Latest Posts

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

a. \(\begin{array}{l}\left ( 0,\frac{\pi }{2} \right )\cup \left ( \pi,\frac{3\pi }{2} \right )\end{array} \) b. \(\begin{array}{l}\left ( 0,\frac{\pi }{4} \right )\cup \left... 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/√2 b. 3√2 c. 3/(2√2) d. 1/(2√2) Answer: (c) (2–i)z = (2+i) \(\begin{array}{l}bar{z}\end{array} \) ⇒(2–i)(x+ iy)=(2+i)(x–iy) ⇒2x–ix + 2iy... 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... 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. 3 b. 2 c. 4 d. 0 Answer: (a) D < 0 (2(3k-1))2 – 4(8k2 – 7) < 0... 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 ↔... 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 \(\begin{array}{l}\frac{x-1}{2} = \frac{y+1}{3} =... View Article

If 0<θ, ϕ < π/2, x = cos²ⁿθ

a. xyz = 4 b. xy – z = (x + y)z c. xy + yz + zx = z... 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... 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... 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. 3/4 b. 1/2 c. 5/8 d. 3/8 Answer: (c) Given that l+m=n ….(1) l2 + m2 – 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. 1/54 b. 1/72 c. 1/36 d. 5/216 Answer: (d) ax2 + bx + c = 0 a,b,c ∈ {1,2,3,4,5,6}... View Article

Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then the probability of event A is equal to

a. 4 / 9 b. 9 / 56 c. 3 / 7 d. 11 / 27 Answer: (a) Total case... View Article

Let the lengths of intercepts on x-axis and y-axis made by the circle x² + y² + ax + 2ay + c = 0, (a < 0) be 2 √2 and 2 √5, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to:

a. √10 b. √6 c. √11 d. √7 Answer: (b) 2 √(a2 / 4 – c) = 2√2 √(a2 –... View Article

Let f be a real-valued function, defined on R – {–1, 1} and given by f(x) = 3 log_e |(x – 1) / (x + 1)| – 2 / (x – 1). Then in which of the following intervals, function f (x) is increasing?

a. (- ∞, – 1) ⋃ ([1 / 2, ∞) – {1}) b. (- 1, 1 / 2] c. (–∞,... View Article

Let A (–1, 1), B (3, 4) and C(2, 0) be given three points. A line y = mx,

Let A (–1, 1), B (3, 4) and C(2, 0) be given three points. A line y = mx, m... View Article

Consider the integral I = ∫₀¹⁰ {[x] e^[x]} / [e^x-1] dx, where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :

a. 45 (e – 1) b. 45 (e + 1) c. 9(e – 1) d. 9(e + 1) Answer: (a)... View Article

If (x, y, z) be an arbitrary point lying on a plane P which passes through the points

If (x, y, z) be an arbitrary point lying on a plane P which passes through the points (42, 0,... View Article

If the foot of the perpendicular from point (4, 3, 8) on the line

If the foot of the perpendicular from point (4, 3, 8) on the line L1 : [x – a] /... View Article

If y = y (x) is the solution of the differential equation (dy / dx) + (tan x) y = sinx, 0 ≤ x ≤ π / 3, with y(0) = 0, then y (π / 4) equal to:

a. loge 2 b. (1 / 2) loge 2 c. (1 / 2 √2) loge 2 d. (1 / 4)... View Article

Let f : S → S where S = (0, ∞) be a twice differentiable function such that f (x + 1) = x f (x). If g : S → R be defined as g (x) = log_ef (x), then the value of |g”(5) – g”(1)| is equal to:

a. 197 / 144 b. 187 / 144 c. 205 / 144 d. 1 Answer: (c) f(x+1) = xf(x) g(x+1)... View Article

«
1
…
2,752
2,753
2,754
2,755
2,756
…
5,472
»