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The set that contains atomic numbers of only transition elements, is

1) 9, 17, 34, 38 2) 21, 25, 42, 72 3) 37, 42, 50, 64 4) 21, 32, 53, 64 Answer: 2 Transition elements = 21 to 30 37 to 48 57 & 72 to 80 Ans.... View Article

Kraft temperature is the temperature

1) Above which the aqueous solution of detergents starts boiling 2) Below which the formation of micelles takes place. 3) Above which the... View Article

The increasing order of pK_b values

The increasing order of pKb values of the following compounds is: The order is I < II < IV < III. Hence option 3 is the answer.... View Article

The major product of the following reaction is

The major product of the following reaction is: Option 2 is the answer.... View Article

The major products of the following reactions

The major products of the following reactions are: Option 1 is the answer.... View Article

In a group of 400 people, 160 are smokers and non-vegetarian….

In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and... View Article

[latex]\lim_{n \rightarrow \infty}[\frac{1}{n} + \frac{n}{(n+1)^2} + \frac{n}{(n+2)^2} +……+ \frac{n}{(2n-1)^2}][/latex] is equal to:

a. 1b. 1/3c. 1/2d. 1/4Answer: (c)... View Article

A hyperbola passes through the foci of the ellipse x²/25 + y²/16 = 1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:

a. x2/9 – y2/4 = 1b. x2/9 – y2/16 = 1c. x2 – y2 = 9d. x2/9 – y2/25 = 1Answer: (b)For ellipse, e1 =... View Article

Solve the intergral problem

a. loge|x2 + 5x – 7| + cb. (1/4) loge |x2 + 5x – 7| + cc. 4 loge|x2 + 5x – 7| + cd. loge √(x2 + 5x – 7) + cAnswer: (c)... View Article

If the curve x² + 2y² = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is:

a. /2 + tan–1(1/4)b. /2 – tan–1(1/4)c. /2 + tan–1(1/3)d. /2 – tan–1(1/3)Answer: (a)Using homogenizationx2... View Article

Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A × B. Then

a. y = 273xb. 2y = 91xc. y = 91xd. 2y = 273xAnswer: (b)Number of elements in A = 3Number of elements in B = 5Number of elements in A × B =... View Article

If for the matrix, [latex]A = begin{bmatrix} 1 & -alpha \ alpha & beta end{bmatrix}[/latex] AA^T = I₂, then the value of α⁴ + β⁴ is:

a. 1 b. 3 c. 2 d. 4 Answer: (a) or the matrix,... View Article

If α, β∈ R are such that 1 – 2i (here i² = –1) is a root of z² + αz + β = 0, then (α – β) is equal to:

a. 7b. -3c. 3d. -7Answer: (d)1-2i is a root of z2 + αz + β = 0.(1-2i) 2 +... View Article

The contrapositive of the statement “If you will work, you will earn money” is:

a. If you will not earn money, you will not workb. You will earn money, if you will not workc. If you will earn money, you will workd. To earn... View Article

A plane passes through the points A(1,2,3), B(2,3,1) and C(2,4,2). If O is the origin and P is (2,–1,1), then the projection of vector(OP) on this plane is of length:

a. √(2/5)b. √(2/3)c. √(2/11)d. √(2/7)Answer: (c)A(1,2,3),B(2,3,1),C(2,4,2),O(0,0,0)Equation of plane passing through A,... View Article

If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle (x – 2)²+ (y – 3)²= 25 at the point (5, 7) is A, then 24A is equal to

Equation of normal at P is(y - 7) = ((7 - 3)/(5 - 2))(x - 5)⇒ 3y - 21 = 4x – 20⇒ 4x - 3y + 1 = 0⇒ M is (-1/4, 0)Equation of... View Article

The sum of first four terms of a geometric progression (G.P.) is 65/12 and the sum of their respective reciprocals is 65/18. If the product of first three terms of the G.P. is 1, and the third term is α then 2α is

Let terms of GP are a, ar, ar2, ar3a + ar + ar2 + ar3 = 65/12 …….(1)1/a + 1/ar + 1/(ar2) + 1/ar3) = 65/18⇒1/a (r3 + r2 + r +... View Article

For integers n and r, let…

For integers n and r, let The maximum value of k for which the sumexists, is equal to ____.Solution: (1+x)10 = 10C0 + 10C1x + 10C2x2 +... View Article

Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (-5, 0). If the locus of the point P is a circle of radius r, then 4r² is equal to

Let P be (h, k), A(5, 0) and B(-5, 0)Given PA = 3PB⇒ PA2 = 9PB2⇒ (h-5)2 + k2 = 9[(h + 5)2 + k2]⇒ 8h2 + 8k2 + 100h + 200 =... View Article

Solve below problem on complex numbers

If i = √-1. If [(-1 + i√3)21/(1 - i)24 + (1 + i√3)21/(1 + i)24 ] = k, and n = [|k| ] be the greatest integral part of |k|.... View Article