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Mathematics · 2016 · 9 Apr · Shift 1

25 questions from this JEE Main paper

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2016 · 9 Apr · Shift 1
Mathematics

Mathematics · 2016 · 9 Apr · Shift 1

25 questions from this JEE Main paper

Sequences and Series1 questions Permutations and Combinations2 questions Binomial Theorem1 questions Matrices and Determinants2 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Functions1 questions Circle1 questions Trigonometric Ratio and Identites1 questions Hyperbola1 questions Vector Algebra1 questions Statistics1 questions 3D Geometry1 questions Probability1 questions Straight Lines and Pair of Straight Lines2 questions Area Under the Curves1 questions Differential Equations1 questions Definite Integration1 questions Indefinite Integrals1 questions Application of Derivatives1 questions Limits Continuity and Differentiability2 questions

Q22.Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5 = (0.1) (600)3. Then x3 + y3 + z3is equal to :
Mathematics · Sequences and Series · MCQ
Q23.If the four letter words (need not be meaningful ) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such words is :
Mathematics · Permutations and Combinations · MCQ
Q24.For x $\in$ R, x $e$ -1, if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + . . . . + x2016 = $i = 0 \sum 2016 a_{i} x^{i},$ then a17 is equal to :
Mathematics · Binomial Theorem · MCQ
Q25.The number of distinct real roots of the equation, $cos x sin x sin x sin x cos x sin x sin x sin x cos x = 0$ in the…
Mathematics · Matrices and Determinants · MCQ
Q26.If P = $[\frac{3}{2} - \frac{1}{2} \frac{1}{2} \frac{3}{2}], A = [1011]$ Q =…
Mathematics · Matrices and Determinants · MCQ
Q27.If the equations x2 + bx−1 = 0 and x2 + x + b = 0 have a common root different from −1, then $∣ b ∣$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q28.The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there $22$ units in the south-westwardsdirection. Then its new position in the Argand plane is at the point…
Mathematics · Complex Numbers · MCQ
Q29.For x $\in$ R, x $e$ 0, Let f0(x) = $\frac{1}{1 - x}$ and fn+1 (x) = f0(fn(x)), n = 0, 1, 2, . . . . Then the value of f100(3) + f1 $(\frac{2}{3})$ + f2 $(\frac{3}{2})$ is equal to :
Mathematics · Functions · MCQ
Q30.The value of $r = 1 \sum 15 r^{2} (\frac{^{15} C _{r}}{^{15} C _{r - 1}})$ is equal to :
Mathematics · Permutations and Combinations · MCQ
Q31.A circle passes through (−2, 4) and touches the y-axis at (0, 2). Which one of the following equations can represent a diameter of this circle?
Mathematics · Circle · MCQ
Q32.If m and M are the minimum and the maximum values of 4 + $\frac{1}{2}$ sin2 2x $-$ 2cos4 x, x $\in$ R, then M $-$ m is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q33.Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation 9e2 − 18e + 5 = 0. If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of this hyperbola, then a2 −…
Mathematics · Hyperbola · MCQ
Q34.In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively 3 $i$ + $j - k$ , $- i$ + 3 $j$ + p $k$ and 5 $i$ + q $j -$ 4 $k$ …
Mathematics · Vector Algebra · MCQ
Q35.If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :
Mathematics · Statistics · MCQ
Q36.The shortest distance between the lines $\frac{x}{2} = \frac{y}{2} = \frac{z}{1}$ and $\frac{x + 2}{- 1} = \frac{y - 4}{8} = \frac{z - 5}{4}$ lies in the interval :
Mathematics · 3D Geometry · MCQ
Q37.If A and B are any two events such that P(A) = $\frac{2}{5}$ and P (A $\cap$ B) = $\frac{3}{20}$ , hen the conditional probability, P(A $∣$ (A' $\cup$ B')), where A' denotes the complement of A, is equal to :
Mathematics · Probability · MCQ
Q38.The point (2, 1) is translated parallel to the line L : x− y = 4 by $23$ units. If the newpoint Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.The area (in sq. units) of the region described by A= {(x, y) $∣$ y $\geq$ x2 $-$ 5x + 4, x + y $\geq$ 1, y $\leq$ 0} is :
Mathematics · Area Under the Curves · MCQ
Q40.If a variable line drawn through the intersection of the lines $\frac{x}{3} + \frac{y}{4} = 1$ and $\frac{x}{4} + \frac{y}{3} = 1,$ meets the coordinate axes at A and B, (A $e$ B), then the locus of the midpoint of AB is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q41.If f(x) is a differentiable function in the interval (0, $\infty$ ) such that f (1) = 1 and $t \to x lim$ $\frac{t ^{2} f ( x ) - x ^{2} f ( t )}{t - x} = 1,$ for each x > 0, then $f (\frac{3}{2})$ …
Mathematics · Differential Equations · MCQ
Q42.If $2 0 \int 1 tan^{- 1} x d x = 0 \int 1 cot^{- 1} (1 - x + x^{2}) d x,$ then $0 \int 1 tan^{- 1} (1 - x + x^{2}) d x$ is equalto :
Mathematics · Definite Integration · MCQ
Q43.If $\int \frac{d x}{c o s ^{3} x 2 s i n 2 x} = (tan x)^{A} + C (tan x)^{B} + k,$ where k is a constant of integration, then A + B +C equals :
Mathematics · Indefinite Integrals · MCQ
Q44.The minimum distance of a point on the curve y = x2−4 from the origin is :
Mathematics · Application of Derivatives · MCQ
Q45.If the function f(x) = ${- x a + cos^{- 1} (x + b), x < 1 1 \leq x \leq 2$ is differentiable at x = 1, then $\frac{a}{b}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q46.If $x \to \infty lim (1 + \frac{a}{x} - \frac{4}{x ^{2}})^{2 x} = e^{3},$ then 'a' is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ