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Mathematics · 2016 · 10 Apr · Shift 1

22 questions from this JEE Main paper

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2016 · 10 Apr · Shift 1
Mathematics

Mathematics · 2016 · 10 Apr · Shift 1

22 questions from this JEE Main paper

Sequences and Series2 questions Permutations and Combinations2 questions Binomial Theorem1 questions Matrices and Determinants2 questions Quadratic Equation and Inequalities1 questions Sets and Relations1 questions Definite Integration2 questions Statistics1 questions Vector Algebra1 questions 3D Geometry1 questions Hyperbola1 questions Differential Equations1 questions Straight Lines and Pair of Straight Lines2 questions Indefinite Integrals1 questions Application of Derivatives1 questions Limits Continuity and Differentiability2 questions

Q21.Let a1, a2, a3, . . . . . . . , an, . . . . . be in A.P. If a3 + a7 + a11 + a15 = 72, then the sum of its first 17 terms is equal to :
Mathematics · Sequences and Series · MCQ
Q22.If $\frac{^{n + 2} C _{6}}{^{n - 2} P _{2}}$ = 11, then n satisfies the equation :
Mathematics · Permutations and Combinations · MCQ
Q23.If the coefficients of x−2 and x−4 in the expansion of $(x^{\frac{1}{3}} + \frac{1}{2 x ^{\frac{1}{3}}})^{18}, (x > 0),$ are m and n respectively, then $\frac{m}{n}$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q24.If A = $[- 4 3 - 1 1]$ , then the determinant of the matrix (A2016 − 2A2015 − A2014) is :
Mathematics · Matrices and Determinants · MCQ
Q25.Let A be a 3 $\times$ 3 matrix such that A2 $-$ 5A + 7I = 0 Statement - I : A $-$ 1 = $\frac{1}{7}$ (5I $-$ A). Statement - II : The polynomial A3 $-$ 2A2 $-$ 3A + I can be reduced to 5(A $-$ 4I). Then :
Mathematics · Matrices and Determinants · MCQ
Q26.If x is a solution of the equation, $2 x + 1 - 2 x - 1 = 1,$ $(x \geq \frac{1}{2}),$ then $4 x^{2} - 1$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q27.Let P = { $θ$ : sin $θ -$ cos $θ$ = $2 cos θ$ } and Q = { $θ$ : sin $θ$ + cos $θ$ = $2 sin θ$ } be two sets. Then
Mathematics · Sets and Relations · MCQ
Q28.The sum $r = 1 \sum 10 (r^{2} + 1) \times (r!)$ is equal to :
Mathematics · Permutations and Combinations · MCQ
Q29.For x $\in$ R, x $e$ 0, if y(x) is a differentiable function such that x $1 \int x y$ (t) dt = (x + 1) $1 \int x t y$ (t) dt, then y (x) equals : (where C is a constant.)
Mathematics · Definite Integration · MCQ
Q30.If A > 0, B > 0 and A + B = $\frac{π}{6}$ , then the minimum value of tanA + tanB is :
Mathematics · Sequences and Series · MCQ
Q31.The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean deviation from the mean of the data is :
Mathematics · Statistics · MCQ
Q32.Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are $a, b, c$ and $\frac{a + b + c}{4}$ …
Mathematics · Vector Algebra · MCQ
Q33.ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C( $λ$ , 5, $μ$ ). If the median through A is equally inclined to the coordinate axes, then the value of ( $λ$ 3 + $μ$ 3 + 5) is :
Mathematics · 3D Geometry · MCQ
Q34.A hyperbola whose transverse axis is along the major axis of the conic, $\frac{x ^{2}}{3} + \frac{y ^{2}}{4} = 4$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\frac{3}{2},$ then which of the…
Mathematics · Hyperbola · MCQ
Q35.The solution of the differential equation $\frac{d y}{d x} + \frac{y}{2} sec x = \frac{t a n x}{2 y},$ where 0 $\leq$ x < $\frac{π}{2}$ , and y (0) = 1, is given by :
Mathematics · Differential Equations · MCQ
Q36.A straight line through origin O meets the lines 3y = 10 − 4x and 8x + 6y + 5 = 0 at points A and B respectively. Then O divides the segment AB in the ratio :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q37.A ray of light is incident along a line which meets another line, 7x − y + 1 = 0, at the point (0, 1). The ray is then reflected from this point along the line, y + 2x = 1. Then the equation of the line of incidence of the ray of light is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.The value of the integral $4 \int 10 \frac{[ x ^{2} ] d x}{[ x ^{2} - 28 x + 196 ] + [ x ^{2} ]},$ where [x] denotes the greatest integer less than or equal to x, is :
Mathematics · Definite Integration · MCQ
Q39.The integral $\int \frac{d x}{( 1 + x ) x - x ^{2}}$ is equal to : (where C is a constant of integration.)
Mathematics · Indefinite Integrals · MCQ
Q40.Let f(x) = sin4x + cos4 x. Then f is an increasing function in the interval :
Mathematics · Application of Derivatives · MCQ
Q41.Let a, b $\in$ R, (a $e$ 0). If the function f defined as $f (x) = ⎩ ⎨ ⎧ \frac{2 x ^{2}}{a}, a, \frac{2 b ^{2} - 4 b}{x ^{3}}, 0 \leq x < 1 1 \leq x < 2 2 \leq x < \infty$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q42. $x \to 0 lim \frac{( 1 - c o s 2 x ) ^{2}}{2 x t a n x - x t a n 2 x}$ is :
Mathematics · Limits Continuity and Differentiability · MCQ