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Mathematics · 2017 · Shift 2

18 questions from this JEE Advanced paper

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JEE Advanced
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2017 · Shift 2
Mathematics

Mathematics · 2017 · Shift 2

18 questions from this JEE Advanced paper

Limits Continuity and Differentiability2 questions Differential Equations2 questions Matrices and Determinants1 questions Probability1 questions Functions1 questions Vector Algebra2 questions 3D Geometry1 questions Application of Derivatives2 questions Definite Integration1 questions Application of Integration1 questions Trigonometric Functions and Equations2 questions Quadratic Equation and Inequalities2 questions

Q19.If f : R $\to$ R is a twice differentiable function such that f"(x) > 0 for all x $\in$ R, and $f (\frac{1}{2}) = \frac{1}{2}$ , f(1) = 1, then
Mathematics · Limits Continuity and Differentiability · MCQ
Q20.If y = y(x) satisfies the differential equation $8 x (9 + x) d y = (4 + 9 + x)^{- 1}$ dx, x > 0 and y(0) = $7$ , then y(256) =
Mathematics · Differential Equations · MCQ
Q21.How many 3 $\times$ 3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of MTM is 5?
Mathematics · Matrices and Determinants · MCQ
Q22.Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is
Mathematics · Probability · MCQ
Q23.Let S = {1, 2, 3, .........., 9}. For k = 1, 2, .........., 5, let Nk be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N1 + N2 + N3 + N4 + N5 =
Mathematics · Functions · MCQ
Q24.Let O be the origin and let PQR be an arbitrary triangle. The point S is such that $O P$ . $O Q$ + $O R$ . $O S$ = $O R$ .…
Mathematics · Vector Algebra · MCQ
Q25.The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y $-$ 2z = 5 and 3x $-$ 6y $-$ 2z = 7 is
Mathematics · 3D Geometry · MCQ
Q26.f : R $\to$ R is a differentiable function such that f'(x) > 2f(x) for all x $\in$ R, and f(0) = 1 then
Mathematics · Application of Derivatives · Multiple correct
Q27.If $I = \sum o l imi t s_{k = 1}^{98} \int_{k}^{k + 1} \frac{k + 1}{x ( x + 1 )} d x$ , then
Mathematics · Definite Integration · Multiple correct
Q28.If the line x = $α$ divides the area of region R = {(x, y) $\in$ R2 : x3 $\leq$ y $\leq$ x, 0 $\leq$ x $\leq$ 1} into two equal parts, then
Mathematics · Application of Integration · Multiple correct
Q29.Let $α$ and $β$ be non zero real numbers such that $2 (cos β - cos α) + cos α cos β = 1$ . Then which of the following is/are true?
Mathematics · Trigonometric Functions and Equations · Multiple correct
Q30.Let $f (x) = \frac{1 - x ( 1 + ∣1 - x ∣ )}{∣1 - x ∣} cos (\frac{1}{1 - x})$ for x $e$ 1. Then
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q31.If $g (x) = \int_{s i n x}^{s i n (2 x)} sin^{- 1} (t) d t$ , then
Mathematics · Differential Equations · Multiple correct
Q32.If $f (x) = cos 2 x - cos x sin x cos 2 x cos x sin x sin 2 x - sin x cos x$ , then
Mathematics · Application of Derivatives · Multiple correct
Q33.Let O be the origin and $O X$ , $O Y$ , $O Z$ be three unit vectors in the directions of the sides $QR$ , $R P$ , $P Q$ respectively, of a…
Mathematics · Trigonometric Functions and Equations · MCQ
Q34.Let O be the origin and $O X$ , $O Y$ , $O Z$ be three unit vectors in the directions of the sides $QR$ , $R P$ , $P Q$ respectively, of a…
Mathematics · Vector Algebra · MCQ
Q35.Let p, q be integers and let $α$ , $β$ be the roots of the equation, x2 $-$ x $-$ 1 = 0 where $α e β$ . For n = 0, 1, 2, ........, let an = p $α$ n + q $β$ n. FACT : If a and b are rational numbers and a + b $5$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q36.Let p, q be integers and let $α$ , $β$ be the roots of the equation, x2 $-$ x $-$ 1 = 0 where $α e β$ . For n = 0, 1, 2, ........, let an = p $α$ n + q $β$ n. FACT : If a and b are rational numbers and a + b $5$ …
Mathematics · Quadratic Equation and Inequalities · MCQ