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Mathematics · 2022 · 24 Jun · Shift 2

24 questions from this JEE Main paper

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2022 · 24 Jun · Shift 2
Mathematics

Mathematics · 2022 · 24 Jun · Shift 2

24 questions from this JEE Main paper

Inverse Trigonometric Functions1 questions Quadratic Equation and Inequalities2 questions Matrices and Determinants2 questions Sequences and Series1 questions Limits Continuity and Differentiability1 questions Definite Integration1 questions Parabola2 questions Ellipse1 questions Straight Lines and Pair of Straight Lines1 questions Probability1 questions 3D Geometry1 questions Vector Algebra1 questions Differentiation1 questions Application of Derivatives1 questions Complex Numbers1 questions Permutations and Combinations1 questions Sets and Relations1 questions Binomial Theorem1 questions Area Under the Curves1 questions Circle1 questions Hyperbola1 questions

Q22.Let $x * y = x^{2} + y^{3}$ and $(x * 1) * 1 = x * (1 * 1)$ . Then a value of $2 sin^{- 1} (\frac{x ^{4} + x ^{2} - 2}{x ^{4} + x ^{2} + 2})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q23.The sum of all the real roots of the equation $(e^{2 x} - 4) (6 e^{2 x} - 5 e^{x} + 1) = 0$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q24.Let the system of linear equations x + y + $α$ z = 2 3x + y + z = 4 x + 2z = 1 have a unique solution (x $^{*}$ , y $^{*}$ , z $^{*}$ ). If ( $α$ , x $^{*}$ ), (y $^{*}$ , $α$ ) and (x $^{*}$ , $-$ y $^{*}$ ) are collinear points, then the…
Mathematics · Matrices and Determinants · MCQ
Q25.Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is
Mathematics · Sequences and Series · MCQ
Q26.Let $f (x) = ⎩ ⎨ ⎧ \frac{sin ( x - [ x ])}{x - [ x ]} max {2 x, 3 [∣ x ∣]} 1, x \in (- 2, - 1), ∣ x ∣ < 1, otherwise$ where $[t]$ denotes greatest integer $m$ . If $m$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.The value of the integral $- π /2 \int π /2 \frac{d x}{( 1 + e ^{x} ) ( s i n ^{6} x + c o s ^{6} x )}$ is equal to
Mathematics · Definite Integration · MCQ
Q28.A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with :
Mathematics · Parabola · MCQ
Q29.Let the maximum area of the triangle that can be inscribed in the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{4} = 1, a > 2$ , having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel…
Mathematics · Ellipse · MCQ
Q30.Let the area of the triangle with vertices A(1, $α$ ), B( $α$ , 0) and C(0, $α$ ) be 4 sq. units. If the points ( $α$ , $- α$ ), ( $- α$ , $α$ ) and ( $α$ 2, $β$ ) are collinear, then $β$ is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.The number of distinct real roots of the equation x7 $-$ 7x $-$ 2 = 0 is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q32.A random variable X has the following probability distribution : The value of P(1 < X < 4 | X $\leq$ 2) is equal to : Includes table
Mathematics · Probability · MCQ
Q33.If the shortest distance between the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{λ}$ and $\frac{x - 2}{1} = \frac{y - 4}{4} = \frac{z - 5}{5}$ is $\frac{1}{3}$ , then the sum of all possible value…
Mathematics · 3D Geometry · MCQ
Q34.Let $a$ and $b$ be two unit vectors such that $∣ (a + b) + 2 (a \times b) ∣ = 2$ . If $θ \in$ (0, $π$ ) is the angle between $a$ and $b$ , then among the statements :…
Mathematics · Vector Algebra · MCQ
Q35.If $y = tan^{- 1} (sec x^{3} - tan x^{3}), \frac{π}{2} < x^{3} < \frac{3 π}{2}$ , then
Mathematics · Differentiation · MCQ
Q36.Let $λ^{*}$ be the largest value of $λ$ for which the function $f_{λ} (x) = 4 λ x^{3} - 36 λ x^{2} + 36 x + 48$ is increasing for all x $\in$ R. Then $f_{λ^{*}} (1) + f_{λ^{*}} (- 1)$ is…
Mathematics · Application of Derivatives · MCQ
Q37.Let S = {z $\in$ C : |z $-$ 3| $\leq$ 1 and z(4 + 3i) + $\overline{z}$ (4 $-$ 3i) $\leq$ 24}. If $α$ + i $β$ is the point in S which is closest to 4i, then 25( $α$ + $β$ ) is equal to .
Mathematics · Complex Numbers · Numerical
Q38.Let $S = {(- 1 0 a b); a, b \in {1, 2, 3, ....100}}$ and let $T_{n} = {A \in S : A^{n (n + 1)} = I}$ . Then the number of elements in $n = 1 ⋂ 100 T_{n}$ …
Mathematics · Matrices and Determinants · Numerical
Q39.The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is .
Mathematics · Permutations and Combinations · Numerical
Q40.The sum of all the elements of the set ${α \in {1, 2, ....., 100} : H C F (α, 24) = 1}$ is .
Mathematics · Sets and Relations · Numerical
Q41.The remainder on dividing 1 + 3 + 32 + 33 + ..... + 32021 by 50 is .
Mathematics · Binomial Theorem · Numerical
Q42.The area (in sq. units) of the region enclosed between the parabola y2 = 2x and the line x + y = 4 is .
Mathematics · Area Under the Curves · Numerical
Q43.Let a circle C : (x $-$ h)2 + (y $-$ k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to …
Mathematics · Circle · Numerical
Q44.Let the hyperbola $H : \frac{x ^{2}}{a ^{2}} - y^{2} = 1$ and the ellipse $E : 3 x^{2} + 4 y^{2} = 12$ be such that the length of latus rectum of H is equal to the length of latus rectum of E. If $e_{H}$ and $e_{E}$ are the eccentricities of H…
Mathematics · Hyperbola · Numerical
Q45.Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with respect to the line x + 2y = 6. Then the directrix of P2 is x + 2y = .
Mathematics · Parabola · Numerical