Mathematics Test 257

Result

Mathematics Test 257

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Question 1
4 / -1

For each t ∈ R, let [t] be the greatest integer less than or equal to t. Then,

A
is equal to 0

B
is equal to 15

C
is equal to 120

D
does not exist (in R)

Solution
Question 2
4 / -1

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square, each of whose sides contains exactly 2 balls less than the number of balls that each side of the triangle contains. Then, the number of balls used to form the equilateral triangle is:

A
190

B
262

C
225

D
157

Solution

Let n be the total number of balls required to formed equilateral triangle, then
Question 3
4 / -1

Consider the following three statements:

P : 5 is a prime number.

Q : 7 is a factor of 192

R : L.C.M. of 5 and 7 is 35.

Then the truth value of which one of the following statements is true?

A
(P ∧ Q) v (~ R)

B
(~ P) ∧ (~ Q ∧ R)

C
(~ P) v (Q ∧ R)

D
P v (~ Q ∧ R)

Solution
Question 4
4 / -1

The differential equation of the family of curves x² = 4b(y + b), b ∈ R is

A
xy' = y

B
x(y')2 = x + 2yy'

C
x(y')2 = x - 2yy'

D
x(y')2 = 2yy' - x

Solution
Question 5
4 / -1

If m is the minimum value of k for which the function is increasing in the interval [0, 3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to

A
(4, 3√2)

B
(4, 3√3)

C
(3, 3√3)

D
(5, 3√6)

Solution
Question 6
4 / -1

Then, in the interval (-2, 2), g is:

A
Differentiable at all points

B
Not differentiable at two points

C
Not continuous

D
Not differentiable at one point

Solution
Question 7
4 / -1

Find the modulus and argument of the complex number

A

B

C

D

Solution
Question 8
4 / -1

Which of the following is correct?

A
Determinant is a square matrix

B
Determinant is a number associated to a matrix.

C
Determinant is a number associated to a square matrix.

D
None of these

Solution

We know that to every square matrix, A = [aij] of order n. We can associate a number called the determinant of square matrix A, where aij = (i, j)th element of A. Thus, the determinant is a number associated with a square matrix.
Question 9
4 / -1

A line with positive direction cosines passes through the point P(2, - 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ is equal to

A
1

B
√2

C
√3

D
2

Solution
Question 10
4 / -1

The curve amongst the family of curves, represented by the differential equation. (x² - y²)dx + 2xy dy = 0 which passes through (1, 1) is:

A
A circle with centre on the y-axis

B
A circle with centre on the x-axis

C
An ellipse with major axis along the y-axis

D
A hyperbola with transverse axis along the x-axis

Solution