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Mathematics · 2021 · 17 Mar · Shift 2

22 questions from this JEE Main paper

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2021 · 17 Mar · Shift 2
Mathematics

Mathematics · 2021 · 17 Mar · Shift 2

22 questions from this JEE Main paper

Permutations and Combinations1 questions Probability1 questions Definite Integration3 questions Complex Numbers1 questions Inverse Trigonometric Functions1 questions Differential Equations2 questions Vector Algebra2 questions Limits Continuity and Differentiability2 questions Application of Derivatives2 questions Matrices and Determinants3 questions Binomial Theorem1 questions Straight Lines and Pair of Straight Lines1 questions Statistics1 questions Area Under the Curves1 questions

Q21.If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :
Mathematics · Permutations and Combinations · MCQ
Q22.Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be $\frac{1}{2}$ and probability of occurrence of 0 at the odd place be $\frac{1}{3}$ . Then the…
Mathematics · Probability · MCQ
Q23.Let f : R $\to$ R be defined as f(x) = e $-$ xsinx. If F : [0, 1] $\to$ R is a differentiable function with that F(x) = $\int_{0}^{x} f (t) d t$ , then the value of $\int_{0}^{1} (F^{'} (x) + f (x)) e^{x} d x$ lies in the interval
Mathematics · Definite Integration · MCQ
Q24.Let S1, S2 and S3 be three sets defined as S1 = {z $\in$ C : |z $-$ 1| $\leq 2$ } S2 = {z $\in$ C : Re((1 $-$ i)z) $\geq$ 1} S3 = {z $\in$ C : Im(z) $\leq$ 1} Then the set S1 $\cap$ S2 $\cap$ S3 :
Mathematics · Complex Numbers · MCQ
Q25.The number of solutions of the equation $sin^{- 1} [x^{2} + \frac{1}{3}] + cos^{- 1} [x^{2} - \frac{2}{3}] = x^{2}$ , for x $\in$ [ $-$ 1, 1], and [x] denotes the greatest integer less than or equal to…
Mathematics · Inverse Trigonometric Functions · MCQ
Q26.If the curve y = y(x) is the solution of the differential equation $2 (x^{2} + x^{5/4}) d y - y (x + x^{1/4}) d x = 2 x^{9/4} d x$ , x > 0 which passes through the point $(1, 1 - \frac{4}{3} lo g_{e} 2)$ , then the value…
Mathematics · Differential Equations · MCQ
Q27.Let O be the origin. Let $O P = x i + y j - k$ and $O Q = - i + 2 j + 3 x k$ , x, y $\in$ R, x > 0, be such that $P Q = 20$ …
Mathematics · Vector Algebra · MCQ
Q28.If the integral $\int_{0}^{10} \frac{[ s i n 2 π x ]}{e ^{x - [x]}} d x = α e^{- 1} + β e^{- \frac{1}{2}} + γ$ , where $α$ , $β$ , $γ$ are integers and [x] denotes the greatest integer less than or equal…
Mathematics · Definite Integration · MCQ
Q29.The value of the limit $θ \to 0 lim \frac{t a n ( π c o s ^{2} θ )}{s i n ( 2 π s i n ^{2} θ )}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.Consider the function $f : R \to R$ defined by $f (x) = ⎩ ⎨ ⎧ (2 - sin (\frac{1}{x})) ∣ x ∣ 0 x \neq = 0 x = 0$ Then $f$ is :
Mathematics · Application of Derivatives · MCQ
Q31.The value of $n \to \infty lim \frac{[ r ] + [ 2 r ] + ... + [ n r ]}{n ^{2}}$ , where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.If x, y, z are in arithmetic progression with common difference d, x $e$ 3d, and the determinant of the matrix $345 4252 k x y z$ …
Mathematics · Matrices and Determinants · MCQ
Q33.Let y = y(x) be the solution of the differential equation $cos x (3 sin x + cos x + 3) d y = (1 + y sin x (3 sin x + cos x + 3)) d x, 0 \leq x \leq \frac{π}{2}, y (0) = 0$ . Then, $y (\frac{π}{3})$ is equal to :
Mathematics · Differential Equations · MCQ
Q34.Let $A = [a c b d]$ and $B = [α β] e [00]$ such that AB = B and…
Mathematics · Matrices and Determinants · Numerical
Q35.Let the coefficients of third, fourth and fifth terms in the expansion of $(x + \frac{a}{x ^{2}})^{n}, x e 0$ , be in the ratio 12 : 8 : 3. Then the term independent of x in the expansion, is equal to …
Mathematics · Binomial Theorem · Numerical
Q36.Let tan $α$ , tan $β$ and tan $γ$ ; $α$ , $β$ , $γ e \frac{( 2 n - 1 ) π}{2}$ , n $\in$ N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of $Δ$ ABC coincides…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q37.Let $x$ be a vector in the plane containing vectors $a = 2 i - j + k$ and $b = i + 2 j - k$ . If the vector $x$ is…
Mathematics · Vector Algebra · Numerical
Q38.Let $I_{n} = \int_{1}^{e} x^{19} (lo g ∣ x ∣)^{n} d x$ , where n $\in$ N. If (20)I10 = $α$ I9 + $β$ I8, for natural numbers $α$ and $β$ , then $α - β$ equals to .
Mathematics · Definite Integration · Numerical
Q39.If 1, log10(4x $-$ 2) and log10 $(4^{x} + \frac{18}{5})$ are in arithmetic progression for a real number x, then the value of the determinant $2 (x - \frac{1}{2}) 1 x x - 1 01 x^{2} x 0$ …
Mathematics · Matrices and Determinants · Numerical
Q40.Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6 and the mean of the remaining n numbers is 3. A new set is constructed by adding 1 into each of first 2n numbers, and subtracting 1 from each of…
Mathematics · Statistics · Numerical
Q41.Let f : [ $-$ 1, 1] $\to$ R be defined as f(x) = ax2 + bx + c for all x $\in$ [ $-$ 1, 1], where a, b, c $\in$ R such that f( $-$ 1) = 2, f'( $-$ 1) = 1 for x $\in$ ( $-$ 1, 1) the maximum value of f ''(x) is $\frac{1}{2}$ . If f(x) $\le…
Mathematics · Application of Derivatives · Numerical
Q42.Let $f : [- 3, 1] \to R$ be given as $f (x) = {min {(x + 6), x^{2}} max {x, x^{2}} - 3 \leq x \leq 0 0 \leq x \leq 1$ If the area bounded by $y = f (x)$ and $x$ -axis is $A$ …
Mathematics · Area Under the Curves · Numerical