32581 + Interview Questions in Mathematics Page 26 InterviewSolution

1251.	THE PERIMETER OF RHOMBUS IS 260 M AND ONE OF ITS DIAGONALS IS 66M. FIND THE AREA OF THE RHOMBUS AND ITS OTHER DIAGONAL
Answer» THE PERIMETER OF RHOMBUS IS 260 M AND ONE OF ITS DIAGONALS IS 66M. FIND THE AREA OF THE RHOMBUS AND ITS OTHER DIAGONAL

Discussion

1252.	D is a point on the side BC of ΔABC such that ∠ADC=∠BAC. Prove that CACD=CBCA or, CA2=CB×CD. [2 MARKS]
Answer» D is a point on the side BC of $Δ A B C$ such that $∠ A D C = ∠ B A C$ . Prove that $\frac{C A}{C D} = \frac{C B}{C A}$ or, $C A^{2} = C B \times C D$ . [2 MARKS]

Discussion

1253.	Let x,y,z are distinct non-zero real numbers such that: x + (1/y) = y + (1/z) = z + (1/x) then the number of possible value of the product xyz is equal to
Answer» Let x,y,z are distinct non-zero real numbers such that: x + (1/y) = y + (1/z) = z + (1/x) then the number of possible value of the product xyz is equal to

Discussion

1254.	Solve the following quadratic equations by factorization:x-5 x-6=25242
Answer» Solve the following quadratic equations by factorization: $(x - 5) (x - 6) = \frac{25}{{(24)}^{2}}$

Discussion

1255.	If the 3rd and 6th terms of a G.P are 12 and 96, then its common ratio is ___.
Answer» If the $3^{rd}$ and $6^{th}$ terms of a G.P are 12 and 96, then its common ratio is ___.

Discussion

1256.	If A=⎡⎢⎣12−35021−11⎤⎥⎦,B=⎡⎢⎣3−12425203⎤⎥⎦ and C=⎡⎢⎣4120321−23⎤⎥⎦, then compute (A+B) and (B−C). Also, verify that A+(B−C)=(A+B)−C.
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 3 5 & 0 & 2 1 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 1 & 2 4 & 2 & 5 2 & 0 & 3 \end{matrix} ⎤ ⎥ ⎦$ and $C = ⎡ ⎢ ⎣ \begin{matrix} 4 & 1 & 2 0 & 3 & 2 1 & - 2 & 3 \end{matrix} ⎤ ⎥ ⎦,$ then compute $(A + B)$ and $(B - C) .$ Also, verify that $A + (B - C) = (A + B) - C$ .

Discussion

1257.	Find the slope of the line which passing through the points (at21, 2 at1) and (at22, 2 at2)
Answer» Find the slope of the line which passing through the points $(a t_{1}^{2}, 2 a t_{1}) a n d (a t_{2}^{2}, 2 a t_{2})$

Discussion

1258.	The given table shows the Marks obtained by students in Mathematics. MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006 Using the table determine the InterQuartile Range by drawing an ogive curve.
Answer» The given table shows the Marks obtained by students in Mathematics. $\begin{matrix} Marks & No. of Students 0 - 10 & 3 10 - 20 & 7 20 - 30 & 12 30 - 40 & 15 40 - 50 & 20 50 - 60 & 9 60 - 70 & 8 70 - 80 & 16 80 - 90 & 14 90 - 100 & 6 \end{matrix}$ Using the table determine the InterQuartile Range by drawing an ogive curve.

1258.

The given table shows the Marks obtained by students in Mathematics. MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006 Using the table determine the InterQuartile Range by drawing an ogive curve.

Answer»

The given table shows the Marks obtained by students in Mathematics.

$\begin{matrix} Marks & No. of Students 0 - 10 & 3 10 - 20 & 7 20 - 30 & 12 30 - 40 & 15 40 - 50 & 20 50 - 60 & 9 60 - 70 & 8 70 - 80 & 16 80 - 90 & 14 90 - 100 & 6 \end{matrix}$

Using the table determine the InterQuartile Range by drawing an ogive curve.

Discussion

1259.	Find the zeros of the following quardric polynomials and verify the relationship between the zeroes and the coefficients. i) x2−2x−8
Answer» Find the zeros of the following quardric polynomials and verify the relationship between the zeroes and the coefficients. i) $x^{2} - 2 x - 8$

Discussion

1260.	(1+tan A)2+(1−tan A)2=
Answer» $(1 + tan A)^{2} + (1 - tan A)^{2} =$

Discussion

1261.	Find the probability that a number selected at random from the numbers 3, 4, 4,4 5, 5, 6, 6, 6, 7 will be their mean.
Answer» Find the probability that a number selected at random from the numbers 3, 4, 4,4 5, 5, 6, 6, 6, 7 will be their mean.

Discussion

1262.	(1)Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case :(i)2x3+x2−5x+2;12.1,−2(2)Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case :(ii)x3−4x2+5x−2;2,1,1
Answer» (1) Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case : $(i) 2 x^{3} + x^{2} - 5 x + 2; \frac{1}{2} . 1, - 2$ (2) Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case : $(i i) x^{3} - 4 x^{2} + 5 x - 2; 2, 1, 1$

Discussion

1263.	Three circles are such that each touch the other two externally.The common tangents are concurrent at P.The length of the tangent to each circle is p.The ratio of the product of their radii to sum of their radii is
Answer» Three circles are such that each touch the other two externally.The common tangents are concurrent at P.The length of the tangent to each circle is p.The ratio of the product of their radii to sum of their radii is

Discussion

1264.	If two of the zeroes of the polynomial f (x) = x4 - 3x3 - x2 + 9x - 6 are -√3 and √3 then all the zeroes are
Answer» If two of the zeroes of the polynomial f (x) = x⁴ - 3x³ - x² + 9x - 6 are -√3 and √3 then all the zeroes are

Discussion

1265.	The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1:5, find the A.P.
Answer» The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1:5, find the A.P.

Discussion

1266.	Question 90 (iii) Factorise the following, using the identity, a2−2ab+b2=(a−b)2. y2−14y+49
Answer» Question 90 (iii) Factorise the following, using the identity, $a^{2} - 2 a b + b^{2} = (a - b)^{2}$ . $y^{2} - 14 y + 49$

Discussion

1267.	If 3cosθ = 1, find the value of 6 sin2 θ+tan2 θ4 cos θ
Answer» If 3cosθ = 1, find the value of $\frac{6 \sin^{2} θ + \tan^{2} θ}{4 \cos θ}$

Discussion

1268.	Three tankers contain 403 lltres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of three containers exact number of times.
Answer» Three tankers contain 403 lltres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of three containers exact number of times.

Discussion

1269.	Prove the following trigonometric identities.secA (1 − sinA) (secA + tanA) = 1
Answer» Prove the following trigonometric identities. secA (1 − sinA) (secA + tanA) = 1

Discussion

1270.	36. If the zeros of the polynomial x-3x+2 are a-b, a and a+b , then the values of a and b respectively are
Answer» 36. If the zeros of the polynomial x-3x+2 are a-b, a and a+b , then the values of a and b respectively are

Discussion

1271.

Marks obtained in a test by X standard students of two sections A and B are given below: Marks No. of students in Section A No. of students in Section B 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50 5 10 25 8 2 5 12 20 8 5 Determine: (i) Which section’s performance is better? And (ii) Which section’s performance is more variable?

Answer»

Marks obtained in a test by X standard students of two sections A and B are given below:

Marks

No. of students in

Section A

No. of students in

Section B

25 – 30

30 – 35

35 – 40

40 – 45

45 – 50

5

10

25

8

2

5

12

20

8

5

Determine: (i) Which section’s performance is better? And (ii) Which section’s performance is more variable?

Discussion

1272.	Arrange the following quadratic equations based on the ascending order of their linear coefficients.
Answer» Arrange the following quadratic equations based on the ascending order of their linear coefficients.

Discussion

1273.	A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles (in the following figure). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region.(Use π = 22/7)
Answer» A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles (in the following figure). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region. (Use π = 22/7)

Discussion

1274.	70. (1) ABCD is a rectangle with angle BAC=40^° . determine angle DBC. (2) PQRS is a parallelogram in which angle SPQ=65^° and angle SQR=50^° .find the measure of angle RSQ and angle PSQ. (3) In the adjoining figure, PQ=PS and RQ=RS. If angle QPO=30^° , angle RSO=55^° .find the measure of angle a,angel b,angel c,angel d and angel e.
Answer» 70. (1) ABCD is a rectangle with angle BAC=40^° . determine angle DBC. (2) PQRS is a parallelogram in which angle SPQ=65^° and angle SQR=50^° .find the measure of angle RSQ and angle PSQ. (3) In the adjoining figure, PQ=PS and RQ=RS. If angle QPO=30^° , angle RSO=55^° .find the measure of angle a,angel b,angel c,angel d and angel e.

Discussion

1275.	In Figure 4, two triangles ABC and DBC are on the same base BC in which ∠A = ∠D = 90°. If CA and BD meet each other at E, show that AE ✕ CE = BE ✕ DE.
Answer» In Figure 4, two triangles ABC and DBC are on the same base BC in which ∠A = ∠D = 90°. If CA and BD meet each other at E, show that AE ✕ CE = BE ✕ DE.

Discussion

1276.	Find the equation of the straight line passing through the pair of points (a, b) and (a + b, a-b).
Answer» Find the equation of the straight line passing through the pair of points (a, b) and (a + b, a-b).

Discussion

1277.	Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Answer» Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Discussion

1278.	Question 3Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
Answer» Question 3 Find the height of a cuboid whose base area is $180 c m^{2}$ and volume is $900 c m^{3}$ ?

Discussion

1279.	From the following particulars, prepare a petty cash book for the month of June 2016. DateParticularsAmt (Rs)June 1Received petty cash2,000June 3Paid for postage300June 5Paid for telephone40June 8Paid for cartage140June 9Paid for postage200June 12Paid for sundries100June 27Paid for taxi fare240 If the imprest amount is Rs 2,000, show what amount the petty cashier would be entitled to draw in the beginning of the next month.
Answer» From the following particulars, prepare a petty cash book for the month of June 2016. $\begin{matrix} Date & Particulars & Amt (Rs) June 1 & Received petty cash & 2, 000 June 3 & Paid for postage & 300 June 5 & Paid for telephone & 40 June 8 & Paid for cartage & 140 June 9 & Paid for postage & 200 June 12 & Paid for sundries & 100 June 27 & Paid for taxi fare & 240 \end{matrix}$ If the imprest amount is Rs 2,000, show what amount the petty cashier would be entitled to draw in the beginning of the next month.

1279.

From the following particulars, prepare a petty cash book for the month of June 2016. DateParticularsAmt (Rs)June 1Received petty cash2,000June 3Paid for postage300June 5Paid for telephone40June 8Paid for cartage140June 9Paid for postage200June 12Paid for sundries100June 27Paid for taxi fare240 If the imprest amount is Rs 2,000, show what amount the petty cashier would be entitled to draw in the beginning of the next month.

Answer»

From the following particulars, prepare a petty cash book for the month of June 2016.

$\begin{matrix} Date & Particulars & Amt (Rs) June 1 & Received petty cash & 2, 000 June 3 & Paid for postage & 300 June 5 & Paid for telephone & 40 June 8 & Paid for cartage & 140 June 9 & Paid for postage & 200 June 12 & Paid for sundries & 100 June 27 & Paid for taxi fare & 240 \end{matrix}$

If the imprest amount is Rs 2,000, show what amount the petty cashier would be entitled to draw in the beginning of the next month.

Discussion

1280.	The sum of three numbers in G.P. is 3910 and their product is 1. Find the numbers.
Answer» The sum of three numbers in G.P. is $\frac{39}{10}$ and their product is 1. Find the numbers.

Discussion

1281.	Given figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.
Answer» Given figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

1281.

Given figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Answer»

Given figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Discussion

1282.	The sum of twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. The sum of thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The smallest of the even numbers is
Answer» The sum of twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. The sum of thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The smallest of the even numbers is

Discussion

1283.	One zero of the polynomial 3x3+16x2+15x-18 is 23. Find the other zeros of the polynomial.
Answer» One zero of the polynomial $3 x^{3} + 16 x^{2} + 15 x - 18 is \frac{2}{3}$ . Find the other zeros of the polynomial.

Discussion

1284.	In triangle ABC ,if DE Parallel BC , and DE :BC = 4:5 , then the ratio of trapezium BCED and triangle ABC IS . And is 9:25
Answer» In triangle ABC ,if DE Parallel BC , and DE :BC = 4:5 , then the ratio of trapezium BCED and triangle ABC IS . And is 9:25

Discussion

1285.	If n is a natural number selected from the first 40 natural numbers, then the probability that it satisfies the inequation n5+40.7n≥5.9 is
Answer» If n is a natural number selected from the first 40 natural numbers, then the probability that it satisfies the inequation $\frac{n}{5} + \frac{40.7}{n} \geq 5.9$ is

Discussion

1286.	Match the following solid objects with the expressions of their volume.
Answer» Match the following solid objects with the expressions of their volume.

Discussion

1287.	A cylindrical vessel of height 35 cm contains 11 litres of juice Find the diameter of the vessel (one litre = 1000 cc.)
Answer» A cylindrical vessel of height 35 cm contains 11 litres of juice Find the diameter of the vessel (one litre = 1000 cc.)

1287.

A cylindrical vessel of height 35 cm contains 11 litres of juice Find the diameter of the vessel (one litre = 1000 cc.)

Answer»

A cylindrical vessel of height 35 cm contains 11 litres of juice Find the diameter of the vessel (one litre = 1000 cc.)

Discussion

1288.	A, B and C are partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2. B decides to retire from the firm. Calculate new profit-sharing ratio of A and C in the following circumstances:(a) If B gives his share to A and C in the original ratio of A and C.(b) If B gives his share to A and C in equal proportion.(c) If B gives his share to A and C in the ratio of 3 : 1.(d) If B gives his share to A only.
Answer» A, B and C are partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2. B decides to retire from the firm. Calculate new profit-sharing ratio of A and C in the following circumstances: (a) If B gives his share to A and C in the original ratio of A and C. (b) If B gives his share to A and C in equal proportion. (c) If B gives his share to A and C in the ratio of 3 : 1. (d) If B gives his share to A only.

Discussion

1289.	If D, E and F are respectively the midpoints of sides AB, BC and CA of △ABC then what is the ratio of the areas of △DEF and △ABC?
Answer» If D, E and F are respectively the midpoints of sides AB, BC and CA of △ABC then what is the ratio of the areas of △DEF and △ABC?

Discussion

1290.	Root of the equation (x+1a)2−b2=0 is
Answer» Root of the equation $(x + \frac{1}{a})^{2} - b^{2} = 0 i s$

Discussion

1291.	\|x-3\|+\|x+5\|=8
Answer» \|x-3\|+\|x+5\|=8

Discussion

1292.	A, B and C are partners sharing profits in the ratio of 5 : 4 : 1. C is given a guarantee that his minimum share of profit in any given year would be at least ₹ 5,000. Deficiency, if any, would be borne by A and B equally. Profit for the year ended 31st March 2019 was ₹ 40,000.Pass necessary Journal entries in the books of the firm.
Answer» A, B and C are partners sharing profits in the ratio of 5 : 4 : 1. C is given a guarantee that his minimum share of profit in any given year would be at least ₹ 5,000. Deficiency, if any, would be borne by A and B equally. Profit for the year ended 31st March 2019 was ₹ 40,000. Pass necessary Journal entries in the books of the firm.

Discussion

1293.	A car has a velocity →v=80km/hr towards east. Another car on the road has a velocity = →−v. The magnitude and direction of velocity of second car is
Answer» A car has a velocity $\to v = 80 k m / h r$ towards east. Another car on the road has a velocity = $\to - v$ . The magnitude and direction of velocity of second car is

Discussion

1294.	The surface of a household radiator has an emissivity of 0.55 and an area of 1.5 m2. Its equilibrium temperature is 50∘C and the surroundings are at 22∘C(Boltzmann constant is σ=5.67×10−8 W/m2K4)Column IColumn IIi. At what rate is radiation a.155 Wemitted by the radiator?ii. At what rate is radiation b.509 Wabsorbed by the radiator?iii What is the net value of c.354 Wradiation from the radiator?
Answer» The surface of a household radiator has an emissivity of $0.55$ and an area of $1.5 m^{2}$ . Its equilibrium temperature is $50^{\circ} C$ and the surroundings are at $22^{\circ} C (Boltzmann constant is σ = 5.67 \times 10^{- 8} {W/m}^{2} K^{4})$ $\begin{matrix} Column I & Column II i. At what rate is radiation & a . 155 W emitted by the radiator ? ii. At what rate is radiation & b . 509 W absorbed by the radiator ? iii What is the net value of & c . 354 W radiation from the radiator ? \end{matrix}$

Discussion

1295.	Show that √p+√q is an irrational number where p and q are prime numbers.
Answer» Show that √p+√q is an irrational number where p and q are prime numbers.

Discussion

1296.	What is the value of x in the figure if BD < DC? 4
Answer» What is the value of x in the figure if BD < DC? 4

Discussion

1297.	Mr. Bajaj needs Rs 30,000 after 2 years. What least money (in multiple of Rs 5) must he deposit every month in a recurring deposit account to get required money at the end of 2 years, the rate of interest being 8% p.a. ?
Answer» Mr. Bajaj needs Rs 30,000 after 2 years. What least money (in multiple of Rs 5) must he deposit every month in a recurring deposit account to get required money at the end of 2 years, the rate of interest being 8% p.a. ?

Discussion

1298.	Factorise: abx+aby−bcx−bcy [2 MARKS]
Answer» Factorise: $a b x + a b y - b c x - b c y$ [2 MARKS]

Discussion

1299.	A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.
Answer» A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.

Discussion

1300.	If [1234]A[−352−4]=[1−511−27], then the matrix A is equal to
Answer» If $[\begin{matrix} 1 & 2 3 & 4 \end{matrix}] A [\begin{matrix} - 3 & 5 2 & - 4 \end{matrix}] = [\begin{matrix} 1 & - 5 11 & - 27 \end{matrix}]$ , then the matrix $A$ is equal to

Discussion

Explore topic-wise InterviewSolutions in .

THE PERIMETER OF RHOMBUS IS 260 M AND ONE OF ITS DIAGONALS IS 66M. FIND THE AREA OF THE RHOMBUS AND ITS OTHER DIAGONAL

D is a point on the side BC of ΔABC such that ∠ADC=∠BAC. Prove that CACD=CBCA or, CA2=CB×CD. [2 MARKS]

Let x,y,z are distinct non-zero real numbers such that: x + (1/y) = y + (1/z) = z + (1/x) then the number of possible value of the product xyz is equal to

Solve the following quadratic equations by factorization:x-5 x-6=25242

If the 3rd and 6th terms of a G.P are 12 and 96, then its common ratio is ___.

If A=⎡⎢⎣12−35021−11⎤⎥⎦,B=⎡⎢⎣3−12425203⎤⎥⎦ and C=⎡⎢⎣4120321−23⎤⎥⎦, then compute (A+B) and (B−C). Also, verify that A+(B−C)=(A+B)−C.

Find the slope of the line which passing through the points (at21, 2 at1) and (at22, 2 at2)

The given table shows the Marks obtained by students in Mathematics. MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006 Using the table determine the InterQuartile Range by drawing an ogive curve.

Find the zeros of the following quardric polynomials and verify the relationship between the zeroes and the coefficients. i) x2−2x−8

(1+tan A)2+(1−tan A)2=

Find the probability that a number selected at random from the numbers 3, 4, 4,4 5, 5, 6, 6, 6, 7 will be their mean.

Three circles are such that each touch the other two externally.The common tangents are concurrent at P.The length of the tangent to each circle is p.The ratio of the product of their radii to sum of their radii is

If two of the zeroes of the polynomial f (x) = x4 - 3x3 - x2 + 9x - 6 are -√3 and √3 then all the zeroes are

The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1:5, find the A.P.

Question 90 (iii) Factorise the following, using the identity, a2−2ab+b2=(a−b)2. y2−14y+49

If 3cosθ = 1, find the value of 6 sin2 θ+tan2 θ4 cos θ

Three tankers contain 403 lltres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of three containers exact number of times.

Prove the following trigonometric identities.secA (1 − sinA) (secA + tanA) = 1

36. If the zeros of the polynomial x-3x+2 are a-b, a and a+b , then the values of a and b respectively are

Arrange the following quadratic equations based on the ascending order of their linear coefficients.

In Figure 4, two triangles ABC and DBC are on the same base BC in which ∠A = ∠D = 90°. If CA and BD meet each other at E, show that AE ✕ CE = BE ✕ DE.

Find the equation of the straight line passing through the pair of points (a, b) and (a + b, a-b).

Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Question 3Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?

The sum of three numbers in G.P. is 3910 and their product is 1. Find the numbers.

Given figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

The sum of twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. The sum of thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The smallest of the even numbers is

One zero of the polynomial 3x3+16x2+15x-18 is 23. Find the other zeros of the polynomial.

In triangle ABC ,if DE Parallel BC , and DE :BC = 4:5 , then the ratio of trapezium BCED and triangle ABC IS . And is 9:25

If n is a natural number selected from the first 40 natural numbers, then the probability that it satisfies the inequation n5+40.7n≥5.9 is

Match the following solid objects with the expressions of their volume.

A cylindrical vessel of height 35 cm contains 11 litres of juice Find the diameter of the vessel (one litre = 1000 cc.)

If D, E and F are respectively the midpoints of sides AB, BC and CA of △ABC then what is the ratio of the areas of △DEF and △ABC?

Root of the equation (x+1a)2−b2=0 is

|x-3|+|x+5|=8

A car has a velocity →v=80km/hr towards east. Another car on the road has a velocity = →−v. The magnitude and direction of velocity of second car is

Show that √p+√q is an irrational number where p and q are prime numbers.

What is the value of x in the figure if BD < DC? 4

Mr. Bajaj needs Rs 30,000 after 2 years. What least money (in multiple of Rs 5) must he deposit every month in a recurring deposit account to get required money at the end of 2 years, the rate of interest being 8% p.a. ?

Factorise: abx+aby−bcx−bcy [2 MARKS]

A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.

If [1234]A[−352−4]=[1−511−27], then the matrix A is equal to