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Mathematics · 2022 · 27 Jun · Shift 1

22 questions from this JEE Main paper

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2022 · 27 Jun · Shift 1
Mathematics

Mathematics · 2022 · 27 Jun · Shift 1

22 questions from this JEE Main paper

Complex Numbers1 questions Matrices and Determinants1 questions Sequences and Series1 questions Limits Continuity and Differentiability1 questions Quadratic Equation and Inequalities2 questions Differentiation1 questions Indefinite Integrals1 questions Definite Integration1 questions Differential Equations1 questions Straight Lines and Pair of Straight Lines1 questions Ellipse1 questions 3D Geometry1 questions Vector Algebra1 questions Probability1 questions Trigonometric Ratio and Identites1 questions Inverse Trigonometric Functions1 questions Functions1 questions Permutations and Combinations1 questions Binomial Theorem1 questions Area Under the Curves1 questions Circle1 questions

Q20.The area of the polygon, whose vertices are the non-real roots of the equation $\overline{z} = i z^{2}$ is :
Mathematics · Complex Numbers · MCQ
Q21.Let the system of linear equations $x + 2 y + z = 2$ , $α x + 3 y - z = α$ , $- α x + y + 2 z = - α$ be inconsistent. Then $α$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q22. $x = n = 0 \sum \infty a^{n}, y = n = 0 \sum \infty b^{n}, z = n = 0 \sum \infty c^{n}$ , where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc $e$ 0, then :
Mathematics · Sequences and Series · MCQ
Q23.Let a be an integer such that $x \to 7 lim \frac{18 - [ 1 - x ]}{[ x - 3 a ]}$ exists, where [t] is greatest integer $\leq$ t. Then a is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q24.The number of distinct real roots of x4 $-$ 4x + 1 = 0 is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q25.If $cos^{- 1} (\frac{y}{2}) = lo g_{e} (\frac{x}{5})^{5}, ∣ y ∣ < 2$ , then :
Mathematics · Differentiation · MCQ
Q26.If $\int \frac{( x ^{2} + 1 ) e ^{x}}{( x + 1 ) ^{2}} d x = f (x) e^{x} + C$ , where C is a constant, then $\frac{d ^{3} f}{d x ^{3}}$ at x = 1 is equal to :
Mathematics · Indefinite Integrals · MCQ
Q27.The value of the integral $- 2 \int 2 \frac{∣ x ^{3} + x ∣}{( e ^{x ∣ x ∣} + 1 )} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q28.If $\frac{d y}{d x} + \frac{2 ^{x - y} ( 2 ^{y} - 1 )}{2 ^{x} - 1} = 0$ , x, y > 0, y(1) = 1, then y(2) is equal to :
Mathematics · Differential Equations · MCQ
Q29.In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4. Let the point B lie on the line x + 3y = 7. If ( $α$ , $β$ ) is the centroid of $Δ$ ABC, then 15( $α$ + $β$ ) is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q30.Let the eccentricity of an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ , $a > b$ , be $\frac{1}{4}$ . If this ellipse passes through the point $(- 4 \frac{2}{5}, 3)$ , then $a^{2} + b^{2}$ is…
Mathematics · Ellipse · MCQ
Q31.If two straight lines whose direction cosines are given by the relations $l + m - n = 0$ , $3 l^{2} + m^{2} + c n l = 0$ are parallel, then the positive value of c is :
Mathematics · 3D Geometry · MCQ
Q32.Let $a = i + j - k$ and $c = 2 i - 3 j + 2 k$ . Then the number of vectors $b$ such that $b \times c = a$ …
Mathematics · Vector Algebra · MCQ
Q33.Five numbers $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ are randomly selected from the numbers 1, 2, 3, ......., 18 and are arranged in the increasing order $(x_{1} < x_{2} < x_{3} < x_{4} < x_{5})$ . The probability that $x_{2} = 7$ and $x_{4} = 11$ …
Mathematics · Probability · MCQ
Q34.The value of $cos (\frac{2 π}{7}) + cos (\frac{4 π}{7}) + cos (\frac{6 π}{7})$ is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q35. $sin^{1} (sin \frac{2 π}{3}) + cos^{- 1} (cos \frac{7 π}{6}) + tan^{- 1} (tan \frac{3 π}{4})$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.Let f : R $\to$ R be a function defined by $f (x) = \frac{2 e ^{2 x}}{e ^{2 x} + e}$ . Then $f (\frac{1}{100}) + f (\frac{2}{100}) + f (\frac{3}{100}) + ..... + f (\frac{99}{100})$ …
Mathematics · Functions · Numerical
Q37.If the sum of all the roots of the equation $e^{2 x} - 11 e^{x} - 45 e^{- x} + \frac{81}{2} = 0$ is $lo g_{e} p$ , then p is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q38.The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is .
Mathematics · Permutations and Combinations · Numerical
Q39.If the coefficient of x10 in the binomial expansion of $(\frac{x}{5 ^{\frac{1}{4}}} + \frac{5}{x ^{\frac{1}{3}}})^{60}$ is $5^{k} . l$ , where l, k $\in$ N and l is co-prime to 5, then k is equal…
Mathematics · Binomial Theorem · Numerical
Q40.Let $A_{1} = {(x, y) : ∣ x ∣ \leq y^{2}, ∣ x ∣ + 2 y \leq 8}$ and $A_{2} = {(x, y) : ∣ x ∣ + ∣ y ∣ \leq k}$ . If 27 (Area A1) = 5 (Area A2), then k is equal to :
Mathematics · Area Under the Curves · Numerical
Q41.A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x $-$ y + 4 = 0, then the area of R is .
Mathematics · Circle · Numerical