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 · 25 Feb · Shift 1

22 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 · 25 Feb · Shift 1
Mathematics

Mathematics · 2021 · 25 Feb · Shift 1

22 questions from this JEE Main paper

Probability2 questions 3D Geometry2 questions Definite Integration1 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations2 questions Differential Equations1 questions Functions1 questions Complex Numbers1 questions Limits Continuity and Differentiability2 questions Indefinite Integrals1 questions Straight Lines and Pair of Straight Lines1 questions Hyperbola1 questions Area Under the Curves1 questions Matrices and Determinants2 questions Sequences and Series1 questions Vector Algebra1 questions Application of Derivatives1 questions

Q24.When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$ . If three missiles are fired…
Mathematics · Probability · MCQ
Q25.The equation of the line through the point (0, 1, 2) and perpendicular to the line $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{- 2}$ is :
Mathematics · 3D Geometry · MCQ
Q26.The value of $- 1 \int 1 x^{2} e^{[x^{3}]} d x$ , where [ t ] denotes the greatest integer $\leq$ t, is :
Mathematics · Definite Integration · MCQ
Q27.The integer 'k', for which the inequality x2 $-$ 2(3k $-$ 1)x + 8k2 $-$ 7 > 0 is valid for every x in R, is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q28.The total number of positive integral solutions (x, y, z) such that xyz = 24 is :
Mathematics · Permutations and Combinations · MCQ
Q29.If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is $\frac{x ^{2} - 4 x + y + 8}{x - 2}$ , then this curve also passes through the point :
Mathematics · Differential Equations · MCQ
Q30.Let f, g : N $\to$ N such that f(n + 1) = f(n) + f(1) $\forall$ n $\in$ N and g be any arbitrary function. Which of the following statements is NOT true?
Mathematics · Functions · MCQ
Q31.Let the lines (2 $-$ i)z = (2 + i) $\overline{z}$ and (2 $+$ i)z + (i $-$ 2) $\overline{z} -$ 4i = 0, (here i2 = $-$ 1) be normal to a circle C. If the line iz + $\overline{z}$ + 1 + i = 0 is tangent to this circle C, then its radius is :
Mathematics · Complex Numbers · MCQ
Q32. $n \to \infty lim (1 + \frac{1 + \frac{1}{2} + ........ + \frac{1}{n}}{n ^{2}})^{n}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q33.Let $α$ be the angle between the lines whose direction cosines satisfy the equations l + m $-$ n = 0 and l2 + m2 $-$ n2 = 0. Then the value of sin4 $α$ + cos4 $α$ is :
Mathematics · 3D Geometry · MCQ
Q34.The value of the integral $\int \frac{s i n θ . s i n 2 θ ( s i n ^{6} θ + s i n ^{4} θ + s i n ^{2} θ ) 2 s i n ^{4} θ + 3 s i n ^{2} θ + 6}{1 - c o s 2 θ} d θ$ is :
Mathematics · Indefinite Integrals · MCQ
Q35.The coefficients a, b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :
Mathematics · Probability · MCQ
Q36.The image of the point (3, 5) in the line x $-$ y + 1 = 0, lies on :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q37.The locus of the point of intersection of the lines $(3) k x + k y - 43 = 0$ and $3 x - y - 4 (3) k = 0$ is a conic, whose eccentricity is .
Mathematics · Hyperbola · Numerical
Q38.The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A4 is equal to .
Mathematics · Area Under the Curves · Numerical
Q39.The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is .
Mathematics · Permutations and Combinations · Numerical
Q40.If $A = [0 tan (\frac{θ}{2}) - tan (\frac{θ}{2}) 0]$ and $(I_{2} + A) (I_{2} - A)^{- 1} = [a b - b a]$ …
Mathematics · Matrices and Determinants · Numerical
Q41.Let A1, A2, A3, ....... be squares such that for each n $\geq$ 1, the length of the side of An equals the length of diagonal of An+1. If the length of A1 is 12 cm, then the smallest value of n for which area of An is less than one, is …
Mathematics · Sequences and Series · Numerical
Q42.If the system of equations kx + y + 2z = 1 3x $-$ y $-$ 2z = 2 $-$ 2x $-$ 2y $-$ 4z = 3 has infinitely many solutions, then k is equal to .
Mathematics · Matrices and Determinants · Numerical
Q43.The number of points, at which the function f(x) = | 2x + 1 | $-$ 3| x + 2 | + | x2 + x $-$ 2 |, x $\in$ R is not differentiable, is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q44.Let $a = i + 2 j - k$ , $b = i - j$ and $c = i - j - k$ be three given vectors. If $r$ is a vector…
Mathematics · Vector Algebra · Numerical
Q45.Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x6 is unity and it has extrema at x = $-$ 1 and x = 1. If $x \to 0 lim \frac{f ( x )}{x ^{3}} = 1$ , then $5. f (2)$ is equal to …
Mathematics · Application of Derivatives · Numerical