The sum of the series ∑n=1∞∞[n2 + 6n + 10] / (2n + 1)! is equal to:
a. (41/ 8) e + (19 / 8) e-1 – 10 b. (- 41/ 8) e + (19 / 8)... View Article
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Let L be a line obtained from the intersection of two planes
Let L be a line obtained from the intersection of two planes x + 2y + z = 6 and... View Article
Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is
a) 3√(5/2) b) 3√5/2 c) √10 d) 2√10 Solution: As we know centroid divides line joining circumcentre and orthocentre internally... View Article
Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series.
Let A be the sum of the first 20 terms and B be the sum of the first 40 terms... View Article
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is
a) at least 500 but less than 750 b) at least 750 but less than 1000 c) at least 1000... View Article
PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR…
PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of... View Article
The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, x+y+z = 7 is
a) 1/3 b) √(2/3) c) 2/√3 d) 2/3 Solution: Direction ratios of AB = (1,0,1) Let be angle between line... View Article
Let u be a vector coplanar with the vectors ….
Let u be a vector coplanar with the vectors \(\begin{array}{l}\vec{a}= 2\hat{i}+3\hat{j}-\hat{k}\end{array} \) and \(\begin{array}{l}\vec{b}= \hat{j}+\hat{k}\end{array} \). If vector u is... View Article
Let y = y(x) be the solution of the differential equation sin x(dy/dx)+y cosx = 4x, x∈(0,π). If y(π/2) = 0, then y(π/6) is equal to
a) (-8/9)π2 b) (-4/9)π2 c) (4/9√3)π2 d) (-8/9√3)π2 Solution: (dy/dx)+y cotx = 4x/sin x IF = e∫cot xdx = elog|sin... View Article
Let S = {t∈R: f(x) = |x-π|(e|x|-1)sin x is not differentiable at t}. Then the set S is equal to:
a) {π} b) {0,π} c) (an empty set) d) {0} Solution: f(x) = |x-π|(e|x|-1) sinx Obviously differentiable at x =... View Article
Solve the integral of fraction – Step by Step Solution
a) 1/(1+cot3x) + C b) -1/(1+cot3x) + C c) 1/3(1+tan3x) + C d) -1/3(1+tan3x) + C where C is the... View Article
If ∑9i=1 (xi-5) = 9 and ∑9i=1 (xi-5)2 = 45, then the standard deviation of the 9 items x1, x2,…x9 is:
a) 2 b) 3 c) 9 d) 4 Solution: Variance = (1/n) Ʃi=1n xi2-[(1/n) Ʃi=1n xi]2 = (1/9)×45-((1/9)×9)2 = 5-1... View Article
For each t ∈ R, let [t] be the greatest integer less than or equal to t.
For each t ∈ R, let [t] be the greatest integer less than or equal to t. Then \(\begin{array}{l}\lim_{x\to0+}x([\frac{1}{x}]+[\frac{2}{x}]+…[\frac{15}{x}])\end{array} \)... View Article
Let g(x) = cos x2, f(x) = √x and α, β(α< β) be the roots
Let g(x) = cos x2, f(x) = √x and α, β(α< β) be the roots of the quadratic equation 18x2-9πx+π2... View Article
The value of [latex]\int_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{\sin ^{2}x}{1+2^{x}}dx[/latex] is:
a) 4π b) π/4 c) π/8 d) π/2 Solution: Answer: (b)
A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is
a) 3x+2y = xy b) 3x+2y = 6xy c) 3x+2y = 6 d) 2x+3y = xy Solution: line y-3 =... View Article
Let a1, a2, a3,..a49 be in A.P
Let a1, a2, a3,..a49 be in A.P such that Ʃk=012 a4k+1 = 416 and a9+a43 = 66. If a12+a22+…+a172 =... View Article
The sum of the coefficients of all odd degree terms in the expansion of (x+√(x3-1))5+(x-√(x3-1))5, (x>) is
a) 1 b) 2 c) -1 d) 0 Solution: (a+b)n+(a-b)n = 2(nC0an + nC2an-2b2+ nC4an-4b4…) (x+√(x3-1))5+(x-√(x3-1))5, (x>) = 2(5C0x5+5C2x3(√(x3-1))2+5C4x(√(x3-1))4) =... View Article
If [latex]\begin{vmatrix} x-4 & 2x &2x \\ 2x& x-4 & 2x\\ 2x& 2x & x-4 \end{vmatrix}[/latex] = (A+Bx)(x-A)2 then the ordered pair (A, B) is equal to
a) (-4, 5) b) (4, 5) c) (-4, -5) d) (-4, 3) Solution: = (5x-4)(-1)(x+4)(x-4-2x) = -1(5x-4)(x+4)(-x-4) = (5x-4)(x+4)(x+4)2 =... View Article
Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB = θ, then a value of tan θ is
a) 3 b) 4/3 c) 1/2 d) 2 Solution: Tangent and normal are drawn at P (16, 16) on y2... View Article
