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Mathematics · 2023 · 31 Jan · Shift 1

23 questions from this JEE Main paper

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2023 · 31 Jan · Shift 1
Mathematics

Mathematics · 2023 · 31 Jan · Shift 1

23 questions from this JEE Main paper

Quadratic Equation and Inequalities1 questions Probability1 questions Inverse Trigonometric Functions1 questions Sequences and Series2 questions Matrices and Determinants2 questions Sets and Relations1 questions Functions1 questions Application of Derivatives1 questions Definite Integration2 questions 3D Geometry1 questions Vector Algebra2 questions Complex Numbers1 questions Differentiation1 questions Binomial Theorem2 questions Permutations and Combinations2 questions Area Under the Curves1 questions Statistics1 questions

Q25.The number of real roots of the equation $x^{2} - 4 x + 3 + x^{2} - 9 = 4 x^{2} - 14 x + 6$ , is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q26.A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is :
Mathematics · Probability · MCQ
Q27.If $sin^{- 1} \frac{α}{17} + cos^{- 1} \frac{4}{5} - tan^{- 1} \frac{77}{36} = 0, 0 < α < 13$ , then $sin^{- 1} (sin α) + cos^{- 1} (cos α)$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q28.If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is
Mathematics · Sequences and Series · MCQ
Q29.For the system of linear equations $x + y + z = 6 α x + β y + 7 z = 3 x + 2 y + 3 z = 14$ which of the following is NOT true ?
Mathematics · Matrices and Determinants · MCQ
Q30.Let $R$ be a relation on $N \times N$ defined by $(a, b) R (c, d)$ if and only if $a d (b - c) = b c (a - d)$ . Then $R$ is
Mathematics · Sets and Relations · MCQ
Q31.If the domain of the function $f (x) = \frac{[ x ]}{1 + x ^{2}}$ , where $[x]$ is greatest integer $[2, 6)$ , is $[2, 6)$ , then its range is
Mathematics · Functions · MCQ
Q32.A wire of length $l_{1}$ is to be cut into two pieces. A piece of length $l_{1}$ is bent to make a square of area $A_{1}$ and the other piece of length $l_{2}$ is made into a circle of area $A_{2}$ . If $2 A_{1} + 3 A_{2}$ is minimum…
Mathematics · Application of Derivatives · MCQ
Q33.Let $α \in (0, 1)$ and $β = lo g_{e} (1 - α)$ . Let $P_{n} (x) = x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3} + ... + \frac{x ^{n}}{n}, x \in (0, 1)$ . Then the integral $0 \int α \frac{t ^{50}}{1 - t} d t$ …
Mathematics · Definite Integration · MCQ
Q34.Let the shortest distance between the lines $L : \frac{x - 5}{- 2} = \frac{y - λ}{0} = \frac{z + λ}{1}, λ \geq 0$ and $L_{1} : x + 1 = y - 1 = 4 - z$ be $26$ . If $(α, β, γ)$ lies on $L$ , then which of the following is…
Mathematics · 3D Geometry · MCQ
Q35.Let $a = 2 \hat{i} + \hat{j} + \hat{k}$ , and $b$ and $c$ be two nonzero vectors such that $∣ a + b + c ∣ = ∣ a + b - c ∣$ and $b \cdot c = 0$ . Consider the following two statements: (A) $∣ a + λ c ∣ \geq ∣ a ∣$ …
Mathematics · Vector Algebra · MCQ
Q36.Let $A = 1000412 0 - 1 - 3$ . Then the sum of the diagonal elements of the matrix $(A + I)^{11}$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q37.For all $z \in C$ on the curve $C_{1} : ∣ z ∣ = 4$ , let the locus of the point $z + \frac{1}{z}$ be the curve $C_{2}$ . Then :
Mathematics · Complex Numbers · MCQ
Q38.The value of $\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{( 2 + 3 s i n x )}{s i n x ( 1 + c o s x )} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q39.Let $y = f (x) = sin^{3} (\frac{π}{3} (cos (\frac{π}{3 2} (- 4 x^{3} + 5 x^{2} + 1)^{\frac{3}{2}})))$ . Then, at x = 1,
Mathematics · Differentiation · MCQ
Q40.The remainder on dividing $5^{99}$ by 11 is .
Mathematics · Binomial Theorem · Numerical
Q41.Let 5 digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is .
Mathematics · Permutations and Combinations · Numerical
Q42.Let $α > 0$ , be the smallest number such that the expansion of $(x^{\frac{2}{3}} + \frac{2}{x ^{3}})^{30}$ has a term $β x^{- α}, β \in N$ . Then $α$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q43.Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to .
Mathematics · Permutations and Combinations · Numerical
Q44.Let $a_{1}, a_{2}, \dots, a_{n}$ be in A.P. If $a_{5} = 2 a_{7}$ and $a_{11} = 18$ , then $12 (\frac{1}{a _{10} + a _{11}} + \frac{1}{a _{11} + a _{12}} + \dots + \frac{1}{a _{17} + a _{18}})$ is equal to …
Mathematics · Sequences and Series · Numerical
Q45.Let $a$ and $b$ be two vectors such that $∣ a ∣ = 14, ∣ b ∣ = 6$ and $∣ a \times b ∣ = 48$ . Then $(a \cdot b)^{2}$ is equal to .
Mathematics · Vector Algebra · Numerical
Q46.Let for $x \in R$ , $f (x) = \frac{x + ∣ x ∣}{2}$ and $g (x) = {x, x^{2}, x < 0 x \geq 0$ . Then area bounded by the curve $y = (f \circ g) (x)$ and the lines $y = 0, 2 y - x = 15$ is equal to …
Mathematics · Area Under the Curves · Numerical
Q47.If the variance of the frequency distribution is 3, then $α$ is equal to . Includes table
Mathematics · Statistics · Numerical