24740 + Interview Questions in Mathematics Page 163 InterviewSolution

8101.	Angle between the pair of lines represented by the equation 2x^2+8y^2-8xy+5x-10y+3=0 is
Answer» Angle between the pair of lines represented by the equation 2x^2+8y^2-8xy+5x-10y+3=0 is

Discussion

8102.	If x=3+8 then x2+1x2=?(a) 34(b) 56(c) 28(d) 63
Answer» If $x = 3 + \sqrt{8} then (x^{2} + \frac{1}{x^{2}}) = ?$ (a) 34 (b) 56 (c) 28 (d) 63

Discussion

8103.	ABCD is a trapezium in which AB \|\| DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the mid-point of BC.
Answer» ABCD is a trapezium in which AB \|\| DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the mid-point of BC.

8103.

ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the mid-point of BC.

Answer»

ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the mid-point of BC.

Discussion

8104.	Write the polynomials in index form. (i) (1, 2, 3) (ii) (5, 0, 0, 0, -1) (iii) (-2, 2,-2, 2)
Answer» Write the polynomials in index form. (i) (1, 2, 3) (ii) (5, 0, 0, 0, $-$ 1) (iii) ( $-$ 2, 2, $-$ 2, 2)

Discussion

8105.	Durations of sunshine (in hours) in Amritsar to first 10 days of August 1997 as reported by the Meteorological Department are given below:9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9(i) Find the mean X.(ii) Verify that ∑i=110 (xi-X¯) = 0
Answer» Durations of sunshine (in hours) in Amritsar to first 10 days of August 1997 as reported by the Meteorological Department are given below: 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9 (i) Find the mean X. (ii) Verify that $\sum_{i = 1}^{10} (x_{i} - \bar{X}) = 0$

Discussion

8106.	AB=CB,AB=CD and EF bisects BD at G. Prove that G is midpoint of EF
Answer» AB=CB,AB=CD and EF bisects BD at G. Prove that G is midpoint of EF

Discussion

8107.	Question 4The cost of 4 pens and 4 pencils boxes is Rs.100. there times the cost of a pen is Rs. 15 more than the cost of a pencil box,. Form the pair of linear equations for the above situation. Find the cost pen and a pencil box be Rs. y.
Answer» Question 4 The cost of 4 pens and 4 pencils boxes is Rs.100. there times the cost of a pen is Rs. 15 more than the cost of a pencil box,. Form the pair of linear equations for the above situation. Find the cost pen and a pencil box be Rs. y.

Discussion

8108.	The perpendicular distance of the point A(3, 4) from the y-axis is(a) 3(b) 4(c) 5(d) 7
Answer» The perpendicular distance of the point A(3, 4) from the y-axis is (a) 3 (b) 4 (c) 5 (d) 7

Discussion

8109.	Parallelogram ABCD and rectangle ABEF are on the same base AB. If AB=14 cm, BC=12 cm, then the possible value for the perimeter of ABEF is
Answer» Parallelogram ABCD and rectangle ABEF are on the same base AB. If AB=14 cm, BC=12 cm, then the possible value for the perimeter of ABEF is

Discussion

8110.	AETB is a straight line such that AE=TB.If ET=30cm,LE=LT=25cm and perimeter of △ LAB is 20 cm more than perimeter of △ LET, then length of AE is
Answer» AETB is a straight line such that AE=TB.If ET=30cm,LE=LT=25cm and perimeter of △ LAB is 20 cm more than perimeter of △ LET, then length of AE is

Discussion

8111.	equation of circle which touches the coordinate axes and passes through the point (2,1) is
Answer» equation of circle which touches the coordinate axes and passes through the point (2,1) is

Discussion

8112.	212+213+214110×25×1256 is equal to:___.(in decimal form)
Answer» $\frac{2 \frac{1}{2} + 2 \frac{1}{3} + 2 \frac{1}{4}}{\frac{1}{10} \times \frac{2}{5} \times \frac{125}{6}}$ is equal to:___.(in decimal form)

Discussion

8113.	Question 2Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.
Answer» Question 2 Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.

Discussion

8114.	46. Prove that the parallelogram circumscribing a circle is rhombus
Answer» 46. Prove that the parallelogram circumscribing a circle is rhombus

Discussion

8115.	A 60∘ angle is constructed with arc radius as 3 cm. Find the perimeter of the △ BOC in cm. 9
Answer» A $60^{\circ}$ angle is constructed with arc radius as 3 cm. Find the perimeter of the $△ B O C$ in cm. 9

Discussion

8116.	if (x-3) and (x+3) are the factors of 4x^2+ax^2+bx, find the value of a and b.
Answer» if (x-3) and (x+3) are the factors of 4x^2+ax^2+bx, find the value of a and b.

Discussion

8117.	Find the edge of a cube whose surface area is 432 m2.
Answer» Find the edge of a cube whose surface area is 432 m².

Discussion

8118.	The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.
Answer» The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm².

Discussion

8119.	A line passes through the point (-4, 6) and is parallel to x-axis. Find its equation.
Answer» A line passes through the point (-4, 6) and is parallel to x-axis. Find its equation.

Discussion

8120.	Factorise the following expression:(l+m)2−4lm
Answer» Factorise the following expression: $(l + m)^{2} - 4 l m$

Discussion

8121.	if P=\sqrt{16+8\sqrt3} - \sqrt{21-12\sqrt3} , then find the value of P ?
Answer» if P=\sqrt{16+8\sqrt3} - \sqrt{21-12\sqrt3} , then find the value of P ?

Discussion

8122.	If A = {1, 2, 3, 4}, B{3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find : (i) A∪B (ii) A∪C (iii) B∪C (iv) B∪D (v) A∪B∪C (vi) A∪B∪D (vii) B∪C∪D
Answer» If A = {1, 2, 3, 4}, B{3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find : (i) $A \cup B$ (ii) $A \cup C$ (iii) $B \cup C$ (iv) $B \cup D$ (v) $A \cup B \cup C$ (vi) $A \cup B \cup D$ (vii) $B \cup C \cup D$

8122.

If A = {1, 2, 3, 4}, B{3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find : (i) A∪B (ii) A∪C (iii) B∪C (iv) B∪D (v) A∪B∪C (vi) A∪B∪D (vii) B∪C∪D

Answer»

If A = {1, 2, 3, 4}, B{3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find :

(i) $A \cup B$ (ii) $A \cup C$

(iii) $B \cup C$ (iv) $B \cup D$

(v) $A \cup B \cup C$ (vi) $A \cup B \cup D$

(vii) $B \cup C \cup D$

Discussion

8123.	Find seven rational numbers between 16 and 521.
Answer» Find seven rational numbers between $\frac{1}{6}$ and $\frac{5}{21}$ .

Discussion

8124.	In a year, Ravi earns ₹3,60,000 and paid ₹24,000 as income tax.Find the ratio of hisa) income to income tax.b) income tax to income after paying income tax.
Answer» In a year, Ravi earns ₹3,60,000 and paid ₹24,000 as income tax. Find the ratio of his a) income to income tax. b) income tax to income after paying income tax.

Discussion

8125.	In the given figure, side BC of ΔABC is produced to point D such that bisectors of ∠ABC and ∠ACD meet at a point E. If ∠BAC = 68°, find ∠BEC.
Answer» In the given figure, side BC of ΔABC is produced to point D such that bisectors of ∠ABC and ∠ACD meet at a point E. If ∠BAC = 68°, find ∠BEC.

Discussion

8126.	A line whose equation is of the type x = a is a line parallel to the y axis, so the line is a vertical line. The line ax + by = ab makes intercepts on the x and y axes
Answer» A line whose equation is of the type x = a is a line parallel to the y axis, so the line is a vertical line. The line ax + by = ab makes intercepts on the x and y axes

8126.

A line whose equation is of the type x = a is a line parallel to the y axis, so the line is a vertical line. The line ax + by = ab makes intercepts on the x and y axes

Answer»

A line whose equation is of the type x = a is a line parallel to the y axis, so the line is a vertical line.

The line ax + by = ab makes intercepts on the x and y axes

Discussion

8127.

Following is the summarised Balance Sheet of Philips India Ltd. as at 31st March 2018: Particulars ulars Note No. 31st March, 2018 (₹) 31st March, 2017 (₹) I. EQUITY AND LIABILITIES 1. Shareholders' Funds (a) Share Capital 13,50,000 13,50,000 (b) Reserves and Surplus 1 11,34,000 10,68,000 2. Non-Current Liabilities Long-term Borrowings: 10% Mortgage Loan 8,10,000 ... 3. Current Liabilities (a) Trade Payables (Creditors) 4,20,000 5,04,000 (b) Short-term Provisions: Provision for Tax 30,000 2,25,000 Total Total Expenses 37,26,000 31,47,000 II. ASSETS 1, Non-Current Assets (a) Fixed Assets (Tangible) 9,60,000 12,00,000 (b) Non-Current Investments 1,80,000 1,50,000 2. Current Assets (a) Current Investments 21,000 17,000 (b) Inventories 63,30,000 7,82,000 (c) Trade Receivables 13,65,000 6,30,000 (c) Cash and Cash Equivalents 5,70,00 4,30,000 Total 37,26,000 31,47,000 Notes to Accounts Particulars 31st March, 2018 (₹) 31st March, 2017 (₹) I. Reserves and Surplus General Reserve 9,30,000 9,00,000 Surplus, i.e., Balance in Statement of Profit and Loss 2,04,000 1,68,000 11,34,000 10,68,000 Additional Information:1. Investments costing ₹ 24,000 were sold during the year for ₹ 25,5000.2. Provistion for Tax made during the year was ₹ 27,000.3. During the year, a part of the Fixed Assets costing ₹ 30,000 was sold for ₹ 36,000. The rofits were included in the Statement of Profit and Loss.4. The Interim Dividend paid during the year amounted to ₹ 1,20,000.You are required to prepare Cash Flow Statement.

Answer» Following is the summarised Balance Sheet of Philips India Ltd. as at 31st March 2018:

Particulars ulars	Note No.	31st March, 2018 (₹)	31st March, 2017 (₹)
I. EQUITY AND LIABILITIES
1. Shareholders' Funds
(a) Share Capital		13,50,000	13,50,000
(b) Reserves and Surplus	1	11,34,000	10,68,000
2. Non-Current Liabilities
Long-term Borrowings: 10% Mortgage Loan		8,10,000	...
3. Current Liabilities
(a) Trade Payables (Creditors)		4,20,000	5,04,000
(b) Short-term Provisions:
Provision for Tax		30,000	2,25,000
Total Total Expenses		37,26,000	31,47,000
II. ASSETS
1, Non-Current Assets
(a) Fixed Assets (Tangible)		9,60,000	12,00,000
(b) Non-Current Investments		1,80,000	1,50,000
2. Current Assets
(a) Current Investments		21,000	17,000
(b) Inventories		63,30,000	7,82,000
(c) Trade Receivables		13,65,000	6,30,000
(c) Cash and Cash Equivalents		5,70,00	4,30,000
Total		37,26,000	31,47,000

Notes to Accounts

Particulars	31st March, 2018 (₹)	31st March, 2017 (₹)
I. Reserves and Surplus
General Reserve	9,30,000	9,00,000
Surplus, i.e., Balance in Statement of Profit and Loss	2,04,000	1,68,000
	11,34,000	10,68,000

Additional Information:

1. Investments costing ₹ 24,000 were sold during the year for ₹ 25,5000.

2. Provistion for Tax made during the year was ₹ 27,000.

3. During the year, a part of the Fixed Assets costing ₹ 30,000 was sold for ₹ 36,000. The rofits were included in the Statement of Profit and Loss.

4. The Interim Dividend paid during the year amounted to ₹ 1,20,000.

You are required to prepare Cash Flow Statement.

Discussion

8128.	Find the area bounded by the curve y²=2y-x and y-axis. NOTE: How to draw the graph of y²=2y-x?
Answer» Find the area bounded by the curve y²=2y-x and y-axis. NOTE: How to draw the graph of y²=2y-x?

Discussion

8129.	If the minimum distance from its opposite side of an equilateral triangle is 4√3 cm, then determine the side length of the triangle.
Answer» If the minimum distance from its opposite side of an equilateral triangle is $4 \sqrt{3}$ cm, then determine the side length of the triangle.

Discussion

8130.	The cost of 5 kg of sugar and 7 kg of rice is ₹153 and the cost of 7 kg of sugar and 5 kg of rice is ₹ 147 find the cost of 6 kg of sugar and 10 kg of rice
Answer» The cost of 5 kg of sugar and 7 kg of rice is ₹153 and the cost of 7 kg of sugar and 5 kg of rice is ₹ 147 find the cost of 6 kg of sugar and 10 kg of rice

Discussion

8131.	If 0∘<θ<90∘, then √sec2θ+cosec2θ =
Answer» If $0^{\circ} < θ < 90^{\circ}$ , then $\sqrt{s e c^{2} θ + c o s e c^{2} θ}$ =

Discussion

8132.	Match the following parallelograms with their respective areas.
Answer» Match the following parallelograms with their respective areas.

Discussion

8133.	The given table shows the rainfall in mm in different cities in India for a year.CitiesRainfall (mm)Delhi44.6Mumbai63.5Kolkata60.7Pune56.2Bangalore60.1Bhubaneswar49.4Chennai61.7Ooty56.9Ahmedabad34.4Jaipur32.5Find the mean rainfall in the year.
Answer» The given table shows the rainfall in mm in different cities in India for a year. $\begin{matrix} Cities & Rainfall (mm) Delhi & 44.6 Mumbai & 63.5 Kolkata & 60.7 Pune & 56.2 Bangalore & 60.1 Bhubaneswar & 49.4 Chennai & 61.7 Ooty & 56.9 Ahmedabad & 34.4 Jaipur & 32.5 \end{matrix}$ Find the mean rainfall in the year.

8133.

The given table shows the rainfall in mm in different cities in India for a year.CitiesRainfall (mm)Delhi44.6Mumbai63.5Kolkata60.7Pune56.2Bangalore60.1Bhubaneswar49.4Chennai61.7Ooty56.9Ahmedabad34.4Jaipur32.5Find the mean rainfall in the year.

Answer»

The given table shows the rainfall in mm in different cities in India for a year.

$\begin{matrix} Cities & Rainfall (mm) Delhi & 44.6 Mumbai & 63.5 Kolkata & 60.7 Pune & 56.2 Bangalore & 60.1 Bhubaneswar & 49.4 Chennai & 61.7 Ooty & 56.9 Ahmedabad & 34.4 Jaipur & 32.5 \end{matrix}$

Find the mean rainfall in the year.

Discussion

8134.	Pescud felt that best-sellers were not realistic as____________. (i) American farmers had nothing in common with European princesses (ii) men generally married girls from a similar background (iii) American men married girls who studied in America (iv) American men did not know fencing and were beaten by the Swiss guards
Answer» Pescud felt that best-sellers were not realistic as____________. (i) American farmers had nothing in common with European princesses (ii) men generally married girls from a similar background (iii) American men married girls who studied in America (iv) American men did not know fencing and were beaten by the Swiss guards

8134.

Pescud felt that best-sellers were not realistic as____________. (i) American farmers had nothing in common with European princesses (ii) men generally married girls from a similar background (iii) American men married girls who studied in America (iv) American men did not know fencing and were beaten by the Swiss guards

Answer»

Pescud felt that
best-sellers were not realistic as____________.

(i) American
farmers had nothing in common with European princesses

(ii) men
generally married girls from a similar background

(iii) American men
married girls who studied in America

(iv) American men
did not know fencing and were beaten by the Swiss guards

Discussion

8135.	Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the cofficients. (1).4x2+8x?
Answer» Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the cofficients. (1).4x2+8x?

Discussion

8136.	Question 9One equation of a pair of dependent linear equations is - 5x + 7y – 2 = 0(A) 10x + 14y + 4 = 0(B) –10x – 14y + 4 = 0(C) –10x + 14y + 4 = 0(D) 10x – 14y = –4
Answer» Question 9 One equation of a pair of dependent linear equations is - 5x + 7y – 2 = 0 (A) 10x + 14y + 4 = 0 (B) –10x – 14y + 4 = 0 (C) –10x + 14y + 4 = 0 (D) 10x – 14y = –4

Discussion

8137.	Find the area of the given polygon:
Answer» Find the area of the given polygon:

Discussion

8138.	Write the coefficient of x2 in each of the following:(i) 17 − 2x + 7x2(ii) 9 − 12x + x3(iii) π6x2-3x+4(iv) 3x-7
Answer» Write the coefficient of x² in each of the following: (i) 17 − 2x + 7x² (ii) 9 − 12x + x³ (iii) $\frac{π}{6} x^{2} - 3 x + 4$ (iv) $\sqrt{3} x - 7$

Discussion

8139.	There is a thin coin of radius 2K mm and thickness 1 mm. Now I place M coins one on top of the other. What is the object formed and what is its volume?
Answer» There is a thin coin of radius 2K mm and thickness 1 mm. Now I place M coins one on top of the other. What is the object formed and what is its volume?

Discussion

8140.	Find the median of the following data: 13, 15, 18, 14, 22, 42, 9, 6, 15, 21.
Answer» Find the median of the following data: 13, 15, 18, 14, 22, 42, 9, 6, 15, 21.

Discussion

8141.	Freddy walks in a straight line from his house having coordinates (1, 3) to the playground having coordinates (4, 5). Find the distance covered by Freddy.
Answer» Freddy walks in a straight line from his house having coordinates (1, 3) to the playground having coordinates (4, 5). Find the distance covered by Freddy.

Discussion

8142.	In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that ∠ADC=95∘ and ∠ECF=20∘ Then, ∠BAD=?. (a) 95∘ (b) 85∘ (c) 105∘ (d) 75∘
Answer» In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that $∠ A D C = 95^{\circ} a n d ∠ E C F = 20^{\circ} T h e n, ∠ B A D = ?$ . (a) $95^{\circ}$ (b) $85^{\circ}$ (c) $105^{\circ}$ (d) $75^{\circ}$

8142.

In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that ∠ADC=95∘ and ∠ECF=20∘ Then, ∠BAD=?. (a) 95∘ (b) 85∘ (c) 105∘ (d) 75∘

Answer»

In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that $∠ A D C = 95^{\circ} a n d ∠ E C F = 20^{\circ} T h e n, ∠ B A D = ?$ .

(a) $95^{\circ}$

(b) $85^{\circ}$

(c) $105^{\circ}$

(d) $75^{\circ}$

Discussion

8143.	Question 39 The sum of angles of a concave quadrilateral is a) More than 360∘ b) Less than 360∘ c) Equal to 360∘ d) Twice of 360∘
Answer» Question 39 The sum of angles of a concave quadrilateral is a) More than $360^{\circ}$ b) Less than $360^{\circ}$ c) Equal to $360^{\circ}$ d) Twice of $360^{\circ}$

Discussion

8144.	If a solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each, then n = _________.
Answer» If a solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each, then n = _________.

Discussion

8145.	If (2a–4,3a–9) lie on Y axis then find the value of a.
Answer» If (2a–4,3a–9) lie on Y axis then find the value of a.

Discussion

8146.	A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Answer» A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

Discussion

8147.	The curved surface of a cylindrical bulb of height 18 cm and base radius 7 cm is to be painted in luminating gold colour such that 23rd of the height of the bulb emits golden light; painting is done at ₹ 5 per sq. cm. The cost of painting the bulb is_____.(use π=227)
Answer» The curved surface of a cylindrical bulb of height $18 c m$ and base radius $7 c m$ is to be painted in luminating gold colour such that ${\frac{2}{3}}^{r d}$ of the height of the bulb emits golden light; painting is done at ₹ 5 per sq. cm. The cost of painting the bulb is_____. $(u s e π = \frac{22}{7})$

Discussion

8148.	The factors of x3 − 1 + y3 + 3xy are(a) (x − 1 + y) (x2 + 1 + y2 + x + y − xy)(b) (x + y + 1) (x2 + y2 + 1 −xy − x − y)(c) (x − 1 + y) (x2 − 1 − y2 + x + y + xy)(d) 3(x + y −1) (x2 + y2 − 1)
Answer» The factors of x³ − 1 + y³ + 3xy are (a) (x − 1 + y) (x² + 1 + y² + x + y − xy) (b) (x + y + 1) (x² + y² + 1 −xy − x − y) (c) (x − 1 + y) (x² − 1 − y² + x + y + xy) (d) 3(x + y −1) (x² + y² − 1)

Discussion

8149.	An angle is 24 less than its compliment, then the measure of angle is
Answer» An angle is 24 less than its compliment, then the measure of angle is

Discussion

8150.

If x - 2 is a factor of each of the following two polynomials, find the values of a in each case : (i) x3−2ax2 + ax - 1 (ii) x5−3x4−ax3+3ax2 + 2ax + 4

Answer»

If x - 2 is a factor of each of the following two polynomials, find the values of a in each case :

(i) $x^{3} - 2 a x^{2}$ + ax - 1

(ii) $x^{5} - 3 x^{4} - a x^{3} + 3 a x^{2}$ + 2ax + 4

Discussion

Explore topic-wise InterviewSolutions in .

Angle between the pair of lines represented by the equation 2x^2+8y^2-8xy+5x-10y+3=0 is

If x=3+8 then x2+1x2=?(a) 34(b) 56(c) 28(d) 63

ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the mid-point of BC.

Write the polynomials in index form. (i) (1, 2, 3) (ii) (5, 0, 0, 0, -1) (iii) (-2, 2,-​2, 2)

Durations of sunshine (in hours) in Amritsar to first 10 days of August 1997 as reported by the Meteorological Department are given below:9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9(i) Find the mean X.(ii) Verify that ∑i=110 (xi-X¯) = 0

AB=CB,AB=CD and EF bisects BD at G. Prove that G is midpoint of EF

Question 4The cost of 4 pens and 4 pencils boxes is Rs.100. there times the cost of a pen is Rs. 15 more than the cost of a pencil box,. Form the pair of linear equations for the above situation. Find the cost pen and a pencil box be Rs. y.

The perpendicular distance of the point A(3, 4) from the y-axis is(a) 3(b) 4(c) 5(d) 7

Parallelogram ABCD and rectangle ABEF are on the same base AB. If AB=14 cm, BC=12 cm, then the possible value for the perimeter of ABEF is

AETB is a straight line such that AE=TB.If ET=30cm,LE=LT=25cm and perimeter of △ LAB is 20 cm more than perimeter of △ LET, then length of AE is

equation of circle which touches the coordinate axes and passes through the point (2,1) is

212+213+214110×25×1256 is equal to:___.(in decimal form)

Question 2Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.

46. Prove that the parallelogram circumscribing a circle is rhombus

A 60∘ angle is constructed with arc radius as 3 cm. Find the perimeter of the △ BOC in cm. 9

if (x-3) and (x+3) are the factors of 4x^2+ax^2+bx, find the value of a and b.

Find the edge of a cube whose surface area is 432 m2.

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.

A line passes through the point (-4, 6) and is parallel to x-axis. Find its equation.

Factorise the following expression:(l+m)2−4lm

if P=\sqrt{16+8\sqrt3} - \sqrt{21-12\sqrt3} , then find the value of P ?

If A = {1, 2, 3, 4}, B{3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find : (i) A∪B (ii) A∪C (iii) B∪C (iv) B∪D (v) A∪B∪C (vi) A∪B∪D (vii) B∪C∪D

Find seven rational numbers between 16 and 521.

In a year, Ravi earns ₹3,60,000 and paid ₹24,000 as income tax.Find the ratio of hisa) income to income tax.b) income tax to income after paying income tax.

In the given figure, side BC of ΔABC is produced to point D such that bisectors of ∠ABC and ∠ACD meet at a point E. If ∠BAC = 68°, find ∠BEC.

A line whose equation is of the type x = a is a line parallel to the y axis, so the line is a vertical line. The line ax + by = ab makes intercepts on the x and y axes

Find the area bounded by the curve y²=2y-x and y-axis. NOTE: How to draw the graph of y²=2y-x?

If the minimum distance from its opposite side of an equilateral triangle is 4√3 cm, then determine the side length of the triangle.

The cost of 5 kg of sugar and 7 kg of rice is ₹153 and the cost of 7 kg of sugar and 5 kg of rice is ₹ 147 find the cost of 6 kg of sugar and 10 kg of rice

If 0∘&lt;θ&lt;90∘, then √sec2θ+cosec2θ =

Match the following parallelograms with their respective areas.

The given table shows the rainfall in mm in different cities in India for a year.CitiesRainfall (mm)Delhi44.6Mumbai63.5Kolkata60.7Pune56.2Bangalore60.1Bhubaneswar49.4Chennai61.7Ooty56.9Ahmedabad34.4Jaipur32.5Find the mean rainfall in the year.

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the cofficients. (1).4x2+8x?

Question 9One equation of a pair of dependent linear equations is - 5x + 7y – 2 = 0(A) 10x + 14y + 4 = 0(B) –10x – 14y + 4 = 0(C) –10x + 14y + 4 = 0(D) 10x – 14y = –4

Find the area of the given polygon:

Write the coefficient of x2 in each of the following:(i) 17 − 2x + 7x2(ii) 9 − 12x + x3(iii) π6x2-3x+4(iv) 3x-7

There is a thin coin of radius 2K mm and thickness 1 mm. Now I place M coins one on top of the other. What is the object formed and what is its volume?

Find the median of the following data: 13, 15, 18, 14, 22, 42, 9, 6, 15, 21.

Freddy walks in a straight line from his house having coordinates (1, 3) to the playground having coordinates (4, 5). Find the distance covered by Freddy.

In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that ∠ADC=95∘ and ∠ECF=20∘ Then, ∠BAD=?. (a) 95∘ (b) 85∘ (c) 105∘ (d) 75∘

Question 39 The sum of angles of a concave quadrilateral is a) More than 360∘ b) Less than 360∘ c) Equal to 360∘ d) Twice of 360∘

If a solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each, then n = _________.

If (2a–4,3a–9) lie on Y axis then find the value of a.

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

The curved surface of a cylindrical bulb of height 18 cm and base radius 7 cm is to be painted in luminating gold colour such that 23rd of the height of the bulb emits golden light; painting is done at ₹ 5 per sq. cm. The cost of painting the bulb is_____.(use π=227)

The factors of x3 − 1 + y3 + 3xy are(a) (x − 1 + y) (x2 + 1 + y2 + x + y − xy)(b) (x + y + 1) (x2 + y2 + 1 −xy − x − y)(c) (x − 1 + y) (x2 − 1 − y2 + x + y + xy)(d) 3(x + y −1) (x2 + y2 − 1)

An angle is 24 less than its compliment, then the measure of angle is

If x - 2 is a factor of each of the following two polynomials, find the values of a in each case : (i) x3−2ax2 + ax - 1 (ii) x5−3x4−ax3+3ax2 + 2ax + 4

Write the polynomials in index form. (i) (1, 2, 3) (ii) (5, 0, 0, 0, -1) (iii) (-2, 2,-2, 2)

If 0∘<θ<90∘, then √sec2θ+cosec2θ =