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Mathematics · 2019 · 10 Jan · Shift 1

21 questions from this JEE Main paper

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2019 · 10 Jan · Shift 1
Mathematics

Mathematics · 2019 · 10 Jan · Shift 1

21 questions from this JEE Main paper

Matrices and Determinants2 questions Statistics1 questions Indefinite Integrals1 questions Vector Algebra1 questions Sets and Relations1 questions Probability1 questions Limits Continuity and Differentiability2 questions Binomial Theorem1 questions Straight Lines and Pair of Straight Lines3 questions Area Under the Curves1 questions Definite Integration1 questions Complex Numbers1 questions Sequences and Series1 questions Application of Derivatives1 questions Quadratic Equation and Inequalities1 questions Differential Equations1 questions Differentiation1 questions

Q24.If the system of equations x + y + z = 5 x + 2y + 3z = 9 x + 3y + az = $β$ has infinitely many solutions, then $β - α$ equals -
Mathematics · Matrices and Determinants · MCQ
Q25.The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -
Mathematics · Statistics · MCQ
Q26.Let n $\geq$ 2 be a natural number and $0 < θ < \frac{π}{2} .$ Then $\int \frac{( s i n ^{n} θ - s i n θ ) ^{1/ n} c o s θ}{s i n ^{n + 1} θ} d θ$ is equal to - (where C is a…
Mathematics · Indefinite Integrals · MCQ
Q27.Let $a = 2 i + λ_{1} j + 3 k, b = 4 i + (3 - λ_{2}) j + 6 k,$ and $c = 3 i + 6 j + (λ_{3} - 1) k$ …
Mathematics · Vector Algebra · MCQ
Q28.In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number…
Mathematics · Sets and Relations · MCQ
Q29.An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards…
Mathematics · Probability · MCQ
Q30.For each t $\in$ R , let [t] be the greatest integer less than or equal to t Then $x \to 1^{+} lim \frac{( 1 - ∣ x ∣ + s i n ∣ 1 - x ∣ ) s i n ( \frac{π}{2} [ 1 - x ] )}{∣ 1 - x ∣ . [ 1 - x ]}$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q31.Let $f (x) = {max {∣ x ∣, x^{2}} 8 - 2 ∣ x ∣ ∣ x ∣ \leq 2 2 < ∣ x ∣ \leq 4$ Let S be the set…
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Let d $\in$ R, and $A = - 2 15 4 + d (sin θ) + 2 (2 sin θ) - d (sin θ) - 2 d (- sin θ) + 2 + 2 d, θ \in [0, 2 π]$ …
Mathematics · Matrices and Determinants · MCQ
Q33.If the third term in the binomial expansion of $(1 + x^{l o g_{2} x})^{5}$ equals 2560, then a possible value of x is -
Mathematics · Binomial Theorem · MCQ
Q34.If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.If the area enclosed between the curves y = kx2 and x = ky2, (k > 0), is 1 square unit. Then k is -
Mathematics · Area Under the Curves · MCQ
Q36.Let $I = a \int b (x^{4} - 2 x^{2}) d x .$ If I is minimum then the ordered pair (a, b) is -
Mathematics · Definite Integration · MCQ
Q37.Let z1 and z2 be any two non-zero complex numbers such that $3 ∣ z_{1} ∣ = 4 ∣ z_{2} ∣ .$ If $z = \frac{3 z _{1}}{2 z _{2}} + \frac{2 z _{2}}{3 z _{1}}$ then :
Mathematics · Complex Numbers · MCQ
Q38.The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -
Mathematics · Sequences and Series · MCQ
Q39.A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R (3, – 2) are fixed points, then the locus of the centroid of $Δ$ PQR is a line :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q40.The shortest distance between the point $(\frac{3}{2}, 0)$ and the curve y = $x$ , (x > 0), is -
Mathematics · Application of Derivatives · MCQ
Q41.Consider the quadratic equation (c – 5)x2 – 2cx + (c – 4) = 0, c $e$ 5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q42.If $\frac{d y}{d x} + \frac{3}{c o s ^{2} x} y = \frac{1}{c o s ^{2} x}, x \in (\frac{- π}{3}, \frac{π}{3})$ and $y (\frac{π}{4}) = \frac{4}{3},$ then $y (- \frac{π}{4})$ …
Mathematics · Differential Equations · MCQ
Q43.Let f : R $\to$ R be a function such that f(x) = x3 + x2f'(1) + xf''(2) + f'''(3), x $\in$ R. Then f(2) equals -
Mathematics · Differentiation · MCQ
Q44.If 5, 5r, 5r2 are the lengths of the sides of a triangle, then r cannot be equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ