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Mathematics · 2021 · 18 Mar · Shift 1

22 questions from this JEE Main paper

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2021 · 18 Mar · Shift 1
Mathematics

Mathematics · 2021 · 18 Mar · Shift 1

22 questions from this JEE Main paper

Straight Lines and Pair of Straight Lines3 questions Matrices and Determinants3 questions Indefinite Integrals2 questions Limits Continuity and Differentiability2 questions Vector Algebra1 questions Complex Numbers2 questions Circle1 questions Functions2 questions Permutations and Combinations3 questions Quadratic Equation and Inequalities1 questions Definite Integration1 questions Statistics1 questions

Q25.The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q26.The solutions of the equation $1 + sin^{2} x cos^{2} x 4 sin 2 x sin^{2} x 1 + cos^{2} x 4 sin 2 x sin^{2} x cos^{2} x 1 + 4 sin 2 x = 0, (0 < x < π)$ …
Mathematics · Matrices and Determinants · MCQ
Q27.Let $α$ , $β$ , $γ$ be the real roots of the equation, x3 + ax2 + bx + c = 0, (a, b, c $\in$ R and a, b $e$ 0). If the system of equations (in u, v, w) given by $α$ u + $β$ v + $γ$ w = 0, $β$ u + $γ$ v + $α$ …
Mathematics · Matrices and Determinants · MCQ
Q28.The integral $\int \frac{( 2 x - 1 ) c o s ( 2 x - 1 ) ^{2} + 5}{4 x ^{2} - 4 x + 6} d x$ is equal to (where c is a constant of integration)
Mathematics · Indefinite Integrals · MCQ
Q29.The equation of one of the straight lines which passes through the point (1, 3) and makes an angles $tan^{- 1} (2)$ with the straight line, y + 1 = 3 $2$ x is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q30.If $x \to 0 lim \frac{s i n ^{- 1} x - t a n ^{- 1} x}{3 x ^{3}}$ is equal to L, then the value of (6L + 1) is
Mathematics · Limits Continuity and Differentiability · MCQ
Q31.A vector $a$ has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, $a$ …
Mathematics · Vector Algebra · MCQ
Q32.If the equation $a ∣ z ∣^{2} + \overline{\overline{α} z + α \overline{z}} + d = 0$ represents a circle where a, d are real constants then which of the following condition is correct?
Mathematics · Complex Numbers · MCQ
Q33.For the four circles M, N, O and P, following four equations are given : Circle M : x2 + y2 = 1 Circle N : x2 + y2 $-$ 2x = 0 Circle O : x2 + y2 $-$ 2x $-$ 2y + 1 = 0 Circle P : x2 + y2 $-$ 2y = 0 If the centre of circle M is joined with…
Mathematics · Circle · MCQ
Q34.The real valued function $f (x) = \frac{c o s e c ^{- 1} x}{x - [ x ]}$ , where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :
Mathematics · Functions · MCQ
Q35.If the functions are defined as $f (x) = x$ and $g (x) = 1 - x$ , then what is the common domain of the following functions : f + g, f $-$ g, f/g, g/f, g $-$ f where $(f \pm g) (x) = f (x) \pm g (x), (f / g) x = \frac{f ( x )}{g ( x )}$
Mathematics · Functions · MCQ
Q36.If $f (x) = {\frac{1}{∣ x ∣} a x^{2} + b; ∣ x ∣ \geq 1; ∣ x ∣ < 1$ is differentiable at every point of the domain, then the values of a and b are respectively :
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.Let $A + 2 B = 16 - 5 2 - 3 3 031$ and $2 A - B = 220 - 1 - 1 1 562$ …
Mathematics · Matrices and Determinants · MCQ
Q38.The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :
Mathematics · Permutations and Combinations · MCQ
Q39.The value of $3 + \frac{1}{4 + \frac{1}{3 + \frac{1}{4 + \frac{1}{3 + ....\infty}}}}$ is equal to
Mathematics · Quadratic Equation and Inequalities · MCQ
Q40.The number of times the digit 3 will be written when listing the integers from 1 to 1000 is :
Mathematics · Permutations and Combinations · Numerical
Q41.Let f(x) and g(x) be two functions satisfying f(x2) + g(4 $-$ x) = 4x3 and g(4 $-$ x) + g(x) = 0, then the value of $- 4 \int 4 f (x)^{2} d x$ is
Mathematics · Definite Integration · Numerical
Q42.The missing value in the following figure is Includes diagram
Mathematics · Permutations and Combinations · Numerical
Q43.Let z1, z2 be the roots of the equation z2 + az + 12 = 0 and z1, z2 form an equilateral triangle with origin. Then, the value of |a| is :
Mathematics · Complex Numbers · Numerical
Q44.The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly…
Mathematics · Statistics · Numerical
Q45.If $f (x) = \int \frac{5 x ^{8} + 7 x ^{6}}{( x ^{2} + 1 + 2 x ^{7} ) ^{2}} d x, (x \geq 0), f (0) = 0$ and $f (1) = \frac{1}{K}$ , then the value of K is
Mathematics · Indefinite Integrals · Numerical
Q46.A square ABCD has all its vertices on the curve x2y2 = 1. The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is .
Mathematics · Straight Lines and Pair of Straight Lines · Numerical