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Mathematics · 2023 · 24 Jan · Shift 1

21 questions from this JEE Main paper

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2023 · 24 Jan · Shift 1
Mathematics

Mathematics · 2023 · 24 Jan · Shift 1

21 questions from this JEE Main paper

Complex Numbers1 questions Probability2 questions Sets and Relations1 questions Limits Continuity and Differentiability2 questions Inverse Trigonometric Functions1 questions Differential Equations1 questions Area Under the Curves1 questions Quadratic Equation and Inequalities2 questions Matrices and Determinants1 questions Sequences and Series2 questions Vector Algebra1 questions 3D Geometry1 questions Ellipse1 questions Permutations and Combinations2 questions Definite Integration2 questions

Q24.Let $p, q \in R$ and $(1 - 3 i)^{200} = 2^{199} (p + i q), i = - 1$ then $p + q + q^{2}$ and $p - q + q^{2}$ are roots of the equation.
Mathematics · Complex Numbers · MCQ
Q25.Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations $x + y + z = 12 x + N y + 2 z = 23 x + 3 y + N z = 3$ has unique solution is $\frac{k}{6}$ , then the sum of value…
Mathematics · Probability · MCQ
Q26.The relation $R = {(a, b) : g cd (a, b) = 1, 2aeb, a, b \in Z}$ is :
Mathematics · Sets and Relations · MCQ
Q27. $t \to 0 lim (1^{\frac{1}{s i n ^{2} t}} + 2^{\frac{1}{s i n ^{2} t}} + ... + n^{\frac{1}{s i n ^{2} t}})^{s i n^{2} t}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q28. $tan^{- 1} (\frac{1 + 3}{3 + 3}) + sec^{- 1} (\frac{8 + 4 3}{6 + 3 3})$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q29.Let $y = y (x)$ be the solution of the differential equation $x^{3} d y + (x y - 1) d x = 0, x > 0, y (\frac{1}{2}) = 3 - e$ . Then y (1) is equal to
Mathematics · Differential Equations · MCQ
Q30.Let $Ω$ be the sample space and $A \subseteq Ω$ be an event. Given below are two statements : (S1) : If P(A) = 0, then A = $ϕ$ (S2) : If P(A) = 1, then A = $Ω$ Then :
Mathematics · Probability · MCQ
Q31.The area enclosed by the curves $y^{2} + 4 x = 4$ and $y - 2 x = 2$ is :
Mathematics · Area Under the Curves · MCQ
Q32.The equation $x^{2} - 4 x + [x] + 3 = x [x]$ , where $[x]$ denotes the greatest integer function, has :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q33.If A and B are two non-zero n $\times$ n matrices such that $A^{2} + B = A^{2} B$ , then :
Mathematics · Matrices and Determinants · MCQ
Q34.For three positive integers p, q, r, $x^{p q^{2}} = y^{q r} = z^{p^{2} r}$ and r = pq + 1 such that 3, 3 log $_{y} x$ , 3 log $_{z} y$ , 7 log $_{x} z$ are in A.P. with common difference $\frac{1}{2}$ . Then r-p-q is equal to
Mathematics · Sequences and Series · MCQ
Q35.Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that $\frac{Q A}{A R} = \frac{R B}{B P} = \frac{P C}{C Q} = \frac{1}{2}$ . Then $\frac{A r e a ( Δ P QR )}{A r e a ( Δ A B C )}$ is equal…
Mathematics · Vector Algebra · MCQ
Q36.Let $f (x) = {x^{2} sin (\frac{1}{x}) 0, x e 0, x = 0$ Then at $x = 0$
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.Let $λ \in R$ and let the equation E be $∣ x ∣^{2} - 2∣ x ∣ + ∣ λ - 3∣ = 0$ . Then the largest element in the set S = { $x + λ : x$ is an integer solution of E} is
Mathematics · Quadratic Equation and Inequalities · Numerical
Q38.The shortest distance between the lines $\frac{x - 2}{3} = \frac{y + 1}{2} = \frac{z - 6}{2}$ and $\frac{x - 6}{3} = \frac{1 - y}{2} = \frac{z + 8}{0}$ is equal to
Mathematics · 3D Geometry · Numerical
Q39.The 4 $^{th}$ term of GP is 500 and its common ratio is $\frac{1}{m}, m \in N$ . Let $S_{n}$ denote the sum of the first n terms of this GP. If $S_{6} > S_{5} + 1$ and $S_{7} < S_{6} + \frac{1}{2}$ , then…
Mathematics · Sequences and Series · Numerical
Q40.Let C be the largest circle centred at (2, 0) and inscribed in the ellipse $\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1$ . If (1, $α$ ) lies on C, then 10 $α^{2}$ is equal to
Mathematics · Ellipse · Numerical
Q41.A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is
Mathematics · Permutations and Combinations · Numerical
Q42.The value of $12 0 \int 3 x^{2} - 3 x + 2 d x$ is
Mathematics · Definite Integration · Numerical
Q43.The value of $\frac{8}{π} 0 \int \frac{π}{2} \frac{( c o s x ) ^{2023}}{( s i n x ) ^{2023} + ( c o s x ) ^{2023}} d x$ is
Mathematics · Definite Integration · Numerical
Q44.The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is .
Mathematics · Permutations and Combinations · Numerical