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The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A⁴ is equal to ___________

The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two... View Article

Let A₁, A₂, A₃,…. be squares such that for each n

Let A1, A2, A3,.... be squares such that for each n ≥ 1, the length of the side of An equals the length of diagonal of An+1. If the length of... View Article

When a missile is fired from a ship, the probability that it is intercepted is

When a missile is fired from a ship, the probability that it is intercepted is 1/3 and the probability that the missile hits the target, given... View Article

The value of [latex]\int_{-1}^1 x^2 e^{x^3}dx[/latex] where [t] denotes the greatest integer ≤ t,is :

a. (e+1)/3b. (e-1)/3ec. (e+1)/3ed. 1/3eAnswer: (c)... View Article

If a curve passes through the origin and the slope of the tangent

If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is Let x – 2 = t ⇒ dx = dtand y + 4 = u... View Article

The total number of positive integral solutions (x, y, z) such that xyz = 24 is

a. 36b. 45c. 24d. 30Answer: (d)x.y.z = 24x.y.z=23.31x=2(a_1 )⋅3(b_1 )y = 2(a_2 )⋅3(b_2 )z = 2(a_3 )⋅3(b_3 )a1, a2, a3 ∈... View Article

Solve limit problem

a. 1/2b. 1/ec. 1d. 0Answer: (c)... View Article

If the curves, [latex]frac{x^2}{a}+frac{y^2}{b}[/latex] and [latex]frac{x^2}{c}+frac{y^2}{d}[/latex] intersect each other at an angle of 90°, then which of the following relations is true ?

a. a + b = c + d b. a- b = c – d c. ab = (c+d)/(a+b) d. a-c = b+d Answer: (b) ………(1) diff : , , ……(2) ………(3) Diff : ………(4)... View Article

The image of the point (3,5) in the line x – y + 1 = 0, lies on :

a. (x – 2)2 + (y – 4) 2 =4b. (x – 4) 2 + (y + 2)2 =16c. (x – 4)2 + (y – 4)2 = 8d. (x – 2)2 + (y – 2)2... View Article

All possible values of θ ∈ [0, 2π] for which sin2θ + tan 2θ > 0 lie in

a. Answer: (b)... View Article

Let the lines (2 – i)z = (2 + i)[latex]bar{z}[/latex] and (2 + i)z + (i – 2)[latex]bar{z}[/latex] – 4i = 0, (here i² = –1) be normal to a circle C. If the line iz + [latex]bar{z}[/latex] + 1 + i = 0 is tangent to this circle C, then its radius is :

a. 3/√2b. 3√2c. 3/(2√2)d. 1/(2√2)Answer: (c)(2–i)z = (2+i) + 1 + i =... View Article

A tangent is drawn to the parabola y² = 6x which is perpendicular to the line 2x + y =1. Which of the following points does NOT lie on it?

a. (0,3) b. (-6,0) c. (4,5) d. (5,4) Answer: (d) Equation of tangent : y = mx + 3/(2m) mT = (1/2) (Because perpendicular to line 2x + y =... View Article

The integer k, for which the inequality x² – 2(3k – 1)x + 8k² – 7 >0 is valid for every x in R is :

a. 3b. 2c. 4d. 0Answer: (a)D < 0(2(3k-1))2 – 4(8k2 – 7) < 04(9k2 – 6k + 1) - 4(8k2 – 7) < 0k2 – 6 k + 8... View Article

The statement A→ (B → A) is equivalent to:

a. A → (A ᐱ B)b. A → (A ᐯ B)c. A → (A → B) d. A → (A ↔ B)Answer: (b) A → (B... View Article

The equation of the line through the point (0,1,2) and perpendicular to the line

The equation of the line through the point (0, 1, 2) and perpendicular to the line λ = 2 / 17Direction ratio of line (21, -28,... View Article

If 0<θ, ϕ < π/2, x = cos²ⁿθ

a. xyz = 4 b. xy – z = (x + y)z c. xy + yz + zx = z d. xy + z = (x+y)z Answer: (d)... View Article

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, the... View Article

The value of the integral

The value of the integral (where c is a constant of integration)a. 1/18[9 - 2 sin6 θ - 3 sin4 θ - 6 sin2 θ ](3/2) + cb. 1/18[11... View Article

Let α be the angle between the lines whose direction cosines satisfy the equations l +m – n = 0 and l² + m² – n² = 0. Then the value of sin⁴ α + cos⁴ α is

a. 3/4b. 1/2c. 5/8d. 3/8Answer: (c)Given that l+m=n ….(1)l2 + m2 – n2 = 0 ….(2)Squaring equation (1)l2 + m2 + 2lm = n2... View Article

The coefficients a,b and c of the quadratic equation, ax² + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is

a. 1/54b. 1/72c. 1/36d. 5/216Answer: (d)ax2 + bx + c = 0a,b,c ∈ {1,2,3,4,5,6}n(s) = 6 × 6 × 6 = 216D=0 ⇒ b2 = 4acac = b2/4,... View Article

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