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Mathematics · 2021 · 27 Aug · Shift 1

18 questions from this JEE Main paper

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2021 · 27 Aug · Shift 1
Mathematics

Mathematics · 2021 · 27 Aug · Shift 1

18 questions from this JEE Main paper

Straight Lines and Pair of Straight Lines1 questions Inverse Trigonometric Functions1 questions Matrices and Determinants2 questions Complex Numbers1 questions Differential Equations2 questions Limits Continuity and Differentiability1 questions Probability1 questions Ellipse1 questions Definite Integration1 questions Application of Derivatives2 questions Vector Algebra1 questions Sets and Relations1 questions Indefinite Integrals1 questions Statistics1 questions Permutations and Combinations1 questions

Q23.Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q24.If $(sin^{- 1} x)^{2} - (cos^{- 1} x)^{2} = a$ ; 0 < x < 1, a $e$ 0, then the value of 2x2 $-$ 1 is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q25.If the matrix $A = (0 K 2 - 1)$ satisfies $A (A^{3} + 3 I) = 2 I$ , then the value of K is :
Mathematics · Matrices and Determinants · MCQ
Q26.If $S = {z \in C : \frac{z - i}{z + 2 i} \in R}$ , then :
Mathematics · Complex Numbers · MCQ
Q27.Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} = 2 (y + 2 sin x - 5) x - 2 cos x$ such that y(0) = 7. Then y( $π$ ) is equal to :
Mathematics · Differential Equations · MCQ
Q28.Let us consider a curve, y = f(x) passing through the point ( $-$ 2, 2) and the slope of the tangent to the curve at any point (x, f(x)) is given by f(x) + xf'(x) = x2. Then :
Mathematics · Differential Equations · MCQ
Q29.If $α$ , $β$ are the distinct roots of x2 + bx + c = 0, then $x \to β lim \frac{e ^{2 (x^{2} + b x + c)} - 1 - 2 ( x ^{2} + b x + c )}{( x - β ) ^{2}}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.When a certain biased die is rolled, a particular face occurs with probability $\frac{1}{6} - x$ and its opposite face occurs with probability $\frac{1}{6} + x$ . All other faces occur with probability $\frac{1}{6}$ . Note that opposite…
Mathematics · Probability · MCQ
Q31.If x2 + 9y2 $-$ 4x + 3 = 0, x, y $\in$ R, then x and y respectively lie in the intervals :
Mathematics · Ellipse · MCQ
Q32. $6 \int 16 \frac{l o g _{e} x ^{2}}{l o g _{e} x ^{2} + l o g _{e} ( x ^{2} - 44 x + 484 )} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q33.A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the…
Mathematics · Application of Derivatives · MCQ
Q34.Let $a = i + 5 j + α k$ , $b = i + 3 j + β k$ and $c = - i + 2 j - 3 k$ be three vectors such that, $b \times c = 53$ …
Mathematics · Vector Algebra · Numerical
Q35.The number of distinct real roots of the equation 3x4 + 4x3 $-$ 12x2 + 4 = 0 is .
Mathematics · Application of Derivatives · Numerical
Q36.If A = {x $\in$ R : |x $-$ 2| > 1}, B = {x $\in$ R : $x^{2} - 3$ > 1}, C = {x $\in$ R : |x $-$ 4| $\geq$ 2} and Z is the set of all integers, then the number of subsets of the set (A $\cap$ B $\cap$ C)c $\cap$ Z is …
Mathematics · Sets and Relations · Numerical
Q37.If $\int \frac{d x}{( x ^{2} + x + 1 ) ^{2}} = a tan^{- 1} (\frac{2 x + 1}{3}) + b (\frac{2 x + 1}{x ^{2} + x + 1}) + C$ , x > 0 where C is the constant of integration, then the value of…
Mathematics · Indefinite Integrals · Numerical
Q38.If the system of linear equations 2x + y $-$ z = 3 x $-$ y $-$ z = $α$ 3x + 3y + $β$ z = 3 has infinitely many solution, then $α$ + $β - α β$ is equal to .
Mathematics · Matrices and Determinants · Numerical
Q39.Let n be an odd natural number such that the variance of 1, 2, 3, 4, ......, n is 14. Then n is equal to .
Mathematics · Statistics · Numerical
Q40.A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is .
Mathematics · Permutations and Combinations · Numerical