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Mathematics · 2022 · 26 Jun · Shift 1

21 questions from this JEE Main paper

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2022 · 26 Jun · Shift 1
Mathematics

Mathematics · 2022 · 26 Jun · Shift 1

21 questions from this JEE Main paper

Functions1 questions Complex Numbers1 questions Matrices and Determinants1 questions Binomial Theorem1 questions Limits Continuity and Differentiability2 questions Application of Derivatives2 questions Area Under the Curves1 questions Straight Lines and Pair of Straight Lines1 questions 3D Geometry1 questions Statistics1 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations1 questions Definite Integration2 questions Differential Equations2 questions Trigonometric Ratio and Identites1 questions Sets and Relations2 questions

Q21.Let $f (x) = \frac{x - 1}{x + 1}, x \in R - {0, - 1, 1}$ . If $f^{n + 1} (x) = f (f^{n} (x))$ for all n $\in$ N, then $f^{6} (6) + f^{7} (7)$ is equal to :
Mathematics · Functions · MCQ
Q22.Let $A = {z \in C : \frac{z + 1}{z - 1} < 1}$ and $B = {z \in C : ar g (\frac{z - 1}{z + 1}) = \frac{2 π}{3}}$ . Then A $\cap$ B is :
Mathematics · Complex Numbers · MCQ
Q23.The ordered pair (a, b), for which the system of linear equations 3x $-$ 2y + z = b 5x $-$ 8y + 9z = 3 2x + y + az = $-$ 1 has no solution, is :
Mathematics · Matrices and Determinants · MCQ
Q24.The remainder when (2021)2023 is divided by 7 is :
Mathematics · Binomial Theorem · MCQ
Q25. $x \to \frac{1}{2} lim \frac{s i n ( c o s ^{- 1} x ) - x}{1 - t a n ( c o s ^{- 1} x )}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.Let f, g : R $\to$ R be two real valued functions defined as $f (x) = {- ∣ x + 3∣ e^{x},, x < 0 x \geq 0$ and $g (x) = {x^{2} + k_{1} x 4 x + k_{2},, x < 0 x \geq 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.The sum of the absolute minimum and the absolute maximum values of the function f(x) = |3x $-$ x2 + 2| $-$ x in the interval [ $-$ 1, 2] is :
Mathematics · Application of Derivatives · MCQ
Q28.The area bounded by the curve y = |x2 $-$ 9| and the line y = 3 is :
Mathematics · Area Under the Curves · MCQ
Q29.Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle. Then the area of $Δ$ PQR is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q30.If the two lines $l_{1} : \frac{x - 2}{3} = \frac{y + 1}{- 2}, z = 2$ and $l_{2} : \frac{x - 1}{1} = \frac{2 y + 3}{α} = \frac{z + 5}{2}$ are perpendicular, then an angle between the lines l2 and $l_{3} : \frac{1 - x}{3} = \frac{2 y - 1}{- 4} = \frac{z}{4}$ …
Mathematics · 3D Geometry · MCQ
Q31.The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to :
Mathematics · Statistics · MCQ
Q32.Let $f (x) = 2 cos^{- 1} x + 4 cot^{- 1} x - 3 x^{2} - 2 x + 10$ , $x \in [- 1, 1]$ . If [a, b] is the range of the function f, then 4a $-$ b is equal to :
Mathematics · Application of Derivatives · MCQ
Q33.The sum of the cubes of all the roots of the equation $x^{4} - 3 x^{3} - 2 x^{2} + 3 x + 1 = 0$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q34.There are ten boys B1, B2, ......., B10 and five girls G1, G2, ........, G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group,…
Mathematics · Permutations and Combinations · Numerical
Q35.Let f(x) = max {|x + 1|, |x + 2|, ....., |x + 5|}. Then $- 6 \int 0 f (x) d x$ is equal to .
Mathematics · Definite Integration · Numerical
Q36.Let the solution curve y = y(x) of the differential equation $(4 + x^{2}) d y - 2 x (x^{2} + 3 y + 4) d x = 0$ pass through the origin. Then y(2) is equal to .
Mathematics · Differential Equations · Numerical
Q37.If $sin^{2} (1 0^{\circ}) sin (2 0^{\circ}) sin (4 0^{\circ}) sin (5 0^{\circ}) sin (7 0^{\circ}) = α - \frac{1}{16} sin (1 0^{\circ})$ , then $16 + α^{- 1}$ is equal to .
Mathematics · Trigonometric Ratio and Identites · Numerical
Q38.Let A = {n $\in$ N : H.C.F. (n, 45) = 1} and Let B = {2k : k $\in$ {1, 2, ......., 100}}. Then the sum of all the elements of A $\cap$ B is .
Mathematics · Sets and Relations · Numerical
Q39.The value of the integral $\frac{48}{π ^{4}} 0 \int π (\frac{3 π x ^{2}}{2} - x^{3}) \frac{s i n x}{1 + c o s ^{2} x} d x$ is equal to .
Mathematics · Definite Integration · Numerical
Q40.Let $A = i = 1 \sum 10 j = 1 \sum 10 min {i, j}$ and $B = i = 1 \sum 10 j = 1 \sum 10 max {i, j}$ . Then A + B is equal to .
Mathematics · Sets and Relations · Numerical
Q41.Let $S = (0, 2 π) - {\frac{π}{2}, \frac{3 π}{4}, \frac{3 π}{2}, \frac{7 π}{4}}$ . Let $y = y (x)$ , x $\in$ S, be the solution curve of the differential equation $\frac{d y}{d x} = \frac{1}{1 + s i n 2 x}, y (\frac{π}{4}) = \frac{1}{2}$ …
Mathematics · Differential Equations · Numerical