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Mathematics · 2022 · 26 Jul · Shift 1

21 questions from this JEE Main paper

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2022 · 26 Jul · Shift 1
Mathematics

Mathematics · 2022 · 26 Jul · Shift 1

21 questions from this JEE Main paper

Limits Continuity and Differentiability4 questions Complex Numbers1 questions Matrices and Determinants1 questions Area Under the Curves1 questions Sequences and Series1 questions Differential Equations1 questions Straight Lines and Pair of Straight Lines2 questions 3D Geometry2 questions Vector Algebra1 questions Probability1 questions Inverse Trigonometric Functions1 questions Quadratic Equation and Inequalities2 questions Permutations and Combinations1 questions Definite Integration1 questions Application of Derivatives1 questions

Q25.Let f : R $\to$ R be a continuous function such that $f (3 x) - f (x) = x$ . If $f (8) = 7$ , then $f (14)$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.Let O be the origin and A be the point $z_{1} = 1 + 2 i$ . If B is the point $z_{2}$ , $Re o l imi t s (z_{2}) < 0$ , such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT…
Mathematics · Complex Numbers · MCQ
Q27.If the system of linear equations. $8 x + y + 4 z = - 2 x + y + z = 0 λ x - 3 y = μ$ has infinitely many solutions, then the distance of the point $(λ, μ, - \frac{1}{2})$ from the plane $8 x + y + 4 z + 2 = 0$ is…
Mathematics · Matrices and Determinants · MCQ
Q28.The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = ya is $\frac{364}{3}$ , is equal to :
Mathematics · Area Under the Curves · MCQ
Q29.Consider two G.Ps. 2, 22, 23, ..... and 4, 42, 43, .... of 60 and n terms respectively. If the geometric mean of all the 60 + n terms is $(2)^{\frac{225}{8}}$ , then $k = 1 \sum n k (n - k)$ is equal to :
Mathematics · Sequences and Series · MCQ
Q30.If the function $f (x) = {\frac{l o g _{e} ( 1 - x + x ^{2} ) + l o g _{e} ( 1 + x + x ^{2} )}{s e c x - c o s x} k,, x \in (\frac{- π}{2}, \frac{π}{2}) - {0} x = 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q31.If $f (x) = {x + a ∣ x - 4∣,, x \leq 0 x > 0$ and $g (x) = {x + 1 (x - 4)^{2} + b,, x < 0 x \geq 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Let $f (x) = {x^{3} - x^{2} + 10 x - 7, - 2 x + lo g_{2} (b^{2} - 4), x \leq 1 x > 1$ . Then the set of all values of b, for which f(x) has maximum value at x = 1,…
Mathematics · Limits Continuity and Differentiability · MCQ
Q33.If $\frac{d y}{d x} + 2 y tan x = sin x, 0 < x < \frac{π}{2}$ and $y (\frac{π}{3}) = 0$ , then the maximum value of $y (x)$ is :
Mathematics · Differential Equations · MCQ
Q34.A point $P$ moves so that the sum of squares of its distances from the points $(1, 2)$ and $(- 2, 1)$ is 14. Let $f (x, y) = 0$ be the locus of $P$ , which intersects the $x$ -axis at the points $A$ , $B$ and the $y$ -axis…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.The length of the perpendicular from the point $(1, - 2, 5)$ on the line passing through $(1, 2, 4)$ and parallel to the line $x + y - z = 0 = x - 2 y + 3 z - 5$ is :
Mathematics · 3D Geometry · MCQ
Q36.Let $a = α \hat{i} + \hat{j} - \hat{k}$ and $b = 2 \hat{i} + \hat{j} - α \hat{k}, α > 0$ . If the projection of $a \times b$ …
Mathematics · Vector Algebra · MCQ
Q37.Let $E_{1}, E_{2}, E_{3}$ be three mutually exclusive events such that $P (E_{1}) = \frac{2 + 3 p}{6}, P (E_{2}) = \frac{2 - p}{8}$ and $P (E_{3}) = \frac{1 - p}{2}$ …
Mathematics · Probability · MCQ
Q38. $tan (2 tan^{- 1} \frac{1}{5} + sec^{- 1} \frac{5}{2} + 2 tan^{- 1} \frac{1}{8})$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q39.If for some $p, q, r \in R$ , not all have same sign, one of the roots of the equation $(p^{2} + q^{2}) x^{2} - 2 q (p + r) x + q^{2} + r^{2} = 0$ …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q40.The number of 5-digit natural numbers, such that the product of their digits is 36 , is .
Mathematics · Permutations and Combinations · Numerical
Q41.The number of distinct real roots of the equation $x^{5} (x^{3} - x^{2} - x + 1) + x (3 x^{3} - 4 x^{2} - 2 x + 4) - 1 = 0$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q42.If $n (2 n + 1) \int_{0}^{1} (1 - x^{n})^{2 n} d x = 1177 \int_{0}^{1} (1 - x^{n})^{2 n + 1} d x$ , then $n \in N$ is equal to …
Mathematics · Definite Integration · Numerical
Q43.The equations of the sides $AB, BC$ and $CA$ of a triangle $ABC$ are $2 x + y = 0, x + p y = 15 a$ and $x - y = 3$ respectively. If its orthocentre is $(2, a), - \frac{1}{2} < a < 2$ , then…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q44.Let the function $f (x) = 2 x^{2} - lo g_{e} x, x > 0$ , be decreasing in $(0, a)$ and increasing in $(a, 4)$ . A tangent to the parabola $y^{2} = 4 a x$ at a point $P$ on it passes through the point $(8 a, 8 a - 1)$ …
Mathematics · Application of Derivatives · Numerical
Q45.Let $Q$ and $R$ be two points on the line $\frac{x + 1}{2} = \frac{y + 2}{3} = \frac{z - 1}{2}$ at a distance $26$ from the point $P (4, 2, 7)$ . Then the square of the area of the triangle $P QR$ is .
Mathematics · 3D Geometry · Numerical