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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 homogenization... 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 = 273x b. 2y = 91x c. y = 91x d. 2y = 273x Answer: (b) Number of... 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, \(\begin{array}{l}A = \begin{bmatrix} 1 & -\alpha \\... 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. 7 b. -3 c. 3 d. -7 Answer: (d) 1-2i is a root of z2 + αz + β... 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 work b. You will earn money, if you will not... 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, B, C will... 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 –... 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, ar3 a + ar + ar2 + ar3 = 65/12 …….(1) 1/a... View Article

For integers n and r, let…

For integers n and r, let The maximum value of k for which the sum exists, is equal to ____.... 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... 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... View Article

If the variance of 10 natural numbers 1,1,1,…,1,k is less than 10, then the maximum possible value of k is

\(\begin{array}{l}sigma ^{2} = frac{Sigma x^{2}}{n} – left (frac{Sigma x}{n} right )^{2}\end{array} \) ⇒ \(\begin{array}{l}sigma ^{2} = frac{9+k^{2}}{10} – left (frac{9+k}{10}... View Article

The students S₁, S₂,… S₁₀ are to be divided into 3 groups A, B, and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is

The students S1, S2,… S10 are to be divided into 3 groups A, B, and C such that each group... View Article

The number of the real roots of the equation (x + 1)² + |x – 5| = 27/4 is

For x ≥ 5, (x + 1)2+ (x – 5) = 27/4 ⇒ x2 + 3x – 4 = 27/4... View Article

The area of the region: R{(x, y): 5x² ≤ y ≤ 2x² + 9} is:

a. 9√3 square units b. 12√3 square units c. 11√3 square units/ d. 6√3 square units Answer: (b) Required area... View Article

If a curve y = f(x) passes through the point (1, 2) and satisfies xdy/dx + y = bx⁴, then for what value of b, [latex]int_{1}^{2}f(x)dx = frac{62}{5}[/latex]

a. 5 b. 62/5 c. 31/5 d. 10 Answer: (d) dy/dx + y/x = bx3 I.F. = \(\begin{array}{l}e^{int frac{dx}{x}}\end{array} \)... View Article

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