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Mathematics · 2021 · 22 Jul · Shift 2

23 questions from this JEE Main paper

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2021 · 22 Jul · Shift 2
Mathematics

Mathematics · 2021 · 22 Jul · Shift 2

23 questions from this JEE Main paper

Sequences and Series2 questions Application of Derivatives1 questions Differential Equations2 questions Probability1 questions Definite Integration1 questions Matrices and Determinants3 questions 3D Geometry1 questions Quadratic Equation and Inequalities1 questions Circle1 questions Complex Numbers1 questions Inverse Trigonometric Functions1 questions Limits Continuity and Differentiability2 questions Ellipse1 questions Functions1 questions Permutations and Combinations1 questions Statistics1 questions Area Under the Curves1 questions Binomial Theorem1 questions

Q24.Let Sn denote the sum of first n-terms of an arithmetic progression. If S10 = 530, S5 = 140, then S20 $-$ S6 is equal to:
Mathematics · Sequences and Series · MCQ
Q25.Let f : R $\to$ R be defined as $f (x) = {- \frac{4}{3} x^{3} + 2 x^{2} + 3 x, 3 x e^{x}, x > 0 x \leq 0$ . Then f is increasing function in the interval
Mathematics · Application of Derivatives · MCQ
Q26.Let y = y(x) be the solution of the differential equation $cos e c^{2} x d y + 2 d x = (1 + y cos 2 x) cos e c^{2} x d x$ , with $y (\frac{π}{4}) = 0$ . Then, the value of $(y (0) + 1)^{2}$ is equal to :
Mathematics · Differential Equations · MCQ
Q27.Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 $\times$ 2 matrices. The probability that such formed matrix have all different entries and are non-singular, is :
Mathematics · Probability · MCQ
Q28.If $0 \int 100 π \frac{s i n ^{2} x}{e ^{(\frac{x}{π} - [\frac{x}{π}])}} d x = \frac{α π ^{3}}{1 + 4 π ^{2}}, α \in R$ where [x] is the greatest integer less than or…
Mathematics · Definite Integration · MCQ
Q29.The values of $λ$ and $μ$ such that the system of equations $x + y + z = 6$ , $3 x + 5 y + 5 z = 26$ , $x + 2 y + λ z = μ$ has no solution, are :
Mathematics · Matrices and Determinants · MCQ
Q30.If the shortest distance between the straight lines $3 (x - 1) = 6 (y - 2) = 2 (z - 1)$ and $4 (x - 2) = 2 (y - λ) = (z - 3), λ \in R$ is $\frac{1}{38}$ , then the integral value of $λ$ is equal to :
Mathematics · 3D Geometry · MCQ
Q31.Let A = [aij] be a real matrix of order 3 $\times$ 3, such that ai1 + ai2 + ai3 = 1, for i = 1, 2, 3. Then, the sum of all the entries of the matrix A3 is equal to :
Mathematics · Matrices and Determinants · MCQ
Q32.Let [x] denote the greatest integer less than or equal to x. Then, the values of x $\in$ R satisfying the equation $[e^{x}]^{2} + [e^{x} + 1] - 3 = 0$ lie in the interval :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q33.Let the circle S : 36x2 + 36y2 $-$ 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x $-$ 2y = 4 and 2x $-$ y = 5 lies inside the circle S, then :
Mathematics · Circle · MCQ
Q34.Let n denote the number of solutions of the equation z2 + 3 $\overline{z}$ = 0, where z is a complex number. Then the value of $k = 0 \sum \infty \frac{1}{n ^{k}}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q35.If the domain of the function $f (x) = \frac{c o s ^{- 1} x ^{2} - x + 1}{s i n ^{- 1} ( \frac{2 x - 1}{2} )}$ is the interval ( $α$ , $β$ ], then $α$ + $β$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.Let f : R $\to$ R be defined as $f (x) = {\frac{x ^{3}}{( 1 - c o s 2 x ) ^{2}} lo g_{e} (\frac{1 + 2 x e ^{- 2 x}}{( 1 - x e ^{- x} ) ^{2}}), α, x e 0 x = 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.Let $E_{1} : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > b$ . Let E2 be another ellipse such that it touches the end points of major axis of E1 and the foci of E2 are the end points of minor axis of E1. If E1 and E2 have…
Mathematics · Ellipse · MCQ
Q38.Let A = {0, 1, 2, 3, 4, 5, 6, 7}. Then the number of bijective functions f : A $\to$ A such that f(1) + f(2) = 3 $-$ f(3) is equal to
Mathematics · Functions · Numerical
Q39.If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to .
Mathematics · Permutations and Combinations · Numerical
Q40.Let $A = 010100001$ . Then the number of 3 $\times$ 3 matrices B with entries from the set {1, 2, 3, 4, 5} and satisfying AB = BA is …
Mathematics · Matrices and Determinants · Numerical
Q41.Consider the following frequency distribution : If mean = $\frac{309}{22}$ and median = 14, then the value (a $-$ b)2 is equal to . Includes table
Mathematics · Statistics · Numerical
Q42.The sum of all the elements in the set {n $\in$ {1, 2, ....., 100} | H.C.F. of n and 2040 is 1} is equal to .
Mathematics · Sequences and Series · Numerical
Q43.The area (in sq. units) of the region bounded by the curves x2 + 2y $-$ 1 = 0, y2 + 4x $-$ 4 = 0 and y2 $-$ 4x $-$ 4 = 0, in the upper half plane is .
Mathematics · Area Under the Curves · Numerical
Q44.Let f : R $\to$ R be a function defined as $f (x) = {3 (1 - \frac{∣ x ∣}{2}) 0 i f i f ∣ x ∣ \leq 2 ∣ x ∣ > 2$ Let g : R $\to$ R be given…
Mathematics · Limits Continuity and Differentiability · Numerical
Q45.If the constant term, in binomial expansion of $(2 x^{r} + \frac{1}{x ^{2}})^{10}$ is 180, then r is equal to .
Mathematics · Binomial Theorem · Numerical
Q46.Let y = y(x) be the solution of the differential equation $((x + 2) e^{(\frac{y + 1}{x + 2})} + (y + 1)) d x = (x + 2) d y$ , y(1) = 1. If the domain of y = y(x) is an open interval ( $α$ , $β$ ), then…
Mathematics · Differential Equations · Numerical