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Mathematics · 2022 · 29 Jun · Shift 2

20 questions from this JEE Main paper

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2022 · 29 Jun · Shift 2
Mathematics

Mathematics · 2022 · 29 Jun · Shift 2

20 questions from this JEE Main paper

Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Limits Continuity and Differentiability1 questions Definite Integration2 questions Differential Equations2 questions Circle1 questions Straight Lines and Pair of Straight Lines1 questions Vector Algebra2 questions Probability1 questions Statistics1 questions Sequences and Series1 questions Area Under the Curves1 questions Differentiation1 questions Binomial Theorem1 questions Permutations and Combinations1 questions Matrices and Determinants1 questions Functions1 questions

Q24.Let $α$ be a root of the equation 1 + x2 + x4 = 0. Then, the value of $α$ 1011 + $α$ 2022 $- α$ 3033 is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q25.Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $-$ 1) $-$ arg(z + 1) = $\frac{π}{4}$ intersect :
Mathematics · Complex Numbers · MCQ
Q26.The value of $x \to 1 lim \frac{( x ^{2} - 1 ) s i n ^{2} ( π x )}{x ^{4} - 2 x ^{3} + 2 x - 1}$ is equal to:
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Let f be a real valued continuous function on [0, 1] and $f (x) = x + 0 \int 1 (x - t) f (t) d t$ . Then, which of the following points (x, y) lies on the curve y = f(x) ?
Mathematics · Definite Integration · MCQ
Q28.If $0 \int 2 (2 x - 2 x - x^{2}) d x = 0 \int 1 (1 - 1 - y^{2} - \frac{y ^{2}}{2}) d y + 1 \int 2 (2 - \frac{y ^{2}}{2}) d y + I$ , then I equals
Mathematics · Definite Integration · MCQ
Q29.If y = y(x) is the solution of the differential equation $(1 + e^{2 x}) \frac{d y}{d x} + 2 (1 + y^{2}) e^{x} = 0$ and y (0) = 0, then $6 (y^{'} (0) + (y (lo g_{e} 3))^{2})$ …
Mathematics · Differential Equations · MCQ
Q30.Let a triangle ABC be inscribed in the circle $x^{2} - 2 (x + y) + y^{2} = 0$ such that $∠ B A C = \frac{π}{2}$ . If the length of side AB is $2$ , then the area of the $Δ$ ABC is equal to :
Mathematics · Circle · MCQ
Q31.The distance of the origin from the centroid of the triangle whose two sides have the equations $x - 2 y + 1 = 0$ and $2 x - y - 1 = 0$ and whose orthocenter is $(\frac{7}{3}, \frac{7}{3})$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q32.Let A, B, C be three points whose position vectors respectively are $a = i + 4 j + 3 k b = 2 i + α j + 4 k, α \in R c = 3 i - 2 j + 5 k$ …
Mathematics · Vector Algebra · MCQ
Q33.The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :
Mathematics · Probability · MCQ
Q34.The number of values of a $\in$ N such that the variance of 3, 7, 12, a, 43 $-$ a is a natural number is :
Mathematics · Statistics · MCQ
Q35.Let $a = i - 2 j + 3 k$ , $b = i + j + k$ and $c$ be a vector such that $a + (b \times c) = 0$ …
Mathematics · Vector Algebra · Numerical
Q36.Let y = y(x), x > 1, be the solution of the differential equation $(x - 1) \frac{d y}{d x} + 2 x y = \frac{1}{x - 1}$ , with $y (2) = \frac{1 + e ^{4}}{2 e ^{4}}$ . If $y (3) = \frac{e ^{α} + 1}{β e ^{α}}$ , then the…
Mathematics · Differential Equations · Numerical
Q37.Let 3, 6, 9, 12, ....... upto 78 terms and 5, 9, 13, 17, ...... upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to .
Mathematics · Sequences and Series · Numerical
Q38.For real numbers a, b (a > b > 0), let Area ${(x, y) : x^{2} + y^{2} \leq a^{2} an d \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} \geq 1} = 30 π$ and Area ${(x, y) : x^{2} + y^{2} \leq b^{2} an d \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} \leq 1} = 18 π$ …
Mathematics · Area Under the Curves · Numerical
Q39.Let f and g be twice differentiable even functions on ( $-$ 2, 2) such that $f (\frac{1}{4}) = 0$ , $f (\frac{1}{2}) = 0$ , $f (1) = 1$ and $g (\frac{3}{4}) = 0$ , $g (1) = 2$ . Then, the minimum…
Mathematics · Differentiation · Numerical
Q40.Let the coefficients of x $-$ 1 and x $-$ 3 in the expansion of $(2 x^{\frac{1}{5}} - \frac{1}{x ^{\frac{1}{5}}})^{15}, x > 0$ , be m and n respectively. If r is a positive integer such that $m n^{2} =^{15} C_{r} . 2^{r}$ …
Mathematics · Binomial Theorem · Numerical
Q41.The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to .
Mathematics · Permutations and Combinations · Numerical
Q42.Let $M = [0 α - α 0]$ , where $α$ is a non-zero real number an $N = k = 1 \sum 49 M^{2 k}$ . If $(I - M^{2}) N = - 2 I$ , then the positive…
Mathematics · Matrices and Determinants · Numerical
Q43.Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If $f (g (x)) = 8 x^{2} - 2 x$ and $g (f (x)) = 4 x^{2} + 6 x + 1$ , then the value of $f (2) + g (2)$ is .
Mathematics · Functions · Numerical