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Mathematics · 2018 · 15 Apr · Shift 2

22 questions from this JEE Main paper

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2018 · 15 Apr · Shift 2
Mathematics

Mathematics · 2018 · 15 Apr · Shift 2

22 questions from this JEE Main paper

Sequences and Series1 questions Matrices and Determinants2 questions Complex Numbers1 questions Permutations and Combinations1 questions Functions1 questions Quadratic Equation and Inequalities1 questions Vector Algebra1 questions Statistics1 questions Probability1 questions 3D Geometry1 questions Parabola1 questions Straight Lines and Pair of Straight Lines2 questions Differential Equations1 questions Indefinite Integrals1 questions Definite Integration2 questions Limits Continuity and Differentiability3 questions Differentiation1 questions

Q23.If a, b, c are in A.P. and a2, b2, c2 are in G.P. such that a < b < c and a + b + c = $\frac{3}{4},$ then the value of a is :
Mathematics · Sequences and Series · MCQ
Q24.If the system of linear equations x + ay + z = 3 x + 2y + 2z = 6 x + 5y + 3z = b has no solution, then :
Mathematics · Matrices and Determinants · MCQ
Q25.If |z $-$ 3 + 2i| $\leq$ 4 then the difference between the greatest value and the least value of |z| is :
Mathematics · Complex Numbers · MCQ
Q26.The number of four letter words that can be formed using the letters of the word BARRACK is :
Mathematics · Permutations and Combinations · MCQ
Q27.Suppose A is any 3 $\times$ 3 non-singular matrix and ( A $-$ 3I) (A $-$ 5I) = O where I = I3 and O = O3. If $α$ A + $β$ A-1 = 4I, then $α$ + $β$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q28.Let f : A $\to$ B be a function defined as f(x) = $\frac{x - 1}{x - 2},$ Where A = R $-$ {2} and B = R $-$ {1}. Then f is :
Mathematics · Functions · MCQ
Q29.If f(x) is a quadratic expression such that f (1) + f (2) = 0, and $-$ 1 is a root of f (x) = 0, then the other root of f(x) = 0 is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q30.If the position vectors of the vertices A, B and C of a $Δ$ ABC are respectively $4 i + 7 j + 8 k, 2 i + 3 j + 4 k,$ and $2 i + 5 j + 7 k,$ then the position…
Mathematics · Vector Algebra · MCQ
Q31.If the mean of the data : 7, 8, 9, 7, 8, 7, $λ$ , 8 is 8, then the variance of this data is :
Mathematics · Statistics · MCQ
Q32.A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game,…
Mathematics · Probability · MCQ
Q33.An angle between the lines whose direction cosines are gien by the equations, $l$ + 3m + 5n = 0 and 5 $l$ m $-$ 2mn + 6n $l$ = 0, is :
Mathematics · 3D Geometry · MCQ
Q34.Tangents drawn from the point ( $-$ 8, 0) to the parabola y2 = 8x touch the parabola at $P$ and $Q .$ If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to :
Mathematics · Parabola · MCQ
Q35.The foot of the perpendicular drawn from the origin, on the line, 3x + y = $λ$ ( $λ e$ 0) is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q36.The sides of a rhombus ABCD are parallel to the lines, x $-$ y + 2 = 0 and 7x $-$ y + 3 = 0. If the diagonals of the rhombus intersect P(1, 2) and the vertex A (different from the origin) is on the y-axis, then the coordinate of A is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q37.The curve satifying the differeial equation, (x2 $-$ y2) dx + 2xydy = 0 and passing through the point (1, 1) is :
Mathematics · Differential Equations · MCQ
Q38.If $\int \frac{2 x + 5}{7 - 6 x - x ^{2}} d x = A 7 - 6 x - x^{2} + B sin^{- 1} (\frac{x + 3}{4}) + C$ (where C is a constant of integration), then the ordered pair (A, B) is equal to :
Mathematics · Indefinite Integrals · MCQ
Q39.If $I_{1} = \int_{0}^{1} e^{- x} cos^{2} x d x; I_{2} = \int_{0}^{1} e^{- x^{2}} cos^{2} x d x$ and $I_{3} = \int_{0}^{1} e^{- x^{3}} d x;$ then
Mathematics · Definite Integration · MCQ
Q40.The value of integral $\int_{\frac{π}{4}}^{\frac{3 π}{4}} \frac{x}{1 + s i n x} d x$ is :
Mathematics · Definite Integration · MCQ
Q41.Let f(x) be a polynomial of degree $4$ having extreme values at $x = 1$ and $x = 2.$ If $x \to 0 l im (\frac{f ( x )}{x ^{2}} + 1) = 3$ then f( $-$ 1) is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q42.If f(x) = sin-1 $(\frac{2 \times 3 ^{x}}{1 + 9 ^{x}}),$ then f' $(- \frac{1}{2})$ equals :
Mathematics · Differentiation · MCQ
Q43.Let f(x) = ${(x - 1)^{\frac{1}{2 - x}}, k x > 1, x e 2, x = 2$ Thevaue of k for which f s continuous at x = 2 is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q44. $x \to 0 lim \frac{x t a n 2 x - 2 x t a n x}{( 1 - c o s 2 x ) ^{2}}$ equals :
Mathematics · Limits Continuity and Differentiability · MCQ