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An equilateral triangle is surrounded by three squares, as shown in the figure. Find the value of x?

Solution of AMBQID 1

In a unit circle, find the area of a shaded region.

Solution of AMBQID 2

Evaluate the expression.

Solution of AMBQID 3

All quadrilaterals are squares. Find the ratio of Ar(Red Square) / Ar(Green Square).

Solution of AMBQID 4

In a circle, C is the centre. If ar(PQR) = 2ar(PSR), then find the angle PRS.

Solution of AMBQID 5

An equilateral triangle is surrounded by three squares, as shown in the figure. Find the value of x?

Solution of AMBQID 6

If BC = AD, then find the angle ABC.

Solution of AMBQID 7

If Area inside the circle but outside the triangle is equal to the area inside the triangle but outside the circle, then find the radius of circle.

Solution of AMBQID 8

In triangle PQR, I (Incenter), O (Orthocentre), C(Circumcircle), Q and R (Vertices) are lie on a circle, then find the angle P.

Solution of AMBQID 9

If 4x = 9 and 9y = 256, then the value of xy is

Solution of AMBQID 10

A square is inside an equilateral triangle. Find (x + y).

Solution of AMBQID 11

If two positive integers x and y (x > y) are the length and breadth respectively such that perimeter of rectangle = area of rectangle, then find (x – y).

Solution of AMBQID 12

If CD = 32 and shaded area is kπ, then find the value of k.

Solution of AMBQID 13

In 10 sided regular polygon, find the value of x.

Solution of AMBQID 14

If ar(ABCD) = 243, then find R.

Solution of AMBQID 15

Two triangles are congruent equilateral triangles, then find x.

Solution of AMBQID 16

An equilateral triangle is inside a regular octagon, then find x.

Solution of AMBQID 17

Red Shared Area is equal to Blue Shaded Area. If the side of the square is 2√π, then find the radius of circle.

Solution of AMBQID 18

If red shared area = 18 cm2, then find the value of x.

Solution of AMBQID 19

If red area = green area = blue area, then find the value of AB/BC.

Solution of AMBQID 20

If (a2 + 1)(b2 + 1) + 16 = 8(a + b), then find the value of (a3 + b3).

Solution of AMBQID 21

Solution of AMBQID 22

If AB = 12 units, then find the yellow shaded area.

Solution of AMBQID 23

If a is the one of the roots of x2 + 2x + 3 = 0, then find the value of (a5 + 3a4 + 3a3 – a2) / (a2 + 3).

Solution of AMBQID 24

Three congruent semi-circles with radius 1 unit inside an equilateral triangle, touching each other as shown in figure. Find x.

Solution of AMBQID 25

In the figure, there is a pattern of four identical rhombuses. Then, find the value of x.

Solution of AMBQID 26

In triangle ABC, PQ || MN such that AP : PB = 5 : 3 and AM : MC = 1 : 4, BQ = 6 and NC = 12. Then, find x.

Solution of AMBQID 27

In right triangle ABC, A is right angle and M is the midpoint of AC. If AP is perpendicular to BM and angle ACB = α and angle PAM = β, then find tanα.tanβ.

Solution of AMBQID 28

Triangle ABC is an isosceles triangle with AB = AC and BL is perpendicular to AC. If BL = 4 cm and BC = 5 cm, then find area of triangle ABC.

Solution of AMBQID 29

Simplify the expression.

Solution of AMBQID 30

ABCD is a rectangle formed by 5 squares each of area 1 sq. units. BD is a diagonal. Then, find shaded area (in sq. units).

Solution of AMBQID 31

If x = 99, then find the value of x(x2 + 3x + 3).

Solution of AMBQID 32

If the central angle of a sector is 60 degree whose radius is OA = OB = 6 units. Then, find the area of circle inscribed in sector.

Solution of AMBQID 33

ABCD is a rectangle. If PC = 8 units, then find the area of rectangle ABCD.

Solution of AMBQID 34

Find the sum of angles (a + b + c + d + e + f + g + h + i).

Solution of AMBQID 35

In triangle ABC, if all the three angles A, B and C (in degrees) are perfect squares, then the triangle ABC is

Solution of AMBQID 36

An equilateral triangle PQR is inside another equilateral triangle ABC such that corresponding sides are parallel. Find (x + y + z).

Solution of AMBQID 37

Rectangle is made of three equal squares of side length 8 units. Find the sum of all angles (α + β + y).

Solution of AMBQID 38

If Tn = 288 – 287 – 286 – 285 – … to n terms, then find the value of T34.

Solution of AMBQID 39

Find the value of FourthRoot(2^4^44).

Solution of AMBQID 40

In the figure, both quadrilaterals are squares. Find the green shaded area.

Solution of AMBQID 41

In the figure, if l1 || l2, then find the angle θ.

Solution of AMBQID 42

Three equal circles of radii 20 have centres at A, B and C. If x = 5, y = 10 and z = 12, then find the perimeter of the triangle ABC.

Solution of AMBQID 43

If O is centre of semi-circle, then find the black shaded area.

Solution of AMBQID 44

If a line from a vertex of a triangle divides the area and the perimeter of the triangle into two equal parts, then the line passes through

Solution of AMBQID 45

If a, b, c are the three factors of x3 – 7x – 6, then find the value of (a + b + c).

Solution of AMBQID 46

Find the value of the expression.

Solution of AMBQID 47

A rectangular sheet is folded along dotted line as shown below. Find x.

Solution of AMBQID 48

In the figure, if AM = MN = BN = NC and angle A = 90 degree, then find x.

Solution of AMBQID 49

Find the value of cosα.cosβ.

Solution of AMBQID 50

An irregular hexagon is inside a circle. Find the value of x?

Solution of AMBQID 51

Two quadrant circles are inside a square. Find Green Shaded Area / Square Area.

Solution of AMBQID 52

The polynomial p(x) = axd + bxc + cxb + exa-9 is complete polynomial and written in decreasing order of degrees. If p(0) = 900, then the value of (a + b + c + d + e).

Solution of AMBQID 53

Two quadrilaterals are unit squares. Find the area of red triangle.

Solution of AMBQID 54

The simplification of ((2019)4 + (2019)2 + 1)/((2019)3 + 1) is a + b/c. Then, find the value of (a + b + c).

Solution of AMBQID 55

If (111… to 109 time) + (222… to 109 time) + (333… to 109 time) + (444… to 109 time) + (555… to 109 time) + (666… to 109 time) + (777… to 109 time) is divided by 37, then find the remainder.

Solution of AMBQID 56

If (x – 8)(x – 10)(x – 12)…(x – 96)(x – 98)(x – 100) < 0 then find the number of positive integral values of x.

Solution of AMBQID 57

If x ≠ 1 and x2 + 15/x = 16, then find the value of x2 + x – 12.

Solution of AMBQID 58

If x is the real number such that x√x = 4√x + √3, then find the value of x – √(3x).

Solution of AMBQID 59

In triangle ABC, I is the incenter, then find the area of triangle ABD.

Solution of AMBQID 60

Find the value of (α + β).

Solution of AMBQID 61

Find the value of θ.

Solution of AMBQID 62

Triangle ABC is an equilateral triangle and AB = BD. Find the value of θ.

Solution of AMBQID 63

Triangle ABC is a right isosceles triangle and BD = BC. Find the value of θ.

Solution of AMBQID 64

Two quarter circles are inside a square. Find Red Shaded Area / Square Area.

Solution of AMBQID 65

The line l passes through the centroid of triangle ABC. Find x.

Solution of AMBQID 66

Two squarea are inside semi-circle. Find the radius of the semicircle.

Solution of AMBQID 67

Don’t use calculator. Find the value of the expression.

Solution of AMBQID 68

Three quarter circles are inside the square. Find R + r.

Solution of AMBQID 69

One circle and two semi circle are inside the square. Find the green shaded region.

Solution of AMBQID 70

Semi circle is in quarter circle. Find semi-circle area/ quarter circle area.

Solution of AMBQID 71

If (x – a)(x + b)(x – 2) is divided by (x2 – 9), then the remainder is (2x + 4). Then, find (b – a).

Solution of AMBQID 72

The sum of the real roots of the equation (x2 – 8x)(x2 – 8x + 1)(x2 – 8x + 2)(x2 – 8x + 3)…(x2 – 8x + 100) = 0 is.

Solution of AMBQID 73

If x = log51000 and y = log72058, then

Solution of AMBQID 74

If x2 – ax + b = 0 has integers roots such that a + b = 4, then find (a – b).

Solution of AMBQID 75

The hundreds digit of 20! – 15! is

Solution of AMBQID 76

If k = 20192 + 22019, then find the unit digit of k2 + 2k.

Solution of AMBQID 77

Find the value of x2.

Solution of AMBQID 78

If x is the real number, then the minimum value of (x + 5)(x + 6)(x + 7)(x + 8) + 2020 is

Solution of AMBQID 79

Find the value of sec(A + B).

Solution of AMBQID 80

If axbxc = 1, then the value of (a + 1)/(ab + a + 1) + (b + 1)/(bc + b + 1) + (c + 1)/(ca + c + 1) is

Solution of AMBQID 81

If p(x) = 2x5 – 43x4 + 98x3 – 61x2 + 80x – 90 is divided by (x – 19), then find the remainder.

Solution of AMBQID 82

Find the area of the quadrilateral ABCD.

Solution of AMBQID 83

Find the value of x?

Solution of AMBQID 84

Find the value of |x – y|.

Solution of AMBQID 85

If tan37 = 3/4, then find the value of tanθ.

Solution of AMBQID 86

A polynomial of least degree with rational coefficients, whose one root is sin10o is

Solution of AMBQID 87

If CN = AN = 2BN, then find CM/AM.

Solution of AMBQID 88

Find the area of the square.

Solution of AMBQID 89

Find the value of (x + y + z)?

Solution of AMBQID 90

All quadrilaterals are square given with their areas. Find the area of the circle.

Solution of AMBQID 91

If a, b, c are the zeroes of the polynomials p(x) = x3 + 4, then find the value of expression.

Solution of AMBQID 92

If the polynomial p(x) = (x5 – 6x + 7)2019 – (x5 – 6x + 9)2020 + 5x5 – 30x + 50 is divided by (x5 – 6x + 8), then find the remainder.

Solution of AMBQID 93

Two equal rectangles and one triangle have same area 12. Find the value of AB.

Solution of AMBQID 94

If x2 + x = 1, then find the value of (x5 + 8)/(x + 1).

Solution of AMBQID 95

Both are semi circle. Find x.

Solution of AMBQID 96

Find the value of (2sin2θ – 1).

Solution of AMBQID 97

Find the orthocenter of the triangle OBC.

Solution of AMBQID 98

In a polygon with 18 sides, three of its vertices adjacent to each other do not send any diagonals. Then, the number of the diagonals in the polygon is

Solution of AMBQID 99

Find sin2θ.

Solution of AMBQID 100