The system of equations x + 2y + 2z = 5, x + 2y + 3z = 6, x + 2y + λz = μ has infinitely many solution if

Correct Answer: Option C - λ = 2, μ = 5.

If the line a^2*x + ay + 1 = 0, for some real number a, is normal to the curve xy = 1, then

Correct Answer: Option A - a < 0.

A coin is thrown 8 number of times. What is the probability of getting a head in an odd number of throw?

Correct Answer: Option C - 1/8.

A critical orthopaedic surgery is performed on 3 patients. The probability of recovering a patient is 0.6. Then the probability that after surgery, exactly two of them will recover is

Correct Answer: Option B - 0.432.

If sin x = sin y and cos x = cos y, then the value of x - y is

Correct Answer: Option D - 2nπ.

If the perpendicular bisector of the line segment joining P(1,4) and Q(k,3) has y-intercept -4, then the possible value of k are

Correct Answer: Option A - -4 and 4.

Find the given numbers below, the smallest number which will be divided by 9, 10, 15 and 20, leaves the remainders 4, 5, 10 and 15 respectively

Correct Answer: Option C - 175.

It is given that the mean, median and mode of a data set is 1, 3^x and 9^x respectively. The possible values of the mode is

Correct Answer: Option A - 1,4.

A man starts at the origin O and walks a distance of 3 units in the north-east direction and then walks a distance of 4 units in the north-west direction to reach the point P, then OP is equal to

Correct Answer: Option D - (1/√2)(-î+7ĵ).

The points (1, 1/2) and (3, -1/2) are

Correct Answer: Option A - In between the lines 2x + 3y = 6 and 2x + 3y = -6.

If (4, -3) and (12, 5) are the two foci of an ellipse passing through the origin, then the eccentricity of the ellipse is

Correct Answer: Option D - √17 / 9.

The value of series 2/3! + 4/5! + 6/7! + ... is

Correct Answer: Option C - e^(-1).

There are 9 bottle labelled 1, 2, 3...9 and 9 boxes labelled 1, 2, 3, ...9. The number of ways one can put these bottles in the boxes so that each box gets one bottle and exactly 5 bottles go in their corresponding numbered boxes is

Correct Answer: Option A - 9 * C(9, 5).

A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is

Correct Answer: Option D - 4/9.

For what values of λ does the equation 6x^2 - xy + λy^2 = 0 represents two perpendicular lines and two lines inclined at an angle of π/4.

Correct Answer: Option C - -6 and -35.

If |F| = 40 N (Newtons), |D| = 3m, and θ = 60°, then the work done by F acting from P to Q is

Correct Answer: Option D - 60 J.

If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is

Correct Answer: Option C - 4/1155.

Let f(x) = {(x^2 * sin(1/x), if x ≠ 0), (0, if x = 0)}. Then which of the following is true

Correct Answer: Option C - f'(x) is not continuous at x = 0.

Which of the following is TRUE?

Correct Answer: Option B - ∫[-5 to 5] e^(x^2) dx = ∫[-5 to -2] e^(x^2) dx + ∫[2 to 5] e^(x^2) dx.

Given a set A with median m1 = 2 and set B with median m2 = 4. What can we say about the median of the combined set?

Correct Answer: Option D - at least 2.

The value of ∑[r=1 to n] (nPr / r!) is

Correct Answer: Option B - 1 - 2^(-n).

The number of one-one function f: {1,2,3} → {a, b, c, d, e} is

Correct Answer: Option D - None of the above.

How much work does it take to slide a crate for a distance of 25m along a loading dock by pulling on it with a 180 N force where the dock is at an angle of 45° from the horizontal?

Correct Answer: Option A - 3.18198 × 10^3 J.

If for non-zero x, c*f(x) + d*f(1/x) = log|x| + 3, where c ≠ d, then ∫[1 to e] f(x)dx

Correct Answer: Option B - (c-d)(3e-2) / (c^2-d^2).

The equation 3x^2 + 10xy + 11y^2 + 14x + 12y + 5 = 0 represent,

Correct Answer: Option B - an ellipse.

Let A and B be two events defined on a sample space Ω. Suppose A^c the complement of A relative to the sample space Ω. Then the probability P((A ∩ B^c ) ∪ (A^c ∩ B)) equal

Correct Answer: Option D - P(A) + P(B) – 2P(A ∩ B).

A speaks truth in 40% and B in 50% of the cases. The probability that they contradict each other while narrating same incident is

Correct Answer: Option B - 1/2.

Which pairs of bits can be joined together to form two words that have opposite meanings? Bits: ER/T (1), UC/E (2), DE/S (3), EN/D (4), EX/P (5), EA/R (6), AN/D (7), SI/P (8), RE/D (9), GO/S (10).

Correct Answer: Option A - (9,2)(5,7).

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The number of solutions of 5^(1+|sin x|+|sin x|^2+...)=25 is for x ∈ (−π, π)

2
0
4
infinite

View Answer & Explanation

Correct Answer: Option C -

Consider the function f(x) = {(-x^3 + 3x^2 + 1, if x ≤ 2), (cos x, if 2 < x ≤ 4), (e^x, if x > 4)}. Which of the following statement about f(x) is true?

f(x) has a local maximum at x = 1, which is also the global maximum
f(x) has a local maximum at x = 2, which is not the global maximum.
f(x) has a local maximum at x = π, but it is not the global maximum.
f(x) has a global maximum at x = 0.

View Answer & Explanation

Correct Answer: Option B -

f(x) has a local maximum at x = 2, which is not the global maximum.

The two parabolas y^2 = 4a(x + c) and y^2 = 4bx, a > b > 0 cannot have a common normal unless

c > 2(a + b)
c > 2(a - b)
c < 2(a – b)
c < 2/(a-c)

View Answer & Explanation

Correct Answer: Option B -

c > 2(a - b)

Let Z be the set of all integers, and consider the sets X = {(x, y): x^2 + 2y^2 = 3, x, y ∈ Z} and Y = {(x, y) : x > y, x, y ∈ Z}. Then the number of elements in X ∩ Y is

View Answer & Explanation

Correct Answer: Option A -

Region R is defined as region in first quadrant satisfying the condition x^2 + y^2 < 4. Given that a point P = (r, s) lies in R, what is the probability that r > s?

View Answer & Explanation

Correct Answer: Option C -

1/2

Let f : R → R be a function such that f(0)= 1/π and f(x) = (e^(πx) - 1) / (e^x - 1) for x ≠ 0

f(x) is not continuous at x = 0
f(x) is continuous but not differentiable at x = 0
f(x) is differentiable at x = 0 and f'(0) = -π/2
None of these

View Answer & Explanation

Correct Answer: Option B -

f(x) is continuous but not differentiable at x = 0

Consider the function f(x) = x^3 (6-x)^2. Which of the following statement is FALSE?

f is increasing in the interval (0, 4)
f is decreasing in the interval (6, ∞)
f has a point of inflection at x = 0
f has a point of inflection at x = 6

View Answer & Explanation

Correct Answer: Option C -

f has a point of inflection at x = 0

The vector A = (2x + 1)î + (x^2 - 6y)ĵ + (xy^2 + 3z)k is a

sink field
solenoidal field
source field
None of these

View Answer & Explanation

Correct Answer: Option A -

sink field

For an invertible matrix A, which of the following is not always true:

|adj(A)| ≠ 0
|A| ≠ 0
|AA^-1| = 1
|A adj(A)| ≠ 1

View Answer & Explanation

Correct Answer: Option D -

|A adj(A)| ≠ 1

The value of the limit lim (x->0) [(1^x + 2^x + 3^x + 4^x) / 4]^(1/x) is

1
(3!)^(1/3!)
(3!)^(1/4)
(4!)^(1/4)

View Answer & Explanation

Correct Answer: Option D -

(4!)^(1/4)

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