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Mathematics · 2018 · Shift 0

18 questions from this JEE Main paper

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JEE Main
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2018 · Shift 0
Mathematics

Mathematics · 2018 · Shift 0

18 questions from this JEE Main paper

Permutations and Combinations1 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Matrices and Determinants2 questions Sets and Relations1 questions Sequences and Series1 questions Probability1 questions Statistics1 questions Vector Algebra1 questions Straight Lines and Pair of Straight Lines1 questions Differential Equations1 questions Indefinite Integrals1 questions Definite Integration1 questions Area Under the Curves1 questions Limits Continuity and Differentiability2 questions Application of Derivatives1 questions

Q27.From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :
Mathematics · Permutations and Combinations · MCQ
Q28.Let S = { $x \in$ R : $x \geq$ 0 and $2 ∣ x - 3 ∣ + x (x - 6) + 6 = 0$ }. Then S
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.If $α, β \in C$ are the distinct roots of the equation x2 - x + 1 = 0, then $α^{101} + β^{107}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q30.If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z), then $\frac{x z}{y ^{2}}$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q31.If $x - 4 2 x 2 x 2 x x - 4 2 x 2 x 2 x x - 4 = (A + B x) (x - A)^{2}$ then the ordered pair (A, B) is…
Mathematics · Matrices and Determinants · MCQ
Q32.Two sets A and B are as under : A = {( $a$ , b) $\in$ R $\times$ R : | $a$ - 5| < 1 and |b - 5| < 1}; B = {( $a$ , b) $\in$ R $\times$ R : 4( $a$ - 6)2 + 9(b - 5)2 $\leq$ 36 }; Then
Mathematics · Sets and Relations · MCQ
Q33.Let $a_{1}$ , $a_{2}$ , $a_{3}$ , ......... , $a_{49}$ be in A.P. such that $k = 0 \sum 12 a_{4 k + 1} = 416$ and $a_{9} + a_{43} = 66$ . $a_{1}^{2} + a_{2}^{2} + ....... + a_{17}^{2} = 140 m$ , then m is equal to
Mathematics · Sequences and Series · MCQ
Q34.A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag,…
Mathematics · Probability · MCQ
Q35.If $i = 1 \sum 9 (x_{i} - 5) = 9$ and $i = 1 \sum 9 (x_{i} - 5)^{2} = 45$ , then the standard deviation of the 9 items $x_{1}, x_{2}, ......., x_{9}$ is
Mathematics · Statistics · MCQ
Q36.Let $u$ be a vector coplanar with the vectors $a = 2 i + 3 j - k$ and $b = j + k$ . If $u$ is perpendicular to $a$ …
Mathematics · Vector Algebra · MCQ
Q37.A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.Let y = y(x) be the solution of the differential equation $sin x \frac{d y}{d x} + y cos x = 4 x$ , $x \in (0, π)$ . If $y (\frac{π}{2}) = 0$ , then $y (\frac{π}{6})$ is equal to :
Mathematics · Differential Equations · MCQ
Q39.The integral $\int \frac{s i n ^{2} x c o s ^{2} x}{( s i n ^{5} x + c o s ^{3} x s i n ^{2} x + s i n ^{3} x c o s ^{2} x + c o s ^{5} x ) ^{2}} d x$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q40.The value of $- π /2 \int π /2 \frac{s i n ^{2} x}{1 + 2 ^{x}} d x$ is
Mathematics · Definite Integration · MCQ
Q41.Let g(x) = cosx2, f(x) = $x$ and $α, β (α < β)$ be the roots of the quadratic equation 18x2 - 9 $π$ x + $π^{2}$ = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the…
Mathematics · Area Under the Curves · MCQ
Q42.Let S = { t $\in R : f (x) = ∣ x - π ∣ . (e^{∣ x ∣} - 1) sin ∣ x ∣$ is not differentiable at t}, then the set S is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q43.Let $f (x) = x^{2} + \frac{1}{x ^{2}}$ and $g (x) = x - \frac{1}{x}$ , $x \in R - {- 1, 0, 1}$ . If $h (x) = \frac{f ( x )}{g ( x )}$ , then the local…
Mathematics · Application of Derivatives · MCQ
Q44.For each t $x \to 0^{+} lim x ([\frac{1}{x}] + [\frac{2}{x}] + ..... + [\frac{15}{x}])$ , let [t] be the greatest integer less than or equal to t. Then $x \to 0^{+} lim x ([\frac{1}{x}] + [\frac{2}{x}] + ..... + [\frac{15}{x}])$ …
Mathematics · Limits Continuity and Differentiability · MCQ