1847 + Interview Questions in Maths in Class 9 Page 28 InterviewSolution

1351.	Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say 'how', if they are not congruent say 'why' and also say if a small modification would them congruent :
Answer» Answer :(i) `DeltaABC~=DeltaPQR` , (ii) `DeltaABD~=DeltaCDB` (III) `Delta~=DeltaPXZ` (IV) `DeltaAOB=DeltaOCD` ,(V) `DeltaAOB~=DeltaOCD` , (vi) `:.DeltaABM~=ACM`

Discussion

1352.	P car complete a piece of wark in 3 days. Q takes triple the time taken by P,R takes 4 times that taken by Q and s takes double the time taken by R to complete the same task. They are grouped in two pairs. One of the pairs takes 2(1)/(2) times the taken by the other pair to complete the work. which is the second pair?
Answer» P,S R,R Q,R Q,S Solution :(i)Q and R take 9 days 36 days respecrtively to COMPLETE a piece of work (ii) Let P take x days, Q takes 3x days, R take 12X days and S take 24 x days (iii) Findthe part of thework done by each perosn, PER day. (iv) Then check from the option

Discussion

1353.	Write the following cubes in the expanded form : (3a+4b)^(3)
Answer» ANSWER :`27 a^(3) + 64b^(3) + 108 a^(2)B + 144 ab^(2)`

Discussion

1354.	The value of tan26^(@).tan64^(@) is……………..
Answer» `(1)/(2)` `sqrt(3)/(2)` 1 0 Answer :C

Discussion

1355.	If the angle of elevation of the Sun is 30^@, then the length of the shadow of a vertical pole of length 15 metre is?
Answer» ANSWER :the train travelled a total distance of 100 KM and the PAST velocity of it was 25km/hour.

Discussion

1356.	Expand : (3x+7y)^(3)
Answer» ANSWER :`27X^(3) + 343y^(3) + 189x^(2)y + 441xy^(2)`

Discussion

1357.	State which of the following expressions are a polynomial in one variable and which are not : sqrt(7)x^(3) + (5)/(3)x^(2) - 9x + 17
Answer» ANSWER :Is a POLYNOMIAL in ONE VARIABLE.

Discussion

1358.	Find the mode of the following marks (out of 10) obtained by 20 students : 4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9
Answer» ANSWER :9

Discussion

1359.	Find the value of k, if x-1 is a factor of p(x) in each of the following cases : p(x) = k x^(2) - 3x + k
Answer» ANSWER :`K= (3)/(2)`

Discussion

1360.	In ΔABC, AB = 4 and BC = 7, Then , .... holds good.
Answer» `AC lt7` `AC gt4` `4 LT AC lt 7` `3 lt AC lt 11` Answer :A::C

Discussion

1361.	Find the value of the polynomial 5x - 4x^(2) + 3 atx = 2.
Answer» ANSWER :`-3`

Discussion

1362.	State the coefficient of x^(2) in each of the following polynomials : x^(4) + 5x^(3) + pi x^(2) - 3x + 11
Answer» ANSWER :`PI`

Discussion

1363.	Find the pair of whole numbers so that their sum cannot exceed 10 and difference of twice the first number and thrice the second number cannot exceed 12
Answer»

Discussion

1364.	A pyramid is a solid figure whose base is
Answer» only a TRIANGLE only a square only a RECTANGLE any polygon Solution :A pyramid is a solid FIGURE WHOSE base in any polygon

Discussion

1365.	(b) Explain rational number in your own words.
Answer» ANSWER :Anumber which can be written in the form `(p)/(Q)` where `q ne0; p,q` are integers, CALLED a rational NUMBER.

Discussion

1366.	Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : The area of an equilateral triangle =………..
Answer» `(1)/(2)xx` BASE `xx` altitude `(SQRT3)/(2)xx("SIDE")^(2)` `(sqrt3)/(4)xx("side")^(2)` base `xx` altitude Answer :B::C::D

Discussion

1367.	Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : The opposite angles of a parallelogram are ………….
Answer» equal unequal REFLEX ANGLES straight angles ANSWER :A

Discussion

1368.	A conical vessel with radius 10 cm and height 15 cm is completely filled with water. This water is poured into a cylinder with radius 5 cm. Find the height of water in the cylinder.
Answer» ANSWER :20 CM

Discussion

1369.	Find for solutions of each of the following equation : x + y = 7
Answer» ANSWER :`(7,0),(0,7),(1,6),(2,5)`

Discussion

1370.	In the previous question, the rate of return is
Answer» EQUAL to the rate of dividend. greater than the rate of dividend. less than the rate of dividend. Either (a) or (B) Solution :SINCE he has to spend more than the face value to PURCHASE each share, `r% LT a%`.

Discussion

1371.	Express the following rational numbers in decimal form. (22)/(7)
Answer» ANSWER :`3.bar(142857)`

Discussion

1372.	Check whether (x-2) is a factor of x ^(3) - 2x ^(2) - 5x +4
Answer» ANSWER :`X ^(2) - 2x ^(2) - 5x +4`

Discussion

1373.	In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that angle BEC = 130^(@) and angle ECD = 20^(@).. Find angle BAC.
Answer» ANSWER :`110^(@)`

Discussion

1374.	Rs,33,000 is to be divided into two parts, such that the income from one part invested in Rs.200 shares at Rs.250 for 10% dividend is the same as that from the other investment which was invested in Rs.120 shares at Rs.150 for 12% dividend. Determine the amountsinvested in the two kinds of sheares.
Answer» ANSWER :Rs.18,000; Rs.15,000

Discussion

1375.	The ratio of the measures of the sides of a triangle is 3 : 4 : 5. If the semiperimeter of the triangle is 36 cm, the measure of the longest side of the triangle is …………..cm.
Answer» 12 15 20 30 Answer :D

Discussion

1376.	Classify the following numbers as rational or irrational. sqrt3+sqrt2
Answer» ANSWER :IRRATIONAL

Discussion

1377.	Evaluate the following products without multiplying directly : 95 xx 96
Answer» ANSWER :9120

Discussion

1378.	Details of shashi 's saving bank account are given below Calculated the total interest earned by him up to 30-4-1999 The rate of interest is as follows (i) 4% per annum up to 28-2-1999 (ii) 35 per annum from 01-3-1999 to 30-4-1999
Answer» ANSWER :RS 31.33

Discussion

1379.	If (y-3) is a factor of y ^(3) - 2y ^(2) - 9y+ 18 then find the other two factors.
Answer» ANSWER :`(y-2) (y +3)`

Discussion

1380.	Express the following in terms of angles between 0^(@) and 45^(@) sin 59^(@)+tan 63^(@)
Answer» ANSWER :`COS31^(@)+cot27^(@)`

Discussion

1381.	ABCD is a square . If ar(ABCD)=36 cm^2 . Then AB=____ cm.
Answer» 18 9 6 12

Discussion

1382.	Expressing 4x = 2y -7 in the y - form , we get y = ......
Answer» `4x +7` `4x +(7)/2` `2X +7/2` `2x -7/2` ANSWER :B

Discussion

1383.	Find the difference between the compound interest compounded yearly and half yearly on Rs 10,000 for 18 months at 10% per annum.
Answer» ANSWER :RS 26,25

Discussion

1384.	If x + 3 is one of the x^(3) + 2x^(2) - m x - 18. then m = …………..
Answer» ANSWER :9

Discussion

1385.	Acylindrical pillar is 50cm in diameter and 3.5m in height. Find the cost ofpainting the curved surface of the pillar at the rate of Rs. 12. 50\ p e r\ m^2dot
Answer» ANSWER :RS. 68.75

Discussion

1386.	If each side of a triangle is doubled, find the ratio of the areas of two triangles, the given triangle & the triangle obtained on doubling the sides. Also find the percentage increase in the area of new triangle.
Answer» ANSWER :(i) 1:4 (II) 300%

Discussion

1387.	Construct a right-angled Delta ABC in which angleA=90^(@), hypotenuse BC=6 cm and AB=4 cm. Justify your construction.
Answer» Solution :STEPS OF CONSTRUCTION (i) Draw a line segment `BC=6` cm. (II) Draw the right BISECTOR of `BC`, cutting `BC` at `O`. (iii) With `O` as centre and radius `OB`, draw a semicircle on `BC`. (iv) With `B` as centre and radius `4 cm`, draw an arc, cutting the semicircle at `A`. (v) JOIN `AB` and `AC.` Then, `Delta ABC` is the required triangle, right angled at `A`. JUSTIFICATION : We know that an angle in a semicircle is a right angle and therefore, `angleBAC=90^(@)`. Also, `BA=4` cm and `BC=6` cm. Hence, `Delta ABC` is the required triangle, right angled at `A`.

Discussion

1388.	Area of a parallelogram =_____
Answer» `1/2` X base x corresponding altitude `1/2` x the PRODUCT the diagonals base x corresponding altitude `1/2` x the product of adjacent SIDES ANSWER :A::B::C::D

Discussion

1389.	The mean of x,x+2,x+4,x+6 and x+8 is 11, find the mean of the first three observations.
Answer» ANSWER :9

Discussion

1390.	John borrowed Rs 20,000 for 4 years under the following conditions : 10% simple interest for the first 2(1)/(2) years. 10% C.I. for the remaining one and a half years on the amount due after 2(1)/(2) years, the interest being compounded half-yearly. Find the total amount to be paid at the end of fourth year.
Answer» ANSWER :RS 28,940-63

Discussion

1391.	If sinx =cosx and x is acute, state the value of x.
Answer» ANSWER :`45^(@)`

Discussion

1392.	How many dimensions does a point have
Answer» 0 1 2 3 Solution :A POINT has 0 DIMENSIONS

Discussion

1393.	Evaluate the following uing suitable identities : (102)^(3)
Answer» ANSWER :10,61,208

Discussion

1394.	Solve for x : sin(x+10^(@))=1/2
Answer» ANSWER :`20^(@)`

Discussion

1395.	Perimeter of a semi circle is 36cm, find itsarea.
Answer»

Discussion

1396.	In the given figure, AB is one of the diameters of the circle and OC is perpendicular to through the centre O. If AC is 9sqrt(2) cm then what is the area of the circle in cm^(2).
Answer» `9picm^(2)` `162picm^(2)` `72picm^(2)` `81picm^(2)` ANSWER :D

Discussion

1397.	There are four unknown numbers. The mean of the first two numbers is 4 and the mean of the first three is 9. The mean of all four number is 15, if one of the four number is 2 find the other numbers.
Answer» Answer :`1^(st)=2; 2^(nd)=6; 3^(RD)=19; 4^(TH)=33`

Discussion

1398.	The median of the following observations arranged in ascending order, is 20. Find x. 3,4,7,8,10,18,x+2,x+4,26,28,31,36,38 and 40.
Answer» ANSWER :17

Discussion

1399.	Find the value of k, if x-1 is a factor of p(x) in each of the following cases : p(x) = kx^(2) - sqrt(2)x + 1
Answer» ANSWER :`K = SQRT(2)-1`

Discussion

1400.	Verify whether 2x ^(4) - 6x ^(3) + 3x ^(2) + 3x -2 is divisible by x ^(2) - 3x +2 or not ? How can you verify using Factor Theorem ?
Answer» ANSWER :`3X -2`

Discussion

Explore topic-wise InterviewSolutions in .

Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say 'how', if they are not congruent say 'why' and also say if a small modification would them congruent :

Write the following cubes in the expanded form : (3a+4b)^(3)

The value of tan26^(@).tan64^(@) is……………..

If the angle of elevation of the Sun is 30^@, then the length of the shadow of a vertical pole of length 15 metre is?

Expand : (3x+7y)^(3)

State which of the following expressions are a polynomial in one variable and which are not : sqrt(7)x^(3) + (5)/(3)x^(2) - 9x + 17

Find the mode of the following marks (out of 10) obtained by 20 students : 4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9

Find the value of k, if x-1 is a factor of p(x) in each of the following cases : p(x) = k x^(2) - 3x + k

In ΔABC, AB = 4 and BC = 7, Then , .... holds good.

Find the value of the polynomial 5x - 4x^(2) + 3 atx = 2.

State the coefficient of x^(2) in each of the following polynomials : x^(4) + 5x^(3) + pi x^(2) - 3x + 11

Find the pair of whole numbers so that their sum cannot exceed 10 and difference of twice the first number and thrice the second number cannot exceed 12

A pyramid is a solid figure whose base is

(b) Explain rational number in your own words.

Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : The area of an equilateral triangle =………..

Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : The opposite angles of a parallelogram are ………….

A conical vessel with radius 10 cm and height 15 cm is completely filled with water. This water is poured into a cylinder with radius 5 cm. Find the height of water in the cylinder.

Find for solutions of each of the following equation : x + y = 7

In the previous question, the rate of return is

Express the following rational numbers in decimal form. (22)/(7)

Check whether (x-2) is a factor of x ^(3) - 2x ^(2) - 5x +4

In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that angle BEC = 130^(@) and angle ECD = 20^(@).. Find angle BAC.

Rs,33,000 is to be divided into two parts, such that the income from one part invested in Rs.200 shares at Rs.250 for 10% dividend is the same as that from the other investment which was invested in Rs.120 shares at Rs.150 for 12% dividend. Determine the amountsinvested in the two kinds of sheares.

The ratio of the measures of the sides of a triangle is 3 : 4 : 5. If the semiperimeter of the triangle is 36 cm, the measure of the longest side of the triangle is …………..cm.

Classify the following numbers as rational or irrational. sqrt3+sqrt2

Evaluate the following products without multiplying directly : 95 xx 96

Details of shashi 's saving bank account are given below Calculated the total interest earned by him up to 30-4-1999 The rate of interest is as follows (i) 4% per annum up to 28-2-1999 (ii) 35 per annum from 01-3-1999 to 30-4-1999

If (y-3) is a factor of y ^(3) - 2y ^(2) - 9y+ 18 then find the other two factors.

Express the following in terms of angles between 0^(@) and 45^(@) sin 59^(@)+tan 63^(@)

ABCD is a square . If ar(ABCD)=36 cm^2 . Then AB=____ cm.

Expressing 4x = 2y -7 in the y - form , we get y = ......

Find the difference between the compound interest compounded yearly and half yearly on Rs 10,000 for 18 months at 10% per annum.

If x + 3 is one of the x^(3) + 2x^(2) - m x - 18. then m = …………..

Acylindrical pillar is 50cm in diameter and 3.5m in height. Find the cost ofpainting the curved surface of the pillar at the rate of Rs. 12. 50\ p e r\ m^2dot

If each side of a triangle is doubled, find the ratio of the areas of two triangles, the given triangle & the triangle obtained on doubling the sides. Also find the percentage increase in the area of new triangle.

Construct a right-angled Delta ABC in which angleA=90^(@), hypotenuse BC=6 cm and AB=4 cm. Justify your construction.

Area of a parallelogram =_____

The mean of x,x+2,x+4,x+6 and x+8 is 11, find the mean of the first three observations.

If sinx =cosx and x is acute, state the value of x.

How many dimensions does a point have

Evaluate the following uing suitable identities : (102)^(3)

Solve for x : sin(x+10^(@))=1/2

Perimeter of a semi circle is 36cm, find itsarea.

In the given figure, AB is one of the diameters of the circle and OC is perpendicular to through the centre O. If AC is 9sqrt(2) cm then what is the area of the circle in cm^(2).

There are four unknown numbers. The mean of the first two numbers is 4 and the mean of the first three is 9. The mean of all four number is 15, if one of the four number is 2 find the other numbers.

The median of the following observations arranged in ascending order, is 20. Find x. 3,4,7,8,10,18,x+2,x+4,26,28,31,36,38 and 40.

Find the value of k, if x-1 is a factor of p(x) in each of the following cases : p(x) = kx^(2) - sqrt(2)x + 1

Verify whether 2x ^(4) - 6x ^(3) + 3x ^(2) + 3x -2 is divisible by x ^(2) - 3x +2 or not ? How can you verify using Factor Theorem ?