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Mathematics · 2021 · 16 Mar · Shift 1

21 questions from this JEE Main paper

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2021 · 16 Mar · Shift 1
Mathematics

Mathematics · 2021 · 16 Mar · Shift 1

21 questions from this JEE Main paper

Vector Algebra1 questions Limits Continuity and Differentiability3 questions 3D Geometry1 questions Sets and Relations1 questions Complex Numbers2 questions Matrices and Determinants2 questions Binomial Theorem1 questions Hyperbola1 questions Statistics1 questions Functions1 questions Trigonometric Ratio and Identites1 questions Probability1 questions Differential Equations2 questions Definite Integration2 questions Sequences and Series1 questions

Q23.Let a vector $α i + β j$ be obtained by rotating the vector $3 i + j$ by an angle 45 $^{\circ}$ about the origin in counterclockwise direction in the first quadrant. Then the area of…
Mathematics · Vector Algebra · MCQ
Q24.Let $S_{k} = r = 1 \sum k tan^{- 1} (\frac{6 ^{r}}{2 ^{2 r + 1} + 3 ^{2 r + 1}})$ . Then $k \to \infty lim S_{k}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q25.Let the position vectors of two points P and Q be 3 $i - j$ + 2 $k$ and $i$ + 2 $j -$ 4 $k$ , respectively. Let R and S be two points such that the direction ratios of lines PR and QS are…
Mathematics · 3D Geometry · MCQ
Q26.The number of elements in the set {x $\in$ R : (|x| $-$ 3) |x + 4| = 6} is equal to :
Mathematics · Sets and Relations · MCQ
Q27.Let a complex number z, |z| $e$ 1, satisfy $lo g_{\frac{1}{2}} (\frac{∣ z ∣ + 11}{( ∣ z ∣ - 1 ) ^{2}}) \leq 2$ . Then, the largest value of |z| is equal to .
Mathematics · Complex Numbers · MCQ
Q28.Let $A = [i - i - i i], i = - 1$ . Then, the system of linear equations $A^{8} [x y] = [864]$ …
Mathematics · Matrices and Determinants · MCQ
Q29.If n is the number of irrational terms in the expansion of $(3^{1/4} + 5^{1/8})^{60}$ , then (n $-$ 1) is divisible by :
Mathematics · Binomial Theorem · MCQ
Q30.The locus of the midpoints of the chord of the circle, x2 + y2 = 25 which is tangent to the hyperbola, $\frac{x ^{2}}{9} - \frac{y ^{2}}{16} = 1$ is :
Mathematics · Hyperbola · MCQ
Q31.Let the functions f : R $\to$ R and g : R $\to$ R be defined as : $f (x) = {x + 2, x^{2}, x < 0 x \geq 0$ and $g (x) = {x^{3}, 3 x - 2, x < 1 x \geq 1$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?
Mathematics · Statistics · MCQ
Q33.The range of a $\in$ R for which the function f(x) = (4a $-$ 3)(x + loge 5) + 2(a $-$ 7) cot $(\frac{x}{2})$ sin2 $(\frac{x}{2})$ , x $e$ 2n $π$ , n $\in$ N has critical points, is :
Mathematics · Functions · MCQ
Q34.If for x $\in$ $(0, \frac{π}{2})$ , log10sinx + log10cosx = $-$ 1 and log10(sinx + cosx) = $\frac{1}{2}$ (log10 n $-$ 1), n > 0, then the value of n is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q35.A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :
Mathematics · Probability · MCQ
Q36.If y = y(x) is the solution of the differential equation, $\frac{d y}{d x} + 2 y tan x = sin x, y (\frac{π}{3}) = 0$ , then the maximum value of the function y(x) over R is equal to:
Mathematics · Differential Equations · MCQ
Q37.Let the curve y = y(x) be the solution of the differential equation, $\frac{d y}{d x}$ = 2(x + 1). If the numerical value of area bounded by the curve y = y(x) and x-axis is $\frac{4 8}{3}$ , then the value of y(1) is equal to …
Mathematics · Differential Equations · Numerical
Q38.Let f : R $\to$ R be a continuous function such that f(x) + f(x + 1) = 2, for all x $\in$ R. If $I_{1} = 0 \int 8 f (x) d x$ and $I_{2} = - 1 \int 3 f (x) d x$ , then the value of I1 + 2I2 is equal to …
Mathematics · Definite Integration · Numerical
Q39.If the normal to the curve y(x) = $0 \int x (2 t^{2} - 15 t + 10) d t$ at a point (a, b) is parallel to the line x + 3y = $-$ 5, a > 1, then the value of | a + 6b | is equal to .
Mathematics · Definite Integration · Numerical
Q40.Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these…
Mathematics · Sequences and Series · Numerical
Q41.If $x \to 0 lim \frac{a e ^{x} - b c o s x + c e ^{- x}}{x s i n x} = 2$ , then a + b + c is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical
Q42.Let z and $ω$ be two complex numbers such that $ω = z \overline{z} - 2 z + 2, \frac{z + i}{z - 3 i} = 1$ and Re( $ω$ ) has minimum value. Then, the minimum value of n $\in$ N for which $ω$ n is real, is…
Mathematics · Complex Numbers · Numerical
Q43.The total number of 3 $\times$ 3 matrices A having entries from the set {0, 1, 2, 3} such that the sum of all the diagonal entries of AAT is 9, is equal to .
Mathematics · Matrices and Determinants · Numerical