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Mathematics · 2022 · 28 Jun · Shift 2

28 questions from this JEE Main paper

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2022 · 28 Jun · Shift 2
Mathematics

Mathematics · 2022 · 28 Jun · Shift 2

28 questions from this JEE Main paper

Sets and Relations1 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations1 questions Binomial Theorem1 questions Sequences and Series2 questions Limits Continuity and Differentiability3 questions Definite Integration2 questions Area Under the Curves1 questions Differential Equations2 questions Straight Lines and Pair of Straight Lines1 questions Hyperbola1 questions Vector Algebra2 questions Parabola1 questions Probability1 questions Trigonometric Ratio and Identites1 questions 3D Geometry1 questions Statistics1 questions Circle1 questions Matrices and Determinants2 questions Complex Numbers1 questions Functions1 questions

Q22.Let R1 = {(a, b) $\in$ N $\times$ N : |a $-$ b| $\leq$ 13} and R2 = {(a, b) $\in$ N $\times$ N : |a $-$ b| $e$ 13}. Then on N :
Mathematics · Sets and Relations · MCQ
Q23.Let f(x) be a quadratic polynomial such that f( $-$ 2) + f(3) = 0. If one of the roots of f(x) = 0 is $-$ 1, then the sum of the roots of f(x) = 0 is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q24.The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives at least 4 and at most 7 candies, C3 receives at least 2 and at most 6 candies, is equal to :
Mathematics · Permutations and Combinations · MCQ
Q25.The term independent of x in the expansion of $(1 - x^{2} + 3 x^{3}) (\frac{5}{2} x^{3} - \frac{1}{5 x ^{2}})^{11}, x e 0$ is :
Mathematics · Binomial Theorem · MCQ
Q26.If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is :
Mathematics · Sequences and Series · MCQ
Q27.Let f, g : R $\to$ R be functions defined by $f (x) = {[x] ∣1 - x ∣,, x < 0 x \geq 0$ and $g (x) = {e^{x} - x (x - 1)^{2} - 1,, x < 0 x \geq 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q28.Let f : R $\to$ R be a differentiable function such that $f (\frac{π}{4}) = 2, f (\frac{π}{2}) = 0$ and $f^{'} (\frac{π}{2}) = 1$ and let $g (x) = \int_{x}^{π /4} (f^{'} (t) sec t + tan t sec t f (t)) d t$ …
Mathematics · Definite Integration · MCQ
Q29.Let f : R $\to$ R be a continuous function satisfying f(x) + f(x + k) = n, for all x $\in$ R where k > 0 and n is a positive integer. If $I_{1} = 0 \int 4 nk f (x) d x$ and $I_{2} = - k \int 3 k f (x) d x$ , then :
Mathematics · Definite Integration · MCQ
Q30.The area of the bounded region enclosed by the curve $y = 3 - x - \frac{1}{2} - ∣ x + 1∣$ and the x-axis is :
Mathematics · Area Under the Curves · MCQ
Q31.Let x = x(y) be the solution of the differential equation $2 y e^{x / y^{2}} d x + (y^{2} - 4 x e^{x / y^{2}}) d y = 0$ such that x(1) = 0. Then, x(e) is equal to :
Mathematics · Differential Equations · MCQ
Q32.Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 $tan x (cos x - y)$ . If the curve passes through the point $(\frac{π}{4}, 0)$ , then the value of $0 \int π /2 y d x$ is equal to :
Mathematics · Differential Equations · MCQ
Q33.Let a triangle be bounded by the lines L1 : 2x + 5y = 10; L2 : $-$ 4x + 3y = 12 and the line L3, which passes through the point P(2, 3), intersects L2 at A and L1 at B. If the point P divides the line-segment AB, internally in the ratio 1…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q34.Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ . Let e' and l' respectively be the eccentricity and length of…
Mathematics · Hyperbola · MCQ
Q35.Let $a = α i + 2 j - k$ and $b = - 2 i + α j + k$ , where $α \in R$ . If the area of the parallelogram whose adjacent sides are…
Mathematics · Vector Algebra · MCQ
Q36.If vertex of a parabola is (2, $-$ 1) and the equation of its directrix is 4x $-$ 3y = 21, then the length of its latus rectum is :
Mathematics · Parabola · MCQ
Q37.The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) $-$ f(c) = f(d) is :
Mathematics · Probability · MCQ
Q38.The value of $n \to \infty lim 6 tan {r = 1 \sum n tan^{- 1} (\frac{1}{r ^{2} + 3 r + 3})}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q39.Let $a$ be a vector which is perpendicular to the vector $3 i + \frac{1}{2} j + 2 k$ . If $a \times (2 i + k) = 2 i - 13 j - 4 k$ …
Mathematics · Vector Algebra · MCQ
Q40.If cot $α$ = 1 and sec $β$ = $- \frac{5}{3}$ , where $π < α < \frac{3 π}{2}$ and $\frac{π}{2} < β < π$ , then the value of $tan (α + β)$ and the quadrant in which $α$ + $β$ lies,…
Mathematics · Trigonometric Ratio and Identites · MCQ
Q41.Let the image of the point P(1, 2, 3) in the line $L : \frac{x - 6}{3} = \frac{y - 1}{2} = \frac{z - 2}{3}$ be Q. Let R ( $α$ , $β$ , $γ$ ) be a point that divides internally the line segment PQ in the ratio 1 : 3. Then the…
Mathematics · 3D Geometry · Numerical
Q42.Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of…
Mathematics · Statistics · Numerical
Q43.If one of the diameters of the circle $x^{2} + y^{2} - 22 x - 62 y + 14 = 0$ is a chord of the circle $(x - 22)^{2} + (y - 22)^{2} = r^{2}$ , then the value of r2 is equal to .
Mathematics · Circle · Numerical
Q44.If $x \to 1 lim \frac{s i n ( 3 x ^{2} - 4 x + 1 ) - x ^{2} + 1}{2 x ^{3} - 7 x ^{2} + a x + b} = - 2$ , then the value of (a $-$ b) is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical
Q45.Let for n = 1, 2, ......, 50, Sn be the sum of the infinite geometric progression whose first term is n2 and whose common ratio is $\frac{1}{( n + 1 ) ^{2}}$ . Then the value of $\frac{1}{26} + n = 1 \sum 50 (S_{n} + \frac{2}{n + 1} - n - 1)$ …
Mathematics · Sequences and Series · Numerical
Q46.If the system of linear equations $2 x - 3 y = γ + 5$ , $α x + 5 y = β + 1$ , where $α$ , $β$ , $γ \in$ R has infinitely many solutions then the value of | 9 $α$ + 3 $β$ + 5 $γ$ | is equal to …
Mathematics · Matrices and Determinants · Numerical
Q47.Let $A = (1 + i - i 10)$ where $i = - 1$ . Then, the number of elements in the set { n } $\in$ {1, 2, ......, 100} : An = A } is .
Mathematics · Matrices and Determinants · Numerical
Q48.Sum of squares of modulus of all the complex numbers z satisfying $\overline{z} = i z^{2} + z^{2} - z$ is equal to .
Mathematics · Complex Numbers · Numerical
Q49.Let S = {1, 2, 3, 4}. Then the number of elements in the set { f : S $\times$ S $\to$ S : f is onto and f (a, b) = f (b, a) $\geq$ a $\forall$ (a, b) $\in$ S $\times$ S } is .
Mathematics · Functions · Numerical