valued differentiable function $y = f (x)$ . If $x \in (- 2, 2)$ …
Mathematics · Application of Integration · MCQ
Q31.Consider the functions defined implicitly by the equation $y^{3} - 3 y + x = 0$ on various intervals in the real line. If $x \in (- \infty, - 2) \cup (2, \infty)$ , the equation implicitly defines a unique real valued differentiable function $y = f (x)$ . If $x \in (- 2, 2)$ …
Mathematics · Differentiation · MCQ
Q32.Let $f (x)$ be a non-constant twice differentiable function defined on $(- \infty, \infty)$ such that $f (x) = f (1 - x)$ and $f^{'} (\frac{1}{4}) = 0.$ Then,
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q33.If $0 < x < 1$ , then $1 + x^{2} [{x cos (cot^{- 1} x) + sin (cot^{- 1} x)}^{2} - 1]^{1/2} =$
Mathematics · Inverse Trigonometric Functions · MCQ
Q34.Consider the two curves $C_{1} : y^{2} = 4 x, C_{2} : x^{2} + y^{2} - 6 x + 1 = 0$ . Then,
Mathematics · Ellipse · MCQ
Q35.Let A, B, C be three sets of complex numbers as defined below $A = {z : Im o l imi t s z \geq 1} B = {z : ∣ z - 2 - i ∣ = 3} C = {z : Re o l imi t s (1 - i) z) = 2}$ …
Mathematics · Complex Numbers · MCQ
Q36.Let $S_{n} = k = 1 \sum n \frac{n}{n ^{2} + k n + k ^{2}}$ and $T_{n} = k = 0 \sum n - 1 \frac{n}{n ^{2} + k n + k ^{2}}$ for $n = 1, 2, 3, ............$ Then,
Mathematics · Sequences and Series · Multiple correct
Q37.A straight line through the vertex p of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then :
Mathematics · Straight Lines and Pair of Straight Lines · Multiple correct
Q38.A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $3 x + y - 6 = 0$ and the point D is $(\frac{3 3}{2}, \frac{3}{2})$ …
Mathematics · Circle · MCQ
Q39.A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $3 x + y - 6 = 0$ and the point D is $(\frac{3 3}{2}, \frac{3}{2})$ …
Mathematics · Circle · MCQ
Q40.A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $3 x + y - 6 = 0$ and the point D is $(\frac{3 3}{2}, \frac{3}{2})$ …
Mathematics · Circle · MCQ
Q41.Let $P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2}), y_{1} < 0, y_{2} < 0,$ be the end points of the latus rectum of the ellipse $x^{2} + 4 y^{2} = 4.$ The equations of parabolas with latus rectum $P Q$ are :
Mathematics · Ellipse · Multiple correct
Q42.Let $f$ and $g$ be real valued functions defined on interval $(- 1, 1)$ such that $g^{''} (x)$ is continuous, $g (0) e 0. g^{'} (0) = 0$ , $g^{''} (0) e 0$ , and $f (x) = g (x) sin x$ …
Mathematics · Differentiation · MCQ
Q43.Let a and b be non-zero real numbers. Then, the equation $(a x^{2} + b y^{2} + c) (x^{2} - 5 x y + 6 y^{2}) = 0$ represents :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q44.Let $g (x) = \frac{( x - 1 ) ^{n}}{l o g c o s ^{m} ( x - 1 )}; 00$ , and let $p$ be the left hand derivative of $∣ x - 1∣$ at $x = 1$ . If $x \to 1^{+} lim g (x) = p$ , then
Mathematics · Limits Continuity and Differentiability · MCQ
Q45.The total number of local maxima and local minima of the function $f (x) = {(2 + x)^{3}, x^{2/3}, - 3 < x \leq - 1 - 1 < x < 2$ is
Mathematics · Application of Derivatives · MCQ
Q46.Consider the system of equations: $x - 2 y + 3 z = - 1 - x + y - 2 z = k x - 3 y + 4 z = 1$ Statement - 1 : The system of equations has no solution for $k e 3$ . and Statement - 2 : The determinant $1 - 1 1 3 - 2 4 - 1 k 1 e 0$ …
Mathematics · Matrices and Determinants · MCQ