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Mathematics · 2019 · 11 Jan · Shift 1

22 questions from this JEE Main paper

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2019 · 11 Jan · Shift 1
Mathematics

Mathematics · 2019 · 11 Jan · Shift 1

22 questions from this JEE Main paper

Circle2 questions Differentiation1 questions Limits Continuity and Differentiability2 questions Matrices and Determinants2 questions Differential Equations1 questions Quadratic Equation and Inequalities1 questions Statistics1 questions Application of Derivatives1 questions Functions2 questions Vector Algebra1 questions Binomial Theorem1 questions Indefinite Integrals1 questions Definite Integration1 questions Sequences and Series2 questions Probability1 questions Complex Numbers1 questions Area Under the Curves1 questions

Q20.The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :
Mathematics · Circle · MCQ
Q21.If xloge(logex) $-$ x2 + y2 = 4(y > 0), then $\frac{d y}{d x}$ at x = e is equal to :
Mathematics · Differentiation · MCQ
Q22.Let [x] denote the greatest integer less than or equal to x. Then $x \to 0 lim \frac{t a n ( π s i n ^{2} x ) + ( ∣ x ∣ - s i n ( x [ x ] ) ) ^{2}}{x ^{2}}$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q23.Let A = $0 p p 2 q q - q r - r r .$ If AAT = I3, then $∣ p ∣$ is :
Mathematics · Matrices and Determinants · MCQ
Q24.If y(x) is the solution of the differential equation $\frac{d y}{d x} + (\frac{2 x + 1}{x}) y = e^{- 2 x}, x > 0,$ where $y (1) = \frac{1}{2} e^{- 2},$ then
Mathematics · Differential Equations · MCQ
Q25.A square is inscribed in the circle x2 + y2 – 6x + 8y – 103 = 0 with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is :
Mathematics · Circle · MCQ
Q26.If one real root of the quadratic equation 81x2 + kx + 256 = 0 is cube of the other root, then a value of k is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q27.The outcome of each of 30 items was observed; 10 items gave an outcome $\frac{1}{2}$ – d each, 10 items gave outcome $\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2}$ + d each. If the variance of this outcome data is $\frac{4}{3}$ …
Mathematics · Statistics · MCQ
Q28.The maximum value of the function f(x) = 3x3 – 18x2 + 27x – 40 on the set S = ${x \in R : x^{2} + 30 \leq 11 x}$ is :
Mathematics · Application of Derivatives · MCQ
Q29.Let f : R $\to$ R be defined by f(x) = $\frac{x}{1 + x ^{2}}, x \in R$ . Then the range of f is :
Mathematics · Functions · MCQ
Q30.Let $a = i + 2 j + 4 k, b = i + λ j + 4 k$ and $c = 2 i + 4 j + (λ^{2} - 1) k$ be…
Mathematics · Vector Algebra · MCQ
Q31.The sum of the real values of x for which the middle term in the binomial expansion of $(\frac{x ^{3}}{3} + \frac{3}{x})^{8}$ equals 5670 is :
Mathematics · Binomial Theorem · MCQ
Q32.If $\int \frac{1 - x ^{2}}{x ^{4}}$ dx = A(x) $(1 - x^{2})^{m}$ + C, for a suitable chosen integer m and a function A(x), where C is a constant of integration, then (A(x))m equals :
Mathematics · Indefinite Integrals · MCQ
Q33.If the system of linear equations 2x + 2y + 3z = a 3x – y + 5z = b x – 3y + 2z = c where a, b, c are non zero real numbers, has more one solution, then :
Mathematics · Matrices and Determinants · MCQ
Q34.The value of the integral $- 2 \int 2 \frac{s i n ^{2} x}{[ \frac{x}{π} ] + \frac{1}{2}} d x$ (where [x] denotes the greatest integer less than or equal to x) is
Mathematics · Definite Integration · MCQ
Q35.The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is $\frac{27}{19}$ .Then the common ratio of this series is :
Mathematics · Sequences and Series · MCQ
Q36.Let $f (x) = {- 1 x^{2} - 1, - 2 \leq x < 0 0 \leq x \leq 2$ and $g (x) = ∣ f (x) ∣ + f (∣ x ∣) .$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.Two integers are selected at random from the set {1, 2, ...., 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :
Mathematics · Probability · MCQ
Q38.Let $(- 2 - \frac{1}{3} i)^{3} = \frac{x + i y}{27} (i = - 1),$ where x and y are real numbers, then y $-$ x equals :
Mathematics · Complex Numbers · MCQ
Q39.Let fk(x) = $\frac{1}{k} (sin^{k} x + cos^{k} x)$ for k = 1, 2, 3, ... Then for all x $\in$ R, the value of f4(x) $-$ f6(x) is equal to
Mathematics · Functions · MCQ
Q40.Let a1, a2, . . . . . ., a10 be a G.P. If $\frac{a _{3}}{a _{1}} = 25,$ then $\frac{a _{9}}{a _{5}}$ equals
Mathematics · Sequences and Series · MCQ
Q41.The area (in sq. units) of the region bounded by the curve x2 = 4y and the straight line x = 4y – 2 is :
Mathematics · Area Under the Curves · MCQ