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Mathematics · 2024 · 29 Jan · Shift 1

30 questions from this JEE Main paper

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2024 · 29 Jan · Shift 1
Mathematics

Mathematics · 2024 · 29 Jan · Shift 1

30 questions from this JEE Main paper

Differentiation1 questions Vector Algebra1 questions Properties of Triangle1 questions Trigonometric Functions and Equations1 questions Sequences and Series2 questions Probability1 questions Matrices and Determinants2 questions Sets and Relations1 questions Functions1 questions 3D Geometry3 questions Straight Lines and Pair of Straight Lines1 questions Indefinite Integrals1 questions Complex Numbers2 questions Application of Derivatives2 questions Definite Integration2 questions Differential Equations2 questions Area Under the Curves2 questions Statistics1 questions Circle1 questions Binomial Theorem1 questions Permutations and Combinations1 questions

Q31.Suppose $f (x) = \frac{( 2 ^{x} + 2 ^{- x} ) t a n x t a n ^{- 1} ( x ^{2} - x + 1 )}{( 7 x ^{2} + 3 x + 1 ) ^{3}}$ . Then the value of $f^{'} (0)$ is equal to
Mathematics · Differentiation · MCQ
Q32.Let $a, b$ and $c$ be three non-zero vectors such that $b$ and $c$ are non-collinear. If $a + 5 b$ is collinear with $c, b + 6 c$ is collinear with $a$ and $a + α b + β c = 0$ …
Mathematics · Vector Algebra · MCQ
Q33.Let $(5, \frac{a}{4})$ be the circumcenter of a triangle with vertices $A (a, - 2), B (a, 6)$ and $C (\frac{a}{4}, - 2)$ . Let $α$ denote the circumradius, $β$ denote the area and $γ$ …
Mathematics · Properties of Triangle · MCQ
Q34.If $α, - \frac{π}{2} < α < \frac{π}{2}$ is the solution of $4 cos θ + 5 sin θ = 1$ , then the value of $tan α$ is
Mathematics · Trigonometric Functions and Equations · MCQ
Q35.If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to
Mathematics · Sequences and Series · MCQ
Q36.A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is
Mathematics · Probability · MCQ
Q37.In an A.P., the sixth term $a_{6} = 2$ . If the product $a_{1} a_{4} a_{5}$ is the greatest, then the common difference of the A.P. is equal to
Mathematics · Sequences and Series · MCQ
Q38. $Let A = 100 0 α β 0 β α and ∣2 A ∣^{3} = 2^{21} where α, β \in Z, Then a value of α is$ …
Mathematics · Matrices and Determinants · MCQ
Q39.Let $R$ be a relation on $Z \times Z$ defined by $(a, b) R (c, d)$ if and only if $a d - b c$ is divisible by 5. Then $R$ is
Mathematics · Sets and Relations · MCQ
Q40.If $f (x) = {2 + 2 x, 1 - \frac{x}{3}, - 1 \leq x < 0 0 \leq x \leq 3; g (x) = {- x, x, - 3 \leq x \leq 0 0 < x \leq 1$ , then range…
Mathematics · Functions · MCQ
Q41.Let $O$ be the origin and the position vectors of $A$ and $B$ be $2 \hat{i} + 2 \hat{j} + \hat{k}$ and $2 \hat{i} + 4 \hat{j} + 4 \hat{k}$ respectively. If the internal bisector of $∠ AOB$ meets the line $AB$ at…
Mathematics · 3D Geometry · MCQ
Q42.In a $△ A B C$ , suppose $y = x$ is the equation of the bisector of the angle $B$ and the equation of the side $A C$ is $2 x - y = 2$ . If $2 A B = B C$ and the points $A$ and $B$ are respectively $(4, 6)$ and $(α, β)$ , then $α + 2 β$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q43.For $x \in (- \frac{π}{2}, \frac{π}{2})$ , if $y (x) = \int \frac{cosec x + s i n x}{cosec x s e c x + t a n x s i n ^{2} x} d x$ , and $lim_{x \to (\frac{π}{2})^{-}} y (x) = 0$ then $y (\frac{π}{4})$ …
Mathematics · Indefinite Integrals · MCQ
Q44.Let $A$ be a square matrix such that $AA^{T} = I$ . Then $\frac{1}{2} A [(A + A^{T})^{2} + (A - A^{T})^{2}]$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q45.If $z = \frac{1}{2} - 2 i$ is such that $∣ z + 1∣ = α z + β (1 + i), i = - 1$ and $α, β \in R$ , then $α + β$ is equal to
Mathematics · Complex Numbers · MCQ
Q46.Consider the function $f : [\frac{1}{2}, 1] \to R$ defined by $f (x) = 42 x^{3} - 32 x - 1$ . Consider the statements (I) The curve $y = f (x)$ intersects the $x$ -axis exactly at one point. (II) The curve $y = f (x)$ …
Mathematics · Application of Derivatives · MCQ
Q47.Let $P QR$ be a triangle with $R (- 1, 4, 2)$ . Suppose $M (2, 1, 2)$ is the mid point of $PQ$ . The distance of the centroid of $△ PQR$ from the point of intersection of the lines $\frac{x - 2}{0} = \frac{y}{2} = \frac{z + 3}{- 1}$ …
Mathematics · 3D Geometry · MCQ
Q48. $x \to \frac{π}{2} lim \frac{1}{( x - \frac{π}{2} ) ^{2}} x^{3} \int (\frac{π}{2})^{3} cos (t^{\frac{1}{3}}) d t$ is equal to
Mathematics · Definite Integration · MCQ
Q49.A function $y = f (x)$ satisfies $f (x) sin 2 x + sin x - (1 + cos^{2} x) f^{'} (x) = 0$ with condition $f (0) = 0$ . Then, $f (\frac{π}{2})$ is equal to
Mathematics · Differential Equations · MCQ
Q50.If the value of the integral $\int_{- \frac{π}{2}}^{\frac{π}{2}} (\frac{x ^{2} c o s x}{1 + π ^{x}} + \frac{1 + s i n ^{2} x}{1 + e ^{s i n x^{2123}}}) d x = \frac{π}{4} (π + a) - 2$ , then the value of $a$ is
Mathematics · Definite Integration · MCQ
Q51.The area (in sq. units) of the part of the circle $x^{2} + y^{2} = 169$ which is below the line $5 x - y = 13$ is $\frac{π α}{2 β} - \frac{65}{2} + \frac{α}{β} sin^{- 1} (\frac{12}{13})$ , where $α, β$ are coprime…
Mathematics · Area Under the Curves · Numerical
Q52.If the mean and variance of the data $65, 68, 58, 44, 48, 45, 60, α, β, 60$ where $α > β$ , are 56 and 66.2 respectively, then $α^{2} + β^{2}$ is equal to .
Mathematics · Statistics · Numerical
Q53.Equations of two diameters of a circle are $2 x - 3 y = 5$ and $3 x - 4 y = 7$ . The line joining the points $(- \frac{22}{7}, - 4)$ and $(- \frac{1}{7}, 3)$ intersects the circle at only one point $P (α, β)$ . Then, $17 β - α$ …
Mathematics · Circle · Numerical
Q54.A line with direction ratios $2, 1, 2$ meets the lines $x = y + 2 = z$ and $x + 2 = 2 y = 2 z$ respectively at the points $P$ and $Q$ . If the length of the perpendicular from the point $(1, 2, 12)$ to the line $PQ$ is $l$ , then $l^{2}$ …
Mathematics · 3D Geometry · Numerical
Q55. $If \frac{^{11} C _{1}}{2} + \frac{^{11} C _{2}}{3} + \dots + \frac{^{11} C _{9}}{10} = \frac{n}{m} with gcd (n, m) = 1, then n + m is equal to$ .
Mathematics · Binomial Theorem · Numerical
Q56.If the points of intersection of two distinct conics $x^{2} + y^{2} = 4 b$ and $\frac{x ^{2}}{16} + \frac{y ^{2}}{b ^{2}} = 1$ lie on the curve $y^{2} = 3 x^{2}$ , then $33$ times the area of the rectangle formed by the intersection points is …
Mathematics · Area Under the Curves · Numerical
Q57.All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is .
Mathematics · Permutations and Combinations · Numerical
Q58.Let $x^{2} - x + 2 = 0$ be the roots of the equation $x^{2} - x + 2 = 0$ with $Im (α) > Im (β)$ . Then $α^{6} + α^{4} + β^{4} - 5 α^{2}$ is equal to .
Mathematics · Complex Numbers · Numerical
Q59.Let $f (x) = 2^{x} - x^{2}, x \in R$ . If $m$ and $n$ are respectively the number of points at which the curves $y = f (x)$ and $y = f^{'} (x)$ intersect the $x$ -axis, then the value of $m + n$ is .
Mathematics · Application of Derivatives · Numerical
Q60.If the solution curve $y = y (x)$ of the differential equation $(1 + y^{2}) (1 + lo g_{e} x) d x + x d y = 0, x > 0$ passes through the point $(1, 1)$ and $y (e) = \frac{α - t a n ( \frac{3}{2} )}{β + t a n ( \frac{3}{2} )}$ …
Mathematics · Differential Equations · Numerical