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Mathematics · 2023 · 10 Apr · Shift 1

23 questions from this JEE Main paper

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2023 · 10 Apr · Shift 1
Mathematics

Mathematics · 2023 · 10 Apr · Shift 1

23 questions from this JEE Main paper

Indefinite Integrals1 questions 3D Geometry1 questions Ellipse1 questions Vector Algebra2 questions Functions1 questions Binomial Theorem2 questions Probability1 questions Application of Derivatives1 questions Trigonometric Ratio and Identites1 questions Matrices and Determinants1 questions Circle1 questions Differential Equations1 questions Sequences and Series1 questions Complex Numbers1 questions Limits Continuity and Differentiability1 questions Area Under the Curves1 questions Sets and Relations1 questions Statistics1 questions Permutations and Combinations2 questions Logarithm1 questions

Q24.If $I (x) = \int e^{s i n^{2} x} (cos x sin 2 x - sin x) d x$ and $I (0) = 1$ , then $I (\frac{π}{3})$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q25.The shortest distance between the lines $\frac{x + 2}{1} = \frac{y}{- 2} = \frac{z - 5}{2}$ and $\frac{x - 4}{1} = \frac{y - 1}{2} = \frac{z + 3}{0}$ is :
Mathematics · 3D Geometry · MCQ
Q26.Let the ellipse $E : x^{2} + 9 y^{2} = 9$ intersect the positive x and y-axes at the points A and B respectively. Let the major axis of E be a diameter of the circle C. Let the line passing through A and B meet the circle C at the point P. If…
Mathematics · Ellipse · MCQ
Q27.Let O be the origin and the position vector of the point P be $- i - 2 j + 3 k$ . If the position vectors of the points A, B and C are $- 2 i + j - 3 k, 2 i + 4 j - 2 k$ …
Mathematics · Vector Algebra · MCQ
Q28.If $f (x) = \frac{( t a n 1 ^{\circ} ) x + l o g _{e} ( 123 )}{x l o g _{e} ( 1234 ) - ( t a n 1 ^{\circ} )}, x > 0$ , then the least value of $f (f (x)) + f (f (\frac{4}{x}))$ is :
Mathematics · Functions · MCQ
Q29.If the coefficient of $x^{7}$ in $(a x - \frac{1}{b x ^{2}})^{13}$ and the coefficient of $x^{- 5}$ in $(a x + \frac{1}{b x ^{2}})^{13}$ are equal, then $a^{4} b^{4}$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q30.An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If $O P = u, O R = v$ , and $O Q = α u + β v$ …
Mathematics · Vector Algebra · MCQ
Q31.Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that $2^{N} < N!$ is $\frac{m}{n}$ , where m and n are coprime, then $4 m - 3 n$ is equal to :
Mathematics · Probability · MCQ
Q32.A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the volume of the box is maximum, then its surface area (in cm $^{2}$ ) is equal to :
Mathematics · Application of Derivatives · MCQ
Q33. $96 cos \frac{π}{33} cos \frac{2 π}{33} cos \frac{4 π}{33} cos \frac{8 π}{33} cos \frac{16 π}{33}$ is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q34.For the system of linear equations $2 x - y + 3 z = 53 x + 2 y - z = 74 x + 5 y + α z = β$ , which of the following is NOT correct?
Mathematics · Matrices and Determinants · MCQ
Q35.A line segment AB of length $λ$ moves such that the points A and B remain on the periphery of a circle of radius $λ$ . Then the locus of the point, that divides the line segment AB in the ratio 2 : 3, is a circle of radius :
Mathematics · Circle · MCQ
Q36.Let $f$ be a differentiable function such that $x^{2} f (x) - x = 4 0 \int x t f (t) d t$ , $f (1) = \frac{2}{3}$ . Then $18 f (3)$ is equal to :
Mathematics · Differential Equations · MCQ
Q37.Let the first term $α$ and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to
Mathematics · Sequences and Series · MCQ
Q38.Let the complex number $z = x + i y$ be such that $\frac{2 z - 3 i}{2 z + i}$ is purely imaginary. If $x + y^{2} = 0$ , then $y^{4} + y^{2} - y$ is equal to :
Mathematics · Complex Numbers · MCQ
Q39.Let $f : (- 2, 2) \to R$ be defined by $f (x) = {x [x], (x - 1) [x], - 2 < x < 0 0 \leq x \leq 2$ where $[x]$ denotes the greatest integer function. If m and n…
Mathematics · Limits Continuity and Differentiability · Numerical
Q40.Let $y = p (x)$ be the parabola passing through the points $(- 1, 0), (0, 1)$ and $(1, 0)$ . If the area of the region ${(x, y) : (x + 1)^{2} + (y - 1)^{2} \leq 1, y \leq p (x)}$ is A, then $12 (π - 4 A)$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q41.The number of elements in the set ${n \in Z : ∣ n^{2} - 10 n + 19∣ < 6}$ is .
Mathematics · Sets and Relations · Numerical
Q42.If the mean of the frequency distribution is 28, then its variance is . Includes table
Mathematics · Statistics · Numerical
Q43.The number of permutations, of the digits 1, 2, 3, ..., 7 without repetition, which neither contain the string 153 nor the string 2467, is .
Mathematics · Permutations and Combinations · Numerical
Q44.The coefficient of $x^{7}$ in $(1 - x + 2 x^{3})^{10}$ is .
Mathematics · Binomial Theorem · Numerical
Q45.Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total number of persons, who participated in the tournament, is …
Mathematics · Permutations and Combinations · Numerical
Q46.Let a, b, c be three distinct positive real numbers such that $(2 a)^{l o g_{e} a} = (b c)^{l o g_{e} b}$ and $b^{l o g_{e} 2} = a^{l o g_{e} c}$ . Then, 6a + 5bc is equal to .
Mathematics · Logarithm · Numerical