SEBA HSLC Maths Question Paper Solution 2022 - Bzziii

CLASS 10 SEBA
Mathematics 2020

Section A

   Which of the following is an irrational number?

(a) 0.142857142857142857...
(b) `22/7`
(c)`\pi`
(d) `\frac{\sqrt{4}}{11}`

   Consider the following pairs of liner equations:

(i) `2x-3y=8`, `4x-6y=9`
(ii) `2x+3y-9=0, 4x+6y-18=0`

Choose the correct alternative:

(a) (a) The pair in (1) has no solution, whereas the pair in (ii) has unique solution
(b) The pair in (i) has infinitely many solutions, whereas the pair in (ii) has no solution
(c) The pairs in (1) and (ii) have no solutions.
(d) The pair in (1) has no solution, whereas the pair in (ii) has infinitely many solution

   The products of the zeroes of `3x^{2}+11x-2` is:

(a) `2/3`
(b) `-\frac{2}{3}`
(c) `11/3`
(d) `-\frac{11}{3}`

   The `26^th` term of the AP 0,-4,-8,-12..... is

(a) -96
(b) -100
(c) -104
(d) -108

   Let ABC be a traingle such that AB=(`X-1`)cm, AC=`2\sqrt{x}`cm, BC=(`x`+1)cm. Then :

(a) A = `90^{0}`
(b) A = `90^{0}`
(c) A = `90^{0}`
(d) none of these

   The point (`x,y`) is equidistant from the point is (7,1) and (3,5). Then:

(a) x+y=2
(b) -x+y=2
(c) x-y=2
(d) -x-y=2

   `8cosec^2A - 8cot^2A` = ?

(a) 0
(b) 1
(c) 8
(d) 16

   A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 30°. Find the height of the tower.

(a) `5\sqrt{3}` m
(b) `15\sqrt{3}` m
(c) 15 m
(d) `\frac{5}{\sqrt{3}}` m

   Which of the following Statement is correct ?

(a) All circles are congruent
(b) All circles are similar
(c) All isosceles traingles are similar
(d) All rectangles are congruent.

   The degree measure of the angle at the centre of a circle is theta. The length of an arc of the sector is:

(a) `\frac{\theta\pi r}{\sqrt{90}}`
(b) `\frac{\theta\pi r}{\sqrt{180}}`
(c) `\frac{\theta\pi r}{\sqrt{270}}`
(d) `\frac{\theta\pi r}{\sqrt{360}}`

Where r is the radius of the circle.

   Two cubes each of volume 64 `"cm"^3` are joined end to end. Find the surface area of the resulting cuboid.

(a) 48 `"cm"^2`
(b) 64 `"cm"^2`
(c) 80 `"cm"^2`
(d) 160 `"cm"^2`

   the sum of probabilities of all the elementary events of an experiment is:

  1
  1.25
  1.5
  2

Section B

   Find the HCF and LCM of 6,72,120 using the prime factorisation method.Is the product of the numbers equalto products of HCF and LCM ?

   5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen by graphical method.

   How many two-Digit numbers are divisible by 5 ?

   Find the cordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3:1 internally.

   If sec A=`13/12`, calculate sin A and cot A. (A is an acute angle.)

   Evaluate:

`\frac{5cos^2 60^0+4sec^2 30^0-tan^2 45^0}{sin^2 30^0+sin^2 60^0}`

   If sec 4A=cosec (A - `20^0`), find the Value of A. (4A is an acute angle)

   Prove that

`(cosec\theta-cos\theta)^2 = \frac{1 - cos\theta}{1 + cos\theta}`

   One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting .

(i) a king of red colour/>
(ii) a spade

Section C

   Prove that `\sqrt{7}` is irrational.

   state the Division Algorithm for polynomials.

Divide the polynomial p(`x`) by the polynomial g(`x`), and the find the quotient and the remainder.

p(`x`)=`x^4-5x+6,` `g(x)= 2-x^2`

   A fraction becomes `9/11`, if 2 is added to both the numerator and denominator. If 3 is added to both the numerator and the denominator, it becomes `5/6`. Find the fraction.

   Solve

`3x^2-2 \sqrt{2}x+2 = 0`

   Sum of the areas of two squares is `468m^2`. If the differences of their perimeters is 24 m, find the sides of two squres.

Divide the polynomial p(`x`) by the polynomial g(`x`), and the find the quotient and the remainder.

p(`x`)=`x^4-5x+6,` `g(x)= 2-x^2`

   Find the coordinates of a point A, where AB is a diameter of a circle whose centre is (2,-3) and B is (1,4).

   Find the sum of first 51 terms of an AP whose secound and third terms are 14 and 18 respectively.

   D and E are points on the sides CA and CB respectively​ of a triangle of a traingal ABC right angled at C. Prove that `AE^2+BD^2`=`AB^2+DE^2`

   Find the area of the traingle formed by joining the middle points of the sides of the traingle whose vertices are (0, -1), (2, 1) and (0, 3)

   Find the area of the sector of a circle with radius 4 cm and angle `30^0`. Also, find the area of the corresponding major sector. (`\pi`= 3.14)

Section D

   Solve the pair of equations by reducing them to a pair of liner equations.

`\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}`

`\frac{1}{2(3x+y)}+\frac{1}{2(3x-y)}=\frac{-1}{ 8}`

   If the areas of two similar traingals are equal, Prove that they are congruent.

   The shadow of a tower standing on a level ground is found to be 40 m longer when Suns altitude is 30 than when it was 60. Find the height of the tower. (Take = `\sqrt{3}` = 1.732)

   If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

   Construct a triangle similar to a given traingle ABC with its sides equal to `5/3` of the corresponding sides of the triangle ABC. (Write the steps of construction.)

Section E

   Find the area of the shaded regionin the figure below, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral traingle OAB of side 12 cm as centre.

   A toy in the form of cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm, find the total surface area of toy.

   The median of the following data is 525. Find the values of `x` and `y`, if the total frequency is 100.

Class interval	0-100	100-200	200-300	300-400	400-500	500-600	600-700	700-800	800-900	900-1000
Frequency	2	5	x	12	17	20	y	9	7	4