32581 + Interview Questions in Mathematics Page 171 InterviewSolution

8501.	If α0,α1,α2…,αn−1 be the n, nth roots of the unity, then the value of ∑n−1i=0αi(3−αi) is equal to
Answer» If $α_{0}, α_{1}, α_{2} \dots, α_{n - 1}$ be the n, nth roots of the unity, then the value of $\sum_{i = 0}^{n - 1} \frac{α_{i}}{(3 - α_{i})}$ is equal to

Discussion

8502.	The median of 19 observations is 30.Two more observations are made and the values of these are 8 and 32.Find the median of the 21 observations taken together.
Answer» The median of 19 observations is 30.Two more observations are made and the values of these are 8 and 32.Find the median of the 21 observations taken together.

Discussion

8503.	Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.
Answer» Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.

Discussion

8504.	If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is
Answer» If $x + 1$ is a factor of the polynomial $2 x^{2} + k x$ , then the value of $k$ is

Discussion

8505.	Select the correct alternative for each of the following questions.(1) The number of tangents that can be drawn to a circle at a point on the circle is ............... .(A) 3 (B) 2 (C) 1 (D) 0(2) The maximum number of tangents that can be drawn to a circle from a point out side it is .............. .(A) 2 (B) 1 (C) one and only one (D) 0(3) If ∆ABC ~ ∆PQR and ABPQ=75, then ...............(A) ∆ABC is bigger.(B) ∆PQR is bigger.(C) Both triangles will be equal.(D) Can not be decided.
Answer» Select the correct alternative for each of the following questions. (1) The number of tangents that can be drawn to a circle at a point on the circle is ............... . (A) 3 (B) 2 (C) 1 (D) 0 (2) The maximum number of tangents that can be drawn to a circle from a point out side it is .............. . (A) 2 (B) 1 (C) one and only one (D) 0 (3) If ∆ABC ~ ∆PQR and $\frac{AB}{PQ} = \frac{7}{5}$ , then ............... (A) ∆ABC is bigger. (B) ∆PQR is bigger. (C) Both triangles will be equal. (D) Can not be decided.

Discussion

8506.	Which of the following is not a measure of central tendency?
Answer» Which of the following is not a measure of central tendency?

Discussion

8507.	If 1x+2y=4 and 3y-1x=11 then(a) x = 2, y = 3 (b) x = − 2, y = 3 (c) x=-12,y=3 (d) x=-12,y=13
Answer» If $\frac{1}{x} + \frac{2}{y} = 4 and \frac{3}{y} - \frac{1}{x} = 11$ then (a) x = 2, y = 3 (b) x = − 2, y = 3 (c) $x = - \frac{1}{2}, y = 3$ (d) $x = - \frac{1}{2}, y = \frac{1}{3}$

Discussion

8508.	Question 34 Kanika was given her pocket money on Jan 1st, 2008. She puts Rs.1 on day 1, Rs.2 on day 2, Rs.3 on day 3 and continued doing so till the end of the month, from this money into her piggy bank she also spent Rs.204 of her pocket money and found that at the end of the month she still had Rs.100 with her. How much was her pocket money for the month?
Answer» Question 34 Kanika was given her pocket money on Jan $1^{s t}$ , 2008. She puts Rs.1 on day 1, Rs.2 on day 2, Rs.3 on day 3 and continued doing so till the end of the month, from this money into her piggy bank she also spent Rs.204 of her pocket money and found that at the end of the month she still had Rs.100 with her. How much was her pocket money for the month?

Discussion

8509.	A 1.8 m tall man is standing at some distance from a building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks 20 m towards the building. Find the height of the building (in m). [Take √3=1.7]18.8
Answer» A 1.8 m tall man is standing at some distance from a building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ}$ to $60^{\circ}$ as he walks 20 m towards the building. Find the height of the building (in m). [Take $\sqrt{3} = 1.7$ ] 18.8

Discussion

8510.	what is cot 150sin 210cosec 330tan 315cos 120sec 240
Answer» what is cot 150 sin 210 cosec 330 tan 315 cos 120 sec 240

Discussion

8511.	The sum of first 7 terms of an AP is 49 and the sum of its first 17 terms is 289. Find the sum of its first n terms.
Answer» The sum of first 7 terms of an AP is 49 and the sum of its first 17 terms is 289. Find the sum of its first n terms.

Discussion

8512.	The mean of 15 numbers is 25. If each number is multiplied by 4, mean of the new numbers is
Answer» The mean of 15 numbers is 25. If each number is multiplied by 4, mean of the new numbers is

Discussion

8513.	In a triangle ABC right angled at B,∠ACB=θ.If tan θ=34,then find sin θ.
Answer» In a triangle ABC right angled at B, $∠ A C B = θ .$ $If t a n θ = \frac{3}{4}, then find s i n θ$ .

Discussion

8514.	Rahul plays a game in which two dice are thrown together. Rahul wins if the product of the two numbers appearing on their tops is even and a multiple of 3. The probability of Rahul lossing the game is
Answer» Rahul plays a game in which two dice are thrown together. Rahul wins if the product of the two numbers appearing on their tops is even and a multiple of 3. The probability of Rahul lossing the game is

Discussion

8515.	Apply the division algorithm to find the quotient and remainder on dividing f(x) by g(x) as given below: f(x)=x4−5x+6, g(x)=2−x2 [4 MARKS]
Answer» Apply the division algorithm to find the quotient and remainder on dividing $f (x)$ by $g (x)$ as given below: $f (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}$ [4 MARKS]

Discussion

8516.	A line passing through point (12,94), has y-intercept of 3. Find the x-intercept of the line.
Answer» A line passing through point ( $\frac{1}{2}, \frac{9}{4}$ ), has y-intercept of 3. Find the x-intercept of the line.

Discussion

8517.	Solve for x where x€R \|x^2-x-6\| = x+2.
Answer» Solve for x where x€R \|x^2-x-6\| = x+2.

Discussion

8518.	(x-2√6)(5√3+5√6)/5√3-5√2=1 find the value of x
Answer» (x-2√6)(5√3+5√6)/5√3-5√2=1 find the value of x

Discussion

8519.	Find the common difference (d) in the following APs respectively. (i) 20, 40, 60, 80, 100,..(ii) 5, 0, -5, -10, -15, ...(iii) 2, 2, 2, 2, 2..
Answer» Find the common difference (d) in the following APs respectively. (i) 20, 40, 60, 80, 100,.. (ii) 5, 0, -5, -10, -15, ... (iii) 2, 2, 2, 2, 2..

8519.

Find the common difference (d) in the following APs respectively. (i) 20, 40, 60, 80, 100,..(ii) 5, 0, -5, -10, -15, ...(iii) 2, 2, 2, 2, 2..

Answer»

Find the common difference (d) in the following APs respectively.

(i) 20, 40, 60, 80, 100,..

(ii) 5, 0, -5, -10, -15, ...

(iii) 2, 2, 2, 2, 2..

Discussion

8520.	Calculation the Standard Deviation from the following set of 10 observations.8, 9, 15, 23, 5, 11, 19, 8, 10 and 12
Answer» Calculation the Standard Deviation from the following set of 10 observations. 8, 9, 15, 23, 5, 11, 19, 8, 10 and 12

8520.

Calculation the Standard Deviation from the following set of 10 observations.8, 9, 15, 23, 5, 11, 19, 8, 10 and 12

Answer»

Calculation the Standard Deviation from the following set of 10 observations.

8, 9, 15, 23, 5, 11, 19, 8, 10 and 12

Discussion

8521.	The area and circumference of a circle are numerically equal. What is the diameter of the circle?
Answer» The area and circumference of a circle are numerically equal. What is the diameter of the circle?

Discussion

8522.	{ Find the co-ordinates of point }P which divides the join of }A(4,-5) and }B}{(6,3) in the ratio }2:5 .
Answer» { Find the co-ordinates of point }P which divides the join of }A(4,-5) and }B}{(6,3) in the ratio }2:5 .

Discussion

8523.	In a mixture of 60 litres, the ratio of milk and water is 2:1. If this ratio is to be 1:2, then the quantity of water to be further added is __________ ___
Answer» In a mixture of 60 litres, the ratio of milk and water is 2:1. If this ratio is to be 1:2, then the quantity of water to be further added is __________ ___

Discussion

8524.	A taxi charges in a city comprise of a fixed charge together with charge for distance covered. For a journey of 10km the charge paid was 75Rs and for 15km the charge was 110Rs. Find the charge for 25km.
Answer» A taxi charges in a city comprise of a fixed charge together with charge for distance covered. For a journey of 10km the charge paid was 75Rs and for 15km the charge was 110Rs. Find the charge for 25km.

Discussion

8525.	The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28 cm. The length of the pipe is 35cm.Find the mass of the pipe, if 1cm3 of wood has a mass of 0.6g.
Answer» The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28 cm. The length of the pipe is 35cm.Find the mass of the pipe, if 1cm³ of wood has a mass of 0.6g.

Discussion

8526.	If x sin (90° − θ) cot (90° − θ) = cos (90° − θ), then x =(a) 0(b) 1(c) −1(d) 2
Answer» If x sin (90° − θ) cot (90° − θ) = cos (90° − θ), then x = (a) 0 (b) 1 (c) −1 (d) 2

Discussion

8527.	11. A boy of height 1.7 is standing 30m away from the flag staff on the same level ground he observes that the angle of elevation of the top of the flagstaff 30 digress calculate the height of the flagstaff
Answer» 11. A boy of height 1.7 is standing 30m away from the flag staff on the same level ground he observes that the angle of elevation of the top of the flagstaff 30 digress calculate the height of the flagstaff

Discussion

8528.	Very-Short and Short-Answer QuestionsHow many three-digit natural numbers are divisible by 7? [CBSE 2013]
Answer» Very-Short and Short-Answer Questions How many three-digit natural numbers are divisible by 7? [CBSE 2013]

Discussion

8529.	On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gain rupees 7. if he sells the tea set at 5% gain and lemon set at 10% gain he gains rupees 13 find the actual price of the tea set and the lemon set
Answer» On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gain rupees 7. if he sells the tea set at 5% gain and lemon set at 10% gain he gains rupees 13 find the actual price of the tea set and the lemon set

Discussion

8530.

Following balances were extracted from the books of Modern Traders on 31st March, 2018: ₹ ₹ Capital 8,50,000 Sundry Creditors 90,000 Drawings 50,000 Sales 12,00,000 Plant and Machinery 4,00,000 Postage and Telegrams 8,000 Accumulated Depreciation 90,000 Bad Debts 4,000 Stock on 1st April, 2017 1,50,000 Provision for Doubtful Debts 8,000 Purchases 8,20,000 Discounts recevied 4,000 Sundry Debtors 2,06,000 Rent Revenue 12,000 Furniture 50,000 Insurance 7,000 Freight Inwards 20,000 Salaries 2,00,000 Carriage Outwards 5,000 Wages 13,000 Rent, Rates and Taxes 46,000 Cash in Hand 62,000 Printing and Stationery 8,000 Cash at Bank 2,55,000 General Reserve 50,000 Prepare Final Accounts for the year ended 31st March, 2018 after taking into account the following:(a) Stock on 31st March, 2018 was valued at ₹ 1,50,000.(b) Outstanding Wages ₹ 5,000.(c) Provision for Doubtful Debts is to be maintaind at 5% of the Sundry Debtors.(d) Prepaid Insurance was ₹ 1,000.(e) An advance paid by the proprietor from his personal bank account of ₹ 50,000 for purchase of a machine on 1st April, 2017 was not recorded in the books. Plant and Machinery was not debited in the books by the amount paid from firm.(f) Provide Depreciation on Plant and Machinery 10% on cost and on Furniture 5%.

Answer» Following balances were extracted from the books of Modern Traders on 31^st March, 2018:

	₹		₹
Capital	8,50,000	Sundry Creditors	90,000
Drawings	50,000	Sales	12,00,000
Plant and Machinery	4,00,000	Postage and Telegrams	8,000
Accumulated Depreciation	90,000	Bad Debts	4,000
Stock on 1st April, 2017	1,50,000	Provision for Doubtful Debts	8,000
Purchases	8,20,000	Discounts recevied	4,000
Sundry Debtors	2,06,000	Rent Revenue	12,000
Furniture	50,000	Insurance	7,000
Freight Inwards	20,000	Salaries	2,00,000
Carriage Outwards	5,000	Wages	13,000
Rent, Rates and Taxes	46,000	Cash in Hand	62,000
Printing and Stationery	8,000	Cash at Bank	2,55,000
		General Reserve	50,000

Prepare Final Accounts for the year ended 31st March, 2018 after taking into account the following:

(a) Stock on 31st March, 2018 was valued at ₹ 1,50,000.

(b) Outstanding Wages ₹ 5,000.

(c) Provision for Doubtful Debts is to be maintaind at 5% of the Sundry Debtors.

(d) Prepaid Insurance was ₹ 1,000.

(e) An advance paid by the proprietor from his personal bank account of ₹ 50,000 for purchase of a machine on 1st April, 2017 was not recorded in the books. Plant and Machinery was not debited in the books by the amount paid from firm.

(f) Provide Depreciation on Plant and Machinery 10% on cost and on Furniture 5%.

Discussion

8531.	A box contains 3 black balls, 4 red balls and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black or green ball?
Answer» A box contains 3 black balls, 4 red balls and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black or green ball?

Discussion

8532.	In the given figure, a line intersects a circle at points A and B. The line is rotated about the point P in both the directions until the points A and B coincide. How many times will they coincide?
Answer» In the given figure, a line intersects a circle at points A and B. The line is rotated about the point P in both the directions until the points A and B coincide. How many times will they coincide?

Discussion

8533.	If θ is acute angle, and tan θ =1√7, then cosec2θ−sec2θcosec2θ+sec2θ=
Answer» If $θ$ is acute angle, and $t a n θ$ = $\frac{1}{\sqrt{7}}$ , then $\frac{c o s e c^{2} θ - s e c^{2} θ}{c o s e c^{2} θ + s e c^{2} θ} =$

Discussion

8534.	If A, B and C are the interior angles of a right-angle triangle, right-angled at B then find the value of A, given that tan2A=cot(A–30∘) and 2A is an acute angle.
Answer» If A, B and C are the interior angles of a right-angle triangle, right-angled at B then find the value of A, given that $tan 2 A = cot (A - 30^{\circ})$ and 2A is an acute angle.

Discussion

8535.	†anα+2†an2α+4†an4α+8†an8α+kcotkα=cotα then k^2-15k+16 is equal t
Answer» †anα+2†an2α+4†an4α+8†an8α+kcotkα=cotα then k^2-15k+16 is equal t

Discussion

8536.	Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm.
Answer» Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm.

Discussion

8537.	Question 4 (ii)State whether the following are true or false. Justify your answer.(ii) The value of sin θ increases as θ increases.
Answer» Question 4 (ii) State whether the following are true or false. Justify your answer. (ii) The value of sin $θ$ increases as $θ$ increases.

Discussion

8538.	From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. Points O and P are joined. The ratio of angles OPR and OPQ is:
Answer» From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. Points O and P are joined. The ratio of angles OPR and OPQ is:

Discussion

8539.	If the points A(1, -2) , B (2,3) , C (a,2) and D (-4,-3) form a parallelogram , find the value of a and height of the parallelogram taking AB as base .
Answer» If the points $A (1, - 2), B (2, 3), C (a, 2) and D (- 4, - 3)$ form a parallelogram , find the value of a and height of the parallelogram taking AB as base .

Discussion

8540.	solve for x and y a(x+y)+b(x-y)=a2-ab+b2 a(x+y)-b(x-y)=a2+ab+b2
Answer» solve for x and y a(x+y)+b(x-y)=a²-ab+b² a(x+y)-b(x-y)=a²+ab+b²

8540.

solve for x and y a(x+y)+b(x-y)=a2-ab+b2 a(x+y)-b(x-y)=a2+ab+b2

Answer»

solve for x and y

a(x+y)+b(x-y)=a²-ab+b²

a(x+y)-b(x-y)=a²+ab+b²

Discussion

8541.	Identify the similar triangles.
Answer» Identify the similar triangles.

Discussion

8542.	Question 6Value(s) of k for which the quadratic equation 2x2 - kx + k = 0 has equal roots is/are(A) 0 only(B) 4(C) 8 only(D) 0, 8
Answer» Question 6 Value(s) of k for which the quadratic equation $2 x^{2}$ - kx + k = 0 has equal roots is/are (A) 0 only (B) 4 (C) 8 only (D) 0, 8

Discussion

8543.	find a rational number between 2/3 and 6/5
Answer» find a rational number between 2/3 and 6/5

Discussion

8544.	Seeds worth Rs 20500, labour Rs 9700 , chemicals and fertilizers Rs 5600, selling price Rs 28640.
Answer» Seeds worth Rs 20500, labour Rs 9700 , chemicals and fertilizers Rs 5600, selling price Rs 28640.

Discussion

8545.	In a single throw of dice,the probability of getting a number greater than 6 is___
Answer» In a single throw of dice,the probability of getting a number greater than 6 is___

Discussion

8546.	Which of the following functions from Z to Z are bijections?(a) f(x) = x3(b) f(x) = x + 2(c) f(x) = 2x + 1(d) f(x) = x2 + 1
Answer» Which of the following functions from Z to Z are bijections? (a) f(x) = x³ (b) f(x) = x + 2 (c) f(x) = 2x + 1 (d) f(x) = x² + 1

Discussion

8547.	The probability of getting a black, face card from a well-shuffled 52 pack card is___
Answer» The probability of getting a black, face card from a well-shuffled 52 pack card is___

Discussion

8548.	Solve the following quadratic equations by factorization:16x-10x=27
Answer» Solve the following quadratic equations by factorization: $16 x - \frac{10}{x} = 27$

Discussion

8549.	Find the indicated terms in each of the following sequences whose nth terms are:(a) an = 5n − 4; a12 and a15(b) an =3n-24n + 5; a7 and a8(c) an = n (n −1) (n − 2); a5 and a8(d) an = (n − 1) (2 − n) (3 + n); a1, a2, a3(e) an = (−1)n n ; a3, a5, a8
Answer» Find the indicated terms in each of the following sequences whose nth terms are: (a) a_n = 5n − 4; a₁₂and a₁₅ (b) $a_{n} = \frac{3 n - 2}{4 n + 5}; a_{7} a n d a_{8}$ (c) a_n = n (n −1) (n − 2); a₅ and a₈ (d) a_n = (n − 1) (2 − n) (3 + n); a₁, a₂, a₃ (e) a_n = (−1)ⁿ n ; a₃, a₅, a₈

Discussion

8550.	The marks obtained by 36 students in a test in statistics (out of 50) are as below.35115354523314021131520474842344345333711132718123739381613185414743Construct a frequency distribution table with equal class intervals, one of them being 10-20(20 is not included).
Answer» The marks obtained by 36 students in a test in statistics (out of 50) are as below. $\begin{matrix} 3 & 5 & 1 & 15 & 35 & 45 & 23 & 31 & 40 & 21 & 13 & 15 20 & 47 & 48 & 42 & 34 & 43 & 45 & 33 & 37 & 11 & 13 & 27 18 & 12 & 37 & 39 & 38 & 16 & 13 & 18 & 5 & 41 & 47 & 43 \end{matrix}$ Construct a frequency distribution table with equal class intervals, one of them being 10-20(20 is not included).

Discussion

Explore topic-wise InterviewSolutions in .

If α0,α1,α2…,αn−1 be the n, nth roots of the unity, then the value of ∑n−1i=0αi(3−αi) is equal to

The median of 19 observations is 30.Two more observations are made and the values of these are 8 and 32.Find the median of the 21 observations taken together.

Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.

If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is

Which of the following is not a measure of central tendency?

If 1x+2y=4 and 3y-1x=11 then(a) x = 2, y = 3 (b) x = − 2, y = 3 (c) x=-12,y=3 (d) x=-12,y=13

A 1.8 m tall man is standing at some distance from a building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks 20 m towards the building. Find the height of the building (in m). [Take √3=1.7]18.8

what is cot 150sin 210cosec 330tan 315cos 120sec 240

The sum of first 7 terms of an AP is 49 and the sum of its first 17 terms is 289. Find the sum of its first n terms.

The mean of 15 numbers is 25. If each number is multiplied by 4, mean of the new numbers is

In a triangle ABC right angled at B,∠ACB=θ.If tan θ=34,then find sin θ.

Rahul plays a game in which two dice are thrown together. Rahul wins if the product of the two numbers appearing on their tops is even and a multiple of 3. The probability of Rahul lossing the game is

Apply the division algorithm to find the quotient and remainder on dividing f(x) by g(x) as given below: f(x)=x4−5x+6, g(x)=2−x2 [4 MARKS]

A line passing through point (12,94), has y-intercept of 3. Find the x-intercept of the line.

Solve for x where x€R |x^2-x-6| = x+2.

(x-2√6)(5√3+5√6)/5√3-5√2=1 find the value of x

Find the common difference (d) in the following APs respectively. (i) 20, 40, 60, 80, 100,..(ii) 5, 0, -5, -10, -15, ...(iii) 2, 2, 2, 2, 2..

Calculation the Standard Deviation from the following set of 10 observations.8, 9, 15, 23, 5, 11, 19, 8, 10 and 12

The area and circumference of a circle are numerically equal. What is the diameter of the circle?

{ Find the co-ordinates of point }P which divides the join of }A(4,-5) and }B}{(6,3) in the ratio }2:5 .

In a mixture of 60 litres, the ratio of milk and water is 2:1. If this ratio is to be 1:2, then the quantity of water to be further added is __________ ___

A taxi charges in a city comprise of a fixed charge together with charge for distance covered. For a journey of 10km the charge paid was 75Rs and for 15km the charge was 110Rs. Find the charge for 25km.

The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28 cm. The length of the pipe is 35cm.Find the mass of the pipe, if 1cm3 of wood has a mass of 0.6g.

If x sin (90° − θ) cot (90° − θ) = cos (90° − θ), then x =(a) 0(b) 1(c) −1(d) 2

11. A boy of height 1.7 is standing 30m away from the flag staff on the same level ground he observes that the angle of elevation of the top of the flagstaff 30 digress calculate the height of the flagstaff

Very-Short and Short-Answer QuestionsHow many three-digit natural numbers are divisible by 7? [CBSE 2013]

On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gain rupees 7. if he sells the tea set at 5% gain and lemon set at 10% gain he gains rupees 13 find the actual price of the tea set and the lemon set

A box contains 3 black balls, 4 red balls and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black or green ball?

In the given figure, a line intersects a circle at points A and B. The line is rotated about the point P in both the directions until the points A and B coincide. How many times will they coincide?

If θ is acute angle, and tan θ =1√7, then cosec2θ−sec2θcosec2θ+sec2θ=

If A, B and C are the interior angles of a right-angle triangle, right-angled at B then find the value of A, given that tan2A=cot(A–30∘) and 2A is an acute angle.

†anα+2†an2α+4†an4α+8†an8α+kcotkα=cotα then k^2-15k+16 is equal t

Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm.

Question 4 (ii)State whether the following are true or false. Justify your answer.(ii) The value of sin θ increases as θ increases.

From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. Points O and P are joined. The ratio of angles OPR and OPQ is:

If the points A(1, -2) , B (2,3) , C (a,2) and D (-4,-3) form a parallelogram , find the value of a and height of the parallelogram taking AB as base .

solve for x and y a(x+y)+b(x-y)=a2-ab+b2 a(x+y)-b(x-y)=a2+ab+b2

Identify the similar triangles.

Question 6Value(s) of k for which the quadratic equation 2x2 - kx + k = 0 has equal roots is/are(A) 0 only(B) 4(C) 8 only(D) 0, 8​​​​​​

find a rational number between 2/3 and 6/5

Seeds worth Rs 20500, labour Rs 9700 , chemicals and fertilizers Rs 5600, selling price Rs 28640.

In a single throw of dice,the probability of getting a number greater than 6 is___

Which of the following functions from Z to Z are bijections?(a) f(x) = x3(b) f(x) = x + 2(c) f(x) = 2x + 1(d) f(x) = x2 + 1

The probability of getting a black, face card from a well-shuffled 52 pack card is___

Solve the following quadratic equations by factorization:16x-10x=27

Find the indicated terms in each of the following sequences whose nth terms are:(a) an = 5n − 4; a12 and a15(b) an =3n-24n + 5; a7 and a8(c) an = n (n −1) (n − 2); a5 and a8(d) an = (n − 1) (2 − n) (3 + n); a1, a2, a3(e) an = (−1)n n ; a3, a5, a8

The marks obtained by 36 students in a test in statistics (out of 50) are as below.35115354523314021131520474842344345333711132718123739381613185414743Construct a frequency distribution table with equal class intervals, one of them being 10-20(20 is not included).

In a mixture of 60 litres, the ratio of milk and water is 2:1. If this ratio is to be 1:2, then the quantity of water to be further added is ________ _

Question 6Value(s) of k for which the quadratic equation 2x2 - kx + k = 0 has equal roots is/are(A) 0 only(B) 4(C) 8 only(D) 0, 8