32581 + Interview Questions in Mathematics Page 130 InterviewSolution

6451.	Two parallel tangents of a circle meet a third tangent at points P and Q. What angle does PQ subtend at the centre?
Answer» Two parallel tangents of a circle meet a third tangent at points P and Q. What angle does PQ subtend at the centre?

Discussion

6452.	(a) Find x if the following numbers are in A.P(1) 4, x, 12(2) 2, (x − 1), 4(3) 6 − a, x, 6 + a(b) Find x if the following numbers are in G.P(1) 16, x, 25(2) 5, x + 1, 20(c) If A, G, H are A.M, G.M, and H.M of the following pair of numbers(a) 1 and 4(b) 2 and 8(c) 9 and 16Verify that (i) A, G, H are in G.P, (ii) A > G > H.
Answer» (a) Find x if the following numbers are in A.P (1) 4, x, 12 (2) 2, (x − 1), 4 (3) 6 − a, x, 6 + a (b) Find x if the following numbers are in G.P (1) 16, x, 25 (2) 5, x + 1, 20 (c) If A, G, H are A.M, G.M, and H.M of the following pair of numbers (a) 1 and 4 (b) 2 and 8 (c) 9 and 16 Verify that (i) A, G, H are in G.P, (ii) A > G > H.

6452.

(a) Find x if the following numbers are in A.P(1) 4, x, 12(2) 2, (x − 1), 4(3) 6 − a, x, 6 + a(b) Find x if the following numbers are in G.P(1) 16, x, 25(2) 5, x + 1, 20(c) If A, G, H are A.M, G.M, and H.M of the following pair of numbers(a) 1 and 4(b) 2 and 8(c) 9 and 16Verify that (i) A, G, H are in G.P, (ii) A > G > H.

Answer»

(a) Find x if the following numbers are in A.P

(1) 4, x, 12

(2) 2, (x − 1), 4

(3) 6 − a, x, 6 + a

(b) Find x if the following numbers are in G.P

(1) 16, x, 25

(2) 5, x + 1, 20

(c) If A, G, H are A.M, G.M, and H.M of the following pair of numbers

(a) 1 and 4

(b) 2 and 8

(c) 9 and 16

Verify that (i) A, G, H are in G.P, (ii) A > G > H.

Discussion

6453.	Question 1 (ii)For which value(s) of λ does the pair of linear equations λx+y=λ2 and x+λy=1 have infinitely many solutions?
Answer» Question 1 (ii) For which value(s) of $λ$ does the pair of linear equations $λ x + y = λ^{2} a n d x + λ y = 1$ have infinitely many solutions?

Discussion

6454.	sin 15° sec 75° + cos 42° cosec 48° = ___.
Answer» sin 15° sec 75° + cos 42° cosec 48° = ___.

Discussion

6455.	The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?
Answer» The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

Discussion

6456.	It is given that ΔABC ~ ΔDEF, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then DE = ______ and ∠F = ______.
Answer» It is given that ΔABC ~ ΔDEF, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then DE = ______ and ∠F = ______.

Discussion

6457.	In an equilateral triangle ABC , if AD is perpendicular to BC , then ___.
Answer» In an equilateral triangle ABC , if AD is perpendicular to BC , then ___.

Discussion

6458.	ab and cd are 2 parallel chords of a circle which are on either sides of the centre such that ab=10 cm and cd =24 cm. find the radius if the dis†an ce between ab and cd is 17 cm with reaso
Answer» ab and cd are 2 parallel chords of a circle which are on either sides of the centre such that ab=10 cm and cd =24 cm. find the radius if the dis†an ce between ab and cd is 17 cm with reaso

Discussion

6459.	97. A circle rolls between pair of lines 9x2+ 24xy + 16y2 -25 0 touching both of them. Then its area is(a) 4 sq. units(c) 12 sq. units(b) 8 sq. units(d) sq. units
Answer» 97. A circle rolls between pair of lines 9x2+ 24xy + 16y2 -25 0 touching both of them. Then its area is(a) 4 sq. units(c) 12 sq. units(b) 8 sq. units(d) sq. units

Discussion

6460.	How to find quadratic polynomial when sum and product of zeroes are given
Answer» How to find quadratic polynomial when sum and product of zeroes are given

Discussion

6461.	How to derive the formula for the volume of the frustum of a cone by integration?
Answer» How to derive the formula for the volume of the frustum of a cone by integration?

Discussion

6462.	The height of a cone is 15 cm. If its volume is 1570 cm3 , find the diameter of its base.(Use π=3.14)
Answer» The height of a cone is 15 cm. If its volume is ${1570 cm}^{3}$ , find the diameter of its base. $(Use π = 3.14)$

Discussion

6463.	What is the ratio ACBC for the line segment AB following the construction method below? Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at A1,A2,...,A30 Step 2. A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17 and meet AB at C.
Answer» What is the ratio $\frac{A C}{B C}$ for the line segment AB following the construction method below? Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_{1}, A_{2}, . . ., A_{30}$ Step 2. A line is drawn from $A_{30}$ to $B$ and a line parallel to $A_{30} B$ is drawn, passing through the point $A_{17}$ and meet AB at C.

Discussion

6464.	if a particle is projected at an angle θ with horizontal then its angle of elevation of particle at maximum height from point of projection
Answer» if a particle is projected at an angle θ with horizontal then its angle of elevation of particle at maximum height from point of projection

Discussion

6465.	If pth, qth and rth terms of an A.P. are a, b, c respectively, then show that: a(q–r)+b(r–p)+c(p–q)=0
Answer» If $p^{t h}$ , $q^{t h}$ and $r^{t h}$ terms of an A.P. are a, b, c respectively, then show that: $a (q - r) + b (r - p) + c (p - q) = 0$

Discussion

6466.	The volume and the height of a cone are 2200 cm3 and 21 cm respectively. Find the diameter of the basic.
Answer» The volume and the height of a cone are 2200 cm³ and 21 cm respectively. Find the diameter of the basic.

6466.

The volume and the height of a cone are 2200 cm3 and 21 cm respectively. Find the diameter of the basic.

Answer»

The volume and the height of a cone are 2200 cm³ and 21 cm respectively. Find the diameter of the basic.

Discussion

6467.	17.A AND B HAVE SOME MARBLES N IF A GIVES SOME MARBLES TO B, THEN B WILL HAVE TWICE AS MANY MARBLES AS A. IF B GIVES SOME MARBLES TO A, THEN A WILL HAVE THRICE AS MANY MARBLES AS B. WHAT IS THE MINIMUM POSSIBLE VALUE OF N FOR WHICH THE ABOVE STATEMENTS ARE TRUE?
Answer» 17.A AND B HAVE SOME MARBLES N IF A GIVES SOME MARBLES TO B, THEN B WILL HAVE TWICE AS MANY MARBLES AS A. IF B GIVES SOME MARBLES TO A, THEN A WILL HAVE THRICE AS MANY MARBLES AS B. WHAT IS THE MINIMUM POSSIBLE VALUE OF N FOR WHICH THE ABOVE STATEMENTS ARE TRUE?

Discussion

6468.	Explain the term trigonometry.
Answer» Explain the term trigonometry.

Discussion

6469.	Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 from its centre. [CBSE 2013]
Answer» Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 from its centre. [CBSE 2013]

Discussion

6470.	How many numbers are there between 101 and 999, which are divisible by both 2 and 5? [CBSE 2014]
Answer» How many numbers are there between 101 and 999, which are divisible by both 2 and 5? [CBSE 2014]

Discussion

6471.	In the given figure, if the length of AB is 6 cm, the length of AD is
Answer» In the given figure, if the length of AB is 6 cm, the length of AD is

6471.

In the given figure, if the length of AB is 6 cm, the length of AD is

Answer»

In the given figure, if the length of AB is 6 cm, the length of AD is

Discussion

6472.	Question 3Factorise the following using appropriate identities:(i) 9x2+6xy+y2(ii) 4y2−4y+1(iii) x2−y2100
Answer» Question 3 Factorise the following using appropriate identities: (i) $9 x^{2} + 6 x y + y^{2}$ (ii) $4 y^{2} - 4 y + 1$ (iii) $x^{2} - \frac{y^{2}}{100}$

Discussion

6473.	If the coordinates of one end of a diameter of the circle x2 + y2 – 4x – 6y + 11 = 0 are (3, 4), then the coordinates of the other end are __________.
Answer» If the coordinates of one end of a diameter of the circle x² + y² – 4x – 6y + 11 = 0 are (3, 4), then the coordinates of the other end are __________.

Discussion

6474.	Point M is the midpoint of seg AB. If AB = 8 then find the length of AM.
Answer» Point M is the midpoint of seg AB. If AB = 8 then find the length of AM.

Discussion

6475.	find the smallest Number which leaves remainder 8 and 12 when divided by 28 and 32 respectively
Answer» find the smallest Number which leaves remainder 8 and 12 when divided by 28 and 32 respectively

Discussion

6476.	If the variance of 1, 2, 3, 4, 5, ...,10 is 334, then the standard deviation of 3, 6, 9, 12, ...33 is ______________.
Answer» If the variance of 1, 2, 3, 4, 5, ...,10 is $\frac{33}{4}$ , then the standard deviation of 3, 6, 9, 12, ...33 is ______________.

Discussion

6477.	If f(x) = ax2 + bx + c has no real zeros and a + b + c = 0, then(a) c = 0(b) c > 0(c) c < 0(d) None of these
Answer» If f(x) = ax² + bx + c has no real zeros and a + b + c = 0, then (a) c = 0 (b) c > 0 (c) c < 0 (d) None of these

Discussion

6478.	tan 5° ✕ tan 30° ✕ 4 tan 85° is equal to(a) 43(b) 43(c) 1(d) 4
Answer» tan 5° ✕ tan 30° ✕ 4 tan 85° is equal to (a) $\frac{4}{\sqrt{3}}$ (b) $4 \sqrt{3}$ (c) 1 (d) 4

Discussion

6479.	Solve :12x2 + 18x + 4218x2 + 12x + 58= 2x + 33x + 2
Answer» Solve : $\frac{12 x^{2} + 18 x + 42}{18 x^{2} + 12 x + 58} = \frac{2 x + 3}{3 x + 2}$

Discussion

6480.	In the given figure, M is the centre of the circle and seg KL is a tangent segment.If MK = 12, KL = 63 then find –(1) Radius of the circle.(2) Measures of ∠K and ∠M.
Answer» In the given figure, M is the centre of the circle and seg KL is a tangent segment. If MK = 12, KL = $6 \sqrt{3}$ then find – (1) Radius of the circle. (2) Measures of ∠K and ∠M.

Discussion

6481.	A circle of radius 3 is drawn with centre at (−2, 1). Find out whether the point (4, 1) lies on the circle, within the circle or outside the circle.
Answer» A circle of radius 3 is drawn with centre at (−2, 1). Find out whether the point (4, 1) lies on the circle, within the circle or outside the circle.

Discussion

6482.	Is it possible to design a rectangular park of perimeter 80m and area 400m2? If so, find its length and breadth.
Answer» Is it possible to design a rectangular park of perimeter 80m and area $400 m^{2}$ ? If so, find its length and breadth.

Discussion

6483.	The sum of the digits of a number lying between 10 and 100 is 9. If the number is multiplied by 7,it becomes four times the number obtained by the digits in reverse order. Find the number.
Answer» The sum of the digits of a number lying between 10 and 100 is 9. If the number is multiplied by 7,it becomes four times the number obtained by the digits in reverse order. Find the number.

Discussion

6484.	If the difference between the 7th term and 2nd term of an A.P. is 45 and 8th term of the A.P is 67, find the sum of first 19 terms.
Answer» If the difference between the $7^{t h}$ term and $2^{n d}$ term of an A.P. is 45 and $8^{t h}$ term of the A.P is 67, find the sum of first 19 terms.

Discussion

6485.	A man invests ₹ 5500 on buying shares of face value of ₹ 100 each at a premium of ₹ 10 %. If he earns ₹ 1600 at the end of the year as dividend, find the number of shares he has in the company
Answer» A man invests ₹ 5500 on buying shares of face value of ₹ 100 each at a premium of ₹ 10 %. If he earns ₹ 1600 at the end of the year as dividend, find the number of shares he has in the company

6485.

A man invests ₹ 5500 on buying shares of face value of ₹ 100 each at a premium of ₹ 10 %. If he earns ₹ 1600 at the end of the year as dividend, find the number of shares he has in the company

Answer»

A man invests ₹ 5500 on buying shares of face value of ₹ 100 each at a premium of ₹ 10 %. If he earns ₹ 1600 at the end of the year as dividend, find the number of shares he has in the company

Discussion

6486.	write the set of values of x satisfying the inequations 5x+2<3x+8 and x+2x−1<4.
Answer» write the set of values of x satisfying the inequations 5x+2<3x+8 and $\frac{x + 2}{x - 1} < 4$ .

Discussion

6487.	A solid metallic right circular cone 20 cm high and whose vertical angle is 60∘, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 112cm, find the length of the wire.
Answer» A solid metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$ , is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{12}$ cm, find the length of the wire.

Discussion

6488.	If the coordinates of the mid points of the sides of a triangle are (1,1), (2,-3) and (3,4), find the vertices of the triangle.
Answer» If the coordinates of the mid points of the sides of a triangle are (1,1), (2,-3) and (3,4), find the vertices of the triangle.

Discussion

6489.	In a line segment AB, P(2,1) and Q(6,2) are the points of trisection. Find the coordinates of A and B (P is closer to A and Q is closer to B).
Answer» In a line segment AB, P(2,1) and Q(6,2) are the points of trisection. Find the coordinates of A and B (P is closer to A and Q is closer to B).

Discussion

6490.	53 The number lies between 100000and110000 which is exactly divisible by 8,15 21 is
Answer» 53 The number lies between 100000and110000 which is exactly divisible by 8,15 21 is

Discussion

6491.	Match the following: ColumnAColumnB1.{1,2,4,8}A.{x:x is a natural even number less than 10}2.{2}B.{x:x is a prime number and a divisor of 8}3.{2,4,6,8}C.{x:x is a divisor of 8}4.{4,6,8,9}D.{x:x is a composite number less than 10}
Answer» Match the following: $\begin{matrix} C o l u m n A & C o l u m n B 1. {1, 2, 4, 8} & A . {x : x i s a n a t u r a l e v e n n u m b e r l e s s t h a n 10} 2. {2} & B . {x : x i s a p r i m e n u m b e r a n d a d i v i s o r o f 8} 3. {2, 4, 6, 8} & C . {x : x i s a d i v i s o r o f 8} 4. {4, 6, 8, 9} & D . {x : x i s a c o m p o s i t e n u m b e r l e s s t h a n 10} \end{matrix}$

Discussion

6492.	Show that the sequence defined by an =5n-7 is an A.P ,find its common differnce
Answer» Show that the sequence defined by a_n=5n-7 is an A.P ,find its common differnce

Discussion

6493.	If x2 + 2 kx + 4 = 0 has a root x = 2, then the value of k is?
Answer» If x² + 2 kx + 4 = 0 has a root x = 2, then the value of k is?

Discussion

6494.

Prepare Bank Reconciliation Statement as on 31st March, 2019 from the following particulars: ₹ (i) Bank balance as per Pass Book. 10,000 (ii) Cheque deposited into the Bank, but no entry was passed in the Cash Book. 500 (iii) Cheque received and entered in the Cash Book but not sent to bank. 1,200 (iv) Credit side of the Cash Book bank column cast short. 200 (v) Insurance premium paid directly by the bank under the standing advice. 600 (vi) Bank charges entered twice in the Cash Book. 20 (vii) Cheque issued but not presented to the bank for payment. 500 (viii) Cheque received entered twice in the Cash Book. 1,000 (ix) Bill discounted dishonoured not recorded in the Cash Book. 5,000 (x) Bank had wrongly allowed interest of ₹ 5,000, which was reversed by it on 5th April, 2019.

Answer» Prepare Bank Reconciliation Statement as on 31st March, 2019 from the following particulars:

		₹
(i)	Bank balance as per Pass Book.	10,000
(ii)	Cheque deposited into the Bank, but no entry was passed in the Cash Book.	500
(iii)	Cheque received and entered in the Cash Book but not sent to bank.	1,200
(iv)	Credit side of the Cash Book bank column cast short.	200
(v)	Insurance premium paid directly by the bank under the standing advice.	600
(vi)	Bank charges entered twice in the Cash Book.	20
(vii)	Cheque issued but not presented to the bank for payment.	500
(viii)	Cheque received entered twice in the Cash Book.	1,000
(ix)	Bill discounted dishonoured not recorded in the Cash Book.	5,000
(x)	Bank had wrongly allowed interest of ₹ 5,000, which was reversed by it on 5th April, 2019.

Discussion

6495.	The probability of getting an even number, when a die is thrown once, is:
Answer» The probability of getting an even number, when a die is thrown once, is:

Discussion

6496.

Following are the balances extracted from the books of Manish on 31st March, 2019: ₹ ₹ Capital 1,90,000 Cash at Bank 26,000 Drawing 7,000 Salaries 8,000 Plant and Machinery 1,20,000 Repairs 1,900 Delivery Vehicle 26,000 Stock on 1st April, 2018 16,000 Sundry Debtors 36,000 Rent 4,500 Sundry Creditors 26,000 Manufacturing Expenses 1,500 Purchases 20,000 Bills Payable 23,500 Sales 42,000 Bad Debts 5,000 Wages 8,000 Carriage 1,600 Prepare Trading and Profit and Loss Account and Balance Sheet as at 31st March, 2019 after following adjustments are made:(i) Closing Stock was ₹ 16,000.(ii) Depreciate Plant and Machinery 10% and Delivery Vehicle 15%.(iii) Unpaid Rent amounted to ₹ 500.

Answer» Following are the balances extracted from the books of Manish on 31st March, 2019:

	₹		₹
Capital	1,90,000	Cash at Bank	26,000
Drawing	7,000	Salaries	8,000
Plant and Machinery	1,20,000	Repairs	1,900
Delivery Vehicle	26,000	Stock on 1st April, 2018	16,000
Sundry Debtors	36,000	Rent	4,500
Sundry Creditors	26,000	Manufacturing Expenses	1,500
Purchases	20,000	Bills Payable	23,500
Sales	42,000	Bad Debts	5,000
Wages	8,000	Carriage	1,600

Prepare Trading and Profit and Loss Account and Balance Sheet as at 31st March, 2019 after following adjustments are made:

(i) Closing Stock was ₹ 16,000.

(ii) Depreciate Plant and Machinery 10% and Delivery Vehicle 15%.

(iii) Unpaid Rent amounted to ₹ 500.

Discussion

6497.	ABDE is a trapezium. with AE∥BD and ED⊥BD, and AC is drawn parallel to the side DE. Find the values of cot θ and cosec θ respectively, from the figure above.
Answer» ABDE is a trapezium. with $A E ∥ B D$ and $E D ⊥ B D$ , and AC is drawn parallel to the side DE. Find the values of $cot θ a n d cosec θ$ respectively, from the figure above.

Discussion

6498.	Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
Answer» Use factor theorem to determine whether x + 3 is factor of x² + 2x − 3 or not.

Discussion

6499.	28. In a trapezium ABCD, AB \|\| DC and DC = 2AB. EF \|\| AB, where E and F lie on BC and AD respectively such that BE/EC = 4/3. Diagonal DB intersects EF at G. Prove that, 7EF = 11AB.
Answer» 28. In a trapezium ABCD, AB \|\| DC and DC = 2AB. EF \|\| AB, where E and F lie on BC and AD respectively such that BE/EC = 4/3. Diagonal DB intersects EF at G. Prove that, 7EF = 11AB.

Discussion

6500.	x+y=7 x+y=11
Answer» x+y=7 x+y=11

Discussion

Explore topic-wise InterviewSolutions in .

Two parallel tangents of a circle meet a third tangent at points P and Q. What angle does PQ subtend at the centre?

Question 1 (ii)For which value(s) of λ does the pair of linear equations λx+y=λ2 and x+λy=1 have infinitely many solutions?

sin 15° sec 75° + cos 42° cosec 48° = ___.

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

It is given that ΔABC ~ ΔDEF, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then DE = ______ and ∠F = ______.

In an equilateral triangle ABC , if AD is perpendicular to BC , then ___.

ab and cd are 2 parallel chords of a circle which are on either sides of the centre such that ab=10 cm and cd =24 cm. find the radius if the dis†an ce between ab and cd is 17 cm with reaso

97. A circle rolls between pair of lines 9x2+ 24xy + 16y2 -25 0 touching both of them. Then its area is(a) 4 sq. units(c) 12 sq. units(b) 8 sq. units(d) sq. units

How to find quadratic polynomial when sum and product of zeroes are given

How to derive the formula for the volume of the frustum of a cone by integration?

The height of a cone is 15 cm. If its volume is 1570 cm3 , find the diameter of its base.(Use π=3.14)

if a particle is projected at an angle θ with horizontal then its angle of elevation of particle at maximum height from point of projection

If pth, qth and rth terms of an A.P. are a, b, c respectively, then show that: a(q–r)+b(r–p)+c(p–q)=0

The volume and the height of a cone are 2200 cm3 and 21 cm respectively. Find the diameter of the basic.

17.A AND B HAVE SOME MARBLES N IF A GIVES SOME MARBLES TO B, THEN B WILL HAVE TWICE AS MANY MARBLES AS A. IF B GIVES SOME MARBLES TO A, THEN A WILL HAVE THRICE AS MANY MARBLES AS B. WHAT IS THE MINIMUM POSSIBLE VALUE OF N FOR WHICH THE ABOVE STATEMENTS ARE TRUE?

Explain the term trigonometry.

Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 from its centre. [CBSE 2013]

How many numbers are there between 101 and 999, which are divisible by both 2 and 5? [CBSE 2014]

In the given figure, if the length of AB is 6 cm, the length of AD is

Question 3Factorise the following using appropriate identities:(i) 9x2+6xy+y2(ii) 4y2−4y+1(iii) x2−y2100

If the coordinates of one end of a diameter of the circle x2 + y2 – 4x – 6y + 11 = 0 are (3, 4), then the coordinates of the other end are __________.

Point M is the midpoint of seg AB. If AB = 8 then find the length of AM.

find the smallest Number which leaves remainder 8 and 12 when divided by 28 and 32 respectively

If the variance of 1, 2, 3, 4, 5, ...,10 is 334, then the standard deviation of 3, 6, 9, 12, ...33 is ______________.

If f(x) = ax2 + bx + c has no real zeros and a + b + c = 0, then(a) c = 0(b) c > 0(c) c < 0(d) None of these

tan 5° ✕ tan 30° ✕ 4 tan 85° is equal to(a) 43(b) 43(c) 1(d) 4

Solve :12x2 + 18x + 4218x2 + 12x + 58= 2x + 33x + 2

In the given figure, M is the centre of the circle and seg KL is a tangent segment.If MK = 12, KL = 63 then find –(1) Radius of the circle.(2) Measures of ∠K and ∠M.

A circle of radius 3 is drawn with centre at (−2, 1). Find out whether the point (4, 1) lies on the circle, within the circle or outside the circle.

Is it possible to design a rectangular park of perimeter 80m and area 400m2? If so, find its length and breadth.

The sum of the digits of a number lying between 10 and 100 is 9. If the number is multiplied by 7,it becomes four times the number obtained by the digits in reverse order. Find the number.

If the difference between the 7th term and 2nd term of an A.P. is 45 and 8th term of the A.P is 67, find the sum of first 19 terms.

A man invests ₹ 5500 on buying shares of face value of ₹ 100 each at a premium of ₹ 10 %. If he earns ₹ 1600 at the end of the year as dividend, find the number of shares he has in the company

write the set of values of x satisfying the inequations 5x+2&lt;3x+8 and x+2x−1&lt;4.

A solid metallic right circular cone 20 cm high and whose vertical angle is 60∘, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 112cm, find the length of the wire.

If the coordinates of the mid points of the sides of a triangle are (1,1), (2,-3) and (3,4), find the vertices of the triangle.

In a line segment AB, P(2,1) and Q(6,2) are the points of trisection. Find the coordinates of A and B (P is closer to A and Q is closer to B).

53 The number lies between 100000and110000 which is exactly divisible by 8,15 21 is

Match the following: ColumnAColumnB1.{1,2,4,8}A.{x:x is a natural even number less than 10}2.{2}B.{x:x is a prime number and a divisor of 8}3.{2,4,6,8}C.{x:x is a divisor of 8}4.{4,6,8,9}D.{x:x is a composite number less than 10}

Show that the sequence defined by an =5n-7 is an A.P ,find its common differnce

If x2 + 2 kx + 4 = 0 has a root x = 2, then the value of k is?

The probability of getting an even number, when a die is thrown once, is:

ABDE is a trapezium.​​​​​​ with AE∥BD and ED⊥BD, and AC is drawn parallel to the side DE. Find the values of cot θ and cosec θ respectively, from the figure above.

Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.

28. In a trapezium ABCD, AB || DC and DC = 2AB. EF || AB, where E and F lie on BC and AD respectively such that BE/EC = 4/3. Diagonal DB intersects EF at G. Prove that, 7EF = 11AB.

x+y=7 x+y=11

It is given that ΔABC ~ ΔDEF, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then DE = and ∠F = .

write the set of values of x satisfying the inequations 5x+2<3x+8 and x+2x−1<4.

ABDE is a trapezium. with AE∥BD and ED⊥BD, and AC is drawn parallel to the side DE. Find the values of cot θ and cosec θ respectively, from the figure above.