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Mathematics · 2021 · 17 Mar · Shift 1

20 questions from this JEE Main paper

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2021 · 17 Mar · Shift 1
Mathematics

Mathematics · 2021 · 17 Mar · Shift 1

20 questions from this JEE Main paper

Straight Lines and Pair of Straight Lines2 questions Limits Continuity and Differentiability2 questions Definite Integration2 questions Differential Equations1 questions Inverse Trigonometric Functions2 questions Quadratic Equation and Inequalities1 questions Functions1 questions Probability2 questions Binomial Theorem2 questions Matrices and Determinants1 questions Sets and Relations1 questions Permutations and Combinations1 questions Complex Numbers1 questions Differentiation1 questions

Q23.In a triangle PQR, the co-ordinates of the points P and Q are ( $-$ 2, 4) and (4, $-$ 2) respectively. If the equation of the perpendicular bisector of PR is 2x $-$ y + 2 = 0, then the centre of the circumcircle of the $Δ$ PQR is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q24.The value of $x \to 0^{+} lim \frac{c o s ^{- 1} ( x - [ x ] ^{2} ) . s i n ^{- 1} ( x - [ x ] ^{2} )}{x - x ^{3}}$ , where [ x ] denotes the greatest integer $\leq$ x is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q25.Which of the following statements is correct for the function g( $α$ ) for $α \in$ R such that $g (α) = \frac{π}{6} \int \frac{π}{3} \frac{s i n ^{α} x}{c o s ^{α} x + s i n ^{α} x} d x$
Mathematics · Definite Integration · MCQ
Q26.Which of the following is true for y(x) that satisfies the differential equation $\frac{d y}{d x}$ = xy $-$ 1 + x $-$ y; y(0) = 0 :
Mathematics · Differential Equations · MCQ
Q27.The sum of possible values of x for tan $-$ 1(x + 1) + cot $-$ 1 $(\frac{1}{x - 1})$ = tan $-$ 1 $(\frac{8}{31})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q28.The value of $4 + \frac{1}{5 + \frac{1}{4 + \frac{1}{5 + \frac{1}{4 + ......\infty}}}}$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.The inverse of $y = 5^{l o g x}$ is :
Mathematics · Functions · MCQ
Q30.Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :
Mathematics · Probability · MCQ
Q31.If the fourth term in the expansion of $(x + x^{l o g_{2} x})^{7}$ is 4480, then the value of x where x $\in$ N is equal to :
Mathematics · Binomial Theorem · MCQ
Q32.The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k2 has no solution if k is equal to :
Mathematics · Matrices and Determinants · MCQ
Q33.In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement? Includes diagram
Mathematics · Sets and Relations · MCQ
Q34.If cot $-$ 1( $α$ ) = cot $-$ 1 2 + cot $-$ 1 8 + cot $-$ 1 18 + cot $-$ 1 32 + ...... upto 100 terms, then $α$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q35.Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :
Mathematics · Permutations and Combinations · MCQ
Q36.The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :
Mathematics · Complex Numbers · MCQ
Q37.If (2021)3762 is divided by 17, then the remainder is .
Mathematics · Binomial Theorem · Numerical
Q38.Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is $α$ , only E2 occurs is $β$ and only E3 occurs is $γ$ . Let 'p' denote the probability of none of events occurs that satisfies the…
Mathematics · Probability · Numerical
Q39.The maximum value of z in the following equation z = 6xy + y2, where 3x + 4y $\leq$ 100 and 4x + 3y $\leq$ 75 for x $\geq$ 0 and y $\geq$ 0 is .
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q40.If [ . ] represents the greatest integer function, then the value of $0 \int \frac{π}{2} [[x^{2}] - cos x] d x$ is .
Mathematics · Definite Integration · Numerical
Q41.If $f (x) = sin (cos^{- 1} (\frac{1 - 2 ^{2 x}}{1 + 2 ^{2 x}}))$ and its first derivative with respect to x is $- \frac{b}{a} lo g_{e} 2$ when x = 1, where a and b are integers, then the minimum…
Mathematics · Differentiation · Numerical
Q42.If the function $f (x) = \frac{c o s ( s i n x ) - c o s x}{x ^{4}}$ is continuous at each point in its domain and $f (0) = \frac{1}{k}$ , then k is .
Mathematics · Limits Continuity and Differentiability · Numerical