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Mathematics · 2024 · 6 Apr · Shift 1

30 questions from this JEE Main paper

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2024 · 6 Apr · Shift 1
Mathematics

Mathematics · 2024 · 6 Apr · Shift 1

30 questions from this JEE Main paper

Circle1 questions Straight Lines and Pair of Straight Lines1 questions Sets and Relations2 questions Parabola3 questions 3D Geometry3 questions Area Under the Curves1 questions Differentiation2 questions Differential Equations2 questions Quadratic Equation and Inequalities2 questions Matrices and Determinants2 questions Definite Integration2 questions Statistics1 questions Permutations and Combinations1 questions Functions1 questions Application of Derivatives1 questions Probability1 questions Binomial Theorem1 questions Sequences and Series1 questions Inverse Trigonometric Functions1 questions Vector Algebra1 questions

Q31.A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are $m$ and $n$ , respectively, then $m + n^{2}$ is equal to
Mathematics · Circle · MCQ
Q32.Let a variable line of slope $m > 0$ passing through the point $(4, - 9)$ intersect the coordinate axes at the points $A$ and $B$ . The minimum value of the sum of the distances of $A$ and $B$ from the origin is
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q33.Let $A = {n \in [100, 700] \cap N : n$ is neither a multiple of 3 nor a multiple of 4 $}$ . Then the number of elements in $A$ is
Mathematics · Sets and Relations · MCQ
Q34.Let $C$ be the circle of minimum area touching the parabola $y = 6 - x^{2}$ and the lines $y = 3 ∣ x ∣$ . Then, which one of the following points lies on the circle $C$ ?
Mathematics · Parabola · MCQ
Q35.If $A (3, 1, - 1), B (\frac{5}{3}, \frac{7}{3}, \frac{1}{3}), C (2, 2, 1)$ and $D (\frac{10}{3}, \frac{2}{3}, \frac{- 1}{3})$ are the vertices of a quadrilateral $A B C D$ , then its area is
Mathematics · 3D Geometry · MCQ
Q36.Let the relations $R_{1}$ and $R_{2}$ on the set $X = {1, 2, 3, \dots, 20}$ be given by $R_{1} = {(x, y) : 2 x - 3 y = 2}$ and $R_{2} = {(x, y) : - 5 x + 4 y = 0}$ . If $M$ and $N$ be the minimum number of elements required to be added in $R_{1}$ and $R_{2}$ ,…
Mathematics · Sets and Relations · MCQ
Q37.Let the area of the region enclosed by the curves $y = 3 x, 2 y = 27 - 3 x$ and $y = 3 x - x x$ be $A$ . Then $10 A$ is equal to
Mathematics · Area Under the Curves · MCQ
Q38. $If f (x) = {x^{3} sin (\frac{1}{x}), 0 x e q 0, x = 0, then$
Mathematics · Differentiation · MCQ
Q39.The shortest distance between the lines $\frac{x - 3}{2} = \frac{y + 15}{- 7} = \frac{z - 9}{5}$ and $\frac{x + 1}{2} = \frac{y - 1}{1} = \frac{z - 9}{- 3}$ is
Mathematics · 3D Geometry · MCQ
Q40.Let $y = y (x)$ be the solution of the differential equation $(2 x lo g_{e} x) \frac{d y}{d x} + 2 y = \frac{3}{x} lo g_{e} x, x > 0$ and $y (e^{- 1}) = 0$ . Then, $y (e)$ is equal to
Mathematics · Differential Equations · MCQ
Q41.Let $x^{2} - (t^{2} - 5 t + 6) x + 1 = 0, t \in R$ be the distinct roots of the equation $x^{2} - (t^{2} - 5 t + 6) x + 1 = 0, t \in R$ and $a_{n} = α^{n} + β^{n}$ . Then the minimum value of $\frac{a _{2023} + a _{2025}}{a _{2024}}$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q42.For $α, β \in R$ and a natural number $n$ , let $A_{r} = r 2 r 3 r - 2 123 \frac{n ^{2}}{2} + α n^{2} - β \frac{n ( 3 n - 1 )}{2}$ . Then $2 A_{10} - A_{8}$ …
Mathematics · Matrices and Determinants · MCQ
Q43.Let $f : (- \infty, \infty) - {0} \to R$ be a differentiable function such that $f^{'} (1) = lim_{a \to \infty} a^{2} f (\frac{1}{a})$ . Then $lim_{a \to \infty} \frac{a ( a + 1 )}{2} tan^{- 1} (\frac{1}{a}) + a^{2} - 2 lo g_{e} a$ …
Mathematics · Differentiation · MCQ
Q44. $0 \int π /4 \frac{c o s ^{2} x s i n ^{2} x}{( c o s ^{3} x + s i n ^{3} x ) ^{2}} d x$ is equal to
Mathematics · Definite Integration · MCQ
Q45.The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is
Mathematics · Statistics · MCQ
Q46.Let $y = y (x)$ be the solution of the differential equation $(1 + x^{2}) \frac{d y}{d x} + y = e^{t a n^{- 1} x}$ , $y (1) = 0$ . Then $y (0)$ is
Mathematics · Differential Equations · MCQ
Q47.The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is
Mathematics · Permutations and Combinations · MCQ
Q48.The function $f (x) = \frac{x ^{2} + 2 x - 15}{x ^{2} - 4 x + 9}, x \in R$ is
Mathematics · Functions · MCQ
Q49.The interval in which the function $f (x) = x^{x}, x > 0$ , is strictly increasing is
Mathematics · Application of Derivatives · MCQ
Q50.A company has two plants $A$ and $B$ to manufacture motorcycles. $60%$ motorcycles are manufactured at plant $A$ and the remaining are manufactured at plant $B .80%$ of the motorcycles manufactured at plant $A$ are rated of the…
Mathematics · Probability · MCQ
Q51.Let $x_{1}, x_{2}, x_{3}, x_{4}$ be the solution of the equation $4 x^{4} + 8 x^{3} - 17 x^{2} - 12 x + 9 = 0$ and $(4 + x_{1}^{2}) (4 + x_{2}^{2}) (4 + x_{3}^{2}) (4 + x_{4}^{2}) = \frac{125}{16} m$ . Then the value of $m$ is …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q52.Let a conic $C$ pass through the point $(4, - 2)$ and $P (x, y), x \geq 3$ , be any point on $C$ . Let the slope of the line touching the conic $C$ only at a single point $P$ be half the slope of the line joining the points $P$ and $(3, - 5)$ . If…
Mathematics · Parabola · Numerical
Q53.If the second, third and fourth terms in the expansion of $(x + y)^{n}$ are 135, 30 and $\frac{10}{3}$ , respectively, then $6 (n^{3} + x^{2} + y)$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q54.Let $α β γ = 45; α, β, γ \in R$ . If $x (α, 1, 2) + y (1, β, 2) + z (2, 3, γ) = (0, 0, 0)$ for some $x, y, z \in R, x y z e q 0$ , then $6 α + 4 β + γ$ is equal to …
Mathematics · Matrices and Determinants · Numerical
Q55.Let $P$ be the point $(10, - 2, - 1)$ and $Q$ be the foot of the perpendicular drawn from the point $R (1, 7, 6)$ on the line passing through the points $(2, - 5, 11)$ and $(- 6, 7, - 5)$ . Then the length of the line segment $P Q$ is equal to …
Mathematics · 3D Geometry · Numerical
Q56.Let the first term of a series be $T_{1} = 6$ and its $r^{th}$ term $T_{r} = 3 T_{r - 1} + 6^{r}, r = 2, 3$ , ............ $n$ . If the sum of the first $n$ terms of this series is $\frac{1}{5} (n^{2} - 12 n + 39) (4 \cdot 6^{n} - 5 \cdot 3^{n} + 1)$ …
Mathematics · Sequences and Series · Numerical
Q57.For $n \in N$ , if $cot^{- 1} 3 + cot^{- 1} 4 + cot^{- 1} 5 + cot^{- 1} n = \frac{π}{4}$ , then $n$ is equal to .
Mathematics · Inverse Trigonometric Functions · Numerical
Q58.Let $r_{k} = \frac{\int _{0}^{1} ( 1 - x ^{7} ) ^{k} d x}{\int _{0}^{1} ( 1 - x ^{7} ) ^{k + 1} d x}, k \in N$ . Then the value of $\sum_{k = 1}^{10} \frac{1}{7 ( r _{k} - 1 )}$ is equal to .
Mathematics · Definite Integration · Numerical
Q59.Let $a = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}, b = 3 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and a vector $c$ be such that $a \times (b + c) + b \times c = \hat{i} + 8 \hat{j} + 13 \hat{k}$ . If $\vec{a} \cdot…
Mathematics · Vector Algebra · Numerical
Q60.Let $L_{1}, L_{2}$ be the lines passing through the point $P (0, 1)$ and touching the parabola $9 x^{2} + 12 x + 18 y - 14 = 0$ . Let $Q$ and $R$ be the points on the lines $L_{1}$ and $L_{2}$ such that the $△ P QR$ is an isosceles triangle with base $QR$ …
Mathematics · Parabola · Numerical