1.

A binary number is represented by (cdccddcccddd)₂, where c > d What is its decimal equivalent ?

• 1848

• 2048

• 2842

• 2872

Let S = {2, 4, 6, 8, ..........20}. What is the maximum number of subsets does S have ?

• 10

• 20

• 512

• 1024

Consider the following statements in respect of the quadratic equation 4(x - p)(x - q) - r² = 0, where p, q and r are real numbers:

1) The roots are real

2) The roots are equal if p = q and r = 0

Where of the above statements is/are correct ?

• 1 only

• 2 only

• Both 1 and 2

• Neither 1 nor 2

How many real roots does the equation x² + 3|x| + 2 = 0 have ?

• 1 only

• 2 Only

• Both 1 and 2

• Neither 1 nor 2

If ${\mathrm{x}}^{{\log }_7\left(\mathrm{x}\right)} > 7 \mathrm{where} \mathrm{x} > 0,$ then which one of the following is correct ?

• $\mathrm{x} \in \left(0, \infty \right)$

• $\mathrm{x} \in \left(\frac{1}{7}, 7\right)$

• $\mathrm{x} \in \left(0, \frac{1}{7}\right) \cup \left(7, \infty \right)$

• $\mathrm{x} \in \left(\frac{1}{7}, \infty \right)$

What is the solution of x ≤ 4, y ≥ 0 and x ≤ - 4, y ≤ 0 ?

• x ≥ - 4, y ≤ 0

• x ≤ 4, y ≥ 0

• x ≤ - 4, y = 0

• x ≥ - 4, y = 0

If 3^rd, 8^th and 13^th terms of a GP are p, q and r respectively, then which one of the following is correct ?

• q² = pr

• r² = pq

• pqr = 1

• 2q = p + r

Let S_n be the sum of the first n terms of an AP. If S_2n = 3n + 14ⁿ², then what is the common difference ?

• 5

• 6

• 7

• 9

How many two-digit numbers are divisible by 4 ?

• 21

• 22

• 24

• 25

Let a, b, c be in AP and k ≠ 0 be a real number. Which of the following are correct ?

1) ka, kb, kc are in AP

2) k –a, k -b, k –c are in AP

3) $\frac{\mathrm{a}}{\mathrm{k}}, \frac{\mathrm{b}}{\mathrm{k}}, \frac{\mathrm{c}}{\mathrm{k}} \mathrm{are} \mathrm{in} \mathrm{AP}$ are in AP

Select the correct answer using the code given below :

• 1 and 2 only

• 2 and 3 only

• 1 and 3 only

• 1, 2 and 3