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Mathematics · 2020 · 9 Jan · Shift 1

20 questions from this JEE Main paper

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2020 · 9 Jan · Shift 1
Mathematics

Mathematics · 2020 · 9 Jan · Shift 1

20 questions from this JEE Main paper

Indefinite Integrals2 questions Definite Integration2 questions Probability1 questions Complex Numbers1 questions Application of Derivatives1 questions Permutations and Combinations1 questions Limits Continuity and Differentiability2 questions 3D Geometry1 questions Differential Equations1 questions Binomial Theorem1 questions Matrices and Determinants1 questions Logarithm1 questions Straight Lines and Pair of Straight Lines1 questions Trigonometric Ratio and Identites1 questions Hyperbola1 questions Statistics1 questions Quadratic Equation and Inequalities1 questions

Q23.If ƒ'(x) = tan–1(secx + tanx), $- \frac{π}{2} < x < \frac{π}{2}$ , and ƒ(0) = 0, then ƒ(1) is equal to :
Mathematics · Indefinite Integrals · MCQ
Q24.The value of $0 \int 2 π \frac{x s i n ^{8} x}{s i n ^{8} x + c o s ^{8} x} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q25.In a box, there are 20 cards, out of which 10 are lebelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second…
Mathematics · Probability · MCQ
Q26.Let z be complex number such that $\frac{z - i}{z + 2 i} = 1$ and |z| = $\frac{5}{2}$ . Then the value of |z + 3i| is :
Mathematics · Complex Numbers · MCQ
Q27.A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness the melts at a rate of 50 cm3/min. When the thickness of ice is 5 cm, then the rate (in cm/min.) at which of the thickness of ice decreases, is :
Mathematics · Application of Derivatives · MCQ
Q28.If the number of five digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to :
Mathematics · Permutations and Combinations · MCQ
Q29.Let ƒ be any function continuous on [a, b] and twice differentiable on (a, b). If for all x $\in$ (a, b), ƒ'(x) > 0 and ƒ''(x) < 0, then for any c $\in$ (a, b), $\frac{f ( c ) - f ( a )}{f ( b ) - f ( c )}$ is greater than :
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.The projection of the line segment joining the points (1, –1, 3) and (2, –4, 11) on the line joining the points (–1, 2, 3) and (3, –2, 10) is .
Mathematics · 3D Geometry · Numerical
Q31.If for x $\geq$ 0, y = y(x) is the solution of the differential equation (x + 1)dy = ((x + 1)2 + y – 3)dx, y(2) = 0, then y(3) is equal to .
Mathematics · Differential Equations · Numerical
Q32.The coefficient of x4 is the expansion of (1 + x + x2)10 is .
Mathematics · Binomial Theorem · Numerical
Q33.If for some $α$ and $β$ in R, the intersection of the following three places x + 4y – 2z = 1 x + 7y – 5z = b x + 5y + $α$ z = 5 is a line in R3, then $α$ + $β$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q34.The number of distinct solutions of the equation $lo g_{\frac{1}{2}} ∣ sin x ∣ = 2 - lo g_{\frac{1}{2}} ∣ cos x ∣$ in the interval [0, 2 $π$ ], is .
Mathematics · Logarithm · Numerical
Q35.The integral $\int \frac{d x}{( x + 4 ) ^{\frac{8}{7}} ( x - 3 ) ^{\frac{6}{7}}}$ is equal to : (where C is a constant of integration)
Mathematics · Indefinite Integrals · MCQ
Q36.If $f (x) = ⎩ ⎨ ⎧ \frac{s i n ( a + 2 ) x + s i n x}{x}; b; \frac{( x + 3 x ^{2} ) ^{\frac{1}{3}} - x ^{\frac{1}{3}}}{x ^{\frac{4}{3}}}; x < 0 x = 0 x > 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y – 1 = 0 and 3x – y + 1 = 0. Then the line passing through the points C and P also passes through the…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.The value of $cos^{3} (\frac{π}{8}) cos (\frac{3 π}{8})$ + $sin^{3} (\frac{π}{8}) sin (\frac{3 π}{8})$ is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q39.If for all real triplets (a, b, c), ƒ(x) = a + bx + cx2; then $0 \int 1 f (x) d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q40.If e1 and e2 are the eccentricities of the ellipse, $\frac{x ^{2}}{18} + \frac{y ^{2}}{4} = 1$ and the hyperbola, $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ respectively and (e1, e2) is a point on the ellipse, 15x2 + 3y2 = k, then k…
Mathematics · Hyperbola · MCQ
Q41.Let the observations xi (1 $\leq$ i $\leq$ 10) satisfy the equations, $i = 1 \sum 10 (x_{1} - 5)$ = 10 and $i = 1 \sum 10 (x_{1} - 5)^{2}$ = 40. If $μ$ and $λ$ are the mean…
Mathematics · Statistics · MCQ
Q42.The number of real roots of the equation, e4x + e3x – 4e2x + ex + 1 = 0 is :
Mathematics · Quadratic Equation and Inequalities · MCQ