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Mathematics · 2021 · 18 Mar · Shift 2

21 questions from this JEE Main paper

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2021 · 18 Mar · Shift 2
Mathematics

Mathematics · 2021 · 18 Mar · Shift 2

21 questions from this JEE Main paper

Differential Equations2 questions Matrices and Determinants2 questions Area Under the Curves1 questions Trigonometric Ratio and Identites1 questions Vector Algebra2 questions Complex Numbers1 questions Limits Continuity and Differentiability2 questions Definite Integration2 questions Statistics1 questions Sets and Relations1 questions Straight Lines and Pair of Straight Lines1 questions Functions2 questions Sequences and Series1 questions Permutations and Combinations1 questions Binomial Theorem1 questions

Q23.Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} = (y + 1) ((y + 1) e^{x^{2} /2} - x)$ , 0 < x < 2.1, with y(2) = 0. Then the value of $\frac{d y}{d x}$ at x = 1 is equal to :
Mathematics · Differential Equations · MCQ
Q24.Let the system of linear equations 4x + $λ$ y + 2z = 0 2x $-$ y + z = 0 $μ$ x + 2y + 3z = 0, $λ$ , $μ \in$ R. has a non-trivial solution. Then which of the following is true?
Mathematics · Matrices and Determinants · MCQ
Q25.The area bounded by the curve 4y2 = x2(4 $-$ x)(x $-$ 2) is equal to :
Mathematics · Area Under the Curves · MCQ
Q26.If 15sin4 $α$ + 10cos4 $α$ = 6, for some $α \in$ R, then the value of 27sec6 $α$ + 8cosec6 $α$ is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q27.Let $a$ and $b$ be two non-zero vectors perpendicular to each other and $∣ a ∣ = ∣ b ∣$ . If $∣ a \times b ∣ = ∣ a ∣$ , then the…
Mathematics · Vector Algebra · MCQ
Q28.Let a complex number be w = 1 $- 3$ i. Let another complex number z be such that |zw| = 1 and arg(z) $-$ arg(w) = $\frac{π}{2}$ . Then the area of the triangle with vertices origin, z and w is equal to :
Mathematics · Complex Numbers · MCQ
Q29.Let $f : R \to R$ be a function defined as $f (x) = ⎩ ⎨ ⎧ \frac{sin ( a + 1 ) x + sin 2 x}{2 x} b \frac{x + b x ^{3} - x}{b x ^{5/2}} if x < 0 if x = 0 if x > 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.Let g(x) = $\int_{0}^{x} f (t) d t$ , where f is continuous function in [ 0, 3 ] such that $\frac{1}{3} \leq$ f(t) $\leq$ 1 for all t $\in$ [0, 1] and 0 $\leq$ f(t) $\leq \frac{1}{2}$ for all t $\in$ (1, 3]. The largest possible interval in which…
Mathematics · Definite Integration · MCQ
Q31.Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $-$ a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively.…
Mathematics · Statistics · MCQ
Q32.In a triangle ABC, if $∣ B C ∣ = 8, ∣ C A ∣ = 7, ∣ A B ∣ = 10$ , then the projection of the vector $A B$ on $A C$ is equal to :
Mathematics · Vector Algebra · MCQ
Q33.Define a relation R over a class of n $\times$ n real matrices A and B as "ARB iff there exists a non-singular matrix P such that PAP $-$ 1 = B". Then which of the following is true?
Mathematics · Sets and Relations · MCQ
Q34.Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line x + y = 3. If R and r be the radius of circumcircle and incircle respectively of $Δ$ ABC,…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.Let f : R $-$ {3} $\to$ R $-$ {1} be defined by f(x) = $\frac{x - 2}{x - 3}$ . Let g : R $\to$ R be given as g(x) = 2x $-$ 3. Then, the sum of all the values of x for which f $-$ 1(x) + g $-$ 1(x) = $\frac{13}{2}$ is equal to :
Mathematics · Functions · MCQ
Q36.Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arithmetic progression. If (S2 $-$ S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :
Mathematics · Sequences and Series · MCQ
Q37.If $r = 1 \sum 10 r! (r^{3} + 6 r^{2} + 2 r + 5) = α (11!)$ , then the value of $α$ is equal to .
Mathematics · Permutations and Combinations · Numerical
Q38.If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x3) + x g(x3) is divisible by x2 + x + 1, then P(1) is equal to .
Mathematics · Functions · Numerical
Q39.The term independent of x in the expansion of $[\frac{x + 1}{x ^{2/3} - x ^{1/3} + 1} - \frac{x - 1}{x - x ^{1/2}}]^{10}$ , x $e$ 1, is equal to .
Mathematics · Binomial Theorem · Numerical
Q40.Let y = y(x) be the solution of the differential equation xdy $-$ ydx = $(x^{2} - y^{2}) d x$ , x $\geq$ 1, with y(1) = 0. If the area bounded by the line x = 1, x = e $π$ , y = 0 and y = y(x) is $α$ e2 $π$ + $β$ , then the…
Mathematics · Differential Equations · Numerical
Q41.Let I be an identity matrix of order 2 $\times$ 2 and P = $[25 - 1 - 3]$ . Then the value of n $\in$ N for which Pn = 5I $-$ 8P is equal to .
Mathematics · Matrices and Determinants · Numerical
Q42.Let f : R $\to$ R satisfy the equation f(x + y) = f(x) . f(y) for all x, y $\in$ R and f(x) $e$ 0 for any x $\in$ R. If the function f is differentiable at x = 0 and f'(0) = 3, then $$\mathop {\lim }\limits_{h \to 0} {1 \over h}(f(h) -…
Mathematics · Limits Continuity and Differentiability · Numerical
Q43.Let P(x) be a real polynomial of degree 3 which vanishes at x = $-$ 3. Let P(x) have local minima at x = 1, local maxima at x = $-$ 1 and $- 1 \int 1 P (x) d x$ = 18, then the sum of all the coefficients of the polynomial P(x) is…
Mathematics · Definite Integration · Numerical