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Mathematics · 2020 · 6 Sep · Shift 2

18 questions from this JEE Main paper

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2020 · 6 Sep · Shift 2
Mathematics

Mathematics · 2020 · 6 Sep · Shift 2

18 questions from this JEE Main paper

Functions2 questions Straight Lines and Pair of Straight Lines1 questions Area Under the Curves1 questions Complex Numbers1 questions Definite Integration1 questions Limits Continuity and Differentiability2 questions Application of Derivatives1 questions Matrices and Determinants2 questions Statistics1 questions Vector Algebra1 questions Permutations and Combinations1 questions Sequences and Series1 questions Quadratic Equation and Inequalities1 questions Probability1 questions Binomial Theorem1 questions

Q18.For a suitably chosen real constant a, let a function, $f : R - {- a} \to R$ be defined by $f (x) = \frac{a - x}{a + x}$ . Further suppose that for any real number $x e - a$ and $f (x) e - a$ , (fof)(x) = x. Then $f (- \frac{1}{2})$ …
Mathematics · Functions · MCQ
Q19.Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (–1, –4) in this line is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q20.The area (in sq. units) of the region enclosed by the curves y = x2 – 1 and y = 1 – x2 is equal to :
Mathematics · Area Under the Curves · MCQ
Q21.Let z = x + iy be a non-zero complex number such that $z^{2} = i ∣ z ∣^{2}$ , where i = $- 1$ , then z lies on the :
Mathematics · Complex Numbers · MCQ
Q22.The integral $1 \int 2 e^{x} . x^{x} (2 + lo g_{e} x) d x$ equals :
Mathematics · Definite Integration · MCQ
Q23.For all twice differentiable functions f : R $\to$ R, with f(0) = f(1) = f'(0) = 0
Mathematics · Limits Continuity and Differentiability · MCQ
Q24.Let f : R $\to$ R be a function defined by f(x) = max {x, x2}. Let S denote the set of all points in R, where f is not differentiable. Then :
Mathematics · Limits Continuity and Differentiability · MCQ
Q25.The set of all real values of $λ$ for which the function $f (x) = (1 - cos^{2} x) (λ + sin x), x \in (- \frac{π}{2}, \frac{π}{2})$ has exactly one maxima and exactly one…
Mathematics · Application of Derivatives · MCQ
Q26.The sum of distinct values of $λ$ for which the system of equations $(λ - 1) x + (3 λ + 1) y + 2 λ z = 0 (λ - 1) x + (4 λ - 2) y + (λ + 3) z = 02 x + (3 λ + 1) y + 3 (λ - 1) z = 0$ …
Mathematics · Matrices and Determinants · Numerical
Q27.Consider the data on x taking the values 0, 2, 4, 8,....., 2n with frequencies nC0 , nC1 , nC2 ,...., nCn respectively. If the mean of this data is $\frac{728}{2 ^{n}}$ , then n is equal to .
Mathematics · Statistics · Numerical
Q28.If $x$ and $y$ be two non-zero vectors such that $x + y = x$ and $2 x + λ y$ is…
Mathematics · Vector Algebra · Numerical
Q29.Suppose that a function f : R $\to$ R satisfies f(x + y) = f(x)f(y) for all x, y $\in$ R and f(1) = 3. If $i = 1 \sum n f (i) = 363$ then n is equal to .
Mathematics · Functions · Numerical
Q30.The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is .
Mathematics · Permutations and Combinations · Numerical
Q31.The common difference of the A.P. b1, b2, … , bm is 2 more than the common difference of A.P. a1, a2, …, an. If a40 = –159, a100 = –399 and b100 = a70, then b1 is equal to :
Mathematics · Sequences and Series · MCQ
Q32.If $α$ and $β$ are the roots of the equation 2x(2x + 1) = 1, then $β$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q33.The probabilities of three events A, B and C are given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5. If P(A $\cup$ B) = 0.8, P(A $\cap$ C) = 0.3, P(A $\cap$ B $\cap$ C) = 0.2, P(B $\cap$ C) = $β$ and P(A $\cup$ B $\cup$ C) = $α$ ,…
Mathematics · Probability · MCQ
Q34.If the constant term in the binomial expansion of $(x - \frac{k}{x ^{2}})^{10}$ is 405, then |k| equals :
Mathematics · Binomial Theorem · MCQ
Q35.Let $θ = \frac{π}{5}$ and $A = [cos θ - sin θ sin θ cos θ]$ . If B = A + A4 , then det (B) :
Mathematics · Matrices and Determinants · MCQ