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Mathematics · 2022 · 26 Jun · Shift 2

22 questions from this JEE Main paper

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2022 · 26 Jun · Shift 2
Mathematics

Mathematics · 2022 · 26 Jun · Shift 2

22 questions from this JEE Main paper

Functions1 questions Matrices and Determinants2 questions Limits Continuity and Differentiability2 questions Application of Derivatives1 questions Area Under the Curves1 questions Indefinite Integrals1 questions Differential Equations2 questions Ellipse1 questions 3D Geometry1 questions Statistics1 questions Trigonometric Ratio and Identites1 questions Inverse Trigonometric Functions1 questions Differentiation1 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Permutations and Combinations1 questions Sequences and Series1 questions Definite Integration1 questions Probability1 questions

Q25.Let f : R $\to$ R be defined as f (x) = x $-$ 1 and g : R $-$ {1, $-$ 1} $\to$ R be defined as $g (x) = \frac{x ^{2}}{x ^{2} - 1}$ . Then the function fog is :
Mathematics · Functions · MCQ
Q26.If the system of equations $α$ x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $β$ has infinitely many solutions, then the ordered pair ( $α$ , $β$ ) is equal to :
Mathematics · Matrices and Determinants · MCQ
Q27. $x \to 0 lim \frac{c o s ( s i n x ) - c o s x}{x ^{4}}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q28.Let f(x) = min {1, 1 + x sin x}, 0 $\leq$ x $\leq$ 2 $π$ . If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q29.Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is :
Mathematics · Application of Derivatives · MCQ
Q30.The area of the region bounded by y2 = 8x and y2 = 16(3 $-$ x) is equal to:
Mathematics · Area Under the Curves · MCQ
Q31.If $\int \frac{1}{x} \frac{1 - x}{1 + x} d x = g (x) + c$ , $g (1) = 0$ , then $g (\frac{1}{2})$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q32.If $y = y (x)$ is the solution of the differential equation $x \frac{d y}{d x} + 2 y = x e^{x}$ , $y (1) = 0$ then the local maximum value of the function $z (x) = x^{2} y (x) - e^{x}, x \in R$ is :
Mathematics · Differential Equations · MCQ
Q33.If the solution of the differential equation $\frac{d y}{d x} + e^{x} (x^{2} - 2) y = (x^{2} - 2 x) (x^{2} - 2) e^{2 x}$ satisfies $y (0) = 0$ , then the value of y(2) is…
Mathematics · Differential Equations · MCQ
Q34.The locus of the mid point of the line segment joining the point (4, 3) and the points on the ellipse $x^{2} + 2 y^{2} = 4$ is an ellipse with eccentricity :
Mathematics · Ellipse · MCQ
Q35.Let $a = i + j + 2 k$ , $b = 2 i - 3 j + k$ and $c = i - j + k$ be three given vectors. Let $v$ …
Mathematics · 3D Geometry · MCQ
Q36.The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct…
Mathematics · Statistics · MCQ
Q37. $16 sin (2 0^{\circ}) sin (4 0^{\circ}) sin (8 0^{\circ})$ is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q38.If the inverse trigonometric functions take principal values then $cos^{- 1} (\frac{3}{10} cos (tan^{- 1} (\frac{4}{3})) + \frac{2}{5} sin (tan^{- 1} (\frac{4}{3})))$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q39.Let f : R $\to$ R satisfy $f (x + y) = 2^{x} f (y) + 4^{y} f (x)$ , $\forall$ x, y $\in$ R. If f(2) = 3, then $14. \frac{f ^{'} ( 4 )}{f ^{'} ( 2 )}$ is equal to .
Mathematics · Differentiation · Numerical
Q40.Let p and q be two real numbers such that p + q = 3 and p4 + q4 = 369. Then $(\frac{1}{p} + \frac{1}{q})^{- 2}$ is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q41.If $z^{2} + z + 1 = 0$ , $z \in C$ , then $n = 1 \sum 15 (z^{n} + (- 1)^{n} \frac{1}{z ^{n}})^{2}$ is equal to .
Mathematics · Complex Numbers · Numerical
Q42.Let $X = 000100010, Y = α I + β X + γ X^{2}$ and $$Z = {\alpha ^2}I - \alpha \beta X + ({\beta ^2} - \alpha \gamma…
Mathematics · Matrices and Determinants · Numerical
Q43.The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is .
Mathematics · Permutations and Combinations · Numerical
Q44.If a1 (> 0), a2, a3, a4, a5 are in a G.P., a2 + a4 = 2a3 + 1 and 3a2 + a3 = 2a4, then a2 + a4 + 2a5 is equal to .
Mathematics · Sequences and Series · Numerical
Q45.The integral $\frac{24}{π} \int_{0}^{2} \frac{( 2 - x ^{2} ) d x}{( 2 + x ^{2} ) 4 + x ^{4}}$ is equal to .
Mathematics · Definite Integration · Numerical
Q46.If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to .
Mathematics · Probability · Numerical