24740 + Interview Questions in Mathematics Page 150 InterviewSolution

7451.	39. Find the value of p when the distance between the points A(3,p) and B(4,1) is 10 ??
Answer» 39. Find the value of p when the distance between the points A(3,p) and B(4,1) is 10 ??

Discussion

7452.	is a terminating decimal.
Answer» is a terminating decimal.

Discussion

7453.	The perimeter of an isosceles triangle is 42 cm and its base is 32 times each of the equal sides. Find the length of each side and area of the triangle.
Answer» The perimeter of an isosceles triangle is 42 cm and its base is $(\frac{3}{2})$ times each of the equal sides. Find the length of each side and area of the triangle.

Discussion

7454.	Question 2If the lengths of the diagonals of a rhombus are 16cm and 12cm. Then the length of the sides of the rhombus is(A) 9 cm(B) 10 cm(C) 8 cm(D) 20 cm
Answer» Question 2 If the lengths of the diagonals of a rhombus are 16cm and 12cm. Then the length of the sides of the rhombus is (A) 9 cm (B) 10 cm (C) 8 cm (D) 20 cm

Discussion

7455.	In the given figure, line AB meets y-axis at point A. Line through C(2, 10) and D intersects line AB at right angle at point P. Find :(i) equation of line AB.(ii) equation of line CD.(iii) co-ordinates of points E and D.
Answer» In the given figure, line AB meets y-axis at point A. Line through C(2, 10) and D intersects line AB at right angle at point P. Find : (i) equation of line AB. (ii) equation of line CD. (iii) co-ordinates of points E and D.

7455.

In the given figure, line AB meets y-axis at point A. Line through C(2, 10) and D intersects line AB at right angle at point P. Find :(i) equation of line AB.(ii) equation of line CD.(iii) co-ordinates of points E and D.

Answer»

In the given figure, line AB meets y-axis at point A. Line through C(2, 10) and D intersects line AB at right angle at point P. Find :

(i) equation of line AB.

(ii) equation of line CD.

(iii) co-ordinates of points E and D.

Discussion

7456.	In the given figure, ar(DRC)=ar(DPC) and ar(BDP)=ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums [4 MARKS]
Answer» In the given figure, ar(DRC)=ar(DPC) and ar(BDP)=ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums [4 MARKS]

Discussion

7457.	Question 5Find a point which is equidistant from the points A(-5,4) and B(-1,6). How many such points are there?
Answer» Question 5 Find a point which is equidistant from the points A(-5,4) and B(-1,6). How many such points are there?

Discussion

7458.	Question 7 The dimensions of a rectangle ABCD are 51cm x 25 cm. A trapezium PQCD with its parallel sides QC and PD in the ratio 9:8, is cut off from the rectangle as shown in the figure. If the area of the trapezium PQCD is 56 th part of the area of the rectangle. Find the lengths QC and PD.
Answer» Question 7 The dimensions of a rectangle ABCD are 51cm x 25 cm. A trapezium PQCD with its parallel sides QC and PD in the ratio 9:8, is cut off from the rectangle as shown in the figure. If the area of the trapezium PQCD is $\frac{5}{6}$ th part of the area of the rectangle. Find the lengths QC and PD.

Discussion

7459.	If x=3+2√2, then the value of (√x−1√x) = _____. 2
Answer» If $x = 3 + 2 \sqrt{2}$ , then the value of $(\sqrt{x} - \frac{1}{\sqrt{x}})$ = _____. 2

Discussion

7460.	If A=[2−3−41], then adj(3A2+12A) is equal to:
Answer» If $A = [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}],$ then adj $(3 A^{2} + 12 A)$ is equal to:

Discussion

7461.	On 31st March, 2017, Pass Book showed a balance of ₹ 25,000. Prepare a Bank Reconciliation Statement from the following particulars:(i) Cheques of ₹ 20,000 were deposited in Bank on 27th March, 2017, out of which cheques of ₹ 5,000 were cleared on 1st April, 2017. Rest are not cleared.(ii) On 28th March, 2017, cheques were issued amounting to ₹ 15,000, out of which cheques of ₹ 3,000 were presented in March, ₹ 4,000 on 2nd April and rest were not presented.(iii) Cheques of ₹ 10,000 were deposited in Bank on 28th March, 2017, out of which cheques of ₹ 4,000 were cleared on 2nd April, 2017 and rest are dishonoured.(iv) Interest on investment collected by bank does not appear in the Cash Book ₹ 800.(v) A B/R of ₹ 9,000 previously discounted from the bank was dishonoured on 30th March, 2017 but no intimation was received from the bank till 31st March.(vi) Bank has debited ₹ 1,500 and credited ₹ 1,200 in our account.
Answer» On 31st March, 2017, Pass Book showed a balance of ₹ 25,000. Prepare a Bank Reconciliation Statement from the following particulars: (i) Cheques of ₹ 20,000 were deposited in Bank on 27th March, 2017, out of which cheques of ₹ 5,000 were cleared on 1st April, 2017. Rest are not cleared. (ii) On 28th March, 2017, cheques were issued amounting to ₹ 15,000, out of which cheques of ₹ 3,000 were presented in March, ₹ 4,000 on 2nd April and rest were not presented. (iii) Cheques of ₹ 10,000 were deposited in Bank on 28th March, 2017, out of which cheques of ₹ 4,000 were cleared on 2nd April, 2017 and rest are dishonoured. (iv) Interest on investment collected by bank does not appear in the Cash Book ₹ 800. (v) A B/R of ₹ 9,000 previously discounted from the bank was dishonoured on 30th March, 2017 but no intimation was received from the bank till 31st March. (vi) Bank has debited ₹ 1,500 and credited ₹ 1,200 in our account.

Discussion

7462.	Find the area in cm2 of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]
Answer» Find the area in $c m^{2}$ of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]

7462.

Find the area in cm2 of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]

Answer»

Find the area in $c m^{2}$ of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]

Discussion

7463.	Plot the graph of 0 (ZERO) Polynomial by constructing a equation and explaining it.
Answer» Plot the graph of 0 (ZERO) Polynomial by constructing a equation and explaining it.

Discussion

7464.	Rectify the following errors found in the books of Mr. B. Trial Balance had ₹ 930 excess credit. The difference has been posted to a Suspense Account:(i) The total of Returns Inward Book has been cast ₹ 1,000 short.(ii) The purchase of an office table costing ₹ 3,000 has been passed through Purchases Book.(iii) ₹ 3,750 paid for wages to workmen for making showcases had been charged to the Wages Account.(iv) A purchases of ₹ 670 had been posted to the Creditors' Account as ₹ 600.(v) A cheque for ₹ 2,000 received from Mr. P.C. Joshi had been dishonoured and was passed to the debit of the Allowances Account.(vi) An amount of ₹ 15,720 due from Prasad written off as had in a previous year, was recovered and credited to the Personal Account of Prasad.After rectification reflect the transactions in the Suspense Account.
Answer» Rectify the following errors found in the books of Mr. B. Trial Balance had ₹ 930 excess credit. The difference has been posted to a Suspense Account: (i) The total of Returns Inward Book has been cast ₹ 1,000 short. (ii) The purchase of an office table costing ₹ 3,000 has been passed through Purchases Book. (iii) ₹ 3,750 paid for wages to workmen for making showcases had been charged to the Wages Account. (iv) A purchases of ₹ 670 had been posted to the Creditors' Account as ₹ 600. (v) A cheque for ₹ 2,000 received from Mr. P.C. Joshi had been dishonoured and was passed to the debit of the Allowances Account. (vi) An amount of ₹ 15,720 due from Prasad written off as had in a previous year, was recovered and credited to the Personal Account of Prasad. After rectification reflect the transactions in the Suspense Account.

Discussion

7465.	Question 2Find six rational numbers between 3 and 4.
Answer» Question 2 Find six rational numbers between 3 and 4.

Discussion

7466.	is the factorization of (xy+x+4y+4).
Answer» is the factorization of $(x y + x + 4 y + 4)$ .

Discussion

7467.	Ifx=213+223,Show that x3−6x=6.
Answer» If $x = 2^{\frac{1}{3}} + 2^{\frac{2}{3}}, S h o w t h a t x^{3} - 6 x = 6.$

Discussion

7468.	A vertical stick 10cm long casts a shadow 8cm long. At the same time, a tower casts a shadow 30m long. Determine the height of the tower?
Answer» A vertical stick 10cm long casts a shadow 8cm long. At the same time, a tower casts a shadow 30m long. Determine the height of the tower?

Discussion

7469.	Mean of 100 observations is found to be 40. At the time of computation two items were wrongly taken as 30 and 27 instead of 3 and 72. Find the correct mean.
Answer» Mean of 100 observations is found to be 40. At the time of computation two items were wrongly taken as 30 and 27 instead of 3 and 72. Find the correct mean.

Discussion

7470.

Sonam keeps his books on single entry and provides you with the following information: 31-12-2017 31-12-2018 ₹ ₹ Furniture and Fitting 50,000 60,000 Stock 30,000 10,000 Sundry Debtors 60,000 70,000 Sundry Creditors 20,000 NIL Prepaid Expenses NIL 2,000 Outstanding Expenses 6,000 10,000 Cash in hand 11,000 3,000 Receipts and Payments in 2018: Receipts from Debtors 2,10,000 Paid to Creditors 1,00,000 Cartage 20,000 Drawings 1,20,000 Sundry Expenses 1,60,000 Furniture Purchased for Cash 10,000 Prepare Trading and Profit & Loss Account for the year ended 31 December, 2018 after providing for bad debts at 10%.There was a considerable amount of Cash Sales.

Answer» Sonam keeps his books on single entry and provides you with the following information:

	31-12-2017	31-12-2018
	₹	₹
Furniture and Fitting	50,000	60,000
Stock	30,000	10,000
Sundry Debtors	60,000	70,000
Sundry Creditors	20,000	NIL
Prepaid Expenses	NIL	2,000
Outstanding Expenses	6,000	10,000
Cash in hand	11,000	3,000
Receipts and Payments in 2018:
Receipts from Debtors		2,10,000
Paid to Creditors		1,00,000
Cartage		20,000
Drawings		1,20,000
Sundry Expenses		1,60,000
Furniture Purchased for Cash		10,000

Prepare Trading and Profit & Loss Account for the year ended 31 December, 2018 after providing for bad debts at 10%.

There was a considerable amount of Cash Sales.

Discussion

7471.	Are non parallel sides of a trepizium are always equal
Answer» Are non parallel sides of a trepizium are always equal

Discussion

7472.	How many litres of water flows out of a pipe having an area of cross section of 5cm2 in 1 minute, if the speed of water in the pipe is 30 cm/sec ?
Answer» How many litres of water flows out of a pipe having an area of cross section of $5 c m^{2}$ in 1 minute, if the speed of water in the pipe is 30 cm/sec ?

Discussion

7473.	Find the value of P if the pair of L.E is coincident. x−2y=−2 and Px−8y=−84
Answer» Find the value of P if the pair of L.E is coincident. $x - 2 y = - 2 a n d P x - 8 y = - 8$ 4

Discussion

7474.	The number of points on x-axis which are at a distance of 25 from the point (7, –4), is __________.
Answer» The number of points on x-axis which are at a distance of $2 \sqrt{5}$ from the point (7, –4), is __________.

Discussion

7475.	The volume of river of width 10 m and depth 6m flowing at a speed of 2 km per hr in 1 min is .
Answer» The volume of river of width 10 m and depth 6m flowing at a speed of 2 km per hr in 1 min is .

Discussion

7476.	7.The sixth HM between 3 and 6/13
Answer» 7.The sixth HM between 3 and 6/13

Discussion

7477.	If B is the mid-point of ¯¯¯¯¯¯¯¯AC and C is the mid-point of ¯¯¯¯¯¯¯¯¯BD, where A, B, C, D lie on a straight line, say why AB = CD?
Answer» If B is the mid-point of $¯ ¯¯¯¯¯¯ ¯ A C$ and C is the mid-point of $¯ ¯¯¯¯¯¯¯ ¯ B D$ , where A, B, C, D lie on a straight line, say why AB = CD?

Discussion

7478.	For three points, X, Y and Z, to be collinear, which of these conditions should be true? Select all that apply.
Answer» For three points, X, Y and Z, to be collinear, which of these conditions should be true? Select all that apply.

Discussion

7479.	In the given figure, if then prove that AOB is a line.
Answer» In the given figure, if then prove that AOB is a line.

7479.

In the given figure, if then prove that AOB is a line.

Answer»

In the given figure, if then prove that AOB is a line.

Discussion

7480.	If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
Answer» If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Discussion

7481.	The lateral or vertical surface area of a cuboidal box of length, breadth and height 6 cm, 8 cm and 6.5 cm respectively is
Answer» The lateral or vertical surface area of a cuboidal box of length, breadth and height 6 cm, 8 cm and 6.5 cm respectively is

Discussion

7482.	The value of 2(\sqrt2 +\sqrt5)/(3\sqrt{2+\sqrt3})+\sqrt{2+\sqrt3}+\sqrt{2-\sqrt3
Answer» The value of 2(\sqrt2 +\sqrt5)/(3\sqrt{2+\sqrt3})+\sqrt{2+\sqrt3}+\sqrt{2-\sqrt3

Discussion

7483.	PQRS is a quadrilateral in which diagonals PR and QS intersect at O. Prove that PQ + QR + RS + SP < 2 (PR + QS).
Answer» PQRS is a quadrilateral in which diagonals PR and QS intersect at O. Prove that PQ + QR + RS + SP < 2 (PR + QS).

Discussion

7484.	In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ΔAPQ is 116 of the area of ΔABC.
Answer» In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of $Δ A P Q$ is $\frac{1}{16}$ of the area of $Δ A B C$ .

7484.

In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ΔAPQ is 116 of the area of ΔABC.

Answer»

In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of $Δ A P Q$ is $\frac{1}{16}$ of the area of $Δ A B C$ .

Discussion

7485.	(√a−√b)×(√a+√b)=
Answer» $(\sqrt{a} - \sqrt{b}) \times (\sqrt{a} + \sqrt{b}) =$

Discussion

7486.	Scientists are supposed to be rational people. Superstitious thoughts go against the principles of rationalism. Therefore scientists are not superstitious. However, there are certain scientists who believe in superstitious thoughts.Such scientists are the single largest obstacle in inculcating a scientific temper in the minds of the people. Why is the author against superstitious scientists?
Answer» Scientists are supposed to be rational people. Superstitious thoughts go against the principles of rationalism. Therefore scientists are not superstitious. However, there are certain scientists who believe in superstitious thoughts.Such scientists are the single largest obstacle in inculcating a scientific temper in the minds of the people. Why is the author against superstitious scientists?

7486.

Scientists are supposed to be rational people. Superstitious thoughts go against the principles of rationalism. Therefore scientists are not superstitious. However, there are certain scientists who believe in superstitious thoughts.Such scientists are the single largest obstacle in inculcating a scientific temper in the minds of the people. Why is the author against superstitious scientists?

Answer»

Scientists are supposed to be rational people. Superstitious thoughts go against the principles of rationalism. Therefore scientists are not superstitious.

However, there are certain scientists who believe in superstitious thoughts.Such scientists are the single largest obstacle in inculcating a scientific temper in the minds of the people.

Why is the author against superstitious scientists?

Discussion

7487.	Factorize 32a3+108b3
Answer» Factorize $32 a^{3} + 108 b^{3}$

Discussion

7488.	Construct a triangle ABC in which BC equal to 7 cm, Angle B equal to 75 degree and AB+AC equal to 13 cm.
Answer» Construct a triangle $A B C$ in which $B C$ equal to $7 c m$ , Angle $B$ equal to $75$ degree and $A B + A C$ equal to $13 c m$ .

Discussion

7489.	A coin is tossed 500 times with the following frequencies of two outcomes:head = 245 timestail = 255 timesWhat is the probability of getting a head in the next throw?
Answer» A coin is tossed 500 times with the following frequencies of two outcomes: head = 245 times tail = 255 times What is the probability of getting a head in the next throw?

Discussion

7490.	Q: If x= 2-√3, then the value of x^2-1/x^2 ?
Answer» Q: If x= 2-√3, then the value of x^2-1/x^2 ?

Discussion

7491.	If 0.75 : x :: 5 : 8, then x = _______
Answer» If 0.75 : x :: 5 : 8, then x = _______

Discussion

7492.	In the figure, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = BC.
Answer» In the figure, O is the centre of the circle, BO is the bisector of $∠ A B C$ . Show that AB = BC.

7492.

In the figure, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = BC.

Answer»

In the figure, O is the centre of the circle, BO is the bisector of $∠ A B C$ . Show that AB = BC.

Discussion

7493.	39. Two circles intersect each other in points X&Y. Secants through X&Y intersect one of the circles in A&D and the other in B&C respectively.A&B are on the opposite side of line DC.Show that line AD is parallel to line BC.
Answer» 39. Two circles intersect each other in points X&Y. Secants through X&Y intersect one of the circles in A&D and the other in B&C respectively.A&B are on the opposite side of line DC.Show that line AD is parallel to line BC.

Discussion

7494.	What is the mean/average of factors of 20 ?
Answer» What is the mean/average of factors of 20 ?

Discussion

7495.	If x= 2(θ +sin θ) and y = 2(1-cosθ) then find dy /dx
Answer» If x= 2(θ +sin θ) and y = 2(1-cosθ) then find dy /dx

Discussion

7496.	Consider the below figure where the diameter AB bisects the chord PQ at the point R. If BR = 4 cm, then what is the radius of the circle?10
Answer» Consider the below figure where the diameter AB bisects the chord PQ at the point R. If BR = 4 cm, then what is the radius of the circle? 10

Discussion

7497.	If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S then PQRS is a (a) rectangle (b) parallelogram (c) rhombus (d) quadrilateral whose opposite angles are supplementary
Answer» If bisectors of $∠ A a n d ∠ B$ of a quadrilateral ABCD intersect each other at P, of $∠ B a n d ∠ C$ at Q, of $∠ C a n d ∠ D$ at R and of $∠ D a n d ∠ A$ at S then PQRS is a (a) rectangle (b) parallelogram (c) rhombus (d) quadrilateral whose opposite angles are supplementary

7497.

If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S then PQRS is a (a) rectangle (b) parallelogram (c) rhombus (d) quadrilateral whose opposite angles are supplementary

Answer»

If bisectors of $∠ A a n d ∠ B$ of a quadrilateral ABCD intersect each other at P, of $∠ B a n d ∠ C$ at Q, of $∠ C a n d ∠ D$ at R and of $∠ D a n d ∠ A$ at S then PQRS is a

(a) rectangle

(b) parallelogram

(c) rhombus

(d) quadrilateral whose opposite angles are supplementary

Discussion

7498.	When are three or more points said to be collinear?
Answer» When are three or more points said to be collinear?

Discussion

7499.	Two cylindrical jars have their diameters in the ratio 3:1, the height 1:3. Then the ratio of their volumes is (a) 1 : 4 (b) 1 : 3 (c) 3 : 1 (d) 2 : 5
Answer» Two cylindrical jars have their diameters in the ratio 3:1, the height 1:3. Then the ratio of their volumes is (a) 1 : 4 (b) 1 : 3 (c) 3 : 1 (d) 2 : 5

7499.

Two cylindrical jars have their diameters in the ratio 3:1, the height 1:3. Then the ratio of their volumes is (a) 1 : 4 (b) 1 : 3 (c) 3 : 1 (d) 2 : 5

Answer»

Two cylindrical jars have their diameters in the ratio 3:1, the height 1:3. Then the ratio of their volumes is

(a) 1 : 4

(b) 1 : 3

(c) 3 : 1

(d) 2 : 5

Discussion

7500.	Write the coefficient of m3 in each of the given polynomial.(i) m3 (ii) -3 2 + m - 3m3 (iii) -23m3 - 5m2 + 7m - 1
Answer» Write the coefficient of m³ in each of the given polynomial. (i) m³ (ii) $\frac{- 3}{2} + m - \sqrt{3} m^{3}$ (iii) $\frac{- 2}{3} m^{3} - 5 m^{2} + 7 m - 1$

Discussion

Explore topic-wise InterviewSolutions in .

39. Find the value of p when the distance between the points A(3,p) and B(4,1) is 10 ??

is a terminating decimal.

The perimeter of an isosceles triangle is 42 cm and its base is 32 times each of the equal sides. Find the length of each side and area of the triangle.

Question 2If the lengths of the diagonals of a rhombus are 16cm and 12cm. Then the length of the sides of the rhombus is(A) 9 cm(B) 10 cm(C) 8 cm(D) 20 cm

In the given figure, line AB meets y-axis at point A. Line through C(2, 10) and D intersects line AB at right angle at point P. Find :(i) equation of line AB.(ii) equation of line CD.(iii) co-ordinates of points E and D.

In the given figure, ar(DRC)=ar(DPC) and ar(BDP)=ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums [4 MARKS]

Question 5Find a point which is equidistant from the points A(-5,4) and B(-1,6). How many such points are there?

Question 7 The dimensions of a rectangle ABCD are 51cm x 25 cm. A trapezium PQCD with its parallel sides QC and PD in the ratio 9:8, is cut off from the rectangle as shown in the figure. If the area of the trapezium PQCD is 56 th part of the area of the rectangle. Find the lengths QC and PD.

If x=3+2√2, then the value of (√x−1√x) = _____. 2

If A=[2−3−41], then adj(3A2+12A) is equal to:

Find the area in cm2 of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]

Plot the graph of 0 (ZERO) Polynomial by constructing a equation and explaining it.

Question 2Find six rational numbers between 3 and 4.

is the factorization of (xy+x+4y+4).

Ifx=213+223,Show that x3−6x=6.

A vertical stick 10cm long casts a shadow 8cm long. At the same time, a tower casts a shadow 30m long. Determine the height of the tower?

Mean of 100 observations is found to be 40. At the time of computation two items were wrongly taken as 30 and 27 instead of 3 and 72. Find the correct mean.

Are non parallel sides of a trepizium are always equal

How many litres of water flows out of a pipe having an area of cross section of 5cm2 in 1 minute, if the speed of water in the pipe is 30 cm/sec ?

Find the value of P if the pair of L.E is coincident. x−2y=−2 and Px−8y=−84

The number of points on x-axis which are at a distance of 25 from the point (7, –4), is __________.

The volume of river of width 10 m and depth 6m flowing at a speed of 2 km per hr in 1 min is .

7.The sixth HM between 3 and 6/13

If B is the mid-point of ¯¯¯¯¯¯¯¯AC and C is the mid-point of ¯¯¯¯¯¯¯¯¯BD, where A, B, C, D lie on a straight line, say why AB = CD?

For three points, X, Y and Z, to be collinear, which of these conditions should be true? Select all that apply.

In the given figure, if then prove that AOB is a line.

If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

The lateral or vertical surface area of a cuboidal box of length, breadth and height 6 cm, 8 cm and 6.5 cm respectively is

The value of 2(\sqrt2 +\sqrt5)/(3\sqrt{2+\sqrt3})+\sqrt{2+\sqrt3}+\sqrt{2-\sqrt3

PQRS is a quadrilateral in which diagonals PR and QS intersect at O. Prove that PQ + QR + RS + SP < 2 (PR + QS).

In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ΔAPQ is 116 of the area of ΔABC.

(√a−√b)×(√a+√b)=

Factorize 32a3+108b3

Construct a triangle ABC in which BC equal to 7 cm, Angle B equal to 75 degree and AB+AC equal to 13 cm.

A coin is tossed 500 times with the following frequencies of two outcomes:head = 245 timestail = 255 timesWhat is the probability of getting a head in the next throw?

Q: If x= 2-√3, then the value of x^2-1/x^2 ?

If 0.75 : x :: 5 : 8, then x = _______

In the figure, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = BC.

39. Two circles intersect each other in points X&Y. Secants through X&Y intersect one of the circles in A&D and the other in B&C respectively.A&B are on the opposite side of line DC.Show that line AD is parallel to line BC.

What is the mean/average of factors of 20 ?

If x= 2(θ +sin θ) and y = 2(1-cosθ) then find dy /dx

Consider the below figure where the diameter AB bisects the chord PQ at the point R. If BR = 4 cm, then what is the radius of the circle?10

If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S then PQRS is a (a) rectangle (b) parallelogram (c) rhombus (d) quadrilateral whose opposite angles are supplementary

When are three or more points said to be collinear?

Two cylindrical jars have their diameters in the ratio 3:1, the height 1:3. Then the ratio of their volumes is (a) 1 : 4 (b) 1 : 3 (c) 3 : 1 (d) 2 : 5

Write the coefficient of m3 in each of the given polynomial.(i) m3 (ii) -3 2 + m - 3m3 (iii) -23m3 - 5m2 + 7m - 1