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Mathematics · 2021 · 26 Aug · Shift 2

23 questions from this JEE Main paper

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2021 · 26 Aug · Shift 2
Mathematics

Mathematics · 2021 · 26 Aug · Shift 2

23 questions from this JEE Main paper

Limits Continuity and Differentiability2 questions Matrices and Determinants1 questions Application of Derivatives1 questions Definite Integration2 questions Differential Equations1 questions Inverse Trigonometric Functions2 questions Probability2 questions Hyperbola1 questions Trigonometric Ratio and Identites1 questions Complex Numbers2 questions Vector Algebra2 questions Circle1 questions Sequences and Series2 questions Area Under the Curves1 questions Quadratic Equation and Inequalities1 questions Statistics1 questions

Q23.Let [t] denote the greatest integer less than or equal to t. Let f(x) = x $-$ [x], g(x) = 1 $-$ x + [x], and h(x) = min{f(x), g(x)}, x $\in$ [ $-$ 2, 2]. Then h is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q24.Let $A = 101010010$ . Then A2025 $-$ A2020 is equal to :
Mathematics · Matrices and Determinants · MCQ
Q25.The local maximum value of the function $f (x) = (\frac{2}{x})^{x^{2}}$ , x > 0, is
Mathematics · Application of Derivatives · MCQ
Q26.If the value of the integral $0 \int 5 \frac{x + [ x ]}{e ^{x - [x]}} d x = α e^{- 1} + β$ , where $α$ , $β \in$ R, 5 $α$ + 6 $β$ = 0, and [x] denotes the greatest integer less than or equal to x;…
Mathematics · Definite Integration · MCQ
Q27.Let y(x) be the solution of the differential equation 2x2 dy + (ey $-$ 2x)dx = 0, x > 0. If y(e) = 1, then y(1) is equal to :
Mathematics · Differential Equations · MCQ
Q28.The domain of the function $cosec o l imi t s^{- 1} (\frac{1 + x}{x})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q29.A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probability P(x $\geq$ 5 | x > 2) is :
Mathematics · Probability · MCQ
Q30.If $r = 1 \sum 50 tan^{- 1} \frac{1}{2 r ^{2}} = p$ , then the value of tan p is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q31.Two fair dice are thrown. The numbers on them are taken as $λ$ and $μ$ , and a system of linear equations x + y + z = 5 x + 2y + 3z = $μ$ x + 3y + $λ$ z = 1 is constructed. If p is the probability that the system has a unique…
Mathematics · Probability · MCQ
Q32.The locus of the mid points of the chords of the hyperbola x2 $-$ y2 = 4, which touch the parabola y2 = 8x, is :
Mathematics · Hyperbola · MCQ
Q33.The value of $2 sin (\frac{π}{8}) sin (\frac{2 π}{8}) sin (\frac{3 π}{8}) sin (\frac{5 π}{8}) sin (\frac{6 π}{8}) sin (\frac{7 π}{8})$ …
Mathematics · Trigonometric Ratio and Identites · MCQ
Q34.If $(3 + i)^{100} = 2^{99} (p + i q)$ , then p and q are roots of the equation :
Mathematics · Complex Numbers · MCQ
Q35.A hall has a square floor of dimension 10 m $\times$ 10 m (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is $cos^{- 1} \frac{1}{5}$ , then the height of the hall (in meters) is : Includes diagram
Mathematics · Vector Algebra · MCQ
Q36.The value of $- \frac{π}{2} \int \frac{π}{2} (\frac{1 + s i n ^{2} x}{1 + π ^{s i n x}}) d x$ is
Mathematics · Definite Integration · MCQ
Q37.A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y $-$ 5 = 0 at two points P and Q such that PQ is a diameter of C1. Then the diameter of C is :
Mathematics · Circle · MCQ
Q38. $x \to 2 lim (n = 1 \sum 9 \frac{x}{n ( n + 1 ) x ^{2} + 2 ( 2 n + 1 ) x + 4})$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q39.The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is .
Mathematics · Sequences and Series · Numerical
Q40.Let a and b respectively be the points of local maximum and local minimum of the function f(x) = 2x3 $-$ 3x2 $-$ 12x. If A is the total area of the region bounded by y = f(x), the x-axis and the lines x = a and x = b, then 4A is equal to …
Mathematics · Area Under the Curves · Numerical
Q41.If the projection of the vector $i + 2 j + k$ on the sum of the two vectors $2 i + 4 j - 5 k$ and $- λ i + 2 j + 3 k$ is 1, then $λ$ is equal to …
Mathematics · Vector Algebra · Numerical
Q42.Let a1, a2, ......., a10 be an AP with common difference $-$ 3 and b1, b2, ........., b10 be a GP with common ratio 2. Let ck = ak + bk, k = 1, 2, ......, 10. If c2 = 12 and c3 = 13, then $k = 1 \sum 10 c_{k}$ is equal to …
Mathematics · Sequences and Series · Numerical
Q43.Let $λ e$ 0 be in R. If $α$ and $β$ are the roots of the equation x2 $-$ x + 2 $λ$ = 0, and $α$ and $γ$ are the roots of equation 3x2 $-$ 10x + 27 $λ$ = 0, then $\frac{β γ}{λ}$ is equal…
Mathematics · Quadratic Equation and Inequalities · Numerical
Q44.Let the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively. Then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x $-$ y is .
Mathematics · Statistics · Numerical
Q45.The least positive integer n such that $\frac{( 2 i ) ^{n}}{( 1 - i ) ^{n - 2}}, i = - 1$ is a positive integer, is .
Mathematics · Complex Numbers · Numerical