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Mathematics · 2021 · 16 Mar · Shift 2

22 questions from this JEE Main paper

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2021 · 16 Mar · Shift 2
Mathematics

Mathematics · 2021 · 16 Mar · Shift 2

22 questions from this JEE Main paper

Differential Equations2 questions Application of Derivatives2 questions Vector Algebra1 questions 3D Geometry1 questions Permutations and Combinations1 questions Limits Continuity and Differentiability3 questions Definite Integration2 questions Sets and Relations1 questions Complex Numbers1 questions Inverse Trigonometric Functions1 questions Circle1 questions Straight Lines and Pair of Straight Lines1 questions Probability1 questions Sequences and Series1 questions Indefinite Integrals1 questions Statistics1 questions Matrices and Determinants1 questions

Q24.If y = y(x) is the solution of the differential equation $\frac{d y}{d x}$ + (tan x) y = sin x, $0 \leq x \leq \frac{π}{3}$ , with y(0) = 0, then $y (\frac{π}{4})$ equal to :
Mathematics · Differential Equations · MCQ
Q25.Let f be a real valued function, defined on R $-$ { $-$ 1, 1} and given by f(x) = 3 loge $\frac{x - 1}{x + 1} - \frac{2}{x - 1}$ . Then in which of the following intervals, function f(x) is increasing?
Mathematics · Application of Derivatives · MCQ
Q26.Let $a$ = $i$ + 2 $j -$ 3 $k$ and $b = 2 i -$ 3 $j$ + 5 $k$ . If $r \times a$ = $b \times r$ , $r$ …
Mathematics · Vector Algebra · MCQ
Q27.If the foot of the perpendicular from point (4, 3, 8) on the line $L_{1} : \frac{x - a}{l} = \frac{y - 2}{3} = \frac{z - b}{4}$ , l $e$ 0 is (3, 5, 7), then the shortest distance between the line L1 and line $L_{2} : \frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}$ …
Mathematics · 3D Geometry · MCQ
Q28.Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let $α$ be the number of triangles having these points from different sides as vertices and $β$ be the number of…
Mathematics · Permutations and Combinations · MCQ
Q29.Let f : S $\to$ S where S = (0, $\infty$ ) be a twice differentiable function such that f(x + 1) = xf(x). If g : S $\to$ R be defined as g(x) = loge f(x), then the value of |g''(5) $-$ g''(1)| is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.Consider the integral $I = \int_{0}^{10} \frac{[ x ] e ^{[x]}}{e ^{x - 1}} d x$ , where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :
Mathematics · Definite Integration · MCQ
Q31.Let C1 be the curve obtained by the solution of differential equation $2 x y \frac{d y}{d x} = y^{2} - x^{2}, x > 0$ . Let the curve C2 be the solution of $\frac{2 x y}{x ^{2} - y ^{2}} = \frac{d y}{d x}$ . If both the curves pass through…
Mathematics · Differential Equations · MCQ
Q32.Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that $\int_{0}^{1} P (x) d x$ = 1 and P(x) leaves remainder 5 when it is divided by (x $-$ 2). Then the value of 9(b + c) is equal to :
Mathematics · Definite Integration · MCQ
Q33.Let A = {2, 3, 4, 5, ....., 30} and ' $≃$ ' be an equivalence relation on A $\times$ A, defined by (a, b) $≃$ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered…
Mathematics · Sets and Relations · MCQ
Q34.The least value of |z| where z is complex number which satisfies the inequality $exp (\frac{( ∣ z ∣ + 3 ) ( ∣ z ∣ - 1 )}{∣∣ z ∣ + 1∣} lo g_{e} 2) \geq lo g_{2} ∣5 7 + 9 i ∣, i = - 1$ , is equal to :
Mathematics · Complex Numbers · MCQ
Q35.Let $α \in$ R be such that the function $f (x) = {\frac{c o s ^{- 1} ( 1 - { x } ^{2} ) s i n ^{- 1} ( 1 - { x })}{{ x } - { x } ^{3}}, α, x e 0 x = 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q36.Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy $sin^{- 1} (\frac{3 x}{5}) + sin^{- 1} (\frac{4 x}{5}) = sin^{- 1} x$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q37.Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2 $2$ and 2 $5$ , respectively. Then the shortest distance from origin to a tangent to this circle which is…
Mathematics · Circle · MCQ
Q38.Let A( $-$ 1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q respectively. Let A1 and A2 be the areas of $Δ$ ABC and $Δ$ PQC respectively, such that A1 = 3A2,…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of event A is equal to :
Mathematics · Probability · MCQ
Q40.The maximum value of $f (x) = sin^{2} x 1 + sin^{2} x sin^{2} x 1 + cos^{2} x cos^{2} x cos^{2} x cos 2 x cos 2 x sin 2 x, x \in R$ …
Mathematics · Application of Derivatives · MCQ
Q41.Let $\frac{1}{16}$ , a and b be in G.P. and $\frac{1}{a}$ , $\frac{1}{b}$ , 6 be in A.P., where a, b > 0. Then 72(a + b) is equal to .
Mathematics · Sequences and Series · Numerical
Q42.For real numbers $α$ , $β$ , $γ$ and $δ$ , if $\int \frac{( x ^{2} - 1 ) + t a n ^{- 1} ( \frac{x ^{2} + 1}{x} )}{( x ^{4} + 3 x ^{2} + 1 ) t a n ^{- 1} ( \frac{x ^{2} + 1}{x} )} d x = α lo g_{e} (tan^{- 1} (\frac{x ^{2} + 1}{x})) + β tan^{- 1} (\frac{γ ( x ^{2} + 1 )}{x}) + δ tan^{- 1} (\frac{x ^{2} + 1}{x}) + C$ …
Mathematics · Indefinite Integrals · Numerical
Q43.Let f : R $\to$ R and g : R $\to$ R be defined as $f (x) = {x + a, ∣ x - 1∣, x < 0 x \geq 0$ and $g (x) = {x + 1, (x - 1)^{2} + b, x < 0 x \geq 0$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q44.Consider the statistics of two sets of observations as follows : If the variance of the combined set of these two observations is $\frac{17}{9}$ , then the value of n is equal to . Includes table
Mathematics · Statistics · Numerical
Q45.Let $A = [a_{1} a_{2}]$ and $B = [b_{1} b_{2}]$ be two 2 $\times$ 1 matrices with real entries such that A = XB, where $X = \frac{1}{3} [11 - 1 k]$ …
Mathematics · Matrices and Determinants · Numerical