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Mathematics · 2023 · 15 Apr · Shift 1

21 questions from this JEE Main paper

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2023 · 15 Apr · Shift 1
Mathematics

Mathematics · 2023 · 15 Apr · Shift 1

21 questions from this JEE Main paper

Differential Equations1 questions Definite Integration1 questions Permutations and Combinations2 questions Vector Algebra1 questions Inverse Trigonometric Functions1 questions Limits Continuity and Differentiability1 questions Statistics1 questions Binomial Theorem1 questions Probability1 questions Quadratic Equation and Inequalities1 questions Straight Lines and Pair of Straight Lines1 questions Sequences and Series1 questions 3D Geometry1 questions Complex Numbers1 questions Ellipse1 questions Area Under the Curves1 questions Indefinite Integrals1 questions Application of Derivatives1 questions Sets and Relations2 questions

Q24.Let $x = x (y)$ be the solution of the differential equation $2 (y + 2) lo g_{e} (y + 2) d x + (x + 4 - 2 lo g_{e} (y + 2)) d y = 0, y > - 1$ with $x (e^{4} - 2) = 1$ . Then $x (e^{9} - 2)$ is equal to :
Mathematics · Differential Equations · MCQ
Q25.If $0 \int 1 \frac{1}{( 5 + 2 x - 2 x ^{2} ) ( 1 + e ^{(2 - 4 x)} )} d x = \frac{1}{α} lo g_{e} (\frac{α + 1}{β}), α, β > 0$ , then $α^{4} - β^{4}$ is equal to :
Mathematics · Definite Integration · MCQ
Q26.The total number of three-digit numbers, divisible by 3, which can be formed using the digits $1, 3, 5, 8$ , if repetition of digits is allowed, is :
Mathematics · Permutations and Combinations · MCQ
Q27.Let $ABCD$ be a quadrilateral. If $E$ and $F$ are the mid points of the diagonals $AC$ and $BD$ respectively and $(A B - B C) + (A D - D C) = k F E$ …
Mathematics · Vector Algebra · MCQ
Q28.If the domain of the function $f (x) = lo g_{e} (4 x^{2} + 11 x + 6) + sin^{- 1} (4 x + 3) + cos^{- 1} (\frac{10 x + 6}{3})$ is $(α, β]$ , then $36∣ α + β ∣$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q29.Let $[x]$ denote the greatest integer function and $f (x) = max {1 + x + [x], 2 + x, x + 2 [x]}, 0 \leq x \leq 2$ . Let $m$ be the number of points in $[0, 2]$ , where $f$ is not continuous and $n$ be the number of points in $(0, 2)$ , where $f$ is not…
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is :
Mathematics · Statistics · MCQ
Q31.Let $(a + b x + c x^{2})^{10} = i = 0 \sum 20 p_{i} x^{i}, a, b, c \in N$ . If $p_{1} = 20$ and $p_{2} = 210$ , then $2 (a + b + c)$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q32.A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is :
Mathematics · Probability · MCQ
Q33.The number of real roots of the equation $x ∣ x ∣ - 5∣ x + 2∣ + 6 = 0$ , is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.If $(α, β)$ is the orthocenter of the triangle $ABC$ with vertices $A (3, - 7), B (- 1, 2)$ and $C (4, 5)$ , then $9 α - 6 β + 60$ is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.Let $A_{1}$ and $A_{2}$ be two arithmetic means and $G_{1}, G_{2}, G_{3}$ be three geometric means of two distinct positive numbers. Then $G_{1}^{4} + G_{2}^{4} + G_{3}^{4} + G_{1}^{2} G_{3}^{2}$ is equal to :
Mathematics · Sequences and Series · MCQ
Q36.Let $S$ be the set of all values of $λ$ , for which the shortest distance between the lines $\frac{x - λ}{0} = \frac{y - 3}{4} = \frac{z + 6}{1}$ and $\frac{x + λ}{3} = \frac{y}{- 4} = \frac{z - 6}{0}$ is 13. Then $8 λ \in S \sum λ$ …
Mathematics · 3D Geometry · MCQ
Q37.If the set ${Re (\frac{z - z ˉ + z z ˉ}{2 - 3 z + 5 z ˉ}) : z \in C, Re (z) = 3}$ is equal to the interval $(α, β]$ , then $24 (β - α)$ is equal to :
Mathematics · Complex Numbers · MCQ
Q38.A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of…
Mathematics · Permutations and Combinations · Numerical
Q39.Let an ellipse with centre $(1, 0)$ and latus rectum of length $\frac{1}{2}$ have its major axis along $x$ -axis. If its minor axis subtends an angle $6 0^{\circ}$ at the foci, then the square of the sum of the lengths of its minor…
Mathematics · Ellipse · Numerical
Q40.If the area bounded by the curve $2 y^{2} = 3 x$ , lines $x + y = 3, y = 0$ and outside the circle $(x - 3)^{2} + y^{2} = 2$ is $A$ , then $4 (π + 4 A)$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q41.Let $f (x) = \int \frac{d x}{( 3 + 4 x ^{2} ) 4 - 3 x ^{2}}, ∣ x ∣0$ , then $α^{2} + β^{2}$ is equal to .
Mathematics · Indefinite Integrals · Numerical
Q42.Consider the triangles with vertices $A (2, 1), B (0, 0)$ and $C (t, 4), t \in [0, 4]$ . If the maximum and the minimum perimeters of such triangles are obtained at $t = α$ and $t = β$ respectively, then $6 α + 21 β$ is equal to …
Mathematics · Application of Derivatives · Numerical
Q43.The number of elements in the set ${n \in N : 10 \leq n \leq 100$ and $3^{n} - 3$ is a multiple of 7 $}$ is .
Mathematics · Sets and Relations · Numerical
Q44.Let $A = {1, 2, 3, 4}$ and $R$ be a relation on the set $A \times A$ defined by $R = {((a, b), (c, d)) : 2 a + 3 b = 4 c + 5 d}$ . Then the number of elements in $R$ is .
Mathematics · Sets and Relations · Numerical