32581 + Interview Questions in Mathematics

1.	Solve each of the following systems of equations graphically: 3x+y+1=0,2x−3y+8=0.
Answer» Solve each of the following systems of equations graphically: $3 x + y + 1 = 0, 2 x - 3 y + 8 = 0.$

1.

Solve each of the following systems of equations graphically: 3x+y+1=0,2x−3y+8=0.

Answer»

Solve each of the following systems of equations graphically:

$3 x + y + 1 = 0, 2 x - 3 y + 8 = 0.$

Discussion

2.	If 3x=cosec θ and 3x=cot θ then 3(x2−1x2) = ? (a) 127 (b) 181 (c) 13 (d) 19
Answer» If $3 x = c o s e c θ$ and $\frac{3}{x} = c o t θ$ then $3 (x^{2} - \frac{1}{x^{2}})$ = ? (a) $\frac{1}{27}$ (b) $\frac{1}{81}$ (c) $\frac{1}{3}$ (d) $\frac{1}{9}$

2.

If 3x=cosec θ and 3x=cot θ then 3(x2−1x2) = ? (a) 127 (b) 181 (c) 13 (d) 19

Answer»

If $3 x = c o s e c θ$ and $\frac{3}{x} = c o t θ$ then $3 (x^{2} - \frac{1}{x^{2}})$ = ?

(a) $\frac{1}{27}$ (b) $\frac{1}{81}$ (c) $\frac{1}{3}$ (d) $\frac{1}{9}$

Discussion

3.	The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.
Answer» The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.

Discussion

4.	Solve for x x2 - 3x - 10 = 0
Answer» Solve for x $x^{2}$ - 3x - 10 = 0

4.

Solve for x x2 - 3x - 10 = 0

Answer»

Solve for x

$x^{2}$ - 3x - 10 = 0

Discussion

5.	Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?
Answer» Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

Discussion

6.	Prove that the points (2a, 4a), (2a, 6a) and (2a+√3a,5a) are the vertices of an equilateral triangle.
Answer» Prove that the points (2a, 4a), (2a, 6a) and $(2 a + \sqrt{3} a, 5 a)$ are the vertices of an equilateral triangle.

Discussion

7.	The angle of elevation of the top of a chimney from the top of a tower is 60∘ and the angle of depression of the foot of the chimney from the top of the tower is 30∘. If the height of the tower is 40m, find the height of the chimney. According to pollution control norms, the minimum height of a smoke emitting chimney should be 100m. State if the height of the above mentioned chimney meets the polution norms. What valued is discussed in this question?
Answer» The angle of elevation of the top of a chimney from the top of a tower is $60^{\circ}$ and the angle of depression of the foot of the chimney from the top of the tower is $30^{\circ}$ . If the height of the tower is $40 m$ , find the height of the chimney. According to pollution control norms, the minimum height of a smoke emitting chimney should be $100 m$ . State if the height of the above mentioned chimney meets the polution norms. What valued is discussed in this question?

Discussion

8.	In Fig. 8.65, BDC is a tangent to the given circle at point D such that BD=30 cm and CD=7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF (ii) radius of the circle.
Answer» In Fig. 8.65, BDC is a tangent to the given circle at point D such that BD=30 cm and CD=7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF (ii) radius of the circle.

8.

In Fig. 8.65, BDC is a tangent to the given circle at point D such that BD=30 cm and CD=7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF (ii) radius of the circle.

Answer»

In Fig. 8.65, BDC is a tangent to the given circle at point D such that BD=30 cm and CD=7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF (ii) radius of the circle.

Discussion

9.	Mr. and Mrs. Ahuja weigh x kg and y kg respectively. They both take a dieting course. at the end of which Mr. Ahuja loses 5 kg and weighs as much as his wife weighed before the course. Mrs. Ahuja loses 4 kg and weighs 78th of what her husband weighed before the course. Form two equations in x and y to find their weights before taking the dieting course.
Answer» Mr. and Mrs. Ahuja weigh x kg and y kg respectively. They both take a dieting course. at the end of which Mr. Ahuja loses 5 kg and weighs as much as his wife weighed before the course. Mrs. Ahuja loses 4 kg and weighs $\frac{7}{8}$ th of what her husband weighed before the course. Form two equations in x and y to find their weights before taking the dieting course.

9.

Mr. and Mrs. Ahuja weigh x kg and y kg respectively. They both take a dieting course. at the end of which Mr. Ahuja loses 5 kg and weighs as much as his wife weighed before the course. Mrs. Ahuja loses 4 kg and weighs 78th of what her husband weighed before the course. Form two equations in x and y to find their weights before taking the dieting course.

Answer»

Mr. and Mrs. Ahuja weigh x kg and y kg respectively. They both take a dieting course. at the end of which Mr. Ahuja loses 5 kg and weighs as much as his wife weighed before the course.

Mrs. Ahuja loses 4 kg and weighs $\frac{7}{8}$ th of what her husband weighed before the course. Form two equations in x and y to find their weights before taking the dieting course.

Discussion

10.	Question 73 In a hurdle race, Nidhi is over hurdle B and 26 of the way through the race, as shown in the given figure. then, answer the following : (a) Where will Nidhi be, when she is 46 of the way through the race? (b) Where will Nidhi be, when she is 56 of the way through the race? (c) Give two fractions to tell what part of the race Nidhi has finished, when she is over hurdle C.
Answer» Question 73 In a hurdle race, Nidhi is over hurdle B and $\frac{2}{6}$ of the way through the race, as shown in the given figure. then, answer the following : (a) Where will Nidhi be, when she is $\frac{4}{6}$ of the way through the race? (b) Where will Nidhi be, when she is $\frac{5}{6}$ of the way through the race? (c) Give two fractions to tell what part of the race Nidhi has finished, when she is over hurdle C.

10.

Question 73 In a hurdle race, Nidhi is over hurdle B and 26 of the way through the race, as shown in the given figure. then, answer the following : (a) Where will Nidhi be, when she is 46 of the way through the race? (b) Where will Nidhi be, when she is 56 of the way through the race? (c) Give two fractions to tell what part of the race Nidhi has finished, when she is over hurdle C.

Answer»

Question 73

In a hurdle race, Nidhi is over hurdle B and $\frac{2}{6}$ of the way through the race, as shown in the given figure.

then, answer the following :
(a) Where will Nidhi be, when she is $\frac{4}{6}$ of the way through the race?
(b) Where will Nidhi be, when she is $\frac{5}{6}$ of the way through the race?
(c) Give two fractions to tell what part of the race Nidhi has finished, when she is over hurdle C.

Discussion

11.	A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of 60∘. After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30∘. Find the distance the boat has to travel to reach a point that is exactly above the submarine. [Tan 30∘=0.57, tan 60∘=1.73]
Answer» A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of $60^{\circ}$ . After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30 $^{\circ}$ . Find the distance the boat has to travel to reach a point that is exactly above the submarine. $[T a n 30^{\circ} = 0.57, t a n 60^{\circ} = 1.73]$

11.

A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of 60∘. After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30∘. Find the distance the boat has to travel to reach a point that is exactly above the submarine. [Tan 30∘=0.57, tan 60∘=1.73]

Answer»

A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of $60^{\circ}$ . After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30 $^{\circ}$ . Find the distance the boat has to travel to reach a point that is exactly above the submarine. $[T a n 30^{\circ} = 0.57, t a n 60^{\circ} = 1.73]$

Discussion

12.	If f(x)=cos(π2]x+cos(−π2]x, where [x] stands for the greatest integer function, then
Answer» If $f (x) = cos (π^{2}] x + cos (- π^{2}] x,$ where [x] stands for the greatest integer function, then

Discussion

13.	The sum of the probabilities of all the elementary events of an experiment is
Answer» The sum of the probabilities of all the elementary events of an experiment is

Discussion

14.	Find solution of the equation 2sin2θ=3cosθ
Answer» Find solution of the equation $2 s i n^{2} θ = 3 c o s θ$

Discussion

15.	AB is a diameter of the circle and A, P, B, R are four points on the circle. The lines AP, RB intersect at Q. Find ∠BPR.
Answer» AB is a diameter of the circle and A, P, B, R are four points on the circle. The lines AP, RB intersect at Q. Find $∠ B P R .$

15.

AB is a diameter of the circle and A, P, B, R are four points on the circle. The lines AP, RB intersect at Q. Find ∠BPR.

Answer»

AB is a diameter of the circle and A, P, B, R are four points on the circle. The lines AP, RB intersect at Q. Find $∠ B P R .$

Discussion

16.	Question 1 (ii) In which of the following situations does the list of numbers involved make an arithmetic progression and why? (ii) The amount of air present in a cylinder when a vacuum pump removes 14 of the air remaining in the cylinder at a time.
Answer» Question 1 (ii) In which of the following situations does the list of numbers involved make an arithmetic progression and why? (ii) The amount of air present in a cylinder when a vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder at a time.

Discussion

17.	The area of a right-angled triangle is 165 sq metres. Then, find its base and altitude if the latter exceeds the former by 7 meters?
Answer» The area of a right-angled triangle is 165 sq metres. Then, find its base and altitude if the latter exceeds the former by 7 meters?

Discussion

18.	What we can say about the nature of roots of x2–2x–3=0 ?
Answer» What we can say about the nature of roots of $x^{2} - 2 x - 3 = 0$ ?

Discussion

19.	How many radii along with the enclosed arc form a sector of a circle?
Answer» How many radii along with the enclosed arc form a sector of a circle?

Discussion

20.	A conical tent is used to accommodate 11 persons. Each person must have 4m2 of the space on the ground and 20 m3 of air to breathe. Find the height of cone.
Answer» A conical tent is used to accommodate 11 persons. Each person must have 4m² of the space on the ground and 20 m³ of air to breathe. Find the height of cone.

Discussion

21.	If p times the pth term is equal to q times the qth term of an A.P. , show that the (p + q)th term is zero.
Answer» If p times the p^th term is equal to q times the q^th term of an A.P. , show that the (p + q)^thterm is zero.

Discussion

22.	In the figure , O is the centre of a circle of radius 9 cm. Semicircle with diameter OA cuts the circle at D. If DP is perpendicular to OA and OA = 15 cm, then DP = _____ cm.
Answer» In the figure , O is the centre of a circle of radius 9 cm. Semicircle with diameter OA cuts the circle at D. If DP is perpendicular to OA and OA = 15 cm, then DP = _____ cm.

22.

In the figure , O is the centre of a circle of radius 9 cm. Semicircle with diameter OA cuts the circle at D. If DP is perpendicular to OA and OA = 15 cm, then DP = _____ cm.

Answer»

In the figure , O is the centre of a circle of radius 9 cm. Semicircle with diameter OA cuts the circle at D.

If DP is perpendicular to OA and OA = 15 cm, then DP = _____ cm.

Discussion

23.	If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then
Answer» If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

Discussion

24.	The base edge of a square pyramid with slant height 24cm is 14cm. Then its lateral edge is:
Answer» The base edge of a square pyramid with slant height 24cm is 14cm. Then its lateral edge is:

Discussion

25.	5th term of an AP is 38 and 8th term is 59. What is the cd of the sequence? Which term of the sequence is 185?
Answer» 5th term of an AP is 38 and 8th term is 59. What is the cd of the sequence? Which term of the sequence is 185?

25.

5th term of an AP is 38 and 8th term is 59. What is the cd of the sequence? Which term of the sequence is 185?

Answer»

5th term of an AP is 38 and 8th term is 59.

What is the cd of the sequence?

Which term of the sequence is 185?

Discussion

26.	If composite number is a product of prime numbers but 15 is a composite number 15=15*1 but if we factorised this then it is not a product of prime numbers.
Answer» If composite number is a product of prime numbers but 15 is a composite number 15=15*1 but if we factorised this then it is not a product of prime numbers.

Discussion

27.	90% acid solution (90% pure acid and 10% water) and 97% acid solution are mixed to obtain 21 litres of 95% acid solution. How many litres of each solution are mixed. Let x litres of 90% and y litres of 97% be mixed; then x + y = 21 and 90% of x + 97% of y = 95% of 21.
Answer» 90% acid solution (90% pure acid and 10% water) and 97% acid solution are mixed to obtain 21 litres of 95% acid solution. How many litres of each solution are mixed. Let x litres of 90% and y litres of 97% be mixed; then x + y = 21 and 90% of x + 97% of y = 95% of 21.

27.

90% acid solution (90% pure acid and 10% water) and 97% acid solution are mixed to obtain 21 litres of 95% acid solution. How many litres of each solution are mixed. Let x litres of 90% and y litres of 97% be mixed; then x + y = 21 and 90% of x + 97% of y = 95% of 21.

Answer»

90% acid solution (90% pure acid and 10% water) and 97% acid solution are mixed to obtain 21 litres of 95% acid solution. How many litres of each solution are mixed.

Let x litres of 90% and y litres of 97% be mixed; then x + y = 21
and 90% of x + 97% of y = 95% of 21.

Discussion

28.	When to use substitution method,cross multiplication method and elimination method during ssolving a linear equation in two variable
Answer» When to use substitution method,cross multiplication method and elimination method during ssolving a linear equation in two variable

Discussion

29.	Determine k so that k^2 + 4k + 8,2k^2 + 3k + 6,3k^2 + 4k + 4 are three consecutive terms of an A.P.
Answer» Determine k so that k^2 + 4k + 8,2k^2 + 3k + 6,3k^2 + 4k + 4 are three consecutive terms of an A.P.

Discussion

30.	A polynomial of degree 1 is called a __ polynomial.
Answer» A polynomial of degree 1 is called a __ polynomial.

Discussion

31.	ABCD is a cyclic quadilateral whose diagonals intersect at a point E. If ∠DBC=70∘ and ∠BAC=30∘, find ∠BCD. Further if AB=BC, find ∠ECD.
Answer» ABCD is a cyclic quadilateral whose diagonals intersect at a point E. If $∠ D B C = 70^{\circ}$ and $∠ B A C = 30^{\circ}$ , find $∠ B C D$ . Further if $A B = B C,$ find $∠ E C D$ .

31.

ABCD is a cyclic quadilateral whose diagonals intersect at a point E. If ∠DBC=70∘ and ∠BAC=30∘, find ∠BCD. Further if AB=BC, find ∠ECD.

Answer»

ABCD is a cyclic quadilateral whose diagonals intersect at a point E. If $∠ D B C = 70^{\circ}$ and $∠ B A C = 30^{\circ}$ , find $∠ B C D$ . Further if $A B = B C,$ find $∠ E C D$ .

Discussion

32.	The tangent at a point C of a circle and a diameter ab when extended intersect it p. If angle PCA = 110, find angle CBA
Answer» The tangent at a point C of a circle and a diameter ab when extended intersect it p. If angle PCA = 110, find angle CBA

Discussion

33.	The Yin-Yang symbol can be explained with the following dimensions. What would be area covered by the Yin (black) region. The radius of the larger circle is, R=8 cm.
Answer» The Yin-Yang symbol can be explained with the following dimensions. What would be area covered by the Yin (black) region. The radius of the larger circle is, $R = 8$ cm.

Discussion

34.	Solve: ax + by = a - b bx - ay = a + b
Answer» Solve: ax + by = a - b bx - ay = a + b

34.

Solve: ax + by = a - b bx - ay = a + b

Answer»

Solve: ax + by = a - b

bx - ay = a + b

Discussion

35.	Tangents AP and AQ are drawn to a circle, with centre O, from an exterior point A. Prove that : ∠PAQ=2∠OPQ
Answer» Tangents AP and AQ are drawn to a circle, with centre O, from an exterior point A. Prove that : $∠ P A Q = 2 ∠ O P Q$

35.

Tangents AP and AQ are drawn to a circle, with centre O, from an exterior point A. Prove that : ∠PAQ=2∠OPQ

Answer»

Tangents AP and AQ are drawn to a circle, with centre O, from an exterior point A. Prove that :

$∠ P A Q = 2 ∠ O P Q$

Discussion

36.	Question 5 The first four terms of an AP whose first term is – 2 and the common difference is – 2 are A) – 2, 0, 2, 4 B) – 2, 4, –8, 16 C) – 2, – 4, – 6 , – 8 D) – 2, – 4, – 8, – 16
Answer» Question 5 The first four terms of an AP whose first term is – 2 and the common difference is – 2 are A) – 2, 0, 2, 4 B) – 2, 4, –8, 16 C) – 2, – 4, – 6 , – 8 D) – 2, – 4, – 8, – 16

Discussion

37.	A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is
Answer» A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is

Discussion

38.	Viv invests Rs.4,500 in 8% Rs.10 shares at Rs.15. He sells the shares when the price rises to Rs.30 & invests the proceeds in 12 % Rs.100 shares at Rs.125. Calculate the change in his annual income
Answer» Viv invests Rs.4,500 in 8% Rs.10 shares at Rs.15. He sells the shares when the price rises to Rs.30 & invests the proceeds in 12 % Rs.100 shares at Rs.125. Calculate the change in his annual income

38.

Viv invests Rs.4,500 in 8% Rs.10 shares at Rs.15. He sells the shares when the price rises to Rs.30 & invests the proceeds in 12 % Rs.100 shares at Rs.125. Calculate the change in his annual income

Answer»

Viv invests Rs.4,500 in 8% Rs.10 shares at Rs.15. He sells the shares when the price rises to Rs.30 & invests the proceeds in 12 % Rs.100 shares at Rs.125.

Calculate the change in his annual income

Discussion

39.	The range of values of m for which the line y = mx + 2 cuts the circle x2+y2=1 at two distinct points, is .
Answer» The range of values of m for which the line y = mx + 2 cuts the circle $x^{2} + y^{2} = 1$ at two distinct points, is .

Discussion

40.	In the adjoining figure 'O' is the center of circle, ∠CAO = 25∘ and ∠CBO = 35∘. What is the value of ∠AOB?
Answer» In the adjoining figure 'O' is the center of circle, $∠$ CAO = $25^{\circ}$ and $∠$ CBO = $35^{\circ}$ . What is the value of $∠$ AOB?

40.

In the adjoining figure 'O' is the center of circle, ∠CAO = 25∘ and ∠CBO = 35∘. What is the value of ∠AOB?

Answer»

In the adjoining figure 'O' is the center of circle, $∠$ CAO = $25^{\circ}$ and $∠$ CBO = $35^{\circ}$ . What is the value of $∠$ AOB?

Discussion

41.	If b2 – 4ac = 0 then The roots of the Quadratic equation ax2 + bx + c = 0 are given by :
Answer» If b² – 4ac = 0 then The roots of the Quadratic equation ax² + bx + c = 0 are given by :

Discussion

42.	Solve the equation 5(+ 2) = 3. Give your answer correct to two decimal places.
Answer» Solve the equation 5(+ 2) = 3. Give your answer correct to two decimal places.

Discussion

43.	If (3x - 9) : (5x + 4) is the triplicate ratio of 3: 4, find the value of x.
Answer» If (3x - 9) : (5x + 4) is the triplicate ratio of 3: 4, find the value of x.

Discussion

44.	Find the values of p, q, r and s in the given cumulative frequency distribution. xfrequencyCumulative frequency103p=−−−−1510q=−−−−2025r=−−−−257s=−−−−30550
Answer» Find the values of p, q, r and s in the given cumulative frequency distribution. $\begin{matrix} x & frequency & Cumulative frequency 10 & 3 & p = - - - - 15 & 10 & q = - - - - 20 & 25 & r = - - - - 25 & 7 & s = - - - - 30 & 5 & 50 \end{matrix}$

Discussion

45.	Three cubical blocks, each of volume 125 cm3, are joined end to end to form a cuboid. What is the total surface area of the cuboid so formed?
Answer» Three cubical blocks, each of volume 125 cm³, are joined end to end to form a cuboid. What is the total surface area of the cuboid so formed?

Discussion

46.	If x = √a tanα and y = √a secα. Find the value of y2 – x2 __
Answer» If x = $\sqrt{a} t a n α$ and y = $\sqrt{a} s e c α$ . Find the value of $y^{2}$ – $x^{2}$ __

Discussion

47.	P and Q are points on the sides AB and AC respectively of a ΔABC. If AP = 2 cm, PB = 4 cm, AQ = 3 cm, and QC = 6 cm, show that BC = 3PQ.
Answer» P and Q are points on the sides AB and AC respectively of a $Δ A B C$ . If AP = 2 cm, PB = 4 cm, AQ = 3 cm, and QC = 6 cm, show that BC = 3PQ.

Discussion

48.	Question 2(ii) (ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. Find out the number of toys produced on that day.
Answer» Question 2(ii) (ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. Find out the number of toys produced on that day.

Discussion

49.	In a right angled △ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of △ABD and △ BCD?
Answer» In a right angled $△$ ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of $△$ ABD and $△$ BCD?

Discussion

50.	The Right to Education Act (RTE) provides free and compulsory education to every person of what age group?
Answer» The $Right to Education Act$ ( $RTE$ ) provides free and compulsory education to every person of what age group?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve each of the following systems of equations graphically: 3x+y+1=0,2x−3y+8=0.

If 3x=cosec θ and 3x=cot θ then 3(x2−1x2) = ? (a) 127 (b) 181 (c) 13 (d) 19

The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.

Solve for x x2 - 3x - 10 = 0

Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

Prove that the points (2a, 4a), (2a, 6a) and (2a+√3a,5a) are the vertices of an equilateral triangle.

In Fig. 8.65, BDC is a tangent to the given circle at point D such that BD=30 cm and CD=7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF (ii) radius of the circle.

If f(x)=cos(π2]x+cos(−π2]x, where [x] stands for the greatest integer function, then

The sum of the probabilities of all the elementary events of an experiment is

Find solution of the equation 2sin2θ=3cosθ

AB is a diameter of the circle and A, P, B, R are four points on the circle. The lines AP, RB intersect at Q. Find ∠BPR.

Question 1 (ii) In which of the following situations does the list of numbers involved make an arithmetic progression and why? (ii) The amount of air present in a cylinder when a vacuum pump removes 14 of the air remaining in the cylinder at a time.

The area of a right-angled triangle is 165 sq metres. Then, find its base and altitude if the latter exceeds the former by 7 meters?

What we can say about the nature of roots of x2–2x–3=0 ?

How many radii along with the enclosed arc form a sector of a circle?

A conical tent is used to accommodate 11 persons. Each person must have 4m2 of the space on the ground and 20 m3 of air to breathe. Find the height of cone.

If p times the pth term is equal to q times the qth term of an A.P. , show that the (p + q)th term is zero.

In the figure , O is the centre of a circle of radius 9 cm. Semicircle with diameter OA cuts the circle at D. If DP is perpendicular to OA and OA = 15 cm, then DP = _____ cm.

If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

The base edge of a square pyramid with slant height 24cm is 14cm. Then its lateral edge is:

5th term of an AP is 38 and 8th term is 59. What is the cd of the sequence? Which term of the sequence is 185?

If composite number is a product of prime numbers but 15 is a composite number 15=15*1 but if we factorised this then it is not a product of prime numbers.

90% acid solution (90% pure acid and 10% water) and 97% acid solution are mixed to obtain 21 litres of 95% acid solution. How many litres of each solution are mixed. Let x litres of 90% and y litres of 97% be mixed; then x + y = 21 and 90% of x + 97% of y = 95% of 21.

When to use substitution method,cross multiplication method and elimination method during ssolving a linear equation in two variable

Determine k so that k^2 + 4k + 8,2k^2 + 3k + 6,3k^2 + 4k + 4 are three consecutive terms of an A.P.

A polynomial of degree 1 is called a __ polynomial.

ABCD is a cyclic quadilateral whose diagonals intersect at a point E. If ∠DBC=70∘ and ∠BAC=30∘, find ∠BCD. Further if AB=BC, find ∠ECD.

The tangent at a point C of a circle and a diameter ab when extended intersect it p. If angle PCA = 110, find angle CBA

The Yin-Yang symbol can be explained with the following dimensions. What would be area covered by the Yin (black) region. The radius of the larger circle is, R=8 cm.

Solve: ax + by = a - b bx - ay = a + b

Tangents AP and AQ are drawn to a circle, with centre O, from an exterior point A. Prove that : ∠PAQ=2∠OPQ

Question 5 The first four terms of an AP whose first term is – 2 and the common difference is – 2 are A) – 2, 0, 2, 4 B) – 2, 4, –8, 16 C) – 2, – 4, – 6 , – 8 D) – 2, – 4, – 8, – 16

A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is

Viv invests Rs.4,500 in 8% Rs.10 shares at Rs.15. He sells the shares when the price rises to Rs.30 &amp; invests the proceeds in 12 % Rs.100 shares at Rs.125. Calculate the change in his annual income

The range of values of m for which the line y = mx + 2 cuts the circle x2+y2=1 at two distinct points, is .

In the adjoining figure 'O' is the center of circle, ∠CAO = 25∘ and ∠CBO = 35∘. What is the value of ∠AOB?

If b2 – 4ac = 0 then The roots of the Quadratic equation ax2 + bx + c = 0 are given by :

Solve the equation 5(+ 2) = 3. Give your answer correct to two decimal places.

If (3x - 9) : (5x + 4) is the triplicate ratio of 3: 4, find the value of x.

Find the values of p, q, r and s in the given cumulative frequency distribution. xfrequencyCumulative frequency103p=−−−−1510q=−−−−2025r=−−−−257s=−−−−30550

Three cubical blocks, each of volume 125 cm3, are joined end to end to form a cuboid. What is the total surface area of the cuboid so formed?

If x = √a tanα and y = √a secα. Find the value of y2 – x2 __

P and Q are points on the sides AB and AC respectively of a ΔABC. If AP = 2 cm, PB = 4 cm, AQ = 3 cm, and QC = 6 cm, show that BC = 3PQ.

In a right angled △ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of △ABD and △ BCD?

The Right to Education Act (RTE) provides free and compulsory education to every person of what age group?

Viv invests Rs.4,500 in 8% Rs.10 shares at Rs.15. He sells the shares when the price rises to Rs.30 & invests the proceeds in 12 % Rs.100 shares at Rs.125. Calculate the change in his annual income