Mensuration Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

According to Pythagorean triplet.

The sum of square of base and perpendicular equal to square of hypotenuse.

By hit and trial method:—

$(2n)^2 + (n^2 – 1)^2 = (n^2 + 1)^2$

$4n^2 + n^4 + 1 – 2n^2 = n^4 + 2n^2$ + 1

$n^4 + 2n^2 + 1 = n^4 + 2n^2$ + 1

LHS = RHS

Answer: (a)

The n-sided polygon can be dinded into 'n' triangle with O, the Centre of the circle as one vertex for each triangle. The altitude of each triangle is r. Let the sides of the polygon be '$a_1 ', a_2 ----- a_n$.(Given $a_1 = a_2 = ------ a_n$)

∴ The area of polygon is ${nr}/2 = {pr}/2$

Area of polygon = ${a_1r}/2 + {a_2r}/2 + --- {a_nr}/2 = {pr}/2$

So, option (a) is correct.

Answer: (c)

Two possibilities are there :

(i) Chemistry part I is available in 8 books with Chemistry part II.

or

(ii) Chemistry part II is not available in 8 books but Chemistry part I is available.

Total No. of ways = 1× 1 ×$^6C_1 + ^7C_3$ = 6 + ${7 × 6 × 5}/{3 × 2}$ = 6 + 35 = 41

Answer: (a)

Area will be maximum when P and B will be same

So $P^2 + P^2 = H^2 ⇒ P^2 = H^2/2$

⇒ P = $H/√2$

Area = $1/2 BP = 1/2 P^2 = 1/2. H^2/2 = H^2/4$

= ${100}/4 = 25 cm^2$

Answer: (a)

Suppose the smaller and larger sides of a right triangle be x and y, respectively.

By given condition,

$x^2 + y^2 = (3 √{10})^2$

⇒ $x^2 + y^2$ = 90 ... (i)

and $9x^2 + 4y^2$ = 405 ... (ii)

On solving Eqs. (i) and (ii), we get

x = 3 units and y = 9 units

Answer: (d)

The tangents drawn from an outer point on a circle are always equal = ∠CBA.

Therefore, ∠CAB = ∠CBA

∴ 45° + x + x = 180°

⇒ 2x = 180° – 45°

⇒ x = 67 ${1°}/2$

∠AQP = ∠x = ∠BQP

= 67 ${1°}/2$

(alternate interior segments properties)

⇒ ∠AQB = ∠AQP + ∠BQP

= $67 {1°}/2 + 67{1°}/2$ = 135°