32581 + Interview Questions in Mathematics Page 32 InterviewSolution

1551.	In Fig., PS is the bisector of ∠QPR of ΔPQR.Prove that QSSR=PQPR.
Answer» In Fig., $P S$ is the bisector of $∠ Q P R$ of $Δ P Q R .$ Prove that $\frac{Q S}{S R} = \frac{P Q}{P R} .$

Discussion

1552.	Find the equation of the line.
Answer» Find the equation of the line.

1552.

Find the equation of the line.

Answer»

Find the equation of the line.

Discussion

1553.	Area of a trapezium is 160 sq cm and the height is 10 cm . Find the sum of its two parallel sides.
Answer» Area of a trapezium is 160 sq cm and the height is 10 cm . Find the sum of its two parallel sides.

Discussion

1554.	If P(A) denotes the probability of an event A, then (a) P(A) < 0 (b) P(A) > 1 (c) 0≤P(A)≤1 (d) −1≤P(A)≤1
Answer» If P(A) denotes the probability of an event A, then (a) P(A) < 0 (b) P(A) > 1 (c) $0 \leq P (A) \leq 1$ (d) $- 1 \leq P (A) \leq 1$

Discussion

1555.	Question 1 The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
Answer» Question 1 The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

Discussion

1556.	Question 14 Prove that √p+√q is irrational, where p and q are primes.
Answer» Question 14 Prove that $\sqrt{p} + \sqrt{q}$ is irrational, where p and q are primes.

Discussion

1557.	What is the area of the minor segment of a circle of radius 14 cm , when the angle of the corresponding sector is 60∘
Answer» What is the area of the minor segment of a circle of radius 14 cm , when the angle of the corresponding sector is $60^{\circ}$

Discussion

1558.	The annual income of two persons are in the ratio 9 : 7 and their expenses are in the ratio 4 : 3. If each of them saves Rs. 2000 per year, then their annual incomes are (1) Rs.18000 and Rs.14000 (2) Rs.27000 and Rs. 21000 (3) Rs. 36000 and Rs. 28000 (4) Rs. 45000 and Rs. 35000
Answer» The annual income of two persons are in the ratio 9 : 7 and their expenses are in the ratio 4 : 3. If each of them saves Rs. 2000 per year, then their annual incomes are (1) Rs.18000 and Rs.14000 (2) Rs.27000 and Rs. 21000 (3) Rs. 36000 and Rs. 28000 (4) Rs. 45000 and Rs. 35000

1558.

The annual income of two persons are in the ratio 9 : 7 and their expenses are in the ratio 4 : 3. If each of them saves Rs. 2000 per year, then their annual incomes are (1) Rs.18000 and Rs.14000 (2) Rs.27000 and Rs. 21000 (3) Rs. 36000 and Rs. 28000 (4) Rs. 45000 and Rs. 35000

Answer»

The annual income of two persons are in the ratio 9 : 7 and their expenses are in the ratio 4 : 3. If each of them saves Rs. 2000 per year, then their annual incomes are

(1) Rs.18000 and Rs.14000

(2) Rs.27000 and Rs. 21000

(3) Rs. 36000 and Rs. 28000

(4) Rs. 45000 and Rs. 35000

Discussion

1559.	Two poles stand on the ground at a distance of 20m and 50 m respectively from a point A on the ground, the taller pole at 30 m from smaller pole. A cable originates from the top pf the taller pole, passing on the other pole ends on a hook at point A. If the length of the cable is 100m, how much of it lies between the the two poles?
Answer» Two poles stand on the ground at a distance of 20m and 50 m respectively from a point A on the ground, the taller pole at 30 m from smaller pole. A cable originates from the top pf the taller pole, passing on the other pole ends on a hook at point A. If the length of the cable is 100m, how much of it lies between the the two poles?

Discussion

1560.	If y= cos ( x^2-4) then the value of dy/dx is
Answer» If y= cos ( x^2-4) then the value of dy/dx is

Discussion

1561.	If radius r and height h of a circular cylinder is increasing at the rate of α and β with time then find the rate of change of volume of the cylinder with time when r = 2 m and h = 5 m.
Answer» If radius r and height h of a circular cylinder is increasing at the rate of α and β with time then find the rate of change of volume of the cylinder with time when r = 2 m and h = 5 m.

Discussion

1562.	Use Euclid's Algorithm to find HCF of 1290 and 23
Answer» Use Euclid's Algorithm to find HCF of 1290 and 23

Discussion

1563.	AB is a tangent to a circle with centre O and A is the point of contact. If , prove that AB = OA.
Answer» AB is a tangent to a circle with centre O and A is the point of contact. If , prove that AB = OA.

Discussion

1564.	8. If a b c are in Arithmetic Progression then the value of (a-c)²/b²-ac
Answer» 8. If a b c are in Arithmetic Progression then the value of (a-c)²/b²-ac

Discussion

1565.	If 2tan−1(cosθ)=tan−1(2cosecθ) then, show that θ=π4.
Answer» If $2 t a n^{- 1} (c o s θ) = t a n^{- 1} (2 c o s e c θ)$ then, show that $θ = \frac{π}{4}$ .

Discussion

1566.	If (x , 2), (−3, −4) and (7, −5) are collinear, then x =(a) 60(b) 63(c) −63(d) −60
Answer» If (x , 2), (−3, −4) and (7, −5) are collinear, then x = (a) 60 (b) 63 (c) −63 (d) −60

Discussion

1567.	The roots of the quadratic equation 2x2 − x − 6 = 0(a) -2, 32(b) 2, -32(c) -2,-32(d) 2, 32
Answer» The roots of the quadratic equation 2x² − x − 6 = 0 (a) $- 2, \frac{3}{2}$ (b) $2, - \frac{3}{2}$ (c) $- 2, - \frac{3}{2}$ (d) $2, \frac{3}{2}$

Discussion

1568.	The value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has non-zero solution, is(a) 0(b) 2(c) 6(d) 8
Answer» The value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has non-zero solution, is (a) 0 (b) 2 (c) 6 (d) 8

Discussion

1569.	Prove the following trigonometric identities.If x = a cos3 θ, y = b sin3 θ, prove that xa2/3+yb2/3=1
Answer» Prove the following trigonometric identities. If x = a cos³ θ, y = b sin³ θ, prove that ${(\frac{x}{a})}^{2 / 3} + {(\frac{y}{b})}^{2 / 3} = 1$

Discussion

1570.

From the following Trial Balance of Shubdo Banerjee, prepare final accounts for the year ended in 31st March, 2018 and Balance Sheet as at that date: Particulars Dr. Balances (₹) Cr. Balances (₹) Land and Building 50,000 Purchases (Adjusted) 2,10,000 Stock (31st March, 2018) 45,000 Returns Inward 1,500 Returns Outward 2,500 Wages 45,300 Salaries 39,000 Office Expenses 15,400 Carriage Inwards 1,200 Carriage Outwards 2,000 Discount allowed 750 Discount received 1,200 Bad Debts 1,200 Sales 3,85,000 Capital Account 1,15,000 Chatterji's Loan A/c (taken on 1st Oct., 2017 18% p.a. 25,000 Insurance 1,500 Commission 1,500 Plant and Machinery 50,000 Furniture and Fixtures 20,000 Bills Receivable 20,000 Sundry Debtors 40,000 Sundry Creditors 25,000 Cash at Bank 16,000 Office Equipments 12,000 Bills Payable 12,350 Expenses Payable 3,300 Total 5,70,850 5,70,850 The following adjustments be taken care of:(i) Depreciate Land and Building 6%, Plant and Machinery 10%, Office equipments 20% and Furniture and Fixtures 15%(ii) Calculate Provision for Doubtful Debts at 2% on Debtors.(iii) Insurance premium includes ₹250 paid in advance.(iv) Provide salary to Banerjee ₹15,000 p.a.(v) Outstanding Salaries ₹11,500.(vi) 10% of the final profit is to be transferred to General Reserve.

Answer» From the following Trial Balance of Shubdo Banerjee, prepare final accounts for the year ended in 31st March, 2018 and Balance Sheet as at that date:


Particulars	Dr. Balances (₹)	Cr. Balances (₹)
Land and Building	50,000
Purchases (Adjusted)	2,10,000
Stock (31st March, 2018)	45,000
Returns Inward	1,500
Returns Outward		2,500
Wages	45,300
Salaries	39,000
Office Expenses	15,400
Carriage Inwards	1,200
Carriage Outwards	2,000
Discount allowed	750
Discount received		1,200
Bad Debts	1,200
Sales		3,85,000
Capital Account		1,15,000
Chatterji's Loan A/c (taken on 1st Oct., 2017 18% p.a.		25,000
Insurance	1,500
Commission		1,500
Plant and Machinery	50,000
Furniture and Fixtures	20,000
Bills Receivable	20,000
Sundry Debtors	40,000
Sundry Creditors		25,000
Cash at Bank	16,000
Office Equipments	12,000
Bills Payable		12,350
Expenses Payable		3,300
Total	5,70,850	5,70,850

The following adjustments be taken care of:

(i) Depreciate Land and Building 6%, Plant and Machinery 10%, Office equipments 20% and Furniture and Fixtures 15%

(ii) Calculate Provision for Doubtful Debts at 2% on Debtors.

(iii) Insurance premium includes ₹250 paid in advance.

(iv) Provide salary to Banerjee ₹15,000 p.a.

(v) Outstanding Salaries ₹11,500.

(vi) 10% of the final profit is to be transferred to General Reserve.

Discussion

1571.	IF [8−3]=[4−5] : find : (i) A + B (ii) B - A
Answer» IF $[\begin{matrix} 8 - 3 \end{matrix}] = [\begin{matrix} 4 - 5 \end{matrix}]$ : find : (i) A + B (ii) B - A

1571.

IF [8−3]=[4−5] : find : (i) A + B (ii) B - A

Answer»

IF $[\begin{matrix} 8 - 3 \end{matrix}] = [\begin{matrix} 4 - 5 \end{matrix}]$ :

find :
(i) A + B (ii) B - A

Discussion

1572.	Find the value of sin(60°+θ)−cos(30°−θ).
Answer» Find the value of $s i n (60 ° + θ) - c o s (30 ° - θ) .$

Discussion

1573.	If f(x)=x-1/x+1 then f(ax) in term of f (x) is given by
Answer» If f(x)=x-1/x+1 then f(ax) in term of f (x) is given by

Discussion

1574.	From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that Δ APB is equilateral.
Answer» From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that Δ APB is equilateral.

Discussion

1575.	If P(a/3,4) is the mid point of the line segment joining the points Q(–6, 5) and R(–2, 3), then the value of 'a' is _________.
Answer» If P(a/3,4) is the mid point of the line segment joining the points Q(–6, 5) and R(–2, 3), then the value of 'a' is _________.

Discussion

1576.	A lateral faces of a square pyramid are equilateral triangles of side 30 centimetres. What is its surface area?
Answer» A lateral faces of a square pyramid are equilateral triangles of side 30 centimetres. What is its surface area?

Discussion

1577.	If [a+2b2c−dc+4d4b−a]=[1023714], then find the values of a, b, c, d respectively.
Answer» If $[\begin{matrix} a + 2 b & 2 c - d c + 4 d & 4 b - a \end{matrix}] = [\begin{matrix} 10 & 2 37 & 14 \end{matrix}]$ , then find the values of $a, b, c, d$ respectively.

Discussion

1578.	How many gold coins of 1.75cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm?
Answer» How many gold coins of 1.75cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm?

Discussion

1579.	Question 9A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume.The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required.[Assume π=227]
Answer» Question 9 A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required. $[A s s u m e π = \frac{22}{7}]$

Discussion

1580.	Write the set of values of a and b for which the following system of equations has infinitely many solutions.2x+3y=72ax+a+by=28
Answer» Write the set of values of a and b for which the following system of equations has infinitely many solutions. $2 x + 3 y = 7 2 a x + (a + b) y = 28$

Discussion

1581.	4s2 -4s+1 Split the middle term and factorise the given expression
Answer» 4s2 -4s+1 Split the middle term and factorise the given expression

1581.

4s2 -4s+1 Split the middle term and factorise the given expression

Answer»

4s2 -4s+1

Split the middle term and factorise the given expression

Discussion

1582.	9x-4y=2000, 7x-3y=2000 solve by substitution method and cross multiplication method
Answer» 9x-4y=2000, 7x-3y=2000 solve by substitution method and cross multiplication method

Discussion

1583.	In the following figure, if LM \|\| CB and LN \|\| CD, prove that AMAB=ANAD.
Answer» In the following figure, if LM \|\| CB and LN \|\| CD, prove that $\frac{A M}{A B} = \frac{A N}{A D}$ .

Discussion

1584.	if alpha and beta are the zeros of the polynomial x^2-ax+a then find the value of alpha^4 - beta^4
Answer» if alpha and beta are the zeros of the polynomial x^2-ax+a then find the value of alpha^4 - beta^4

Discussion

1585.	Describe the locus for questions 1 to 13 given below: The locus of a point in rhombus ABCD, so that it is equidistant from (i) AB and BC; (ii) B and D.
Answer» Describe the locus for questions 1 to 13 given below: The locus of a point in rhombus ABCD, so that it is equidistant from (i) AB and BC; (ii) B and D.

1585.

Describe the locus for questions 1 to 13 given below: The locus of a point in rhombus ABCD, so that it is equidistant from (i) AB and BC; (ii) B and D.

Answer»

Describe the locus for questions 1 to 13 given below:

The locus of a point in rhombus ABCD, so that it is equidistant from

(i) AB and BC; (ii) B and D.

Discussion

1586.	Rakesh invested Rs 43,920 to buy shares of a company whose market value is Rs 122 each. The face value of a share is Rs 100. (i) Find the number of shares purchased. (ii) Also, find his yearly dividend, if the dividend is 10% per annum. [4 MARKS]
Answer» Rakesh invested Rs 43,920 to buy shares of a company whose market value is Rs 122 each. The face value of a share is Rs 100. (i) Find the number of shares purchased. (ii) Also, find his yearly dividend, if the dividend is $10 %$ per annum. [4 MARKS]

Discussion

1587.	The orthocentre of the triangle with vertices(2,√3−12),(12,−12)and(2,−12) is
Answer» The orthocentre of the triangle with vertices $(2, \frac{\sqrt{3} - 1}{2}), (\frac{1}{2}, - \frac{1}{2}) a n d (2, - \frac{1}{2})$ is

Discussion

1588.	could help me with Q.no.11 pg.31
Answer» could help me with Q.no.11 pg.31

Discussion

1589.	Show that the square of an odd positive integer can be of the form 6q+1 or 6q+3 for some integer q.
Answer» Show that the square of an odd positive integer can be of the form $6 q + 1$ or $6 q + 3$ for some integer $q$ .

Discussion

1590.	If A is an m × n matrix and B is a matrix such that both AB and BA are defined, then the order of B is ___________.
Answer» If A is an m × n matrix and B is a matrix such that both AB and BA are defined, then the order of B is ___________.

Discussion

1591.	A juice seller fills juice into cylindrical glasses from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹10/- for a glass of height 10 cm and radius 4 cm. The amount he earns by selling the juice is ____. (Use π=227)
Answer» A juice seller fills juice into cylindrical glasses from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹10/- for a glass of height 10 cm and radius 4 cm. The amount he earns by selling the juice is ____. $(U s e π = \frac{22}{7})$

Discussion

1592.	A man buys ₹ 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
Answer» A man buys ₹ 20 shares paying $9 %$ dividend. The man wants to have an interest of $12 %$ on his money. The market value of each share is:

Discussion

1593.	A sailor goes 8 km downstream in 40 minutes and returns in 1 hours. Determine the speed of the sailor in still water and the speed of the current.
Answer» A sailor goes 8 km downstream in 40 minutes and returns in 1 hours. Determine the speed of the sailor in still water and the speed of the current.

Discussion

1594.	Ashok invested Rs 26,400 on 12%, Rs 25 shares of a company. If he receives a dividend of Rs 2,475, find the : i) Number of shares he bought ii) Market value of each share [3 MARKS]
Answer» Ashok invested Rs 26,400 on 12%, Rs 25 shares of a company. If he receives a dividend of Rs 2,475, find the : i) Number of shares he bought ii) Market value of each share [3 MARKS]

Discussion

1595.	A table marked at Rs 15000 is available for Rs 14400. What is the discount %?
Answer» A table marked at $R s 15000$ is available for $R s 14400$ . What is the discount $%$ ?

Discussion

1596.	Mark the correct alternative in each of the following:A number is selected at random from the numbers 1 to 30. The probability that it is a prime number is(a) 23 (b) 16 (c) 13 (d) 1130 [CBSE 2014]
Answer» Mark the correct alternative in each of the following: A number is selected at random from the numbers 1 to 30. The probability that it is a prime number is (a) $\frac{2}{3}$ (b) $\frac{1}{6}$ (c) $\frac{1}{3}$ (d) $\frac{11}{30}$ [CBSE 2014]

Discussion

1597.	If x1, x2,........x18 are 18 observations such that ∑i=118(xi-8)=9 and ∑i=118(xi-8)2=45, then the standard deviation of these observations is _________________.
Answer» If x₁, x₂,........x₁₈ are 18 observations such that $\sum_{i = 1}^{18} (x_{i} - 8) = 9 and \sum_{i = 1}^{18} {(x_{i} - 8)}^{2} = 45,$ then the standard deviation of these observations is _________________.

Discussion

1598.	From a thin metallic piece in the shape of a trapezium ABCD in which AB \|\| CD and ∠BCD = 90°, a quarter circle BFEC is removed. Given, AB = BC = 3.5 cm and DE = 2 cm, calculate the area of remaining (shaded) part of metal sheet. [CBSE 2011]
Answer» From a thin metallic piece in the shape of a trapezium ABCD in which AB \|\| CD and ∠BCD = 90°, a quarter circle BFEC is removed. Given, AB = BC = 3.5 cm and DE = 2 cm, calculate the area of remaining (shaded) part of metal sheet. [CBSE 2011]

Discussion

1599.	For what value of k will the following system of linear equations has no solution:3x + y = 1(2k − 1)x + (k − 1)y = 2k + 1
Answer» For what value of k will the following system of linear equations has no solution: 3x + y = 1 (2k − 1)x + (k − 1)y = 2k + 1

Discussion

1600.	In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C.
Answer» In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C.

Discussion

Explore topic-wise InterviewSolutions in .

In Fig., PS is the bisector of ∠QPR of ΔPQR.Prove that QSSR=PQPR.

Find the equation of the line.

Area of a trapezium is 160 sq cm and the height is 10 cm . Find the sum of its two parallel sides.

If P(A) denotes the probability of an event A, then (a) P(A) &lt; 0 (b) P(A) &gt; 1 (c) 0≤P(A)≤1 (d) −1≤P(A)≤1

Question 1 The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

Question 14 Prove that √p+√q is irrational, where p and q are primes.

What is the area of the minor segment of a circle of radius 14 cm , when the angle of the corresponding sector is 60∘

The annual income of two persons are in the ratio 9 : 7 and their expenses are in the ratio 4 : 3. If each of them saves Rs. 2000 per year, then their annual incomes are (1) Rs.18000 and Rs.14000 (2) Rs.27000 and Rs. 21000 (3) Rs. 36000 and Rs. 28000 (4) Rs. 45000 and Rs. 35000

If y= cos ( x^2-4) then the value of dy/dx is

If radius r and height h of a circular cylinder is increasing at the rate of α and β with time then find the rate of change of volume of the cylinder with time when r = 2 m and h = 5 m.

Use Euclid's Algorithm to find HCF of 1290 and 23

AB is a tangent to a circle with centre O and A is the point of contact. If , prove that AB = OA.

8. If a b c are in Arithmetic Progression then the value of (a-c)²/b²-ac

If 2tan−1(cosθ)=tan−1(2cosecθ) then, show that θ=π4.

If (x , 2), (−3, −4) and (7, −5) are collinear, then x =(a) 60(b) 63(c) −63(d) −60

The roots of the quadratic equation 2x2 − x − 6 = 0(a) -2, 32(b) 2, -32(c) -2,-32(d) 2, 32

The value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has non-zero solution, is(a) 0(b) 2(c) 6(d) 8

Prove the following trigonometric identities.If x = a cos3 θ, y = b sin3 θ, prove that xa2/3+yb2/3=1

IF [8−3]=[4−5] : find : (i) A + B (ii) B - A

Find the value of sin(60°+θ)−cos(30°−θ).

If f(x)=x-1/x+1 then f(ax) in term of f (x) is given by

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that Δ APB is equilateral.

If P(a/3,4) is the mid point of the line segment joining the points Q(–6, 5) and R(–2, 3), then the value of 'a' is _________.

A lateral faces of a square pyramid are equilateral triangles of side 30 centimetres. What is its surface area?

If [a+2b2c−dc+4d4b−a]=[1023714], then find the values of a, b, c, d respectively.

How many gold coins of 1.75cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm?

Question 9A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume.The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required.[Assume π=227]

Write the set of values of a and b for which the following system of equations has infinitely many solutions.2x+3y=72ax+a+by=28

4s2 -4s+1 Split the middle term and factorise the given expression

9x-4y=2000, 7x-3y=2000 solve by substitution method and cross multiplication method

In the following figure, if LM || CB and LN || CD, prove that AMAB=ANAD.

if alpha and beta are the zeros of the polynomial x^2-ax+a then find the value of alpha^4 - beta^4

Describe the locus for questions 1 to 13 given below: The locus of a point in rhombus ABCD, so that it is equidistant from (i) AB and BC; (ii) B and D.

Rakesh invested Rs 43,920 to buy shares of a company whose market value is Rs 122 each. The face value of a share is Rs 100. (i) Find the number of shares purchased. (ii) Also, find his yearly dividend, if the dividend is 10% per annum. [4 MARKS]

The orthocentre of the triangle with vertices(2,√3−12),(12,−12)and(2,−12) is

could help me with Q.no.11 pg.31

Show that the square of an odd positive integer can be of the form 6q+1 or 6q+3 for some integer q.

If A is an m × n matrix and B is a matrix such that both AB and BA are defined, then the order of B is ___________.

A juice seller fills juice into cylindrical glasses from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹10/- for a glass of height 10 cm and radius 4 cm. The amount he earns by selling the juice is ____. (Use π=227)

A man buys ₹ 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:

A sailor goes 8 km downstream in 40 minutes and returns in 1 hours. Determine the speed of the sailor in still water and the speed of the current.

Ashok invested Rs 26,400 on 12%, Rs 25 shares of a company. If he receives a dividend of Rs 2,475, find the : i) Number of shares he bought ii) Market value of each share [3 MARKS]

A table marked at Rs 15000 is available for Rs 14400. What is the discount %?

Mark the correct alternative in each of the following:A number is selected at random from the numbers 1 to 30. The probability that it is a prime number is(a) 23 (b) 16 (c) 13 (d) 1130 [CBSE 2014]

If x1, x2,........x18 are 18 observations such that ∑i=118(xi-8)=9 and ∑i=118(xi-8)2=45, then the standard deviation of these observations is _________________.

From a thin metallic piece in the shape of a trapezium ABCD in which AB || CD and ∠BCD = 90°, a quarter circle BFEC is removed. Given, AB = BC = 3.5 cm and DE = 2 cm, calculate the area of remaining (shaded) part of metal sheet. [CBSE 2011]

For what value of k will the following system of linear equations has no solution:3x + y = 1(2k − 1)x + (k − 1)y = 2k + 1

In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C.

If P(A) denotes the probability of an event A, then (a) P(A) < 0 (b) P(A) > 1 (c) 0≤P(A)≤1 (d) −1≤P(A)≤1