Circles Class 10 ICSE ML Aggarwal Chapter Test

ML Aggarwal Class 10 Solutions Circles Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test.

Question 1.
(a) In the figure (i) given below, triangle ABC is equilateral. Find ∠BDC and ∠BEC.
(b) In the figure (ii) given below, AB is a diameter of a circle with centre O. OD is perpendicular to AB and C is a point on the arc DB. Find ∠BAD and ∠ACD
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q1.1
Solution:
(a) ∆ABC is an equilateral triangle.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q1.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q1.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q1.4

Question 2.
(a) In the figure given below, AB is a diameter of the circle. If AE = BE and ∠ADC = 118°, find
(i) ∠BDC (ii) ∠CAE.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q2.1
(b) In the figure given below, AB is the diameter of the semi-circle ABCDE with centre O. If AE = ED and ∠BCD = 140°, find ∠AED and ∠EBD. Also Prove that OE is parallel to BD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q2.2
Solution:
(a) Join DB, CA and CB.
∠ADC = 118° (given)
and ∠ADB = 90°
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q2.3
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Question 3.
(a) In the figure (i) given below, O is the centre of the circle. Prove that ∠AOC = 2 (∠ACB + ∠BAC).
(b) In the figure (ii) given below, O is the centre of the circle. Prove that x + y = z.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q3.1
Solution:
(a) Given : O is the centre of the circle.
To Prove : ∠AOC = 2 (∠ACB + ∠BAC).
Proof: In ∆ABC,
∠ACB + ∠BAC + ∠ABC = 180°
(Angles of a triangle)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q3.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q3.3
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ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q3.5

Question 4.
(a) In the figure (i) given below, AB is diameter of a circle. If DC is parallel to AB and ∠CAB = 25°, find :
(i)∠ADC (ii) ∠DAC.
(b) In the figure (ii) given below, the centre O of the smaller circle lies on the circumference of the bigger circle. If ∠APB = 70° and ∠BCD = 60°, find :
(i) ∠AOB (ii) ∠ACB
(iii) ∠ABD (iv) ∠ADB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q4.1
Solution:
(a) AB is diameter and DC || AB,
∠CAB = 25°, join AD,BD
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q4.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q4.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q4.4

Question 5.
(a) In the figure (i) given below, ABCD is a cyclic quadrilateral. If AB = CD, Prove that AD = BC.
(b) In the figure (ii) given below, ABC is an isosceles triangle with AB = AC. If ∠ABC = 50°, find ∠BDC and ∠BEC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q5.1
Solution:
(a) Given : ABDC is a cyclic quadrilateral AB = CD.
To Prove: AD = BC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q5.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q5.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q5.4

Question 6.
A point P is 13 cm from the centre of a circle. The length of the tangent drawn from P to the circle is 12 cm. Find the distance of P from the nearest point of the circle.
Solution:
Join OT, OP = 13 cm and TP = 12 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q6.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q6.2

Question 7.
Two circles touch each other internally. Prove that the tangents drawn to the two circles from any point on the common tangent are equal in length.
Solution:
Given : Two circles with centre O and O’ touch each other internally at P.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q7.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q7.2

Question 8.
From a point outside a circle, with centre O, tangents PA and PB are drawn. Prove that
(i) ∠AOP = ∠BOP.
(ii) OP is the perpendicular bisector of the chord AB.
Solution:
Given : From a point P, outside the circle with centre O. PA and PB are the tangents to the circle, OA, OB and OP are joined.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q8.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q8.2

Question 9.
(a) The figure given below shows two circles with centres A, B and a transverse common tangent to these circles meet the straight line AB in C. Prove that:
AP : BQ = PC : CQ.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q9.1
(b) In the figure (ii) given below, PQ is a tangent to the circle with centre O and AB is a diameter of the circle. If QA is parallel to PO, prove that PB is tangent to the circle.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q9.2
Solution:
(a) Given : Two circles with centres A and B and a transverse common tangent to these circles meet AB at C.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q9.3
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ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q9.5

Question 10.
In the figure given below, two circles with centres A and B touch externally. PM is a tangent to the circle with centre A and QN is a tangent to the circle with centre B. If PM = 15 cm, QN = 12 cm, PA = 17 cm and QB = 13 cm, then find the distance between the centres A and B of the circles.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q10.1
Solution:
In the given figure, two chords with centre A and B touch externally. PM is a tangent to the circle with centre A and QN is tangent to the circle with centre B. PM = 15 cm, QN = 12 cm, PA = 17 cm, QB = 13 cm. We have to find AB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q10.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q10.3

Question 11.
Two chords AB, CD of a circle intersect externally at a point P. If PB = 7 cm, AB = 9 cm and PD = 6 cm, find CD.
Solution:
∵ AB and CD are two chords of a circle which intersect each other at P, outside the circle.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q11.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q11.2

Question 12.
(a) In the figure (i) given below, chord AB and diameter CD of a circle with centre O meet at P. PT is tangent to the circle at T. If AP = 16 cm, AB = 12 cm and DP = 2 cm, find the length of PT and the radius of the circle
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q12.1
(b) In the figure (ii) given below, chord AB and diameter CD of a circle meet at P. If AB = 8 cm, BP = 6 cm and PD = 4 cm, find the radius of the circle. Also find the length of the tangent drawn from P to the circle. .
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q12.2
Solution:
Given : (a) AB is chord of a circle with centre O and PT is tangent and CD is the diameter of the circle which meet at P.
AP = 16 cm, AB = 12 cm, OP = 2 cm
∴PB = PA – AB = 16 – 12 = 4 cm
∵ABP is a secant and PT is tangent.
∴PT² = PA x PB .
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q12.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q12.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q12.5

Question 13.
In the figure given below, chord AB and diameter PQ of a circle with centre O meet at X. If BX = 5 cm, OX = 10 cm and.the radius of the circle is 6 cm, compute the length of AB. Also find the length of tangent drawn from X to the circle.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q13.1
Solution:
Chord AB and diameter PQ meet at X on producing outside the circle
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q13.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q13.3

Question 14.
(a) In the figure (i) given below, ∠CBP = 40°, ∠CPB = q° and ∠DAB = p°. Obtain an equation connecting p and q. If AC and BD meet at Q so that ∠AQD = 2 q° and the points C, P, B and Q are concyclic, find the values of p and q.
(b) In the figure (ii) given below, AC is a diameter of the circle with centre O. If CD || BE, ∠AOB = 130° and ∠ACE = 20°, find:
(i)∠BEC (ii) ∠ACB
(iii) ∠BCD (iv) ∠CED.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q14.1
Solution:
(a) (i) Given : ABCD is a cyclic quadrilateral.
Ext. ∠PBC = ∠ADC
=> 40° = ∠ADC
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q14.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q14.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q14.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q14.5

Question 15.
(a) In the figure (i) given below, APC, AQB and BPD are straight lines.
(i) Prove that ∠ADB + ∠ACB = 180°.
(ii) If a circle can be drawn through A, B, C and D, Prove that it has AB as diameter
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q15.1
(b) In the figure (ii) given below, AQB is a straight line. Sides AC and BC of ∆ABC cut the circles at E and D respectively. Prove that the points C, E, P and D are concyclic.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q15.2
Solution:
(a) Given : In the figure, APC, AQB and BPD are straight lines.
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ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q15.4
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ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q15.6

Question 16.
(a) In the figure (i) given below, chords AB, BC and CD of a circle with centre O are equal. If ∠BCD = 120°, find
(i) ∠BDC (ii) ∠BEC
(iii) ∠AEC (iv) ∠AOB.
Hence Prove that AOAB is equilateral.
(b) In the figure (ii) given below, AB is a diameter of a circle with centre O. The chord BC of the circle is parallel to the radius OD and the lines OC and BD meet at E. Prove that
(i) ∠CED = 3 ∠CBD (ii) CD = DA.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q16.1
Solution:
(a) In ∆BCD, BC = CD
∠CBD = ∠CDB
But ∠BCD + ∠CBD + ∠CDB = 180°
(∵ Angles of a triangle)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q16.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q16.3
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ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q16.5

Question 17.
(a) In the adjoining figure, (i) given below AB and XY are diameters of a circle with centre O. If ∠APX = 30°, find
(i) ∠AOX (ii) ∠APY (iii) ∠BPY (iv) ∠OAX.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q17.1
(b) In the figure (ii) given below, AP and BP are tangents to the circle with centre O. If ∠CBP = 25° and ∠CAP = 40°, find :
(i) ∠ADB (ii) ∠AOB (iii) ∠ACB (iv) ∠APB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q17.2
Solution:
(a) AB and XY are diameters of a circle with centre O.
∠APX = 30°.
To find :
(i) ∠AOX (ii) ∠APY
(iii) ∠BPY (iv) ∠OAX
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q17.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q17.5
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 16 Circles Chapter Test Q17.6

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Locus Class 10 ICSE ML Aggarwal Chapter Test

ML Aggarwal Class 10 Solutions Locus Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Locus Chapter Test.

Question 1.
Draw a straight line AB of length 8 cm. Draw the locus of all points which are equidistant from A and B. Prove your statement.
Solution:
(i) Draw a line segment AB = 8 cm.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Locus Chapter Test Q1.1
(ii) Draw the perpendicular bisector of AB intersecting AB at D.
∴ Every point P on it will be equidistant from A and B.
(iii) Take a point P on the perpendicular bisector.
(iv) Join PA and PB.
Proof : In ∆PAD and ∆PBD
PD = PD (common)
AD = BD (D is mid-point of AB)
∠PDA = ∠PDB (each 90°)
∴ ∆ PAD ≅ ∆ PBD (SAS axiom of congruency)
∴PA = PB (c.p.c.t.)
Similarly we can prove any other point on the perpendicular bisector of AB is equidistant from A and B.
Hence Proved.

Question 2.
A point P is allowed to travel in space. State the locus of P so that it always remains at a constant distance from a fixed point C.
Solution:
The point P is moving in the space and it is at a constant distance from a fixed point C.
∴ Its locus is a sphere.

Question 3.
Draw a line segment AB of length 7 cm. Construct the locus of a point P such that area of triangle PAB is 14 cm².
Solution:
Base of ∆PAB = 7 cm
and its area = 14 cm²
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Locus Chapter Test Q3.1
Now draw a line XY parallel to AB at a distance of 4 cm.
Now take any point P on XY
Join PA and PB
area of ∆PAB = 14 cm.
Hence locus of P is the line XY which is parallel to AB at distance of 4 cm.

Question 4.
Draw a line segment AB of length 12 cm. Mark M, the mid-point of AB. Draw and describe the locus of a point which is
(i) at a distance of 3 cm from AB.
(ii) at a distance of 5 cm from the point M. Mark the points P, Q, R, S which satisfy both the above conditions. What kind of quadrilateral is PQRS ? Compute the area of the quadrilateral PQRS.
Solution:
Steps of Construction :
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Locus Chapter Test Q4.1
(i) Take a line AB = 12 cm
(ii) Take M, the mid point of AB.
(iii) Draw straight lines CD and EF parallel to AB at a distance of 3 cm.
(iv) With centre M and radius 5 cm, draw areas which intersects CD at P and Q and EF at R and S.
(v) Join QR and PS.
PQRS is a rectangle where length
PQ = 8 cm.
Area of rectangle PQRS = PQ x RS = 8 x 6 = 48 cm²

Question 5.
AB and CD are two intersecting lines. Find the position of a point which is at a distance of 2 cm from AB and 1.6 cm from CD.
Solution:
(i) AB and CD are the intersecting lines which intersect each other at O.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Locus Chapter Test Q5.1
(ii) Draw a line EF parallel to AB and GH parallel to CD intersecting each other at P
P is the required point.

Question 6.
Two straight lines PQ and PK cross each other at P at an angle of 75°. S is a stone on the road PQ, 800 m from P towards Q. By drawing a figure to scale 1 cm = 100 m, locate the position of a flag staff X, which is equidistant from P and S, and is also equidistant from the road.
Solution:
1 cm = 100 cm
800 m = 8 cm.
Steps of Construction :
(i) Draw the lines PQ and PK intersecting each other at P making an angle of 75°.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Locus Chapter Test Q6.1
(ii) Take a point S on PQ such that PS = 8 cm.
(iii) Draw the perpendicular bisector of PS.
(iv) Draw the angle bisector of ∠KPS intersecting the perpendicular bisector at X. X is the required point which is equidistant from P and S and also from PQ and PK.

Question 7.
Construct a rhombus PQRS whose diagonals PR, QS are 8 cm and 6 cm respectively. Find by construction a point X equidistant from PQ, PS and equidistant from R, S. Measure XR.
Solution:
Steps of Construction :
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Locus Chapter Test Q7.1
(i) Take PR = 8 cm and draw the perpendicular bisector of PR intersecting it at O.
(ii) From O, out. off OS = OQ = 3 cm
(iii) Join PQ, QR, RS and SP.
PQRS is a rhombus. Whose diagonal are PR and QS.
(iv) PR is the bisector of ∠SPQ.
(v) Draw the perpendicular bisector of SR intersecting PR at X
∴ X is equidistant from PQ and PS and also from S and R.
On measuring length of XR = 3.2 cm (approx)

Question 8.
Without using set square or protractor, construct the parallelogram ABCD in which AB = 5.1 cm. the diagonal AC = 5.6 cm and the diagonal BD = 7 cm. Locate the point P on DC, which is equidistant from AB and BC.
Solution:
Steps of Construction :
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Locus Chapter Test Q8.1
(i) Take AB = 5.1 cm
(ii) At A, with readius \(\\ \frac { 5.6 }{ 2 } \) = 2.8 cm and at B with radius \(\\ \frac { 7.0 }{ 2 } \) = 3.5 cm, draw two arcs
intersecting each other at O.
(iii) Join AO and produce it to C such that OC = AD = 2.8 cm and join BO and produce it to D such that BO = OD = 3.5 cm
(iv) Join BC, CD, DA
ABCD is a parallelogram.
(v) Draw the angle bisector of ∠ABC intersecting CD at P. P is the required point which is equidistant from AB and BC.

Question 9.
By using ruler and compass only, construct a quadrilateral ABCD in which AB = 6.5 cm, AD = 4cm and ∠DAB = 75°. C is equidistant from the sides AB and AD, also C is equidistant from the points A and B.
Solution:
Steps of Construction :
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Locus Chapter Test Q9.1
(i) Draw a line segment AB = 6.5 cm.
(ii) At A, draw a ray making an angle of 75° and cut off AD = 4 cm.
(iii) Draw the bisector of ∠DAB.
(iv) Draw perpendicular bisector of AB intersecting the angle bisector at C.
(v) Join CB and CD.
ABCD is the required quadrilateral.

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Equation of a Straight Line Class 10 ICSE ML Aggarwal Chapter Test

ML Aggarwal Class 10 Solutions Equation of a Straight Line Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test.

Question 1.
Find the equation of a line whose inclination is 60° and y-intercept is – 4.
Solution:
Angle of inclination = 60°
Slope = tan θ = tan 60° = √3
Equation of the line will be,
y = mx + c = √3x + ( – 4)
=> y – √3x – 4 Ans.

Question 2.
Write down the gradient and the intercept on the y-axis of the line 3y + 2x = 12.
Solution:
Slope of the line 3y + 2x = 12
=> 3y = 12 – 2x
=> 3y = – 2x + 12
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q2.1

Question 3.
If the equation of a line is y – √3x + 1, find its inclination.
Solution:
In the line
y = √3 x + 1
Slope = √3 => tan θ = √3
θ = 60° (∵ tan 60° = √3)

Question 4.
If the line y = mx + c passes through the points (2, – 4) and ( – 3, 1), determine the values of m and c.
Solution:
The equation of line y = mx + c
∵ it passes through (2, – 4) and ( – 3, 1)
Now substituting the value of these points – 4 = 2 m + c …(i)
and 1 = – 3 m + c …(ii)
Subtracting we get,
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q4.1

Question 5.
If the point (1, 4), (3, – 2) and (p, – 5) lie on a st. line, find the value of p.
Solution:
Let the points to be A (1, 4), B (3, – 2) and C (p, – 5) are collinear and let B (3, – 2)
divides AC in the ratio of m1 : m2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q5.1

Question 6.
Find the inclination of the line joining the points P (4, 0) and Q (7, 3).
Solution:
Slope of the line joining the points P (4, 0) and Q (7, 3)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q6.1

Question 7.
Find the equation of the line passing through the point of intersection of the lines 2x + y = 5 and x – 2y = 5 and having y-intercept equal to \(– \frac { 3 }{ 7 } \)
Solution:
Equation of lines are
2x + y = 5 …(i)
x – 2y = 5 …(ii)
Multiply (i) by 2 and (ii) by 1, we get
4x + 2y = 10
x – 2y = 5
Adding we get,
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q7.1

Question 8.
If the point A is reflected in the y-axis, the co-ordinates of its image A1, are (4, – 3),
(i) Find the co-ordinates of A
(ii) Find the co-ordinates of A2, A3 the images of the points A, A1, Respectively under reflection in the line x = – 2
Solution:
(i) ∵ A is reflected in the y-axis and its image is A1 (4, – 3)
Co-ordinates of A will be ( – 4, – 3)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q8.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q8.2

Question 9.
If the lines \(\frac { x }{ 3 } +\frac { y }{ 4 } =7 \) and 3x + ky = 11 are perpendicular to each other, find the value of k.
Solution:
Given
Equation of lines are
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q9.1

Question 10.
Write down the equation of a line parallel to x – 2y + 8 = 0 and passing through the point (1, 2).
Solution:
The equation of the line is x – 2y + 8 = 0
=> 2y = x + 8
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q10.1

Question 11.
Write down the equation of the line passing through ( – 3, 2) and perpendicular to the line 3y = 5 – x.
Solution:
Equations of the line is
3y = 5 – x
=> 3y = – x + 5
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q11.1

Question 12.
Find the equation of the line perpendicular to the line joining the points A (1, 2) and B (6, 7) and passing through the point which divides the line segment AB in the ratio 3 : 2.
Solution:
Let slope of the line joining the points A (1, 2) and B (6, 7) be m1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q12.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q12.2

Question 13.
The points A (7, 3) and C (0, – 4) are two opposite vertices of a rhombus ABCD. Find the equation of the diagonal BD.
Solution:
Slope of line AC (m1)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q13.2

Question 14.
A straight line passes through P (2, 1) and cuts the axes in points A, B. If BP : PA = 3 : 1, find:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q14.1
(i) the co-ordinates of A and B
(ii) the equation of the line AB
Solution:
A lies on x-axis and B lies on y-axis
Let co-ordinates of A be (x, 0) and B be (0, y) , and P (2, 1) divides BA in the ratio 3 : 1.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q14.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q14.3

Question 15.
A straight line makes on the co-ordinates axes positive intercepts whose sum is 7. If the line passes through the point ( – 3, 8), find its equation.
Solution:
Let the line make intercept a and b with the x-axis and y-axis respectively then the line passes through
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q15.2

Question 16.
If the coordinates of the vertex A of a square ABCD are (3, – 2) and the quation of diagonal BD is 3 x – 7 y + 6 = 0, find the equation of the diagonal AC. Also find the co-ordinates of the centre of the square.
Solution:
Co-ordinates of A are (3, – 2).
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q16.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q16.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q16.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Chapter Test Q16.4

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Section Formula Class 10 ICSE ML Aggarwal Chapter Test

ML Aggarwal Class 10 Solutions Section Formula Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test.

Question 1.
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of the point C are (0, – 3). If origin is the mid-point of the base BC, find the coordinates of the points A and B
Solution:
Base BC of an equilateral ∆ABC lies on y-axis co-ordinates of point C are (0, – 3), origin (0, 0) is the mid-point of BC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q1.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q1.2

Question 2.
A and B have co-ordinates (4, 3) and (0, 1), Find
(i) the image A’ of A under reflection in the y – axis.
(ii) the image of B’ of B under reflection in the lineAA’.
(iii) the length of A’B’.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q2.1
(i) Co-ordinates of A’, the image of A (4, 3) reflected in y-axis will be ( – 4, 3).
(ii) Co-ordinates of B’ the image of B (0, 1) reflected in the line AA’ will be (0, 5).
(iii) Length A’B’
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q2.2

Question 3.
Find the co-ordinates of the point that divides the line segment joining the points P (5, – 2) and Q (9, 6) internally in the ratio of 3 : 1.
Solution:
Let R be the point whose co-ordinates are (x, y) which divides PQ in the ratio of 3:1.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q3.1

Question 4.
Find the coordinates of the point P which is three-fourth of the way from A (3, 1) to B ( – 2, 5).
Solution:
Co-ordinates of A (3, 1) and B ( – 2, 5)
P lies on AB such that
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q4.1

Question 5.
P and Q are the points on the line segment joining the points A (3, – 1) and B ( – 6, 5) such that AP = PQ = QB. Find the co-ordinates of P and Q.
Solution:
Given
AP = PQ = QB
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q5.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q5.2

Question 6.
The centre of a circle is (α + 2, α – 5). Find the value of a given that the circle passes through the points (2, – 2) and (8, – 2).
Solution:
Let A (2, – 2), B (8, – 2) and centre of the circle be
O (α + 2, α – 5)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q6.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q6.2

Question 7.
The mid-point of the line joining A (2, p) and B (q, 4) is (3, 5). Calculate the numerical values of p and q.
Solution:
Given
(3, 5) is the mid-point of A (2, p) and B (q, 4)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q7.1

Question 8.
The ends of a diameter of a circle have the co-ordinates (3, 0) and ( – 5, 6). PQ is another diameter where Q has the coordinates ( – 1, – 2). Find the co-ordinates of P and the radius of the circle.
Solution:
Let AB be the diameter where co-ordinates of A are (3, 0) and of B are ( – 5, 6).
Co-ordinates of its origin O will be
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q8.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q8.2

Question 9.
In what ratio does the point ( – 4, 6) divide the line segment joining the points A( – 6, 10) and B (3, – 8) ?
Solution:
Let the point ( – 4, 6) divides the line segment joining the points
A ( – 6, 10) and B (3, – 8), in the ratio m : n
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q9.1

Question 10.
Find the ratio in which the point P ( – 3, p) divides the line segment joining the points ( – 5, – 4) and ( – 2, 3). Hence find the value of p.
Solution:
Let P ( – 3, p) divides AB in the ratio of m1 : m2 coordinates of
A ( – 5, – 4) and B ( – 2, 3)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q10.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q10.2

Question 11.
In what ratio is the line joining the points (4, 2) and (3, – 5) divided by the x-axis? Also find the co-ordinates of the point of division.
Solution:
Let the point P which is on x-axis, divides the line segment joining the points A (4, 2) and B (3, – 5) in the ratio of m1 : m2.
and let co-ordinates of P be (x, 0)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q11.1

Question 12.
If the abscissa of a point P is 2, find the ratio in which it divides the line segment joining the points ( – 4 – 3) and (6, 3). Hence, find the co-ordinates of P.
Solution:
Let co-ordinates of A be ( – 4, 3) and of B (6, 3) and of P be (2, y)
Let the ratio in which the P divides AB be m1 : m2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q12.1

Question 13.
Determine the ratio in which the line 2x + y – 4 = 0 divide the line segment joining the points A (2, – 2) and B (3, 7). Also find the co-ordinates of the point of division.
Solution:
Points are given A (2, – 2), B (3, 7)
and let the line 2x + y – 4 = 0 divides AB in the ratio m1 : m2 at P and let co-ordinates of
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q13.1

Question 14.
The point A(2, – 3) is reflected in the v-axis onto the point A’. Then the point A’ is reflected in the line x = 4 onto the:point A”.
(i) Write the coordinates of A’ and A”.
(ii) Find the ratio in which the line segment AA” is divided by the x-axis. Also find the coordinates of the point of division.
Solution:
A’ is the reflection of A(2, – 3) in the x-axis
(i) ∴ Co-ordinates of A’ will be (2, 3)
Draw a line x = 4 which is parallel to y-axis
A” is the reflection of A’ (2, 3)
∴Co-ordinates OA” will be (6, 3)
(ii) Join AA” which intersects x-axis at P whose
co-ordinate are (4, 0)
Let P divide AA” in the ratio in m1 : m2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q14.1
Hence P(4, 0) divides AA” in the ratio 1 : 1

Question 15.
ABCD is a parallelogram. If the coordinates of A, B and D are (10, – 6), (2, – 6) and (4, – 2) respectively, find the co-ordinates of C.
Solution:
Let the co-ordinates of C be (x, y) and other three vertices of the given parallelogram are A (10, – 6), B, (2, – 6) and D (4, – 2)
∴ ABCD is a parallelogram
Its diagonals bisect each other.
Let AC and BD intersect each other at O.
∴O is mid-points of BD
∴ Co-ordinates of O will be
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q15.1

Question 16.
ABCD is a parallelogram whose vertices A and B have co-ordinates (2, – 3) and ( – 1, – 1) respectively. If the diagonals of the parallelogram meet at the point M(1, – 4), find the co-ordinates of C and D. Hence, find the perimeter of the parallelogram. find the perimeter of the parallelogram.
Solution:
ABCD is a || gm , m which co-ordinates of A are (2, – 3) and B (-1, -1)
Its diagonals AC and BD bisect each other at M (1, – 4)
∴ M is mid point of AC and BD Let co-ordinates of C be (x1, y1) and of D be (x2, y2) when M is mid point of AC then
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q16.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q16.2

Question 17.
In the adjoining figure, P (3, 1) is the point on the line segment AB such that AP : PB = 2 : 3. Find the co-ordinates of A and B.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q17.1
Solution:
A lies on x-axis and
B lies on y-axis
Let co-ordinates of A be (x, 0) and B be (0, y) and P (3, 1) divides it in the ratio of 2 : 3.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q17.2

Question 18.
Given, O, (0, 0), P(1, 2), S( – 3, 0) P divides OQ in the ratio of 2 : 3 and OPRS is a parallelogram.
Find : (i) the co-ordinates of Q.
(ii)the co-ordinates of R.
(iii) the ratio in which RQ is divided by y-axis.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q18.1
Solution:
(i) Let co-ordinates of Q be (x’, y’) and of R (x”,y”)
Point P (1, 2) divides OQ in the ratio of 2 : 3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q18.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q18.3

Question 19.
If A (5, – 1), B ( – 3, – 2) and C ( – 1, 8) are the vertices of a triangle ABC, find the length of the median through A and the co-ordinates of the centroid of triangle ABC.
Solution:
A (5, – 1), B ( – 3, – 2) and C ( – 1, 8) are the vertices of ∆ABC
D, E and F are the midpoints of sides BC, CA and AB respectively and G is the centroid of the ∆ABC
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q19.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test Q19.2

Hope given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 11 Section Formula Chapter Test are helpful to complete your math homework.

If you have any doubts, please comment below. APlusTopper try to provide online math tutoring for you.

Matrices Class 10 ICSE ML Aggarwal Chapter Test

ML Aggarwal Class 10 Solutions Matrices Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test.

Question 1.
Find the values of a and below
\(\begin{bmatrix} a+3 & { b }^{ 2 }+2 \\ 0 & -6 \end{bmatrix}=\begin{bmatrix} 2a+1 & 3b \\ 0 & { b }^{ 2 }-5b \end{bmatrix}\)
Solution:
\(\begin{bmatrix} a+3 & { b }^{ 2 }+2 \\ 0 & -6 \end{bmatrix}=\begin{bmatrix} 2a+1 & 3b \\ 0 & { b }^{ 2 }-5b \end{bmatrix}\)
comparing the corresponding elements
a + 3 = 2a + 1
=> 2a – a =3 – 1
=> a = 2
b² + 2 = 3b
=>b² – 3b + 2 = 0
=> b² – b – 2b + 2 = 0
=> b (b – 1) – 2 (b – 1) = 0
=> (b – 1) (b – 2) = 0.
Either b – 1 = 0, then b = 1 or b – 2 = 0,
then b = 2
Hence a = 2, 5 = 2 or 1 Ans.

Question 2.
Find a, b, c and d if \(3\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 4 & a+b \\ c+d & 3 \end{bmatrix}+\begin{bmatrix} a & 6 \\ -1 & 2d \end{bmatrix}\)
Solution:
Given
\(3\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 4 & a+b \\ c+d & 3 \end{bmatrix}+\begin{bmatrix} a & 6 \\ -1 & 2d \end{bmatrix}\)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q2.1

Question 3.
Find X if Y = \(\begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix} \) and 2X + Y = \(\begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix} \)
Solution:
Given
2X + Y = \(\begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix} \)
=> 2X = 2X + Y = \(\begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix} \) – Y
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q3.1

Question 4.
Determine the matrices A and B when
A + 2B = \(\begin{bmatrix} 1 & 2 \\ 6 & -3 \end{bmatrix} \) and 2A – B = \(\begin{bmatrix} 2 & -1 \\ 2 & -1 \end{bmatrix} \)
Solution:
A + 2B = \(\begin{bmatrix} 1 & 2 \\ 6 & -3 \end{bmatrix} \)…..(i)
2A – B = \(\begin{bmatrix} 2 & -1 \\ 2 & -1 \end{bmatrix} \)…….(ii)
Multiplying (i) by 1 and (ii) by 2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q4.1

Question 5.
(i) Find the matrix B if A = \(\begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix} \) and A² = A + 2B
(ii) If A = \(\begin{bmatrix} 1 & 2 \\ -3 & 4 \end{bmatrix} \), B = \(\begin{bmatrix} 0 & 1 \\ -2 & 5 \end{bmatrix} \)
and C = \(\begin{bmatrix} -2 & 0 \\ -1 & 1 \end{bmatrix} \) find A(4B – 3C)
Solution:
A = \(\begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix} \)
let B = \(\begin{bmatrix} a & b \\ c & d \end{bmatrix} \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q5.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q5.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q5.3

Question 6.
If A = \(\begin{bmatrix} 1 & 4 \\ 1 & 0 \end{bmatrix} \), B = \(\begin{bmatrix} 2 & 1 \\ 3 & -1 \end{bmatrix} \) and C = \(\begin{bmatrix} 2 & 3 \\ 0 & 5 \end{bmatrix} \) compute (AB)C = (CB)A ?
Solution:
Given
A = \(\begin{bmatrix} 1 & 4 \\ 1 & 0 \end{bmatrix} \),
B = \(\begin{bmatrix} 2 & 1 \\ 3 & -1 \end{bmatrix} \) and
C = \(\begin{bmatrix} 2 & 3 \\ 0 & 5 \end{bmatrix} \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q6.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q6.2

Question 7.
If A = \(\begin{bmatrix} 3 & 2 \\ 0 & 5 \end{bmatrix} \) and B = \(\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix} \) find the each of the following and state it they are equal:
(i) (A + B)(A – B)
(ii)A² – B²
Solution:
Given
A = \(\begin{bmatrix} 3 & 2 \\ 0 & 5 \end{bmatrix} \) and
B = \(\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix} \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q7.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q7.2

Question 8.
If A = \(\begin{bmatrix} 3 & -5 \\ -4 & 2 \end{bmatrix} \) find A² – 5A – 14I
Where I is unit matrix of order 2 x 2
Solution:
Given
A = \(\begin{bmatrix} 3 & -5 \\ -4 & 2 \end{bmatrix} \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q8.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q8.2

Question 9.
If A = \(\begin{bmatrix} 3 & 3 \\ p & q \end{bmatrix} \) and A² = 0 find p and q
Solution:
Given
A = \(\begin{bmatrix} 3 & 3 \\ p & q \end{bmatrix} \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q9.1

Question 10.
If A = \(\begin{bmatrix} \frac { 3 }{ 5 } & \frac { 2 }{ 5 } \\ x & y \end{bmatrix} \) and A² = I, find x,y
Solution:
Given
A = \(\begin{bmatrix} \frac { 3 }{ 5 } & \frac { 2 }{ 5 } \\ x & y \end{bmatrix} \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q10.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q10.2

Question 11.
If \(\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \) find a,b,c and d
Solution:
Given
\(\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q11.1

Question 12.
Find a and b if
\(\begin{bmatrix} a-b & b-4 \\ b+4 & a-2 \end{bmatrix}\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}=\begin{bmatrix} -2 & -2 \\ 14 & 0 \end{bmatrix} \)
Solution:
Given
\(\begin{bmatrix} a-b & b-4 \\ b+4 & a-2 \end{bmatrix}\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}=\begin{bmatrix} -2 & -2 \\ 14 & 0 \end{bmatrix} \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q12.1

Question 13.
If A = \(\begin{bmatrix} { sec60 }^{ o } & { cos90 }^{ o } \\ { -3tan45 }^{ o } & { sin90 }^{ o } \end{bmatrix} \) and B = \(\begin{bmatrix} 0 & { cos45 }^{ o } \\ -2 & { 3sin90 }^{ o } \end{bmatrix} \)
Find (i) 2A – 3B (ii) A² (iii) BA
Solution:
Given
A = \(\begin{bmatrix} { sec60 }^{ o } & { cos90 }^{ o } \\ { -3tan45 }^{ o } & { sin90 }^{ o } \end{bmatrix} \) and
B = \(\begin{bmatrix} 0 & { cos45 }^{ o } \\ -2 & { 3sin90 }^{ o } \end{bmatrix} \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test Q13.2

Hope given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Matrices Chapter Test are helpful to complete your math homework.

If you have any doubts, please comment below. APlusTopper try to provide online math tutoring for you.