11.

A good Mathematics textbook contains a lot of

• questions for practice

• questions for exploration

• worked out,examples

• theorems and proofs

Consider the following statement. "Every odd natural number is a prime number." Which of the following methods of "proof can be used to prove/disprove the above statement?

• Direct proof

• Method of disproof

• Proof by contrapositive

• Proof by contradiction

$\mathrm{Which} \mathrm{of} \mathrm{the} \mathrm{following} \mathrm{numbers} \mathrm{does} \mathrm{not} \mathrm{lie} \mathrm{between} \frac{ - 5}{6} \mathrm{and} \frac{7}{8}$

• $\frac{ - 17}{24}$

• $\frac{5}{6}$

• $\frac{ - 3}{4}$

• $\frac{ - 11}{12}$

$$\begin{gathered} \mathrm{If} \mathrm{x}\sqrt{243} = \mathrm{y}\sqrt{867}, \mathrm{where} \mathrm{x} \mathrm{and} \mathrm{y} \mathrm{are} \mathrm{co}-\mathrm{prime} \mathrm{numbers}, \\ \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of}(\mathrm{x} - \mathrm{y}) \mathrm{is} \end{gathered}$$

• 3

• 8

• 4

• 6

On dividing the polynomial

$8{\mathrm{x}}^3 - 6{\mathrm{x}}^2 +\hspace{0.17em}10\mathrm{x} +\hspace{0.17em}3 \mathrm{by} \left(4\mathrm{x} + 1\right), \mathrm{the} \mathrm{quotient} \mathrm{is} 2{\mathrm{x}}^2 + \mathrm{k}, \mathrm{where} \mathrm{k} \mathrm{is} \mathrm{equal} \mathrm{to}$

• 3  - 2x

•  - 3 + 2x

• 3 + 2x

•  - 3 - 2x

In the product of (9x + 15 - x) and ( - 1 - x + x²), if A, B and C are the coefficients of x³, x² and x respectively, then the value of (A + B - C) is

•  - 3

• 14

• - 17

• 11

A person marks his goods 40% above the cost price and allows 40% discount on the marked price. His loss/gain percent is

• loss, 8%

• No loss/gain

• gain, 10%

• loss, 16%

Two sides of a right triangle measure 15 cm and 17 cm. Which of the following statements can be true of the length of the third side of the triangle ?

A. It is between 4 cm and 7 cm.

B. It is between 20 cm and 23 cm.

C. It is less than 10 cm

• Only B

• A and C

• A and B

• B and C

$$\begin{gathered} \mathrm{In} ∆\mathrm{ABC}, \mathrm{AB} =4\mathrm{cm}, \mathrm{AC} =5 \mathrm{cm} \mathrm{and} \mathrm{BC} = 6 \mathrm{cm}. \\ \mathrm{In} ∆\mathrm{PQR}, \mathrm{PR} = 4 \mathrm{cm}, \mathrm{PQ} = 5 \mathrm{cm} \mathrm{and} \mathrm{RQ} = 6 \mathrm{cm}. ∆\mathrm{ABC} \mathrm{is} \mathrm{congruent} \mathrm{to} \end{gathered}$$

• $∆\mathrm{PQR}$

• $∆\mathrm{RPQ}$

• $∆\mathrm{PRQ}$

• $∆\mathrm{QRP}$

A tank is in the form of a cuboid. It holds a maximum of 540 m³ water. If the tank is 8 m long and 15 m wide, then how many metres,deep must the water be when the tank is full ?

• 2

• 4.5

• 2.5

• 3