If two sets A and B have 17 elements in common, then the number of elements common to the set A \(\times\)B and B \(\times\)A is

(a)

2¹⁷

(b)

17²

(c)

34

(d)

insufficient data

Which one of the following statements is false? The graph of the function \(f(x)={1\over x}\)

(a)

exist is the first and third quadrant only

(b)

is a reciprocal function

(c)

is defined at x = 0

(d)

it is symmetric about y = x and y = - x.

If |x + 3| ≥ 10 then ___________

(a)

x ∊ (-13, 7]

(b)

x ∊ [-13, 7)

(c)

x ∊ (-∞, -13] \(\cup\) [7, ∞)

(d)

x ∊ (-∞, -13] \(\cup\) [7, ∞)

The quadratic equation whose roots are tan 75° and cot 75° is _______________

(a)

x²+4x+ 1 = 0

(b)

4x²-x+ 1 = 0

(c)

4x²+ 4x - 1 = 0

(d)

x² - 4x + 1 = 0

If 10ⁿ + 3 \(\times\) 4ⁿ⁺²+\(\lambda \) is divisible by 9 for all n \(\in \)N, then the least positive integral value of \(\lambda \) is _________

(a)

5

(b)

3

(c)

7

(d)

1

The number of integers greater than 6000 that can be formed, using the digits 3, 5, 6, 7 and 8 without repetition  _________

(a)

216

(b)

192

(c)

120

(d)

72

The sum of the digits in the unit's place of all the 4- digit numbers formed by 3, 4, 5 and 6, without repetition, is _______.

(a)

432

(b)

108

(c)

36

(d)

72

\(\frac{2}{1!}+\frac{4}{3!}+\frac{6}{5!}+. . .\infty =\) ______________

(a)

e

(b)

2e

(c)

\(\frac{1}{e}\)

(d)

e²

If the square of the matrix \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is the unit matrix of order 2, then \(\alpha ,\beta \) and \(\gamma\) should satisfy the relation.

(a)

1 + \(\alpha ^2+\beta \gamma=0\)

(b)

1 - \(\alpha ^2-\beta \gamma=0\)

(c)

1 - \(\alpha ^2+\beta \gamma=0\)

(d)

1 + \(\alpha ^2-\beta \gamma=0\)

If the projection of \(5\hat{i}-\hat{j}-3\hat{k}\) on the vector \(\hat{i}+3\hat{j}+\lambda\hat{k}\) is same as the projection of \(\hat{i}+3\hat{j}+\lambda\hat{k}\) on \(5\hat{i}-\hat{j}-3\hat{k}\), then \(\lambda\) is equal to

(a)

\(\pm 4\)

(b)

\(\pm 3\)

(c)

\(\pm 5\)

(d)

\(\pm 1\)