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Mathematics · 2023 · 25 Jan · Shift 2

25 questions from this JEE Main paper

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2023 · 25 Jan · Shift 2
Mathematics

Mathematics · 2023 · 25 Jan · Shift 2

25 questions from this JEE Main paper

Parabola1 questions 3D Geometry3 questions Functions3 questions Probability2 questions Limits Continuity and Differentiability1 questions Matrices and Determinants2 questions Hyperbola1 questions Application of Derivatives1 questions Complex Numbers1 questions Definite Integration2 questions Permutations and Combinations4 questions Differential Equations1 questions Binomial Theorem1 questions Sequences and Series1 questions Quadratic Equation and Inequalities1 questions

Q22.The equations of two sides of a variable triangle are $x = 0$ and $y = 3$ , and its third side is a tangent to the parabola $y^{2} = 6 x$ . The locus of its circumcentre is :
Mathematics · Parabola · MCQ
Q23.The foot of perpendicular of the point (2, 0, 5) on the line $\frac{x + 1}{2} = \frac{y - 1}{5} = \frac{z + 1}{- 1}$ is ( $α, β, γ$ ). Then, which of the following is NOT correct?
Mathematics · 3D Geometry · MCQ
Q24.The number of functions $f : {1, 2, 3, 4} \to {a \in Z ∣ a ∣ \leq 8}$ satisfying $f (n) + \frac{1}{n} f (n + 1) = 1, \forall n \in {1, 2, 3}$ is
Mathematics · Functions · MCQ
Q25.Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N - 2, 3 N, N + 2$ are in geometric progression be $\frac{k}{48}$ . Then the value of k is :
Mathematics · Probability · MCQ
Q26.If the function $f (x) = ⎩ ⎨ ⎧ (1 + ∣ cos x ∣)^{\frac{λ}{∣ c o s x ∣}} μ e^{\frac{c o t 6 x}{c o t 4 x}},,, 0 < x < \frac{π}{2} x = \frac{π}{2} \frac{π}{2} < x < π$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Let A, B, C be 3 $\times$ 3 matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements (S1) A $^{13}$ B $^{26} -$ B $^{26}$ A $^{13}$ is symmetric (S2) A $^{26}$ C $^{13} -$ C $^{13}$ A $^{26}$ is symmetric…
Mathematics · Matrices and Determinants · MCQ
Q28.The shortest distance between the lines $x + 1 = 2 y = - 12 z$ and $x = y + 2 = 6 z - 6$ is :
Mathematics · 3D Geometry · MCQ
Q29.Let T and C respectively be the transverse and conjugate axes of the hyperbola $16 x^{2} - y^{2} + 64 x + 4 y + 44 = 0$ . Then the area of the region above the parabola $x^{2} = y + 4$ , below the transverse axis T and on the right of the…
Mathematics · Hyperbola · MCQ
Q30.Let the function $f (x) = 2 x^{3} + (2 p - 7) x^{2} + 3 (2 p - 9) x - 6$ have a maxima for some value of $x 0$ . Then, the set of all values of p is
Mathematics · Application of Derivatives · MCQ
Q31.Let $z$ be a complex number such that $\frac{z - 2 i}{z + i} = 2, z e - i$ . Then $z$ lies on the circle of radius 2 and centre :
Mathematics · Complex Numbers · MCQ
Q32.The integral $16 1 \int 2 \frac{d x}{x ^{3} ( x ^{2} + 2 ) ^{2}}$ is equal to
Mathematics · Definite Integration · MCQ
Q33.Let $f : R \to R$ be a function defined by $f (x) = lo g_{m} {2 (sin x - cos x) + m - 2}$ , for some $m$ , such that the range of $f$ is [0, 2]. Then the value of $m$ is
Mathematics · Functions · MCQ
Q34.The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is :
Mathematics · Permutations and Combinations · MCQ
Q35.Let $y = y (t)$ be a solution of the differential equation $\frac{d y}{d t} + α y = γ e^{- β t}$ where, $α > 0, β > 0$ and $γ > 0$ . Then $t \to \infty lim y (t)$
Mathematics · Differential Equations · MCQ
Q36.Let $A = [\frac{1}{10} \frac{- 3}{10} \frac{3}{10} \frac{1}{10}]$ and $B = [10 - i 1]$ …
Mathematics · Matrices and Determinants · MCQ
Q37. $k = 0 \sum 6^{51 - k} C_{3}$ is equal to :
Mathematics · Permutations and Combinations · MCQ
Q38.Let $f (x) = 2 x^{n} + λ, λ \in R, n \in N$ , and $f (4) = 133, f (5) = 255$ . Then the sum of all the positive integer divisors of $(f (3) - f (2))$ is
Mathematics · Functions · MCQ
Q39.25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is $\frac{k}{10}$ . Then the value of k…
Mathematics · Probability · Numerical
Q40.A triangle is formed by X-axis, Y-axis and the line $3 x + 4 y = 60$ . Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is .
Mathematics · Permutations and Combinations · Numerical
Q41.The remainder when (2023) $^{2023}$ is divided by 35 is .
Mathematics · Binomial Theorem · Numerical
Q42.If $\frac{1}{3} \int 3 ∣ lo g_{e} x ∣ d x = \frac{m}{n} lo g_{e} (\frac{n ^{2}}{e})$ , where m and n are coprime natural numbers, then $m^{2} + n^{2} - 5$ is equal to .
Mathematics · Definite Integration · Numerical
Q43.Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given,…
Mathematics · Permutations and Combinations · Numerical
Q44.For the two positive numbers $a, b,$ if $\frac{1}{18}$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{a}, 10$ and $\frac{1}{b}$ are in an arithmetic progression, then $16 a + 12 b$ is equal to .
Mathematics · Sequences and Series · Numerical
Q45.If the shortest distance between the line joining the points (1, 2, 3) and (2, 3, 4), and the line $\frac{x - 1}{2} = \frac{y + 1}{- 1} = \frac{z - 2}{0}$ is $α$ , then 28 $α^{2}$ is equal to .
Mathematics · 3D Geometry · Numerical
Q46.Let $α \in R$ and let $x^{2} + 6 0^{\frac{1}{4}} x + a = 0$ be the roots of the equation $x^{2} + 6 0^{\frac{1}{4}} x + a = 0$ . If $α^{4} + β^{4} = - 30$ , then the product of all possible values of $a$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical