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Mathematics · 2019 · 10 Apr · Shift 1

21 questions from this JEE Main paper

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2019 · 10 Apr · Shift 1
Mathematics

Mathematics · 2019 · 10 Apr · Shift 1

21 questions from this JEE Main paper

Probability1 questions Matrices and Determinants2 questions 3D Geometry1 questions Differential Equations1 questions Complex Numbers1 questions Quadratic Equation and Inequalities2 questions Straight Lines and Pair of Straight Lines1 questions Limits Continuity and Differentiability3 questions Functions2 questions Sequences and Series1 questions Permutations and Combinations1 questions Statistics1 questions Vector Algebra1 questions Indefinite Integrals1 questions Definite Integration1 questions Hyperbola1 questions

Q23.Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is :
Mathematics · Probability · MCQ
Q24.If $Δ_{1} = x - sin θ cos θ sin θ - x 1 cos θ 1 x$ and $Δ_{2} = x - sin 2 θ cos 2 θ sin 2 θ - x 1 cos 2 θ 1 x$ …
Mathematics · Matrices and Determinants · MCQ
Q25.If the length of the perpendicular from the point ( $β$ , 0, $β$ ) ( $β e$ 0) to the line, $\frac{x}{1} = \frac{y - 1}{0} = \frac{z + 1}{- 1}$ is $\frac{3}{2}$ , then $β$ is equal to :
Mathematics · 3D Geometry · MCQ
Q26.If y = y(x) is the solution of the differential equation $\frac{d y}{d x} = (tan x - y) sec^{2} x$ , $x \in (- \frac{π}{2}, \frac{π}{2})$ , such that y (0) = 0, then $y (- \frac{π}{4})$ …
Mathematics · Differential Equations · MCQ
Q27.If a > 0 and z = $\frac{( 1 + i ) ^{2}}{a - i}$ , has magnitude $\frac{2}{5}$ , then $\overline{z}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q28.If $α$ and $β$ are the roots of the quadratic equation, x2 + x sin $θ$ - 2 sin $θ$ = 0, $θ \in (0, \frac{π}{2})$ , then $\frac{α ^{12} + β ^{12}}{( α ^{- 12} + β ^{- 12} ) . ( α - β ) ^{24}}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.All the pairs (x, y) that satisfy the inequality $2^{s i n^{2} x - 2 s i n x + 5} . \frac{1}{4 ^{s i n^{2} y}} \leq 1$ also satisfy the equation
Mathematics · Quadratic Equation and Inequalities · MCQ
Q30.The region represented by| x – y | $\leq$ 2 and | x + y| $\leq$ 2 is bounded by a :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.If $f (x) = ⎩ ⎨ ⎧ \frac{s i n ( p + 1 ) x + s i n x}{x} q \frac{x + x ^{2} - x}{x ^{\frac{3}{2}}}, x < 0, x = 0, x > 0$ is continuous at x =…
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Let f(x) = ex – x and g(x) = x2 – x, $\forall$ x $\in$ R. Then the set of all x $\in$ R, where the function h(x) = (fog) (x) is increasing, is :
Mathematics · Functions · MCQ
Q33.If a1, a2, a3, ............... an are in A.P. and a1 + a4 + a7 + ........... + a16 = 114, then a1 + a6 + a11 + a16 is equal to :
Mathematics · Sequences and Series · MCQ
Q34.The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is :
Mathematics · Permutations and Combinations · MCQ
Q35.If for some x $\in$ R, the frequency distribution of the marks obtained by 20 students in a test is : then the mean of the marks is Includes table
Mathematics · Statistics · MCQ
Q36.If the system of linear equations x + y + z = 5 x + 2y + 2z = 6 x + 3y + $λ$ z = $μ$ , ( $λ$ , $μ \in$ R), has infinitely many solutions, then the value of $λ$ + $μ$ is :
Mathematics · Matrices and Determinants · MCQ
Q37.Let A (3, 0, –1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the ratio, 2 : 1, then cos ( $∠$ GOA) (O being the origin) is equal to :
Mathematics · Vector Algebra · MCQ
Q38.If $\int \frac{d x}{( x ^{2} - 2 x + 10 ) ^{2}} = A (tan^{- 1} (\frac{x - 1}{3}) + \frac{f ( x )}{x ^{2} - 2 x + 10}) + C$ where C is a constant of integration then :
Mathematics · Indefinite Integrals · MCQ
Q39.Let f : R $\to$ R be differentiable at c $\in$ R and f(c) = 0. If g(x) = |f(x)| , then at x = c, g is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q40.The value of $0 \int 2 π [sin 2 x (1 + cos 3 x)] d x$ , where [t] denotes the greatest integer function is :
Mathematics · Definite Integration · MCQ
Q41.If a directrix of a hyperbola centred at the origin and passing through the point (4, –2 $3$ ) is 5x = 4 $5$ and its eccentricity is e, then :
Mathematics · Hyperbola · MCQ
Q42.If $x \to 1 lim \frac{x ^{4} - 1}{x - 1} = x \to k lim \frac{x ^{3} - k ^{3}}{x ^{2} - k ^{2}}$ , then k is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q43.Let f(x) = x2 , x $\in$ R. For any A $\subseteq$ R, define g (A) = { x $\in$ R : f(x) $\in$ A}. If S = [0,4], then which one of the following statements is not true ?
Mathematics · Functions · MCQ