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Mathematics · 2022 · 30 Jun · Shift 1

19 questions from this JEE Main paper

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2022 · 30 Jun · Shift 1
Mathematics

Mathematics · 2022 · 30 Jun · Shift 1

19 questions from this JEE Main paper

Quadratic Equation and Inequalities2 questions Complex Numbers1 questions Matrices and Determinants1 questions Binomial Theorem1 questions Application of Derivatives3 questions Inverse Trigonometric Functions2 questions Straight Lines and Pair of Straight Lines1 questions Ellipse1 questions Permutations and Combinations1 questions Limits Continuity and Differentiability1 questions Area Under the Curves1 questions Definite Integration1 questions Parabola1 questions 3D Geometry1 questions Probability1 questions

Q23.Let $S_{1} = {x \in R - {1, 2} : \frac{( x + 2 ) ( x ^{2} + 3 x + 5 )}{- 2 + 3 x - x ^{2}} \geq 0}$ and $S_{2} = {x \in R : 3^{2 x} - 3^{x + 1} - 3^{x + 2} + 27 \leq 0}$ . Then, $S_{1} \cup S_{2}$ is…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q24.The real part of the complex number $\frac{( 1 + 2 i ) ^{8} . ( 1 - 2 i ) ^{2}}{( 3 + 2 i ) . ( 4 - 6 i )}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q25.Let S be the set of all integral values of $α$ for which the sum of squares of two real roots of the quadratic equation $3 x^{2} + (α - 6) x + (α + 3) = 0$ is minimum. Then S :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q26.Let $A = [1 α - 2 2 α - 1]$ and $B = 2 - 1 4 α 2 - 5, α \in C$ …
Mathematics · Matrices and Determinants · MCQ
Q27.For two positive real numbers a and b such that $\frac{1}{a ^{2}} + \frac{1}{b ^{3}} = 4$ , then minimum value of the constant term in the expansion of $(a x^{\frac{1}{8}} + b x^{- \frac{1}{12}})^{10}$ is :
Mathematics · Binomial Theorem · MCQ
Q28.If xy4 attains maximum value at the point (x, y) on the line passing through the points (50 + $α$ , 0) and (0, 50 + $α$ ), $α$ > 0, then (x, y) also lies on the line :
Mathematics · Application of Derivatives · MCQ
Q29.Let $f (x) = 4 x^{3} - 11 x^{2} + 8 x - 5, x \in R$ . Then f :
Mathematics · Application of Derivatives · MCQ
Q30.Let m and M respectively be the minimum and the maximum values of $f (x) = sin^{- 1} 2 x + sin 2 x + cos^{- 1} 2 x + cos 2 x, x \in [0, \frac{π}{8}]$ . Then m + M is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q31.Let $α$ 1, $α$ 2 ( $α$ 1 2) be the values of $α$ fo the points ( $α$ , $-$ 3), (2, 0) and (1, $α$ ) to be collinear. Then the equation of the line, passing through ( $α$ 1, $α$ 2) and making an angle of $\frac{π}{3}$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q32.Let the eccentricity of the ellipse $x^{2} + a^{2} y^{2} = 25 a^{2}$ be b times the eccentricity of the hyperbola $x^{2} - a^{2} y^{2} = 5$ , where a is the minimum distance between the curves y = ex and y = logex. Then $a^{2} + \frac{1}{b ^{2}}$ …
Mathematics · Ellipse · MCQ
Q33.Let $α = tan (\frac{5 π}{16} sin (2 cos^{- 1} (\frac{1}{5})))$ and $β = cos (sin^{- 1} (\frac{4}{5}) + sec^{- 1} (\frac{5}{3}))$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q34.The number of 6-digit numbers made by using the digits 1, 2, 3, 4, 5, 6, 7, without repetition and which are multiple of 15 is .
Mathematics · Permutations and Combinations · Numerical
Q35.Suppose $x \to 0 lim \frac{F ( x )}{x ^{3}}$ exists and is equal to L, where $F (x) = a + sin \frac{x}{2} - b cos x 0 - b cos x 0 a + sin \frac{x}{2} 0 a + sin \frac{x}{2} - b cos x$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q36.If for some $α$ > 0, the area of the region ${(x, y) : ∣ x + α ∣ \leq y \leq 2 - ∣ x ∣}$ is equal to $\frac{3}{2}$ , then the area of the region ${(x, y) : 0 \leq y \leq x + 2 α, ∣ x ∣ \leq 1}$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q37.Let $f (t) = 0 \int t e^{x^{3}} (\frac{x ^{8}}{( x ^{6} + 2 x ^{3} + 2 ) ^{2}}) d x$ . If $f (1) + f^{'} (1) = α e - \frac{1}{6}$ , then the value of 150 $α$ is equal to .
Mathematics · Definite Integration · Numerical
Q38.A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some virus. Assume that the rate at which the virus spreads is directly proportional to the product of the number of…
Mathematics · Application of Derivatives · Numerical
Q39.Let PQ be a focal chord of length 6.25 units of the parabola y2 = 4x. If O is the vertex of the parabola, then 10 times the area (in sq. units) of $Δ$ POQ is equal to .
Mathematics · Parabola · Numerical
Q40.Consider a triangle ABC whose vertices are A(0, $α$ , $α$ ), B( $α$ , 0, $α$ ) and C( $α$ , $α$ , 0), $α$ > 0. Let D be a point moving on the line x + z $-$ 3 = 0 = y and G be the centroid of $Δ$ ABC. If…
Mathematics · 3D Geometry · Numerical
Q41.The probability distribution of X is : For the minimum possible value of d, sixty times the mean of X is equal to . Includes table
Mathematics · Probability · Numerical