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Mathematics · 2021 · 26 Feb · Shift 2

22 questions from this JEE Main paper

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2021 · 26 Feb · Shift 2
Mathematics

Mathematics · 2021 · 26 Feb · Shift 2

22 questions from this JEE Main paper

Limits Continuity and Differentiability3 questions Circle2 questions Matrices and Determinants2 questions Permutations and Combinations1 questions Inverse Trigonometric Functions1 questions Definite Integration3 questions Functions1 questions Area Under the Curves1 questions Vector Algebra1 questions Probability1 questions Sequences and Series2 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Statistics1 questions Application of Derivatives1 questions

Q26.Let f(x) be a differentiable function at x = a with f'(a) = 2 and f(a) = 4. Then $x \to a lim \frac{x f ( a ) - a f ( x )}{x - a}$ equals :
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Let A(1, 4) and B(1, $-$ 5) be two points. Let P be a point on the circle (x $-$ 1)2 + (y $-$ 1)2 = 1 such that (PA)2 + (PB)2 have maximum value, then the points, P, A and B lie on :
Mathematics · Circle · MCQ
Q28.Consider the following system of equations : x + 2y $-$ 3z = a 2x + 6y $-$ 11z = b x $-$ 2y + 7z = c, where a, b and c are real constants. Then the system of equations :
Mathematics · Matrices and Determinants · MCQ
Q29.A natural number has prime factorization given by n = 2x3y5z, where y and z are such that y + z = 5 and y $-$ 1 + z $-$ 1 = $\frac{5}{6}$ , y > z. Then the number of odd divisions of n, including 1, is :
Mathematics · Permutations and Combinations · MCQ
Q30.If 0 < a, b < 1, and tan $-$ 1a + tan $-$ 1b = $\frac{π}{4}$ , then the value of $(a + b) - (\frac{a ^{2} + b ^{2}}{2}) + (\frac{a ^{3} + b ^{3}}{3}) - (\frac{a ^{4} + b ^{4}}{4}) + .....$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q31.Let $f (x) = 0 \int x e^{t} f (t) d t + e^{x}$ be a differentiable function for all x $\in$ R. Then f(x) equals :
Mathematics · Definite Integration · MCQ
Q32.For x > 0, if $f (x) = 1 \int x \frac{l o g _{e} t}{( 1 + t )} d t$ , then $f (e) + f (\frac{1}{e})$ is equal to :
Mathematics · Definite Integration · MCQ
Q33.Let $A = {1, 2, 3, ...., 10}$ and $f : A \to A$ be defined as $f (k) = {k + 1 k i f k i s o dd i f k i s e v e n$ Then the number of possible functions $g : A \to A$ such that…
Mathematics · Functions · MCQ
Q34.Let A1 be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in the first quadrant. Also, let A2 be the area of the region bounded by the curves y = sinx, y = cosx, x-axis and x = $\frac{π}{2}$ in the first…
Mathematics · Area Under the Curves · MCQ
Q35.Let $f (x) = sin^{- 1} x$ and $g (x) = \frac{x ^{2} - x - 2}{2 x ^{2} - x - 6}$ . If $g (2) = x \to 2 lim g (x)$ , then the domain of the function fog is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q36.Let $f : R \to R$ be defined as $f (x) = ⎩ ⎨ ⎧ 2 sin (- \frac{π x}{2}) ∣ a x^{2} + x + b ∣ sin (π x) if x < - 1 if - 1 \leq x \leq 1 if x > 1$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circle of radius r, then r is equal to :
Mathematics · Circle · MCQ
Q38.If vectors $a_{1} = x i - j + k$ and $a_{2} = i + y j + z k$ are collinear, then a possible unit vector parallel to the vector $x i + y j + z k$ …
Mathematics · Vector Algebra · MCQ
Q39.A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is :
Mathematics · Probability · MCQ
Q40.The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is .
Mathematics · Sequences and Series · Numerical
Q41.If the matrix $A = 103020 00 - 1$ satisfies the equation $A^{20} + α A^{19} + β A = 100040001$ …
Mathematics · Matrices and Determinants · Numerical
Q42.Let $α$ and $β$ be two real numbers such that $α$ + $β$ = 1 and $α β$ = $-$ 1. Let pn = ( $α$ )n + ( $β$ )n, pn $-$ 1 = 11 and pn+1 = 29 for some integer n $\geq$ 1. Then, the value of p $_{n}^{2}$ is …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q43.Let z be those complex numbers which satisfy | z + 5 | $\leq$ 4 and z(1 + i) + $\overline{z}$ (1 $-$ i) $- 1$ 10, i = $- 1$ . If the maximum value of | z + 1 |2 is $α$ + $β 2$ , then the value of ( $α$ + $β$ ) is …
Mathematics · Complex Numbers · Numerical
Q44.If the arithmetic mean and geometric mean of the pth and qth terms of the sequence $-$ 16, 8, $-$ 4, 2, ...... satisfy the equation 4x2 $-$ 9x + 5 = 0, then p + q is equal to .
Mathematics · Sequences and Series · Numerical
Q45.If $I_{m, n} = 0 \int 1 x^{m - 1} (1 - x)^{n - 1} d x$ , for m, $n \geq 1$ , and $0 \int 1 \frac{x ^{m - 1} + x ^{n - 1}}{( 1 + x ) ^{m + 1}} d x = α I_{m, n} α \in R$ , then $α$ equals …
Mathematics · Definite Integration · Numerical
Q46.Let X1, X2, ......., X18 be eighteen observations such that $i = 1 \sum 18 (X_{i} - α) = 36$ and $i = 1 \sum 18 (X_{i} - β)^{2} = 90$ , where $α$ and $β$ are distinct real numbers. If the…
Mathematics · Statistics · Numerical
Q47.Let a be an integer such that all the real roots of the polynomial 2x5 + 5x4 + 10x3 + 10x2 + 10x + 10 lie in the interval (a, a + 1). Then, |a| is equal to .
Mathematics · Application of Derivatives · Numerical