Mathematics and Pedagogy MCQ Questions with Answer

Solution: $\frac{\mathrm{x}}{\mathrm{y}}=\frac{3}{5}$

Using Dividendo and Componendo

$\Longrightarrow \frac{\mathrm{x}-\mathrm{y}}{\mathrm{x}=\mathrm{y}}=\frac{3-5}{3+5}=-\frac{1}{4}\,\,$

Solution: Clearly, defined absolute value i.e | x| = – x

Solution: N = 35 x 45 x 55 x 60 x 124 x 75

= 3 × 5 × 3 × 3 × 5 × 5 × 11 × 5 × 12 × 124 × 5 × 5 × 3

= 5⁶ × 3⁴ × 11 × 12 × 124

Since N is is divisible by 5^m

∴ 5^m = 5⁶ or m = 6

Solution: Let the number = x

52x – 25x = 324

⇒ 27x = 324

⇒x = 12

Solution: I. f(k) = 4k+3

For k=1, f(k) = 7; for k=2, f(k) = 11; for k=3, f(k) = 15

Values of f(k) cannot be expressed as sum of two squares for k = 1, 2, 3, …

II. f(k) = 8k+1

For k=1, f(k) = 9= 3²; for k=2, f(k) = 17; for k=3, f(k) = 25 = 5²

for k=4, f(k) = 33; for k=5, f(k) = 41

Values of f(k) is square of an odd integer only for some values of k

So, only statement I is correct

Solution: $\sqrt{\left( 2013 \right) ^2+2013+2014}$

= $\sqrt{\left( 2013 \right) ^2+2.2013.1+1}$

= $\sqrt{\left( 2013+1 \right) ^2}$

= 2014

Solution: LCM = prime factor with highest powe = 2⁴ x 3 x 5 x 7

Solution: $\frac{\left( 0.5 \right) ^4-\left( 0.4 \right) ^4}{\left( 0.5 \right) ^2+\left( 0.4 \right) ^2}$

= $\frac{\left( \left( 0.5 \right) ^2+\left( 0.4 \right) ^2 \right) .\left( \left( 0.5 \right) ^2-\left( 0.4 \right) ^2 \right)}{\left( \left( 0.5 \right) ^2+\left( 0.4 \right) ^2 \right)}$

= (0.5 + 0.4) (0.5 – 0.4) = 0.09

Solution: sum of all interior angles of a regular convex polygon = (2n – 4)×90°

∴ (2n – 4)×90 = 1080

⇒ 2n – 4 = 12

⇒2n = 16

⇒ n = 8

∴ each interior  angles of a regular convex polygon = $\frac{1080\degree}{8}=135\degree$

Solution: Arranging the given data in a table with their frequency:

From the table Range  = 7 – 0 = 7

Mode = 2 ( frequency 4)

Median = 3

∴ mean of range, mode and median = $\frac{7 +\,\,2 +3}{3}=4$