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Mathematics · 2021 · 24 Feb · Shift 1

22 questions from this JEE Main paper

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2021 · 24 Feb · Shift 1
Mathematics

Mathematics · 2021 · 24 Feb · Shift 1

22 questions from this JEE Main paper

Indefinite Integrals1 questions Limits Continuity and Differentiability2 questions Differential Equations1 questions Functions1 questions Application of Derivatives2 questions Definite Integration2 questions Permutations and Combinations1 questions Straight Lines and Pair of Straight Lines1 questions Quadratic Equation and Inequalities1 questions Area Under the Curves1 questions Trigonometric Ratio and Identites1 questions Parabola1 questions Matrices and Determinants3 questions Complex Numbers1 questions Sets and Relations1 questions Circle1 questions Probability1 questions

Q23.If $\int \frac{c o s x - s i n x}{8 - s i n 2 x} d x = a sin^{- 1} (\frac{s i n x + c o s x}{b}) + c$ , where c is a constant of integration, then the ordered pair (a, b) is equal to :
Mathematics · Indefinite Integrals · MCQ
Q24.If f : R $\to$ R is a function defined by f(x)= [x - 1] $cos (\frac{2 x - 1}{2}) π$ , where [.] denotes the greatest integer function, then f is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q25.The population P = P(t) at time 't' of a certain species follows the differential equation $\frac{d P}{d t}$ = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is :
Mathematics · Differential Equations · MCQ
Q26.Let f : R → R be defined as f (x) = 2x – 1 and g : R - {1} → R be defined as g(x) = $\frac{x - \frac{1}{2}}{x - 1}$ . Then the composition function f(g(x)) is :
Mathematics · Functions · MCQ
Q27.The function f(x) = $\frac{4 x ^{3} - 3 x ^{2}}{6} - 2 sin x + (2 x - 1) cos x$ :
Mathematics · Application of Derivatives · MCQ
Q28. $x \to 0 lim \frac{0 \int x ^{2} ( s i n t ) d t}{x ^{3}}$ is equal to :
Mathematics · Definite Integration · MCQ
Q29.A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is :
Mathematics · Permutations and Combinations · MCQ
Q30.A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $\frac{1}{4}$ . Three stones A, B and C are placed at the points (1, 1), (2, 2) and (4, 4) respectively.…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.Let p and q be two positive numbers such that p + q = 2 and p4+q4 = 272. Then p and q are roots of the equation :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q32.The area (in sq. units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is :
Mathematics · Area Under the Curves · MCQ
Q33.If $e^{(c o s^{2} x + c o s^{4} x + c o s^{6} x + ...\infty) l o g_{e} 2}$ satisfies the equation t2 - 9t + 8 = 0, then the value of $\frac{2 s i n x}{s i n x + 3 c o s x} (0 < x < \frac{π}{2})$ …
Mathematics · Trigonometric Ratio and Identites · MCQ
Q34.The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a moving point of the parabola, is another parabola whose directrix is :
Mathematics · Parabola · MCQ
Q35.The system of linear equations 3x - 2y - kz = 10 2x - 4y - 2z = 6 x+2y - z = 5m is inconsistent if :
Mathematics · Matrices and Determinants · MCQ
Q36.Let P = $323 - 1 0 - 5 - 2 α 0$ , where $α \in$ R. Suppose Q = [ qij] is a matrix satisfying PQ = kl3 for some non-zero k…
Mathematics · Matrices and Determinants · Numerical
Q37.The minimum value of $α$ for which the equation $\frac{4}{s i n x} + \frac{1}{1 - s i n x} = α$ has at least one solution in $(0, \frac{π}{2})$ is .......
Mathematics · Application of Derivatives · Numerical
Q38.If the least and the largest real values of a, for which the equation z + $α$ |z – 1| + 2i = 0 (z $\in$ C and i = $- 1$ ) has a solution, are p and q respectively; then 4(p2 + q2) is equal to .
Mathematics · Complex Numbers · Numerical
Q39. $n \to \infty lim tan {r = 1 \sum n tan^{- 1} (\frac{1}{1 + r + r ^{2}})}$ is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical
Q40.Let A = {n $\in$ N: n is a 3-digit number} B = {9k + 2: k $\in$ N} and C = {9k + $l$ : k $\in$ N} for some $l (0 < l < 9)$ If the sum of all the elements of the set A $\cap$ (B $\cup$ C) is 274 $\times$ 400, then $l$ is equal to …
Mathematics · Sets and Relations · Numerical
Q41.If one of the diameters of the circle x2 + y2 - 2x - 6y + 6 = 0 is a chord of another circle 'C', whose center is at (2, 1), then its radius is .
Mathematics · Circle · Numerical
Q42.If $- a \int a (∣ x ∣ + ∣ x - 2 ∣) d x = 22$ , (a > 2) and [x] denotes the greatest integer $\leq$ x, then $- a \int a (x + [x]) d x$ is equal to…
Mathematics · Definite Integration · Numerical
Q43.Let M be any 3 $\times$ 3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of MTM is seven, is .
Mathematics · Matrices and Determinants · Numerical
Q44.Let Bi (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is $α$ , only B2 occurs is $β$ and only B3 occurs is $γ$ . Let p be the probability that none of the events Bi occurs and…
Mathematics · Probability · Numerical