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Mathematics · 2021 · 25 Jul · Shift 2

23 questions from this JEE Main paper

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2021 · 25 Jul · Shift 2
Mathematics

Mathematics · 2021 · 25 Jul · Shift 2

23 questions from this JEE Main paper

Binomial Theorem4 questions Statistics1 questions Definite Integration2 questions Trigonometric Ratio and Identites1 questions Vector Algebra3 questions Quadratic Equation and Inequalities3 questions Matrices and Determinants2 questions Functions1 questions Probability2 questions Permutations and Combinations1 questions Differential Equations1 questions Limits Continuity and Differentiability1 questions Complex Numbers1 questions

Q24.The sum of all those terms which are rational numbers in the expansion of (21/3 + 31/4)12 is :
Mathematics · Binomial Theorem · MCQ
Q25.The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation $13.44$ , then the standard deviation of the second sample is :
Mathematics · Statistics · MCQ
Q26.If $f (x) = ⎩ ⎨ ⎧ 0 \int x (5 + ∣ 1 - t ∣) d t, 5 x + 1, x > 2 x \leq 2$ , then
Mathematics · Definite Integration · MCQ
Q27.If the greatest value of the term independent of 'x' in the expansion of $(x sin α + a \frac{c o s α}{x})^{10}$ is $\frac{10 !}{( 5 !) ^{2}}$ , then the value of 'a' is equal to :
Mathematics · Binomial Theorem · MCQ
Q28.The value of $cot \frac{π}{24}$ is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q29.The lowest integer which is greater than $(1 + \frac{1}{10 ^{100}})^{10^{100}}$ is .
Mathematics · Binomial Theorem · MCQ
Q30.The value of the integral $- 1 \int 1 lo g (x + x^{2} + 1) d x$ is :
Mathematics · Definite Integration · MCQ
Q31.Let a, b and c be distinct positive numbers. If the vectors $a i + a j + c k, i + k$ and $c i + c j + b k$ are co-planar, then c is equal to :
Mathematics · Vector Algebra · MCQ
Q32.If [x] be the greatest integer less than or equal to x, then $n = 8 \sum 100 [\frac{( - 1 ) ^{n} n}{2}]$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q33.The number of distinct real roots of $sin x cos x cos x cos x sin x cos x cos x cos x sin x = 0$ in the interval $- \frac{π}{4} \leq x \leq \frac{π}{4}$ …
Mathematics · Matrices and Determinants · MCQ
Q34.If $a = 2, b = 5$ and $a \times b$ = 8, then $a . b$ is equal to :
Mathematics · Vector Algebra · MCQ
Q35.The number of real solutions of the equation, x2 $-$ |x| $-$ 12 = 0 is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q36.Consider function f : A $\to$ B and g : B $\to$ C (A, B, C $\subseteq$ R) such that (gof) $-$ 1 exists, then :
Mathematics · Functions · MCQ
Q37.If $P = [1 \frac{1}{2} 01]$ , then P50 is :
Mathematics · Matrices and Determinants · MCQ
Q38.Let X be a random variable such that the probability function of a distribution is given by $P (X = 0) = \frac{1}{2}, P (X = j) = \frac{1}{3 ^{j}} (j = 1, 2, 3, ..., \infty)$ . Then the mean of the distribution and P(X is positive and even)…
Mathematics · Probability · MCQ
Q39.If $^{n} P_{r} =^{n} P_{r + 1}$ and $^{n} C_{r} =^{n} C_{r - 1}$ , then the value of r is equal to :
Mathematics · Permutations and Combinations · MCQ
Q40.Let y = y(x) be the solution of the differential equation xdy = (y + x3 cosx)dx with y( $π$ ) = 0, then $y (\frac{π}{2})$ is equal to :
Mathematics · Differential Equations · MCQ
Q41.Consider the function where P(x) is a polynomial such that P'' (x) is always a constant and P(3) = 9. If f(x) is continuous at x = 2, then P(5) is equal to . Includes diagram
Mathematics · Limits Continuity and Differentiability · Numerical
Q42.The equation of a circle is Re(z2) + 2(Im(z))2 + 2Re(z) = 0, where z = x + iy. A line which passes through the center of the given circle and the vertex of the parabola, x2 $-$ 6x $-$ y + 13 = 0, has y-intercept equal to …
Mathematics · Complex Numbers · Numerical
Q43.If $(a + 3 b)$ is perpendicular to $(7 a - 5 b)$ and $(a - 4 b)$ is perpendicular to $(7 a - 2 b)$ …
Mathematics · Vector Algebra · Numerical
Q44.If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a4 + b4 + c4 is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q45.A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is .
Mathematics · Probability · Numerical
Q46.If the co-efficient of x7 and x8 in the expansion of $(2 + \frac{x}{3})^{n}$ are equal, then the value of n is equal to .
Mathematics · Binomial Theorem · Numerical