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Mathematics · 2019 · 8 Apr · Shift 1

23 questions from this JEE Main paper

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2019 · 8 Apr · Shift 1
Mathematics

Mathematics · 2019 · 8 Apr · Shift 1

23 questions from this JEE Main paper

Inverse Trigonometric Functions1 questions Area Under the Curves1 questions Quadratic Equation and Inequalities1 questions Probability1 questions Sequences and Series1 questions Matrices and Determinants2 questions Functions1 questions Straight Lines and Pair of Straight Lines2 questions Application of Derivatives2 questions Definite Integration1 questions Statistics1 questions Limits Continuity and Differentiability1 questions 3D Geometry1 questions Complex Numbers1 questions Differential Equations1 questions Trigonometric Ratio and Identites1 questions Indefinite Integrals1 questions Permutations and Combinations1 questions Differentiation1 questions Circle1 questions

Q23.If $α = cos^{- 1} (\frac{3}{5})$ , $β = tan^{- 1} (\frac{1}{3})$ where $0 < α, β < \frac{π}{2}$ , then $α$ - $β$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q24.The area (in sq. units) of the region A = { (x, y) $\in$ R × R| 0 $\leq$ x $\leq$ 3, 0 $\leq$ y $\leq$ 4, y $\leq$ x2 + 3x} is :
Mathematics · Area Under the Curves · MCQ
Q25.The sum of the solutions of the equation $∣ x - 2 ∣ + x (x - 4) + 2 = 0$ (x > 0) is equal to:
Mathematics · Quadratic Equation and Inequalities · MCQ
Q26.Let A and B be two non-null events such that A $\subset$ B . Then, which of the following statements is always correct?
Mathematics · Probability · MCQ
Q27.The sum of all natural numbers 'n' such that 100 < n < 200 and H.C.F. (91, n) > 1 is :
Mathematics · Sequences and Series · MCQ
Q28.Let $A = (cos α sin α - sin α cos α)$ , ( $α \in$ R) such that $A^{32} = (01 - 1 0)$ …
Mathematics · Matrices and Determinants · MCQ
Q29.If $f (x) = lo g_{e} (\frac{1 - x}{1 + x})$ , $∣ x ∣ < 1$ then $f (\frac{2 x}{1 + x ^{2}})$ is equal to
Mathematics · Functions · MCQ
Q30.Let O(0, 0) and A(0, 1) be two fixed points. Then the locus of a point P such that the perimeter of $Δ$ AOP is 4, is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.If S1 and S2 are respectively the sets of local minimum and local maximum points of the function, ƒ(x) = 9x4 + 12x3 – 36x2 + 25, x $\in$ R, then :
Mathematics · Application of Derivatives · MCQ
Q32.If $f (x) = \frac{2 - x c o s x}{2 + x c o s x}$ and g(x) = logex, (x > 0) then the value of integral $- \frac{π}{4} \int \frac{π}{4} g (f (x)) d x$ is
Mathematics · Definite Integration · MCQ
Q33.The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is :
Mathematics · Statistics · MCQ
Q34. $x \to 0 lim \frac{s i n ^{2} x}{2 - 1 + c o s x}$ equals:
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.The length of the perpendicular from the point (2, –1, 4) on the straight line, $\frac{x + 3}{10}$ = $\frac{y - 2}{- 7}$ = $\frac{z}{1}$ is :
Mathematics · 3D Geometry · MCQ
Q36.A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate axes will lie only in :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q37.If $α$ and $β$ be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which $(\frac{α}{β})^{n} = 1$ is :
Mathematics · Complex Numbers · MCQ
Q38.Let y = y(x) be the solution of the differential equation, $(x^{2} + 1)^{2} \frac{d y}{d x} + 2 x (x^{2} + 1) y = 1$ such that y(0) = 0. If $a y (1)$ = $\frac{π}{32}$ , then the value of 'a' is :
Mathematics · Differential Equations · MCQ
Q39.The greatest value of c $\in$ R for which the system of linear equations x – cy – cz = 0 cx – y + cz = 0 cx + cy – z = 0 has a non-trivial solution, is :
Mathematics · Matrices and Determinants · MCQ
Q40.If cos( $α$ + $β$ ) = 3/5 ,sin ( $α$ - $β$ ) = 5/13 and 0 < $\frac{π}{4}$ < $\frac{π}{4}$ , then tan(2 $α$ ) is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q41. $\int \frac{s i n \frac{5 x}{2}}{s i n \frac{x}{2}} d x$ is equal to (where c is a constant of integration)
Mathematics · Indefinite Integrals · MCQ
Q42.All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is :
Mathematics · Permutations and Combinations · MCQ
Q43.If $2 y = (cot^{- 1} (\frac{3 c o s x + s i n x}{c o s x - 3 s i n x}))^{2}$ , x $\in$ $(0, \frac{π}{2})$ then $\frac{d y}{d x}$ is equal to:
Mathematics · Differentiation · MCQ
Q44.The sum of the squares of the lengths of the chords intercepted on the circle, x2 + y2 = 16, by the lines, x + y = n, n $\in$ N, where N is the set of all natural numbers, is :
Mathematics · Circle · MCQ
Q45.Let ƒ : [0, 2] $\to$ R be a twice differentiable function such that ƒ''(x) > 0, for all x $\in$ (0, 2). If $ϕ$ (x) = ƒ(x) + ƒ(2 – x), then $ϕ$ is :
Mathematics · Application of Derivatives · MCQ