32581 + Interview Questions in Mathematics Page 104 InterviewSolution

5151.	Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution: 3x+2y=11 2x−3y+10=0
Answer» Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution: $3 x + 2 y = 11$ $2 x - 3 y + 10 = 0$

5151.

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution: 3x+2y=11 2x−3y+10=0

Answer»

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution:

$3 x + 2 y = 11$

$2 x - 3 y + 10 = 0$

5152.	Choose the equation of the line with slope of 2 and meets the y-axis at (0,12).
Answer» Choose the equation of the line with slope of 2 and meets the y-axis at (0,12).

Discussion

5153.	Apurva deposited ₹200 per month for 36 months in a bank’s recurring deposit account. The bank pays interest rate of 11% per annum. Calculate the amount that she will receive on the maturity.
Answer» Apurva deposited ₹200 per month for 36 months in a bank’s recurring deposit account. The bank pays interest rate of 11% per annum. Calculate the amount that she will receive on the maturity.

Discussion

5154.	A bag contains lemon-flavoured candies only. Hema takes out one candy without lookking into the bag. What is the probability that she takes out (i) an orange - flavoured candy? (ii) a lemon - flavoured candy?
Answer» A bag contains lemon-flavoured candies only. Hema takes out one candy without lookking into the bag. What is the probability that she takes out (i) an orange - flavoured candy? (ii) a lemon - flavoured candy?

Discussion

5155.	Find the roots of the following quadratic equations, if they exist, by the method of completing the square:4x2+4√3x+3=0
Answer» Find the roots of the following quadratic equations, if they exist, by the method of completing the square: $4 x^{2} + 4 \sqrt{3} x + 3 = 0$

Discussion

5156.	ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. ∠ADP = ∠BEQ = 100∘. What is value of ∠PRD?
Answer» ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. $∠$ ADP = $∠$ BEQ = $100^{\circ}$ . What is value of $∠$ PRD?

5156.

ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. ∠ADP = ∠BEQ = 100∘. What is value of ∠PRD?

Answer»

ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. $∠$ ADP = $∠$ BEQ = $100^{\circ}$ . What is value of $∠$ PRD?

Discussion

5157.	The probability of it being a rainy day is 0.75, then the probability of it not being a rainy day is ___
Answer» The probability of it being a rainy day is 0.75, then the probability of it not being a rainy day is ___

Discussion

5158.	Two tangents are drawn onto a circle with centre O and radius r, from an external point P. These tangents touch the circle at points A and B respectively. The triangle ABP is definitely a ______________ .
Answer» Two tangents are drawn onto a circle with centre O and radius r, from an external point P. These tangents touch the circle at points A and B respectively. The triangle ABP is definitely a ______________ .

Discussion

5159.	Capacity of an isolated sphere is increased n times when it is enclosed by earthed concentric sphere. Find the ratio of their radii.
Answer» Capacity of an isolated sphere is increased n times when it is enclosed by earthed concentric sphere. Find the ratio of their radii.

Discussion

5160.	Let a,b and c be the sides opposite to angles A, B and C in a triangle ABC. If sinA(sinA+cosB−sinB)+cosA(cosA+sinB+cosB)=1+sinC and a=4,b=3, then area (in sq. units) of the triangle ABC is
Answer» Let $a, b$ and $c$ be the sides opposite to angles $A,$ $B$ and $C$ in a triangle $A B C .$ If $sin A (sin A + cos B - sin B) + cos A (cos A + sin B + cos B) = 1 + sin C$ and $a = 4, b = 3,$ then area (in sq. units) of the triangle $A B C$ is

Discussion

5161.	Find the volume of a structure of dimensions 10×10×10.
Answer» Find the volume of a structure of dimensions $10 \times 10 \times 10$ .

Discussion

5162.	Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
Answer» Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .

Discussion

5163.	A bucket of height 24 cm is in the form of frustum of a cone whose circular ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of ₹30 per litre, which the bucket can hold. [CBSE 2013C]
Answer» A bucket of height 24 cm is in the form of frustum of a cone whose circular ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of ₹30 per litre, which the bucket can hold. [CBSE 2013C]

Discussion

5164.	D is any point on the side AC of ΔABC with AB = AC. Show that CD < BD.
Answer» D is any point on the side AC of ΔABC with AB = AC. Show that CD < BD.

Discussion

5165.	The angles of depression of the top and bottom of a 8 m tall building from the top of a tower are 30° and 45° respectively. Find the height of the tower and the distance between the tower and the building.
Answer» The angles of depression of the top and bottom of a 8 m tall building from the top of a tower are 30° and 45° respectively. Find the height of the tower and the distance between the tower and the building.

Discussion

5166.	The difference between the sides of right angles in a right angles triangle is 14 cm .The area of the triangle is 120 cm sq . Calculate the perimeter of the triangle
Answer» The difference between the sides of right angles in a right angles triangle is 14 cm .The area of the triangle is 120 cm sq . Calculate the perimeter of the triangle

Discussion

5167.	Arrange the fractions in ascending order.
Answer» Arrange the fractions in ascending order.

Discussion

5168.	A boy is excited about his approaching birthday. He collects 1 leaf on the first day of the month, 2 leaves on the second day and 3 leaves on the third day of the month and so on. On his birthday, he finds that he has collected 210 leaves in all. On which day of the month is his birthday?
Answer» A boy is excited about his approaching birthday. He collects 1 leaf on the first day of the month, 2 leaves on the second day and 3 leaves on the third day of the month and so on. On his birthday, he finds that he has collected 210 leaves in all. On which day of the month is his birthday?

Discussion

5169.	The monthly pocket money of Ravi and Sanjeev are in the ratio 5: 7. Their expenditures are in the ratio 3: 5. If each saves Rs. 80 every month, find their monthly pocket money.
Answer» The monthly pocket money of Ravi and Sanjeev are in the ratio 5: 7. Their expenditures are in the ratio 3: 5. If each saves Rs. 80 every month, find their monthly pocket money.

Discussion

5170.	A coin is tossed three times, where E is the event of atmost two tails, F is the event of atleast one tail. Then the value of P(E/F) is:
Answer» A coin is tossed three times, where $E$ is the event of atmost two tails, $F$ is the event of atleast one tail. Then the value of $P (E / F)$ is:

Discussion

5171.	Two chords AB and AC of a circle with centre O are on the opposite sides of OA. If angle AOB = angle AOC , then prove that AB=AC and angle OAB = angle OAC.
Answer» Two chords AB and AC of a circle with centre O are on the opposite sides of OA. If angle AOB = angle AOC , then prove that AB=AC and angle OAB = angle OAC.

Discussion

5172.	\lbrack Pt(en)3\rbrack x \lbrack PtCl4\rbrack y possible value of x + y in complex will be :-
Answer» \lbrack Pt(en)3\rbrack x \lbrack PtCl4\rbrack y possible value of x + y in complex will be :-

Discussion

5173.	What is the maximum number of solutions that a pair of linear equations can have?
Answer» What is the maximum number of solutions that a pair of linear equations can have?

Discussion

5174.	Find the area of the major segment APB of a circle of radius 35 cm and ∠AOB = 90°, as shown in the given figure.
Answer» Find the area of the major segment APB of a circle of radius 35 cm and ∠AOB = 90°, as shown in the given figure.

Discussion

5175.	Show that the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Answer» Show that the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Discussion

5176.	A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number.
Answer» A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number.

Discussion

5177.	In the given figure, radius of the circle is 7 cm and m ( arc MBN) = 60°,find (1) Area of the circle . (2) A(O - MBN) . (3) A(O - MCN) .
Answer» In the given figure, radius of the circle is 7 cm and m ( arc MBN) = 60^°, find (1) Area of the circle . (2) A(O - MBN) . (3) A(O - MCN) .

Discussion

5178.	In a rectangle ABCD, P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively and T is the point on RS such that RT = 2TS. If the area of ABCD is 'k' times the area of ∆PQT then 'k' is
Answer» In a rectangle ABCD, P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively and T is the point on RS such that RT = 2TS. If the area of ABCD is 'k' times the area of ∆PQT then 'k' is

Discussion

5179.	A tower is vertically place on a horizontal plane.If angle of elevation of sun is 30^° and length of shadow of tower is 45m,then find height of the tower
Answer» A tower is vertically place on a horizontal plane.If angle of elevation of sun is 30^° and length of shadow of tower is 45m,then find height of the tower

Discussion

5180.	62.If the points A(2, 3), B(4, 5) and C(x, y) are collinear,then(1)x+y+1=0(3) x -y+ 10(2) x + 2y 10(4) 3x + 2y 0
Answer» 62.If the points A(2, 3), B(4, 5) and C(x, y) are collinear,then(1)x+y+1=0(3) x -y+ 10(2) x + 2y 10(4) 3x + 2y 0

Discussion

5181.	Question 9 (iv)Solve the following pairs of equation12x−1y=−1, 1x+12y=8,x,y ≠0
Answer» Question 9 (iv) Solve the following pairs of equation $\frac{1}{2 x} - \frac{1}{y} = - 1, \frac{1}{x} + \frac{1}{2 y} = 8, x, y \neq 0$

Discussion

5182.	In the given figure, there are two concentric circles with centre O. PR and PQS are tangents to the inner circle from point plying on the outer circle. If PR = 7.5 cm, then PS is equal to(a) 10 cm(b) 12 cm(c) 15 cm(d) 18 cm
Answer» In the given figure, there are two concentric circles with centre O. PR and PQS are tangents to the inner circle from point plying on the outer circle. If PR = 7.5 cm, then PS is equal to (a) 10 cm (b) 12 cm (c) 15 cm (d) 18 cm

Discussion

5183.	The algebraic forms of some sequence are given below. Check whether each of them is an arithmetic sequence or not; also find out the first term and the common difference of the arithmetic sequence(i) xn = 4 − 3n(ii) xn = n2 + 2(iii) (iv) (v) xn = (n + 1)2 − (n − 1)2
Answer» The algebraic forms of some sequence are given below. Check whether each of them is an arithmetic sequence or not; also find out the first term and the common difference of the arithmetic sequence (i) x_n = 4 − 3n (ii) x_n = n² + 2 (iii) (iv) (v) x_n = (n + 1)² − (n − 1)²

5183.

The algebraic forms of some sequence are given below. Check whether each of them is an arithmetic sequence or not; also find out the first term and the common difference of the arithmetic sequence(i) xn = 4 − 3n(ii) xn = n2 + 2(iii) (iv) (v) xn = (n + 1)2 − (n − 1)2

Answer»

The algebraic forms of some sequence are given below. Check whether each of them is an arithmetic sequence or not; also find out the first term and the common difference of the arithmetic sequence

(i) x_n = 4 − 3n

(ii) x_n = n² + 2

(iii)

(iv)

(v) x_n = (n + 1)² − (n − 1)²

Discussion

5184.	A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?
Answer» A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?

Discussion

5185.	Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.
Answer» Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.

Discussion

5186.	Find the next number in the sequence 1,2,6,42,__
Answer» Find the next number in the sequence 1,2,6,42,__

Discussion

5187.	Solve the following inequation:−15≤3x10+1<25 [4 MARKS]
Answer» Solve the following inequation: $- \frac{1}{5} \leq \frac{3 x}{10} + 1 < \frac{2}{5}$ [4 MARKS]

Discussion

5188.	In a triangle, r1=2r2=3r3 then ab+bc+ca is equal to:
Answer» In a triangle, $r_{1} = 2 r_{2} = 3 r_{3}$ then $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ is equal to:

Discussion

5189.	The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be(a) 3 or −9(b) −3 or 9(c) 6 or 27(d) −6 or −27
Answer» The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be (a) 3 or −9 (b) −3 or 9 (c) 6 or 27 (d) −6 or −27

Discussion

5190.	A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of 30∘ to the ground. What should be the length of the slide?
Answer» A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of $30^{\circ}$ to the ground. What should be the length of the slide?

Discussion

5191.	A box contain 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ___________.
Answer» A box contain 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ___________.

Discussion

5192.	The number which should be added to x2+6x+5 so that the resulting polynomial is completely divisible by x+3 _______. 4
Answer» The number which should be added to $x^{2} + 6 x + 5$ so that the resulting polynomial is completely divisible by $x + 3$ _______. 4

Discussion

5193.	19. Find the values of a and b so that the polynomial (x + ax - 7x + 8x + b) is exactly divisible by (x+2) as well as (x+3).
Answer» 19. Find the values of a and b so that the polynomial (x + ax - 7x + 8x + b) is exactly divisible by (x+2) as well as (x+3).

Discussion

5194.	Assertion-and-Reason Type Each question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code: (a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. Assertion (A)Reason (R)Consider the following frequencyThe value of the variable whichdistribution:occurs most often is the modeClass interval3−66−99−1212−1515−1818−21Frequency2521231012The mode of the above data is 12.4. The correct answer is:(a)/(b)/(c)/(d).
Answer» Assertion-and-Reason Type Each question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code: (a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. $\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) C o n s i d e r t h e f o l l o w i n g f r e q u e n c y & T h e v a l u e o f t h e v a r i a b l e w h i c h d i s t r i b u t i o n : & o c c u r s m o s t o f t e n i s t h e m o d e \begin{matrix} C l a s s i n t e r v a l & 3 - 6 & 6 - 9 & 9 - 12 & 12 - 15 & 15 - 18 & 18 - 21 F r e q u e n c y & 2 & 5 & 21 & 23 & 10 & 12 \end{matrix} T h e m o d e o f t h e a b o v e d a t a i s 12.4. \end{matrix}$ The correct answer is:(a)/(b)/(c)/(d).

5194.

Assertion-and-Reason Type Each question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code: (a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. Assertion (A)Reason (R)Consider the following frequencyThe value of the variable whichdistribution:occurs most often is the modeClass interval3−66−99−1212−1515−1818−21Frequency2521231012The mode of the above data is 12.4. The correct answer is:(a)/(b)/(c)/(d).

Answer»

Assertion-and-Reason Type

Each question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) C o n s i d e r t h e f o l l o w i n g f r e q u e n c y & T h e v a l u e o f t h e v a r i a b l e w h i c h d i s t r i b u t i o n : & o c c u r s m o s t o f t e n i s t h e m o d e \begin{matrix} C l a s s i n t e r v a l & 3 - 6 & 6 - 9 & 9 - 12 & 12 - 15 & 15 - 18 & 18 - 21 F r e q u e n c y & 2 & 5 & 21 & 23 & 10 & 12 \end{matrix} T h e m o d e o f t h e a b o v e d a t a i s 12.4. \end{matrix}$

The correct answer is:(a)/(b)/(c)/(d).

Discussion

5195.	Using trigonometric tables, find the value of cos(85.2)∘.
Answer» Using trigonometric tables, find the value of $c o s (85.2)^{\circ}$ .

Discussion

5196.	If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution then the values of k are __________________.
Answer» If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution then the values of k are __________________.

Discussion

5197.	In the given right angle triangle if AC = 10 cm and θ = 30∘. The vertical height of given triangle is ___ cm.
Answer» In the given right angle triangle if AC = 10 cm and $θ$ = $30^{\circ}$ . The vertical height of given triangle is ___ cm.

5197.

In the given right angle triangle if AC = 10 cm and θ = 30∘. The vertical height of given triangle is ___ cm.

Answer»

In the given right angle triangle if AC = 10 cm and $θ$ = $30^{\circ}$ . The vertical height of given triangle is ___ cm.

Discussion

5198.	From a point Q, 13 cm away from the centre of a circle, the length of tangent PQ to the circle is 12 cm. The radius of the circle (in cm) is(a) 25(b) 313(c) 5(d) 1
Answer» From a point Q, 13 cm away from the centre of a circle, the length of tangent PQ to the circle is 12 cm. The radius of the circle (in cm) is (a) 25 (b) $\sqrt{313}$ (c) 5 (d) 1

Discussion

5199.	Question 1Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8cm is a tangent to the inner circle,. Find the radius of the inner circle.
Answer» Question 1 Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8cm is a tangent to the inner circle,. Find the radius of the inner circle.

Discussion

5200.	If one zero of the quadratic polynomial x2 + 3x + k is 2 , then the value of k is (a) 10 (b)-10 (c) 5 (d)-5
Answer» If one zero of the quadratic polynomial x² + 3x + k is 2 , then the value of k is (a) 10 (b) $-$ 10 (c) 5 (d) $-$ 5

Discussion

Explore topic-wise InterviewSolutions in .

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution: 3x+2y=11 2x−3y+10=0

Choose the equation of the line with slope of 2 and meets the y-axis at (0,12).

Apurva deposited ₹200 per month for 36 months in a bank’s recurring deposit account. The bank pays interest rate of 11% per annum. Calculate the amount that she will receive on the maturity.

A bag contains lemon-flavoured candies only. Hema takes out one candy without lookking into the bag. What is the probability that she takes out (i) an orange - flavoured candy? (ii) a lemon - flavoured candy?

Find the roots of the following quadratic equations, if they exist, by the method of completing the square:4x2+4√3x+3=0

ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. ∠ADP = ∠BEQ = 100∘. What is value of ∠PRD?

The probability of it being a rainy day is 0.75, then the probability of it not being a rainy day is ___

Two tangents are drawn onto a circle with centre O and radius r, from an external point P. These tangents touch the circle at points A and B respectively. The triangle ABP is definitely a ______________ .

Capacity of an isolated sphere is increased n times when it is enclosed by earthed concentric sphere. Find the ratio of their radii.

Let a,b and c be the sides opposite to angles A, B and C in a triangle ABC. If sinA(sinA+cosB−sinB)+cosA(cosA+sinB+cosB)=1+sinC and a=4,b=3, then area (in sq. units) of the triangle ABC is

Find the volume of a structure of dimensions 10×10×10.

Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .

A bucket of height 24 cm is in the form of frustum of a cone whose circular ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of ₹30 per litre, which the bucket can hold. [CBSE 2013C]

D is any point on the side AC of ΔABC with AB = AC. Show that CD < BD.

The angles of depression of the top and bottom of a 8 m tall building from the top of a tower are 30° and 45° respectively. Find the height of the tower and the distance between the tower and the building.

The difference between the sides of right angles in a right angles triangle is 14 cm .The area of the triangle is 120 cm sq . Calculate the perimeter of the triangle

Arrange the fractions in ascending order.

A boy is excited about his approaching birthday. He collects 1 leaf on the first day of the month, 2 leaves on the second day and 3 leaves on the third day of the month and so on. On his birthday, he finds that he has collected 210 leaves in all. On which day of the month is his birthday?

The monthly pocket money of Ravi and Sanjeev are in the ratio 5: 7. Their expenditures are in the ratio 3: 5. If each saves Rs. 80 every month, find their monthly pocket money.

A coin is tossed three times, where E is the event of atmost two tails, F is the event of atleast one tail. Then the value of P(E/F) is:

Two chords AB and AC of a circle with centre O are on the opposite sides of OA. If angle AOB = angle AOC , then prove that AB=AC and angle OAB = angle OAC.

\lbrack Pt(en)3\rbrack x \lbrack PtCl4\rbrack y possible value of x + y in complex will be :-

What is the maximum number of solutions that a pair of linear equations can have?

Find the area of the major segment APB of a circle of radius 35 cm and ∠AOB = 90°, as shown in the given figure.

Show that the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number.

In the given figure, radius of the circle is 7 cm and m ( arc MBN) = 60°,find (1) Area of the circle . (2) A(O - MBN) . (3) A(O - MCN) .

In a rectangle ABCD, P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively and T is the point on RS such that RT = 2TS. If the area of ABCD is 'k' times the area of ∆PQT then 'k' is

A tower is vertically place on a horizontal plane.If angle of elevation of sun is 30^° and length of shadow of tower is 45m,then find height of the tower

62.If the points A(2, 3), B(4, 5) and C(x, y) are collinear,then(1)x+y+1=0(3) x -y+ 10(2) x + 2y 10(4) 3x + 2y 0

Question 9 (iv)Solve the following pairs of equation12x−1y=−1, 1x+12y=8,x,y ≠0

In the given figure, there are two concentric circles with centre O. PR and PQS are tangents to the inner circle from point plying on the outer circle. If PR = 7.5 cm, then PS is equal to(a) 10 cm(b) 12 cm(c) 15 cm(d) 18 cm

The algebraic forms of some sequence are given below. Check whether each of them is an arithmetic sequence or not; also find out the first term and the common difference of the arithmetic sequence(i) xn = 4 − 3n(ii) xn = n2 + 2(iii) (iv) (v) xn = (n + 1)2 − (n − 1)2

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?

Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.

Find the next number in the sequence 1,2,6,42,__

Solve the following inequation:−15≤3x10+1&lt;25 [4 MARKS]

In a triangle, r1=2r2=3r3 then ab+bc+ca is equal to:

The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be(a) 3 or −9(b) −3 or 9(c) 6 or 27(d) −6 or −27

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of 30∘ to the ground. What should be the length of the slide?

A box contain 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ___________.

The number which should be added to x2+6x+5 so that the resulting polynomial is completely divisible by x+3 _______. 4

19. Find the values of a and b so that the polynomial (x + ax - 7x + 8x + b) is exactly divisible by (x+2) as well as (x+3).

Using trigonometric tables, find the value of cos(85.2)∘.

If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution then the values of k are __________________.

In the given right angle triangle if AC = 10 cm and θ = 30∘. The vertical height of given triangle is ___ cm.

From a point Q, 13 cm away from the centre of a circle, the length of tangent PQ to the circle is 12 cm. The radius of the circle (in cm) is(a) 25(b) 313(c) 5(d) 1

Question 1Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8cm is a tangent to the inner circle,. Find the radius of the inner circle.

If one zero of the quadratic polynomial x2 + 3x + k is 2 , then the value of k is (a) 10 (b)-10 (c) 5 (d)-5

Solve the following inequation:−15≤3x10+1<25 [4 MARKS]