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Mathematics · 2018 · 16 Apr · Shift 1

23 questions from this JEE Main paper

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2018 · 16 Apr · Shift 1
Mathematics

Mathematics · 2018 · 16 Apr · Shift 1

23 questions from this JEE Main paper

Matrices and Determinants2 questions Definite Integration1 questions Indefinite Integrals1 questions Differentiation1 questions Limits Continuity and Differentiability2 questions Application of Derivatives1 questions Sequences and Series1 questions Permutations and Combinations1 questions Area Under the Curves1 questions Sets and Relations1 questions Quadratic Equation and Inequalities2 questions Complex Numbers1 questions Probability2 questions Statistics1 questions Vector Algebra1 questions 3D Geometry1 questions Ellipse1 questions Circle1 questions Hyperbola1 questions

Q25.Let A = $111011001$ and B = A20. Then the sum of the elements of the first column of B is :
Mathematics · Matrices and Determinants · MCQ
Q26.If $f (x) = 0 \int x t (sin x - sin t) d t$ then :
Mathematics · Definite Integration · MCQ
Q27.If $\int \frac{t a n x}{1 + t a n x + t a n ^{2} x} d x = x - \frac{K}{A} tan^{- 1} (\frac{K t a n x + 1}{A}) + C, (C$ is a constant of integration) then the ordered pair (K, A) is equal to :
Mathematics · Indefinite Integrals · MCQ
Q28.If $x = 2^{c o s e c^{- 1}}$ and $y = 2^{se c^{- 1} t} (∣ t ∣ \geq 1),$ then $\frac{d y}{d x}$ is equal to :
Mathematics · Differentiation · MCQ
Q29.If the function f defined as $f (x) = \frac{1}{x} - \frac{k - 1}{e ^{2 x} - 1}, x e 0,$ is continuous at x = 0, then the ordered pair (k, f(0)) is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x3 $-$ 9x2 + 12x + 5 in the interval [0, 3]. Then M $-$ m is equal to :
Mathematics · Application of Derivatives · MCQ
Q31.Let $\frac{1}{x _{1}}, \frac{1}{x _{2}}, ..., \frac{1}{x _{n}}$ (xi $e$ 0 for i = 1, 2, ..., n) be in A.P. such that x1=4 and x21 = 20. If n is the least positive integer for which $x_{n} > 50,$ then $i = 1 \sum n (\frac{1}{x _{i}})$ …
Mathematics · Sequences and Series · MCQ
Q32. $x \to 0 lim \frac{( 27 + x ) ^{\frac{1}{3}} - 3}{9 - ( 27 + x ) ^{\frac{2}{3}}}$ equals.
Mathematics · Limits Continuity and Differentiability · MCQ
Q33.The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is :
Mathematics · Permutations and Combinations · MCQ
Q34.The number of values of k for which the system of linear equations, (k + 2)x + 10y = k kx + (k +3)y = k -1 has no solution, is :
Mathematics · Matrices and Determinants · MCQ
Q35.If the area of the region bounded by the curves, $y = x^{2}, y = \frac{1}{x}$ and the lines y = 0 and x= t (t >1) is 1 sq. unit, then t is equal to :
Mathematics · Area Under the Curves · MCQ
Q36.Let N denote the set of all natural numbers. Define two binary relations on N as R = {(x, y) $\in$ N $\times$ N : 2x + y = 10} and R2 = {(x, y) $\in$ N $\times$ N : x + 2y = 10}. Then :
Mathematics · Sets and Relations · MCQ
Q37.Let p, q and r be real numbers (p $e$ q, r $e$ 0), such that the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q38.The least positive integer n for which $(\frac{1 + i 3}{1 - i 3})^{n} = 1,$ is :
Mathematics · Complex Numbers · MCQ
Q39.Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to…
Mathematics · Probability · MCQ
Q40.If an angle A of a $Δ$ ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equation, 9x2 + 27x + 20 = 0 are :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q41.The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :
Mathematics · Statistics · MCQ
Q42.Let A, B and C be three events, which are pair-wise independent and $E$ denotes the completement of an event E. If $P (A \cap B \cap C) = 0$ and $P (C) > 0,$ then $P [(\overline{A} \cap \overline{B}) ∣ C]$ …
Mathematics · Probability · MCQ
Q43.Let $a = i + j + k, c = j - k$ and a vector $b$ be such that $a \times b = c$ and $a . b = 3.$ …
Mathematics · Vector Algebra · MCQ
Q44.If the angle between the lines, $\frac{x}{2} = \frac{y}{2} = \frac{z}{1}$ and $\frac{5 - x}{- 2} = \frac{7 y - 14}{p} = \frac{z - 3}{4}$ is $cos^{- 1} (\frac{2}{3}),$ then p is equal to :
Mathematics · 3D Geometry · MCQ
Q45.If the length of the latus rectum of an ellipse is 4 units and the distance between a focus an its nearest vertex on the major axis is $\frac{3}{2}$ units, then its eccentricity is :
Mathematics · Ellipse · MCQ
Q46.If a circle C, whose radius is 3, touches externally the circle, $x^{2} + y^{2} + 2 x - 4 y - 4 = 0$ at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :
Mathematics · Circle · MCQ
Q47.The locus of the point of intersection of the lines, $2 x - y + 42 k = 0$ and $2 k x + k y - 42 = 0$ (k is any non-zero real parameter), is :
Mathematics · Hyperbola · MCQ