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Mathematics · 2021 · 24 Feb · Shift 2

19 questions from this JEE Main paper

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2021 · 24 Feb · Shift 2
Mathematics

Mathematics · 2021 · 24 Feb · Shift 2

19 questions from this JEE Main paper

Matrices and Determinants2 questions Definite Integration3 questions 3D Geometry2 questions Application of Derivatives1 questions Parabola1 questions Probability1 questions Inverse Trigonometric Functions1 questions Area Under the Curves1 questions Circle1 questions Statistics1 questions Functions1 questions Complex Numbers1 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations1 questions Sequences and Series1 questions

Q23.Let A and B be 3 $\times$ 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2 $-$ B2A2) X = O, where X is a 3 $\times$ 1 column matrix of unknown variables and O is a 3 $\times$ …
Mathematics · Matrices and Determinants · MCQ
Q24.The value of the integral, $1 \int 3 [x^{2} - 2 x - 2] d x$ , where [x] denotes the greatest integer less than or equal to x, is :
Mathematics · Definite Integration · MCQ
Q25.Let a, b $\in$ R. If the mirror image of the point P(a, 6, 9) with respect to the line $\frac{x - 3}{7} = \frac{y - 2}{5} = \frac{z - 1}{- 9}$ is (20, b, $-$ a $-$ 9), then | a + b |, is equal to :
Mathematics · 3D Geometry · MCQ
Q26.For the system of linear equations: $x - 2 y = 1, x - y + k z = - 2, k y + 4 z = 6, k \in R$ , consider the following statements : (A) The system has unique solution if $k e 2, k e - 2$ . (B) The system has unique solution if k = $-$ 2 (C) The…
Mathematics · Matrices and Determinants · MCQ
Q27.Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2 $-$ x) for all x $\in$ (0, 2), f(0) = 1 and f(2) = e2. Then the value of $0 \int 2 f (x) d x$ is :
Mathematics · Definite Integration · MCQ
Q28.Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) $e$ 0 for all x $\in$ R. If $f (x) f^{'} (x) f^{'} (x) f^{''} (x)$ = 0, for all x $\in$ …
Mathematics · Definite Integration · MCQ
Q29.Let $f : R \to R$ be defined as $f (x) = ⎩ ⎨ ⎧ - 55 x, 2 x^{3} - 3 x^{2} - 120 x, 2 x^{3} - 3 x^{2} - 36 x - 336, i f x < - 5 i f - 5 \leq x \leq 4 i f x > 4,$ Let…
Mathematics · Application of Derivatives · MCQ
Q30.If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x $-$ 1, then the co-ordinates of P are :
Mathematics · Parabola · MCQ
Q31.The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :
Mathematics · Probability · MCQ
Q32.A possible value of $tan (\frac{1}{4} sin^{- 1} \frac{63}{8})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q33.The area of the region : $R = {(x, y) : 5 x^{2} \leq y \leq 2 x^{2} + 9}$ is :
Mathematics · Area Under the Curves · MCQ
Q34.Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point ( $-$ 5, 0). If the locus of the point P is a circle of radius r, then 4r2 is equal to
Mathematics · Circle · Numerical
Q35.If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is .
Mathematics · Statistics · Numerical
Q36.Let $λ$ be an integer. If the shortest distance between the lines x $- λ$ = 2y $-$ 1 = $-$ 2z and x = y + 2 $λ$ = z $- λ$ is $\frac{7}{2 2}$ , then the value of | $λ$ | is .
Mathematics · 3D Geometry · Numerical
Q37.If a + $α$ = 1, b + $β$ = 2 and $a f (x) + α f (\frac{1}{x}) = b x + \frac{β}{x}, x e 0$ , then the value of the expression $\frac{f ( x ) + f ( \frac{1}{x} )}{x + \frac{1}{x}}$ is …
Mathematics · Functions · Numerical
Q38.Let $i = - 1$ . If $\frac{( - 1 + i 3 ) ^{21}}{( 1 - i ) ^{24}} + \frac{( 1 + i 3 ) ^{21}}{( 1 + i ) ^{24}} = k$ , and $n = [∣ k ∣]$ be the greatest integral part of | k |. Then…
Mathematics · Complex Numbers · Numerical
Q39.The number of the real roots of the equation $(x + 1)^{2} + ∣ x - 5∣ = \frac{27}{4}$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q40.The students S1, S2, ....., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is …
Mathematics · Permutations and Combinations · Numerical
Q41.The sum of first four terms of a geometric progression (G. P.) is $\frac{65}{12}$ and the sum of their respective reciprocals is $\frac{65}{18}$ . If the product of first three terms of the G.P. is 1, and the third term is $α$ ,…
Mathematics · Sequences and Series · Numerical