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Mathematics · 2019 · 10 Jan · Shift 2

24 questions from this JEE Main paper

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2019 · 10 Jan · Shift 2
Mathematics

Mathematics · 2019 · 10 Jan · Shift 2

24 questions from this JEE Main paper

Definite Integration2 questions Differential Equations2 questions Limits Continuity and Differentiability1 questions Matrices and Determinants2 questions Complex Numbers1 questions Binomial Theorem1 questions Quadratic Equation and Inequalities1 questions Vector Algebra1 questions Ellipse1 questions Straight Lines and Pair of Straight Lines2 questions Sequences and Series1 questions Permutations and Combinations1 questions Trigonometric Ratio and Identites1 questions Statistics1 questions Inverse Trigonometric Functions1 questions Application of Derivatives1 questions Indefinite Integrals1 questions Circle1 questions Parabola1 questions Functions1 questions

Q23.If $0 \int x$ f(t) dt = x2 + $x \int 1$ t2f(t) dt then f ' $(\frac{1}{2})$ is -
Mathematics · Definite Integration · MCQ
Q24.Let f be a differentiable function such that f '(x) = 7 - $\frac{3}{4} \frac{f ( x )}{x},$ (x > 0) and f(1) $e$ 4. Then $x \to 0^{'} lim$ xf $(\frac{1}{x})$ :
Mathematics · Differential Equations · MCQ
Q25.Let f : ( $-$ 1, 1) $\to$ R be a function defined by f(x) = max ${- ∣ x ∣, - 1 - x^{2}} .$ If K be the set of all points at which f is not differentiable, then K has exactly -
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.The number of values of $θ \in$ (0, $π$ ) for which the system of linear equations x + 3y + 7z = 0 $-$ x + 4y + 7z = 0 (sin3 $θ$ )x + (cos2 $θ$ )y + 2z = 0. has a non-trival solution, is -
Mathematics · Matrices and Determinants · MCQ
Q27.The curve amongst the family of curves represented by the differential equation, (x2 – y2)dx + 2xy dy = 0 which passes through (1, 1) is :
Mathematics · Differential Equations · MCQ
Q28.Let $z = (\frac{3}{2} + \frac{i}{2})^{5} + (\frac{3}{2} - \frac{i}{2})^{5} .$ If R(z) and 1(z) respectively denote the real and imaginary parts of z, then :
Mathematics · Complex Numbers · MCQ
Q29.The positive value of $λ$ for which the co-efficient of x2 in the expression x2 $(x + \frac{λ}{x ^{2}})^{10}$ is 720, is -
Mathematics · Binomial Theorem · MCQ
Q30.The value of $λ$ such that sum of the squares of the roots of the quadratic equation, x2 + (3 – $λ$ )x + 2 = $λ$ has the least value is -
Mathematics · Quadratic Equation and Inequalities · MCQ
Q31.Let A = $2 b 1 b b^{2} + 1 b 1 b 2$ where b > 0. Then the minimum value of $\frac{d e t ( A )}{b}$ is -
Mathematics · Matrices and Determinants · MCQ
Q32.If $α$ = $(λ - 2) a + b$ and $β = (4 λ - 2) a + 3 b$ be two given vectors $a$ …
Mathematics · Vector Algebra · MCQ
Q33.Let S = ${(x, y) \in R^{2} : \frac{y ^{2}}{1 + r} - \frac{x ^{2}}{1 - r}}; r e \pm 1.$ Then S represents :
Mathematics · Ellipse · MCQ
Q34.The value of $- π /2 \int π /2 \frac{d x}{[ x ] + [ s i n x ] + 4},$ where [t] denotes the greatest integer less than or equal to t, is
Mathematics · Definite Integration · MCQ
Q35.Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which quadrant :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q36.Let a1, a2, a3, ..... a10 be in G.P. with ai > 0 for i = 1, 2, ….., 10 and S be the set of pairs (r, k), r, k $\in$ N (the set of natural numbers) for which $lo g_{e} a_{1}^{r} a_{2}^{k} lo g_{e} a_{4}^{r} a_{5}^{k} lo g_{e} a_{7}^{r} a_{8}^{k} lo g_{e} a_{2}^{r} a_{3}^{k} lo g_{e} a_{5}^{r} a_{6}^{k} lo g_{e} a_{8}^{r} a_{9}^{k} lo g_{e} a_{3}^{r} a_{4}^{k} lo g_{e} a_{6}^{r} a_{7}^{k} lo g_{e} a_{9}^{r} a_{10}^{k}$ …
Mathematics · Sequences and Series · MCQ
Q37.If $r = 0 \sum 25 {^{50} C_{r} .^{50 - r} C_{25 - r}} = K (^{50} C_{25}),$ then K is equal to :
Mathematics · Permutations and Combinations · MCQ
Q38.The value of $cos \frac{π}{2 ^{2}} . cos \frac{π}{2 ^{3}} ..... cos \frac{π}{2 ^{10}} . sin \frac{π}{2 ^{10}}$ is -
Mathematics · Trigonometric Ratio and Identites · MCQ
Q39.If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2, ….., x5 and –50 is equal to
Mathematics · Statistics · MCQ
Q40.The value of $cot (n = 1 \sum 19 cot^{- 1} (1 + p = 1 \sum n 2 p))$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q41.Two sides of a parallelogram are along the lines, x + y = 3 & x – y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q42.A helicopter is flying along the curve given by y – x3/2 = 7, (x $\geq$ 0). A soldier positioned at the point $(\frac{1}{2}, 7)$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is -
Mathematics · Application of Derivatives · MCQ
Q43.If $\int$ x5.e $-$ 4x3 dx = $\frac{1}{48}$ e $-$ 4x3 f(x) + C, where C is a constant of inegration, then f(x) is equal to -
Mathematics · Indefinite Integrals · MCQ
Q44.If the area of an equilateral triangle inscribed in the circle x2 + y2 + 10x + 12y + c = 0 is $273$ sq units then c is equal to :
Mathematics · Circle · MCQ
Q45.The length of the chord of the parabola x2 $=$ 4y having equation x – $2 y + 42 = 0$ is -
Mathematics · Parabola · MCQ
Q46.Let N be the set of natural numbers and two functions f and g be defined as f, g : N $\to$ N such that f(n) = ${\frac{n + 1}{2}; \frac{n}{2}; i f n i s o dd i f n i s e v e n$ …
Mathematics · Functions · MCQ