Let X1, X2, …. X18 be eighteen observation such that ∑i=118 (Xi – ɑ) = 36 and
Answer: 4 Solution: Given, ∑i=118 (Xi – ɑ) = 36 ∑xi – 18ɑ = 36 ∑xi = 18 (ɑ +... View Article
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Let ɑ and β be two real numbers such that ɑ + β = 1 and ɑ β = – 1.
Let ɑ and β be two real numbers such that ɑ + β = 1 and ɑ β = –... View Article
The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is
Answer: 1000 Since the required number has G.C.D with 18 as 3. It must be an odd multiple of ‘3’... View Article
The triangle of the maximum area that can be inscribed in a given circle of radius ‘r’ is:
a. A right-angle triangle having two of its sides of length 2r and r. b. An equilateral triangle of height... View Article
Let f (x) = ∫0x et f (t) dt + ex be a differentiable function for all x ∈ R. Then f (x) equals
a. 2eex-1 – 1 b. e(e^x-1) c. 2ee^x – 1 d. ee^x – 1 Solution: Answer: (a) Given, f (x)... View Article
Let f (x) = sin-1 x and g (x) = [x2 – x – 2] / [2x2 – x – 6]. If g (2) = limx→2 g (x), then then the domain of the function fog is:
a. (- ∞, – 2] ⋃ [- 4 / 3, ∞] b. (- ∞, – 1] ⋃ [2, ∞) c.... View Article
A natural number has prime factorization given by n = 2x3y5z, where..
A natural number has prime factorization given by n = 2x3y5z, where y and z are such that y +... View Article
Find the number of possible functions g
Let A = {1, 2, 3 ……. , 10} and f : A → A be defined as \(\begin{array}{l}f(k) =... View Article
Let f : R → R be defined as
Let f : R → R be defined as If f (x) is continuous on R, then a + b... View Article
For x > 0, if f (x) = ∫1x loge t / [1 + t] dt, then f (e) + f (1 / e) is equal to:
a. 1 / 2 b. -1 c. 1 d. 0 Solution: Answer: (a)
If vectors a1 = xi – j + k and a2 = i + yj + zk are collinear, then a possible unit vector parallel to the vector xi + yj + zk is
a. (1 / √2) (- j + k) b. (1 / √2) (i – j) c. (1 / √3) (i... View Article
A seven-digit number is formed using the digit 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is:
a. 6 / 7 b. 4 / 7 c. 3 / 7 d. 1 / 7 Solution: Answer: (3) n... View Article
Consider the following system of equations:
Question 10: Consider the following system of equations: x + 2y – 3z = a 2x + 6y – 11... View Article
Let F1 (A, B, C) = (A ∧ ~B) ∨ [~C ∧….
Question 9: Let F1 (A, B, C) = (A ∧ ~B) ∨ [~C ∧ (A ∨ B)] ∨ ~A and... View Article
If 0 < a, b < 1, and tan-1 a + tan-1 b = π / 4, then the value of (a + b) – [a2 + b2] / 2 + [a3 + b3 ] / 3 – [a4 + b4] / 4 + …. is
a. loge2 b. loge (e / 2) c. e d. e2 – 1 Solution: Answer: (a) tan-1 {[a + b]... View Article
Let A1 be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in the first quadrant.
Let A1 be the area of the region bounded by the curves y = sinx, y = cosx and y-axis... View Article
Let the slope of the tangent line to a curve at any point P (x, y) be given by [xy2 + y] / x. If the curve intersects the line x + 2y = 4 at x = – 2, then the value of y, for which the point (3, y) lies on the curve, is:
a. – 18 / 11 b. – 18 / 19 c. – 4 / 3 d. 18 / 35 Solution:... View Article
If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circle of the radius r, then r is equal to
a. 14 b. 12 c. 1 d. 13 Solution: Answer: (b) P ≡ (2h – 3), (2k – 2) →... View Article
Let A (1, 4) and B (1, – 5) be two points. Let P be a point on the circle (x – 1)2 + (y – 1)2 = 1 such that (PA)2 + (PB)2 have maximum value, then the points P, A and B lie on
a. a parabola b. a straight line c. a hyperbola d. an ellipse Solution: Answer: (b) PA2 = cos2 θ... View Article
Let f(x) be a differentiable function at x = a with f’ (a) = 2 and f (a) = 4. Then limx→a [x f (a) – a f (x)] / [x – a] equals:
a. 2a + 4 b. 2a – 4 c. 4 – 2a d. a + 4 Solution: Answer: (c) By... View Article
