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Mathematics · 2021 · 27 Jul · Shift 1

25 questions from this JEE Main paper

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2021 · 27 Jul · Shift 1
Mathematics

Mathematics · 2021 · 27 Jul · Shift 1

25 questions from this JEE Main paper

Statistics1 questions Vector Algebra2 questions Definite Integration3 questions Complex Numbers1 questions Area Under the Curves1 questions Ellipse1 questions Binomial Theorem1 questions Trigonometric Ratio and Identites1 questions Matrices and Determinants3 questions Limits Continuity and Differentiability3 questions Differential Equations2 questions Circle2 questions Quadratic Equation and Inequalities1 questions Probability1 questions Sequences and Series1 questions Functions1 questions

Q23.If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and $\frac{37}{4}$ respectively, then (a $-$ b)2 is equal to :
Mathematics · Statistics · MCQ
Q24.Let $a = i + j + 2 k$ and $b = - i + 2 j + 3 k$ . Then the vector product $(a + b) \times ((a \times ((a - b) \times b)) \times b)$ …
Mathematics · Vector Algebra · MCQ
Q25.The value of the definite integral $- \frac{π}{4} \int \frac{π}{4} \frac{d x}{( 1 + e ^{x c o s x} ) ( s i n ^{4} x + c o s ^{4} x )}$ is equal to :
Mathematics · Definite Integration · MCQ
Q26.Let C be the set of all complex numbers. Let $S_{1} = {z \in C ∣∣ z - 3 - 2 i ∣^{2} = 8}$ $S_{2} = {z \in C ∣ Re o l imi t s (z) \geq 5}$ and $S_{3} = {z \in C ∣∣ z - \overline{z} ∣ \geq 8}$ . Then the number of elements in $S_{1} \cap S_{2} \cap S_{3}$ …
Mathematics · Complex Numbers · MCQ
Q27.If the area of the bounded region $R = {(x, y) : max {0, lo g_{e} x} \leq y \leq 2^{x}, \frac{1}{2} \leq x \leq 2}$ is , $α (lo g_{e} 2)^{- 1} + β (lo g_{e} 2) + γ$ , then the value of $(α + β - 2 λ)^{2}$ …
Mathematics · Area Under the Curves · MCQ
Q28.A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity $\frac{1}{3}$ and the distance of the nearer focus from…
Mathematics · Ellipse · MCQ
Q29.If the coefficients of x7 in $(x^{2} + \frac{1}{b x})^{11}$ and x $-$ 7 in $(x - \frac{1}{b x ^{2}})^{11}$ , b $e$ 0, are equal, then the value of b is equal to :
Mathematics · Binomial Theorem · MCQ
Q30.If $sin θ + cos θ = \frac{1}{2}$ , then 16(sin(2 $θ$ ) + cos(4 $θ$ ) + sin(6 $θ$ )) is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q31.Let $A = [1 - 1 24]$ . If A $-$ 1 = $α$ I + $β$ A, $α$ , $β \in$ R, I is a 2 $\times$ 2 identity matrix then 4( $α - β$ ) is equal to :
Mathematics · Matrices and Determinants · MCQ
Q32.Let $f : (- \frac{π}{4}, \frac{π}{4}) \to R$ be defined as $f (x) = ⎩ ⎨ ⎧ (1 + ∣ sin x ∣)^{\frac{3 a}{∣ s i n x ∣}} b e^{c o t 4 x / c o t 2 x},,, - \frac{π}{4} < x < 0 x = 0 0 < x < \frac{π}{4}$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q33.Let y = y(x) be solution of the differential equation $lo g (\frac{d y}{d x}) = 3 x + 4 y$ , with y(0) = 0. If $y (- \frac{2}{3} lo g_{e} 2) = α lo g_{e} 2$ , then the value of $α$ is equal…
Mathematics · Differential Equations · MCQ
Q34.Let f : R $\to$ R be a function such that f(2) = 4 and f'(2) = 1. Then, the value of $x \to 2 lim \frac{x ^{2} f ( 2 ) - 4 f ( x )}{x - 2}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to :
Mathematics · Circle · MCQ
Q36.Let $α$ , $β$ be two roots of the equation x2 + (20)1/4x + (5)1/2 = 0. Then $α$ 8 + $β$ 8 is equal to
Mathematics · Quadratic Equation and Inequalities · MCQ
Q37.The probability that a randomly selected 2-digit number belongs to the set {n $\in$ N : (2n $-$ 2) is a multiple of 3} is equal to :
Mathematics · Probability · MCQ
Q38.Let $A = {(x, y) \in R \times R ∣2 x^{2} + 2 y^{2} - 2 x - 2 y = 1}$ , $B = {(x, y) \in R \times R ∣4 x^{2} + 4 y^{2} - 16 y + 7 = 0}$ and $C = {(x, y) \in R \times R ∣ x^{2} + y^{2} - 4 x - 2 y + 5 \leq r^{2}}$ . Then the minimum value of |r|…
Mathematics · Circle · MCQ
Q39.For real numbers $α$ and $β$ , consider the following system of linear equations : x + y $-$ z = 2, x + 2y + $α$ z = 1, 2x $-$ y + z = $β$ . If the system has infinite solutions, then $α$ + $β$ is equal to …
Mathematics · Matrices and Determinants · Numerical
Q40.Let $a = i + j + k, b$ and $c = j - k$ be three vectors such that $a \times b = c$ and $a . b = 1$ …
Mathematics · Vector Algebra · Numerical
Q41.If $lo g_{3} 2, lo g_{3} (2^{x} - 5), lo g_{3} (2^{x} - \frac{7}{2})$ are in an arithmetic progression, then the value of x is equal to .
Mathematics · Sequences and Series · Numerical
Q42.Let the domain of the function $f (x) = lo g_{4} (lo g_{5} (lo g_{3} (18 x - x^{2} - 77)))$ be (a, b). Then the value of the integral $a \int b \frac{s i n ^{3} x}{( s i n ^{3} x + s i n ^{3} ( a + b - x )} d x$ …
Mathematics · Definite Integration · Numerical
Q43.Let $f (x) = sin^{2} x 2 + sin^{2} x sin^{2} x - 2 + cos^{2} x cos^{2} x cos^{2} x cos 2 x cos 2 x 1 + cos 2 x, x \in [0, π]$ …
Mathematics · Matrices and Determinants · Numerical
Q44.Let $F : [3, 5] \to R$ be a twice differentiable function on (3, 5) such that $F (x) = e^{- x} 3 \int x (3 t^{2} + 2 t + 4 F^{'} (t)) d t$ . If $F^{'} (4) = \frac{α e ^{β} - 224}{( e ^{β} - 4 ) ^{2}}$ , then $α$ + $β$ is…
Mathematics · Definite Integration · Numerical
Q45.Let S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f : S $\to$ S such that f(m . n) = f(m) . f(n) for every m, n $\in$ S and m . n $\in$ S is equal to .
Mathematics · Functions · Numerical
Q46.If $y = y (x), y \in [0, \frac{π}{2})$ is the solution of the differential equation $sec y \frac{d y}{d x} - sin (x + y) - sin (x - y) = 0$ , with y(0) = 0, then $5 y^{'} (\frac{π}{2})$ is equal to …
Mathematics · Differential Equations · Numerical
Q47.Let $f : [0, 3] \to R$ be defined by $f (x) = min {x - [x], 1 + [x] - x}$ where [x] is the greatest integer less than or equal to x. Let P denote the set containing all x $\in$ [0, 3] where f i discontinuous, and Q denote the set containing…
Mathematics · Limits Continuity and Differentiability · Numerical