32581 + Interview Questions in Mathematics

1.	___ is modified form of an inclined plane.
Answer» ___ is modified form of an inclined plane.

Discussion

2.	Which country has the longest coastline than any other in the world?
Answer» Which country has the longest coastline than any other in the world?

Discussion

3.	Prove that√1−sinθ1+sinθ=secθ−tanθ
Answer» Prove that $\sqrt{\frac{1 - s i n θ}{1 + s i n θ}} = s e c θ - t a n θ$

Discussion

4.	If cos θ = 45 then tan θ = ? (a) 34 (b) 43 (c) 35 (d) 53
Answer» If cos $θ$ = $\frac{4}{5}$ then tan $θ$ = ? (a) $\frac{3}{4}$ (b) $\frac{4}{3}$ (c) $\frac{3}{5}$ (d) $\frac{5}{3}$

4.

If cos θ = 45 then tan θ = ? (a) 34 (b) 43 (c) 35 (d) 53

Answer»

If cos $θ$ = $\frac{4}{5}$ then tan $θ$ = ?

(a) $\frac{3}{4}$ (b) $\frac{4}{3}$ (c) $\frac{3}{5}$ (d) $\frac{5}{3}$

Discussion

5.	The cost harvesting a square field at Rs.900 per hectare is Rs.8100. Find the cost of putting a fence around it at Rs.18 per metre.
Answer» The cost harvesting a square field at Rs.900 per hectare is Rs.8100. Find the cost of putting a fence around it at Rs.18 per metre.

Discussion

6.	Find two consecutive multiples of 3 whose product is 648.
Answer» Find two consecutive multiples of 3 whose product is 648.

Discussion

7.	Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.
Answer» Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.

7.

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.

Answer»

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.

Discussion

8.	Find the values of k for which the given quadratic equation has real and distinct roots: (i)kx2+2x+1=0 (ii)kx2+6x+1=0
Answer» Find the values of k for which the given quadratic equation has real and distinct roots: $(i) k x^{2} + 2 x + 1 = 0 (i i) k x^{2} + 6 x + 1 = 0$

Discussion

9.	The zeros of the polynomial 4x2+5√2x−3 are
Answer» The zeros of the polynomial $4 x^{2} + 5 \sqrt{2} x - 3$ are

9.

The zeros of the polynomial 4x2+5√2x−3 are

Answer»

The zeros of the polynomial $4 x^{2} + 5 \sqrt{2} x - 3$ are

Discussion

10.	If θ is a positive acute angle such that sec θ=cosec 60∘, find the value of 2cos2 θ−1.
Answer» If $θ$ is a positive acute angle such that $s e c θ = c o s e c 60^{\circ}$ , find the value of $2 c o s^{2} θ - 1$ .

Discussion

11.	What is the probability of getting all heads or all tails, when three coins are tossed simultaneously?
Answer» What is the probability of getting all heads or all tails, when three coins are tossed simultaneously?

Discussion

12.	If radius of the base of a right circular cone is increased by 15%, then its volume will increase by:
Answer» If radius of the base of a right circular cone is increased by 15%, then its volume will increase by:

Discussion

13.	If LCM of two numbers is equal to the greater number, then its HCF ____.
Answer» If LCM of two numbers is equal to the greater number, then its HCF ____.

Discussion

14.	Question 14 A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q . If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.
Answer» Question 14 A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q . If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.

Discussion

15.	Question 9 The ratio of the corresponding altitudes of two similar triangles is 3 : 5. Is it correct to say that ratio of their areas is 6 : 5? Why?
Answer» Question 9 The ratio of the corresponding altitudes of two similar triangles is 3 : 5. Is it correct to say that ratio of their areas is 6 : 5? Why?

Discussion

16.	In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT=40∘,∠RPT=95∘ and ∠TSQ=75∘, find ∠SQT.
Answer» In the given figure, if lines PQ and RS intersect at point T, such that $∠ P R T = 40^{\circ}, ∠ R P T = 95^{\circ} a n d ∠ T S Q = 75^{\circ}$ , find $∠ S Q T .$

Discussion

17.	log8 17log9 23−log2√2 17log3 23 is equal to
Answer» $\frac{l o g_{8} 17}{l o g_{9} 23} - \frac{l o g_{2 \sqrt{2}} 17}{l o g_{3} 23}$ is equal to

Discussion

18.	A series in G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio will be equal to
Answer» A series in G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio will be equal to

Discussion

19.	What will be the circumference of a circle having area 9 times the area of a circle with diameter 8 cm?
Answer» What will be the circumference of a circle having area 9 times the area of a circle with diameter 8 cm?

Discussion

20.	Solve the following quadratic equation: x2=15
Answer» Solve the following quadratic equation: $x^{2} = 15$

Discussion

21.	Question 13 If P(a3,4) is mid-point of the line segment joining points Q(-6,5) and R(-2,3), then value of a is (A) – 4 (B) – 12 (C) 12 (D) – 6
Answer» Question 13 If $P (\frac{a}{3}, 4)$ is mid-point of the line segment joining points Q(-6,5) and R(-2,3), then value of a is (A) – 4 (B) – 12 (C) 12 (D) – 6

Discussion

22.	The zero of the polynomial x-3 is
Answer» The zero of the polynomial x-3 is

Discussion

23.	If →a,→b,→c are vectors such that →a.→b=0 and →a+→b=→c, then
Answer» If $\to a, \to b, \to c$ are vectors such that $\to a . \to b = 0$ and $\to a + \to b = \to c$ , then

Discussion

24.	In fig., DE ∥ BC and CD ∥ EF. Prove that AD2= AB x AF.
Answer» In fig., DE $∥$ BC and CD $∥$ EF. Prove that AD²= AB x AF.

24.

In fig., DE ∥ BC and CD ∥ EF. Prove that AD2= AB x AF.

Answer»

In fig., DE $∥$ BC and CD $∥$ EF. Prove that AD²= AB x AF.

Discussion

25.	Construct a line segment of 6 cm. Divide this line segment in the ratio 3:2. [2 MARKS]
Answer» Construct a line segment of 6 cm. Divide this line segment in the ratio 3:2. [2 MARKS]

Discussion

26.	If a and b are real and a ≠ b then show that the roots of the equation (a−b)x2+5(a+b)x−2(a−b)=0 are real and unequal.
Answer» If a and b are real and a $\neq$ b then show that the roots of the equation $(a - b) x^{2} + 5 (a + b) x - 2 (a - b) = 0$ are real and unequal.

Discussion

27.	What is the tangent-secant theorem?
Answer» What is the tangent-secant theorem?

Discussion

28.	Evaluate each of the following 2sin2 30o−3cos2 45o+tan2 60o
Answer» Evaluate each of the following $2 s i n^{2} 30^{o} - 3 c o s^{2} 45^{o} + t a n^{2} 60^{o}$

28.

Evaluate each of the following 2sin2 30o−3cos2 45o+tan2 60o

Answer»

Evaluate each of the following

$2 s i n^{2} 30^{o} - 3 c o s^{2} 45^{o} + t a n^{2} 60^{o}$

Discussion

29.	Explain the steps to construct tangents to a circle from a point P outside the circle and prove that they are tangents to the circle.
Answer» Explain the steps to construct tangents to a circle from a point P outside the circle and prove that they are tangents to the circle.

Discussion

30.	A chord of a circle of radius 12 cm subtends an angle of 120∘ at the centre. Find the area in cm2 of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73) ___
Answer» A chord of a circle of radius 12 cm subtends an angle of $120^{\circ}$ at the centre. Find the area in $c m^{2}$ of the corresponding segment of the circle. (Use $π$ = 3.14 and $\sqrt{3}$ = 1.73) ___

Discussion

31.	The decimal expansions of 136250 is
Answer» The decimal expansions of $\frac{13}{6250}$ is

Discussion

32.	The taxable value of a shirt is ₹500. Rate of GST is 18%. What is the price of the shirt for the consumer?
Answer» The taxable value of a shirt is ₹ $500$ . Rate of GST is $18 %$ . What is the price of the shirt for the consumer?

Discussion

33.	The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is
Answer» The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is

Discussion

34.	Question 10 (ii) CD and GH are respectively the bisectors of angleACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC∼ΔFEG, Show that (ii)ΔDCB∼ΔHGE
Answer» Question 10 (ii) CD and GH are respectively the bisectors of $a n g l e A C B$ and $∠ E G F$ such that D and H lie on sides AB and FE of $Δ A B C$ and $Δ E F G$ respectively. If $Δ A B C \sim Δ F E G$ , Show that $(i i) Δ D C B \sim Δ H G E$

Discussion

35.	Find the point where 2x-3y = 12 cuts the x axis
Answer» Find the point where 2x-3y = 12 cuts the x axis

Discussion

36.	State the co-ordinates of the following points under reflection in y-axis : (i) (6, -3) (ii) (-1, 0) (iii) (-8, -2)
Answer» State the co-ordinates of the following points under reflection in y-axis : (i) (6, -3) (ii) (-1, 0) (iii) (-8, -2)

36.

State the co-ordinates of the following points under reflection in y-axis : (i) (6, -3) (ii) (-1, 0) (iii) (-8, -2)

Answer»

State the co-ordinates of the following points under reflection in y-axis :

(i) (6, -3) (ii) (-1, 0) (iii) (-8, -2)

Discussion

37.	If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 64 : 189, then the common ratio r is _______.
Answer» If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 64 : 189, then the common ratio r is _______.

Discussion

38.	Match the following (i) MeanA.Typical value(ii) MedianB.Most popular value(iii) ModeC.Gets highly affected by extreme values
Answer» Match the following $\begin{matrix} (i) M e a n & A . T y p i c a l v a l u e (i i) M e d i a n & B . M o s t p o p u l a r v a l u e (i i i) M o d e & C . G e t s h i g h l y a f f e c t e d b y e x t r e m e v a l u e s \end{matrix}$

Discussion

39.	If a side of a cyclic quadrilateral is produced, then prove that the exterior angle is equal to the interior opposite angle. [3 MARKS]
Answer» If a side of a cyclic quadrilateral is produced, then prove that the exterior angle is equal to the interior opposite angle. [3 MARKS]

Discussion

40.	Question 8 Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.
Answer» Question 8 Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Discussion

41.	The incentre of a triangle is the ______.
Answer» The incentre of a triangle is the ______.

Discussion

42.	Kamal Ltd., was formed for purpose of purchasing Rajesh Ltd. and was registered with a nominal capital of Rs 2,00,000 divided into 2,000 equity shares of Rs 100 each. 1,000 shares were issued as fully paid to the vendors in payment of the purchase consideration. You are required to give necessary journal entries to record the above transactions.
Answer» Kamal Ltd., was formed for purpose of purchasing Rajesh Ltd. and was registered with a nominal capital of Rs 2,00,000 divided into 2,000 equity shares of Rs 100 each. 1,000 shares were issued as fully paid to the vendors in payment of the purchase consideration. You are required to give necessary journal entries to record the above transactions.

42.

Kamal Ltd., was formed for purpose of purchasing Rajesh Ltd. and was registered with a nominal capital of Rs 2,00,000 divided into 2,000 equity shares of Rs 100 each. 1,000 shares were issued as fully paid to the vendors in payment of the purchase consideration. You are required to give necessary journal entries to record the above transactions.

Answer»

Kamal Ltd., was formed for purpose of purchasing Rajesh Ltd. and was registered with a nominal capital of Rs 2,00,000 divided into 2,000 equity shares of Rs 100 each. 1,000 shares were issued as fully paid to the vendors in payment of the purchase consideration.

You are required to give necessary journal entries to record the above transactions.

Discussion

43.	Factorise : a2−3a−40
Answer» Factorise : $a^{2} - 3 a - 40$

43.

Factorise : a2−3a−40

Answer»

Factorise :

$a^{2} - 3 a - 40$

Discussion

44.	In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square, where O and O' are centres of the circles. Find the area of shaded region.
Answer» In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square, where O and O' are centres of the circles. Find the area of shaded region.

44.

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square, where O and O' are centres of the circles. Find the area of shaded region.

Answer»

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square, where O and O' are centres of the circles. Find the area of shaded region.

Discussion

45.	In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 4 cm and 3 cm respectively. If the area Δ ABC = 21 cm2 then find the lengths of sides AB and AC.
Answer» In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 4 cm and 3 cm respectively. If the area $Δ$ ABC = 21 $c m^{2}$ then find the lengths of sides AB and AC.

45.

In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 4 cm and 3 cm respectively. If the area Δ ABC = 21 cm2 then find the lengths of sides AB and AC.

Answer»

In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 4 cm and 3 cm respectively. If the area $Δ$ ABC = 21 $c m^{2}$ then find the lengths of sides AB and AC.

Discussion

46.	A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/hr more. Find the original speed of the train.
Answer» A train, travelling at a uniform speed for $360 k m$ , would have taken $48$ minutes less to travel the same distance if its speed were $5 k m / h r$ more. Find the original speed of the train.

Discussion

47.	If the sum of first n terms of an A.P. is 2n2−n+1, then the tenth term of this A.P. is:
Answer» If the sum of first n terms of an A.P. is $2 n^{2} - n + 1$ , then the tenth term of this A.P. is:

Discussion

48.	Question 7 Consider the following frequency distribution Class0.56−1112−1718−2324−29Frequency131015811 The upper limit of the median class is (a) 17 (b) 17.5 (c) 18 (d) 18.5
Answer» Question 7 Consider the following frequency distribution $\begin{matrix} C l a s s & 0.5 & 6 - 11 & 12 - 17 & 18 - 23 & 24 - 29 F r e q u e n c y & 13 & 10 & 15 & 8 & 11 \end{matrix}$ The upper limit of the median class is (a) 17 (b) 17.5 (c) 18 (d) 18.5

Discussion

49.	3 person can built a small house in 8 days to built same house in 6 days how many person are required
Answer» 3 person can built a small house in 8 days to built same house in 6 days how many person are required

Discussion

50.	A woman increased her weight by 5:4. Her original weight is 60kg. Find her increase in weight.
Answer» A woman increased her weight by 5:4. Her original weight is 60kg. Find her increase in weight.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

___ is modified form of an inclined plane.

Which country has the longest coastline than any other in the world?

Prove that√1−sinθ1+sinθ=secθ−tanθ

If cos θ = 45 then tan θ = ? (a) 34 (b) 43 (c) 35 (d) 53

The cost harvesting a square field at Rs.900 per hectare is Rs.8100. Find the cost of putting a fence around it at Rs.18 per metre.

Find two consecutive multiples of 3 whose product is 648.

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.

Find the values of k for which the given quadratic equation has real and distinct roots: (i)kx2+2x+1=0 (ii)kx2+6x+1=0

The zeros of the polynomial 4x2+5√2x−3 are

If θ is a positive acute angle such that sec θ=cosec 60∘, find the value of 2cos2 θ−1.

What is the probability of getting all heads or all tails, when three coins are tossed simultaneously?

If radius of the base of a right circular cone is increased by 15%, then its volume will increase by:

If LCM of two numbers is equal to the greater number, then its HCF ____.

Question 14 A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q . If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.

Question 9 The ratio of the corresponding altitudes of two similar triangles is 3 : 5. Is it correct to say that ratio of their areas is 6 : 5? Why?

In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT=40∘,∠RPT=95∘ and ∠TSQ=75∘, find ∠SQT.

log8 17log9 23−log2√2 17log3 23 is equal to

A series in G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio will be equal to

What will be the circumference of a circle having area 9 times the area of a circle with diameter 8 cm?

Solve the following quadratic equation: x2=15

Question 13 If P(a3,4) is mid-point of the line segment joining points Q(-6,5) and R(-2,3), then value of a is (A) – 4 (B) – 12 (C) 12 (D) – 6

The zero of the polynomial x-3 is

If →a,→b,→c are vectors such that →a.→b=0 and →a+→b=→c, then

In fig., DE ∥ BC and CD ∥ EF. Prove that AD2= AB x AF.

Construct a line segment of 6 cm. Divide this line segment in the ratio 3:2. [2 MARKS]

If a and b are real and a ≠ b then show that the roots of the equation (a−b)x2+5(a+b)x−2(a−b)=0 are real and unequal.

What is the tangent-secant theorem?

Evaluate each of the following 2sin2 30o−3cos2 45o+tan2 60o

Explain the steps to construct tangents to a circle from a point P outside the circle and prove that they are tangents to the circle.

A chord of a circle of radius 12 cm subtends an angle of 120∘ at the centre. Find the area in cm2 of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73) ___

The decimal expansions of 136250 is

The taxable value of a shirt is ₹500. Rate of GST is 18%. What is the price of the shirt for the consumer?

The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is

Question 10 (ii) CD and GH are respectively the bisectors of angleACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC∼ΔFEG, Show that (ii)ΔDCB∼ΔHGE

Find the point where 2x-3y = 12 cuts the x axis

State the co-ordinates of the following points under reflection in y-axis : (i) (6, -3) (ii) (-1, 0) (iii) (-8, -2)

If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 64 : 189, then the common ratio r is _______.

Match the following (i) MeanA.Typical value(ii) MedianB.Most popular value(iii) ModeC.Gets highly affected by extreme values

If a side of a cyclic quadrilateral is produced, then prove that the exterior angle is equal to the interior opposite angle. [3 MARKS]

Question 8 Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

The incentre of a triangle is the ______.

Factorise : a2−3a−40

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square, where O and O' are centres of the circles. Find the area of shaded region.

In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 4 cm and 3 cm respectively. If the area Δ ABC = 21 cm2 then find the lengths of sides AB and AC.

A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/hr more. Find the original speed of the train.

If the sum of first n terms of an A.P. is 2n2−n+1, then the tenth term of this A.P. is:

Question 7 Consider the following frequency distribution Class0.56−1112−1718−2324−29Frequency131015811 The upper limit of the median class is (a) 17 (b) 17.5 (c) 18 (d) 18.5

3 person can built a small house in 8 days to built same house in 6 days how many person are required

A woman increased her weight by 5:4. Her original weight is 60kg. Find her increase in weight.