New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Mathematics · 2021 · 1 Sep · Shift 2

23 questions from this JEE Main paper

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Papers
2021 · 1 Sep · Shift 2
Mathematics

Mathematics · 2021 · 1 Sep · Shift 2

23 questions from this JEE Main paper

Definite Integration3 questions Inverse Trigonometric Functions1 questions Matrices and Determinants1 questions Probability2 questions Differential Equations1 questions Application of Derivatives1 questions Area Under the Curves1 questions 3D Geometry1 questions Quadratic Equation and Inequalities2 questions Permutations and Combinations2 questions Functions1 questions Sequences and Series1 questions Limits Continuity and Differentiability2 questions Complex Numbers1 questions Straight Lines and Pair of Straight Lines2 questions Vector Algebra1 questions

Q24.Let f : R $\to$ R be a continuous function. Then $x \to \frac{π}{4} lim \frac{\frac{π}{4} 2 \int s e c ^{2} x f ( x ) d x}{x ^{2} - \frac{π ^{2}}{16}}$ is equal to :
Mathematics · Definite Integration · MCQ
Q25. $cos^{- 1} (cos (- 5)) + sin^{- 1} (sin (6)) - tan^{- 1} (tan (12))$ is equal to : (The inverse trigonometric functions take the principal values)
Mathematics · Inverse Trigonometric Functions · MCQ
Q26.Consider the system of linear equations $-$ x + y + 2z = 0 3x $-$ ay + 5z = 1 2x $-$ 2y $-$ az = 7 Let S1 be the set of all a $\in$ R for which the system is inconsistent and S2 be the set of all a $\in$ R for which the system has…
Mathematics · Matrices and Determinants · MCQ
Q27.Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is : Includes diagram
Mathematics · Probability · MCQ
Q28.If y = y(x) is the solution curve of the differential equation $x^{2} d y + (y - \frac{1}{x}) d x = 0$ ; x > 0 and y(1) = 1, then $y (\frac{1}{2})$ is equal to :
Mathematics · Differential Equations · MCQ
Q29.The function $f (x) = x^{3} - 6 x^{2} + a x + b$ is such that $f (2) = f (4) = 0$ . Consider two statements : Statement 1 : there exists x1, x2 $\in$ (2, 4), x1 < x2, such that f'(x1) = $-$ 1 and f'(x2) = 0. Statement 2 : there exists x3, x4 $\in$ …
Mathematics · Application of Derivatives · MCQ
Q30.Let $J_{n, m} = 0 \int \frac{1}{2} \frac{x ^{n}}{x ^{m} - 1} d x$ , $\forall$ n > m and n, m $\in$ N. Consider a matrix $A = [a_{ij}]_{3 \times 3}$ where $a_{ij} = {j_{6 + i, 3} - j_{i + 3, 3}, 0, i \leq j i > j$ …
Mathematics · Definite Integration · MCQ
Q31.The area, enclosed by the curves $y = sin x + cos x$ and $y = ∣ cos x - sin x ∣$ and the lines $x = 0, x = \frac{π}{2}$ , is :
Mathematics · Area Under the Curves · MCQ
Q32.The distance of line $3 y - 2 z - 1 = 0 = 3 x - z + 4$ from the point (2, $-$ 1, 6) is :
Mathematics · 3D Geometry · MCQ
Q33.The numbers of pairs (a, b) of real numbers, such that whenever $α$ is a root of the equation x2 + ax + b = 0, $α$ 2 $-$ 2 is also a root of this equation, is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.Let P1, P2, ......, P15 be 15 points on a circle. The number of distinct triangles formed by points Pi, Pj, Pk such that i +j + k $e$ 15, is :
Mathematics · Permutations and Combinations · MCQ
Q35.The range of the function, $f (x) = lo g_{5} (3 + cos (\frac{3 π}{4} + x) + cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) - cos (\frac{3 π}{4} - x))$ …
Mathematics · Functions · MCQ
Q36.Let a1, a2, ..........., a21 be an AP such that $n = 1 \sum 20 \frac{1}{a _{n} a _{n + 1}} = \frac{4}{9}$ . If the sum of this AP is 189, then a6a16 is equal to :
Mathematics · Sequences and Series · MCQ
Q37.The function f(x), that satisfies the condition $f (x) = x + 0 \int π /2 sin x . cos y f (y) d y$ , is :
Mathematics · Definite Integration · MCQ
Q38.Let X be a random variable with distribution. If the mean of X is 2.3 and variance of X is $σ$ 2, then 100 $σ$ 2 is equal to : Includes table
Mathematics · Probability · Numerical
Q39.Let $f (x) = x^{6} + 2 x^{4} + x^{3} + 2 x + 3$ , x $\in$ R. Then the natural number n for which $x \to 1 lim \frac{x ^{n} f ( 1 ) - f ( x )}{x - 1} = 44$ is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q40.If for the complex numbers z satisfying | z $-$ 2 $-$ 2i | $\leq$ 1, the maximum value of | 3iz + 6 | is attained at a + ib, then a + b is equal to .
Mathematics · Complex Numbers · Numerical
Q41.Let the points of intersections of the lines x $-$ y + 1 = 0, x $-$ 2y + 3 = 0 and 2x $-$ 5y + 11 = 0 are the mid points of the sides of a triangle $Δ$ ABC. Then, the area of the $Δ$ ABC is .
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q42.Let f(x) be a polynomial of degree 3 such that $f (k) = - \frac{2}{k}$ for k = 2, 3, 4, 5. Then the value of 52 $-$ 10f(10) is equal to :
Mathematics · Quadratic Equation and Inequalities · Numerical
Q43.All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial…
Mathematics · Permutations and Combinations · Numerical
Q44.Let $a = 2 i - j + 2 k$ and $b = i + 2 j - k$ . Let a vector $v$ be in the plane containing $a$ and $b$ .…
Mathematics · Vector Algebra · Numerical
Q45.Let [t] denote the greatest integer $\leq$ t. The number of points where the function $f (x) = [x] x^{2} - 1 + sin (\frac{π}{[ x ] + 3}) - [x + 1], x \in (- 2, 2)$ is not continuous is …
Mathematics · Limits Continuity and Differentiability · Numerical
Q46.A man starts walking from the point P( $-$ 3, 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $50 ((P R)^{2} + (R Q)^{2})$ …
Mathematics · Straight Lines and Pair of Straight Lines · Numerical