24740 + Interview Questions in Mathematics

1.	Two angles measure a-60 and 123-2a.if each one is opposite to equal sides of an isosceles triangle,then find the value of a
Answer» Two angles measure a-60 and 123-2a.if each one is opposite to equal sides of an isosceles triangle,then find the value of a

Discussion

2.	If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder ? (a) 4 (b) 1√2 (c) 2 (d) 12
Answer» If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder ? (a) 4 (b) $\frac{1}{\sqrt{2}}$ (c) 2 (d) $\frac{1}{2}$

2.

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder ? (a) 4 (b) 1√2 (c) 2 (d) 12

Answer»

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder ?

(a) 4 (b) $\frac{1}{\sqrt{2}}$

(c) 2 (d) $\frac{1}{2}$

Discussion

3.	Prove that line is a circle of infinite radius.
Answer» Prove that line is a circle of infinite radius.

Discussion

4.	The simplest form of 4√2434√3 is
Answer» The simplest form of $\frac{\sqrt[4]{243}}{\sqrt[4]{3}}$ is

Discussion

5.	Factorise 5√5x+30x+8√5
Answer» Factorise 5√5x+30x+8√5

Discussion

6.	Question. The perimeter of a rectangle is 240 cm. If its length is decreased by 10% and breadth is increased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.
Answer» Question. The perimeter of a rectangle is 240 cm. If its length is decreased by 10% and breadth is increased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.

Discussion

7.	Find the surface area of a park which is in the shape of a rectangle whose one side is thrice the other side and the length of its boundary is 200 m.
Answer» Find the surface area of a park which is in the shape of a rectangle whose one side is thrice the other side and the length of its boundary is 200 m.

Discussion

8.	Question 2 The perimeter of a triangle is 50cm. one side of a triangle is 4cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.
Answer» Question 2 The perimeter of a triangle is 50cm. one side of a triangle is 4cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.

Discussion

9.	Question 145 In rectangle PAIR, find ∠ARI,∠RMI and ∠PMA.
Answer» Question 145 In rectangle PAIR, find $∠ A R I, ∠ R M I$ and $∠ P M A$ .

Discussion

10.	The following scores were obtained in a statistics exam class interval[50,60)[60,70)[70,80)[80,90)[90,100)Class value xi 5565758595Frequency fi14652 Find: i) Considering the class value, the average score of the whole class. ii) The ratio of the no. of students who scored above 80 to the ratio no. of students who scored below 70.
Answer» The following scores were obtained in a statistics exam $\begin{matrix} c l a s s i n t e r v a l & [50, 60) & [60, 70) & [70, 80) & [80, 90) & [90, 100) C l a s s v a l u e x_{i} & 55 & 65 & 75 & 85 & 95 F r e q u e n c y f_{i} & 1 & 4 & 6 & 5 & 2 \end{matrix}$ Find: i) Considering the class value, the average score of the whole class. ii) The ratio of the no. of students who scored above 80 to the ratio no. of students who scored below 70.

10.

The following scores were obtained in a statistics exam class interval[50,60)[60,70)[70,80)[80,90)[90,100)Class value xi 5565758595Frequency fi14652 Find: i) Considering the class value, the average score of the whole class. ii) The ratio of the no. of students who scored above 80 to the ratio no. of students who scored below 70.

Answer»

The following scores were obtained in a statistics exam

$\begin{matrix} c l a s s i n t e r v a l & [50, 60) & [60, 70) & [70, 80) & [80, 90) & [90, 100) C l a s s v a l u e x_{i} & 55 & 65 & 75 & 85 & 95 F r e q u e n c y f_{i} & 1 & 4 & 6 & 5 & 2 \end{matrix}$

Find:

i) Considering the class value, the average score of the whole class.

ii) The ratio of the no. of students who scored above 80 to the ratio no. of students who scored below 70.

Discussion

11.	Find the probability that a number is multiple of 7 selected at random from the numbers 1,2,3.....35
Answer» Find the probability that a number is multiple of 7 selected at random from the numbers 1,2,3.....35

Discussion

12.	Why do we multiply a constant if it is given as a no. A is inversely proportional to B then , A= KB (where K is constant)?
Answer» Why do we multiply a constant if it is given as a no. A is inversely proportional to B then , A= KB (where K is constant)?

Discussion

13.	If 22x+4−17×2x+1=−4, then which of the following is true?
Answer» If $2^{2 x + 4} - 17 \times 2^{x + 1} = - 4$ , then which of the following is true?

Discussion

14.	XY is a line parallel to side BC of a triangle ABC. If BE\|\|AC and CF\|\|AB meet XY at E and F respectively, show that ar(ΔABE)=ar(ΔACF)
Answer» XY is a line parallel to side BC of a triangle ABC. If BE\|\|AC and CF\|\|AB meet XY at E and F respectively, show that $a r (Δ A B E) = a r (Δ A C F)$

Discussion

15.	P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, Show that ar(ΔPBQ)=ar(ΔARC).
Answer» P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, Show that $a r (Δ P B Q) = a r (Δ A R C)$ .

Discussion

16.	In the given figure, O is a point in the interior of a triangle. ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Then, AF2+BD2+CE2=AE2+CD2+BF2
Answer» In the given figure, O is a point in the interior of a triangle. ABC, OD $⊥$ BC, OE $⊥$ AC and OF $⊥$ AB. Then, $A F^{2} + B D^{2} + C E^{2} = A E^{2} + C D^{2} + B F^{2}$

Discussion

17.	The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5 √5 cm. Its surface area is
Answer» The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is $5 \sqrt{5} c m .$ Its surface area is

Discussion

18.	Question 1 (i) ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that ΔABD≅ΔACD
Answer» Question 1 (i) $Δ$ ABC and $Δ$ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that $Δ A B D ≅ Δ A C D$

Discussion

19.	If the given system of equation is 3x + 2y = 2xy; 6x + 2y = 3xy, then the first step to solve such eqs is
Answer» If the given system of equation is 3x + 2y = 2xy; 6x + 2y = 3xy, then the first step to solve such eqs is

Discussion

20.	Question 68 Fill in the blanks to make the statements true. A regular polygon is a polygon whose all sides are equal and all ___ are equal.
Answer» Question 68 Fill in the blanks to make the statements true. A regular polygon is a polygon whose all sides are equal and all ___ are equal.

Discussion

21.	AB and CD are parallel lines. Then,
Answer» AB and CD are parallel lines. Then,

Discussion

22.	Find the range of x for the following expression: ∣∣x2−3x+2x2+3x+2∣∣≥1
Answer» Find the range of $x$ for the following expression: $∣ ∣ \frac{x^{2} - 3 x + 2}{x^{2} + 3 x + 2} ∣ ∣ \geq 1$

22.

Find the range of x for the following expression: ∣∣x2−3x+2x2+3x+2∣∣≥1

Answer»

Find the range of $x$ for the following expression:

$∣ ∣ \frac{x^{2} - 3 x + 2}{x^{2} + 3 x + 2} ∣ ∣ \geq 1$

Discussion

23.	The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
Answer» The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

Discussion

24.	In the figure below, it is given that chords AB = PQ. The ∠AOB=550, and ∠POQ=x0, find x.
Answer» In the figure below, it is given that chords AB = PQ. The $∠ A O B = 55^{0}$ , and $∠ P O Q = x^{0}$ , find $x$ .

24.

In the figure below, it is given that chords AB = PQ. The ∠AOB=550, and ∠POQ=x0, find x.

Answer»

In the figure below, it is given that chords AB = PQ. The $∠ A O B = 55^{0}$ , and $∠ P O Q = x^{0}$ , find $x$ .

Discussion

25.	Two dice are thrown simultaneously. The probability of getting a doublet is
Answer» Two dice are thrown simultaneously. The probability of getting a doublet is

Discussion

26.	The total distance travelled if you start walking along the edge of a shape is known as its:
Answer» The total distance travelled if you start walking along the edge of a shape is known as its:

Discussion

27.	ABCD is a parallelogram and A1 and B1 are the mid-points of the sides BC and CD respectively. If →AA1+→AB1=λ →AC, then ′λ′ is equal to
Answer» ABCD is a parallelogram and $A_{1}$ and $B_{1}$ are the mid-points of the sides BC and CD respectively. $I f \to A A_{1} + \to A B_{1} = λ \to A C,$ then $^{'} λ^{'}$ is equal to

Discussion

28.	The graph of f(x) = x2 lies in:
Answer» The graph of f(x) = x² lies in:

Discussion

29.	A circus artist is climbing a 30m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The height of the pole, if the angle made by the rope with the ground level is 30∘ __ m.
Answer» A circus artist is climbing a 30m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The height of the pole, if the angle made by the rope with the ground level is $30^{\circ}$ __ m.

Discussion

30.	After having the straight line 180∘, we should __ this angle to get 90∘
Answer» After having the straight line $180^{\circ}$ , we should __ this angle to get $90^{\circ}$

Discussion

31.	The perimeter of an isosceles right angled triangle having an area of 200 cm2 is
Answer» The perimeter of an isosceles right angled triangle having an area of 200 cm² is

Discussion

32.	Question 4(iii) Identify the greater number, wherever possible, in each of the following: (iii) 28 or 82
Answer» Question 4(iii) Identify the greater number, wherever possible, in each of the following: (iii) $2^{8} o r 8^{2}$

Discussion

33.	The value of tan63∘+cot23∘tan27∘+cot67∘−tan63∘tan67∘ is
Answer» The value of $\frac{t a n 63^{\circ} + c o t 23^{\circ}}{t a n 27^{\circ} + c o t 67^{\circ}} - t a n 63^{\circ} t a n 67^{\circ}$ is

Discussion

34.	Two points A & B are marked on the number line as shown in figure. A = -7 and distance between them is 10 units. The point B is
Answer» Two points A & B are marked on the number line as shown in figure. A = -7 and distance between them is 10 units. The point B is

34.

Two points A & B are marked on the number line as shown in figure. A = -7 and distance between them is 10 units. The point B is

Answer»

Two points A & B are marked on the number line as shown in figure. A = -7 and distance between them is 10 units. The point B is

Discussion

35.	The passage given below is followed by four summaries. Choose the option that best captures the author's position?
Answer» The passage given below is followed by four summaries. Choose the option that best captures the author's position?

Discussion

36.	If A is the set of all xϵR such that x(log x)2−3 log x+1>1000, and A=(a,∞) then √10a will be ___. ( (Base of logx is 10).
Answer» If A is the set of all $x ϵ R$ such that $x^{(l o g x)^{2} - 3 l o g x + 1} > 1000$ , and $A = (a, \infty)$ then $\sqrt{10 a}$ will be ___. ( (Base of logx is 10).

Discussion

37.	In geometry, is the fundamental unit which exists by itself.
Answer» In geometry, is the fundamental unit which exists by itself.

Discussion

38.	The cost of a room in a hotel is partially fixed and partially varying with the number of hours. A person staying for 10 hours paid Rs. 600 and a person staying for 15 hours paid Rs. 840. Find the fixed cost and the variable cost per hour.
Answer» The cost of a room in a hotel is partially fixed and partially varying with the number of hours. A person staying for 10 hours paid Rs. 600 and a person staying for 15 hours paid Rs. 840. Find the fixed cost and the variable cost per hour.

Discussion

39.	Question 5 The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is A) 13 B) 65 C) 875 D) 1750
Answer» Question 5 The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is A) 13 B) 65 C) 875 D) 1750

Discussion

40.	In the figure given below, if ∠AOP=75∘ and ∠AOB=120∘, the what is ∠AQP?
Answer» In the figure given below, if $∠ A O P = 75^{\circ}$ and $∠ A O B = 120^{\circ}$ , the what is $∠ A Q P$ ?

Discussion

41.	Draw a histogram for the following data: Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163 Using this histogram, draw the frequency polygon on the same graph
Answer» Draw a histogram for the following data: $\begin{matrix} Class interval & 600 - 640 & 640 - 680 & 680 - 720 & 720 - 760 & 760 - 800 & 800 - 840 Frequency & 18 & 45 & 153 & 288 & 171 & 63 \end{matrix}$ Using this histogram, draw the frequency polygon on the same graph

41.

Draw a histogram for the following data: Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163 Using this histogram, draw the frequency polygon on the same graph

Answer»

Draw a histogram for the following data:

$\begin{matrix} Class interval & 600 - 640 & 640 - 680 & 680 - 720 & 720 - 760 & 760 - 800 & 800 - 840 Frequency & 18 & 45 & 153 & 288 & 171 & 63 \end{matrix}$
Using this histogram, draw the frequency polygon on the same graph

Discussion

42.	Differentiate the following w.r.t xex[log(a)]+ea[log(x)]+ea[log(a)]
Answer» Differentiate the following w.r.t $x e^{x} [l o g (a)] + e^{a} [l o g (x)] + e^{a} [l o g (a)]$

Discussion

43.	If x = y and y = 8, then find the value of 2x+x2 using Euclid's axioms.20
Answer» $If x = y and y = 8, then find the value of 2 x + \frac{x}{2} using Euclid's axioms.$ 20

Discussion

44.	Question 24 Which of the following is an equiangular and equilateral polygon? a) Square b) Rectangle c) Rhombus d) Right angled Triangle
Answer» Question 24 Which of the following is an equiangular and equilateral polygon? a) Square b) Rectangle c) Rhombus d) Right angled Triangle

Discussion

45.	Question 9 In figure X and Y are the mid - points of AC and AB respectively, QP \|\| BC and CYQ and BXP are straight lines. Prove that ar(ΔABP)=ar(ΔACQ).
Answer» Question 9 In figure X and Y are the mid - points of AC and AB respectively, QP \|\| BC and CYQ and BXP are straight lines. Prove that $a r (Δ A B P) = a r (Δ A C Q)$ .

Discussion

46.	if b is not equal to 0 how can we showthat a by b is a rational number
Answer» if b is not equal to 0 how can we showthat a by b is a rational number

Discussion

47.	The mid points of an equilateral triangle of side 10 cm are joined to form a triangle. What type of triangle is obtained by joining the mid points?
Answer» The mid points of an equilateral triangle of side 10 cm are joined to form a triangle. What type of triangle is obtained by joining the mid points?

Discussion

48.	If ΔABC∼ΔPQR, identify the pairs of corresponding angles.
Answer» If $Δ ABC \sim Δ PQR$ , identify the pairs of corresponding angles.

Discussion

49.	Question 03. In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?
Answer» Question 03. In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?

Discussion

50.	Question 180(iv) Simplify (15)45×(15)−60−(15)28×(15)−43
Answer» Question 180(iv) Simplify ${(\frac{1}{5})}^{45} \times {(\frac{1}{5})}^{- 60} - {(\frac{1}{5})}^{28} \times {(\frac{1}{5})}^{- 43}$

50.

Question 180(iv) Simplify (15)45×(15)−60−(15)28×(15)−43

Answer»

Question 180(iv)

Simplify

${(\frac{1}{5})}^{45} \times {(\frac{1}{5})}^{- 60} - {(\frac{1}{5})}^{28} \times {(\frac{1}{5})}^{- 43}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Two angles measure a-60 and 123-2a.if each one is opposite to equal sides of an isosceles triangle,then find the value of a

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder ? (a) 4 (b) 1√2 (c) 2 (d) 12

Prove that line is a circle of infinite radius.

The simplest form of 4√2434√3 is

Factorise 5√5x+30x+8√5

Question. The perimeter of a rectangle is 240 cm. If its length is decreased by 10% and breadth is increased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.

Find the surface area of a park which is in the shape of a rectangle whose one side is thrice the other side and the length of its boundary is 200 m.

Question 2 The perimeter of a triangle is 50cm. one side of a triangle is 4cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.

Question 145 In rectangle PAIR, find ∠ARI,∠RMI and ∠PMA.

Find the probability that a number is multiple of 7 selected at random from the numbers 1,2,3.....35

Why do we multiply a constant if it is given as a no. A is inversely proportional to B then , A= KB (where K is constant)?

If 22x+4−17×2x+1=−4, then which of the following is true?

XY is a line parallel to side BC of a triangle ABC. If BE||AC and CF||AB meet XY at E and F respectively, show that ar(ΔABE)=ar(ΔACF)

P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, Show that ar(ΔPBQ)=ar(ΔARC).

In the given figure, O is a point in the interior of a triangle. ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Then, AF2+BD2+CE2=AE2+CD2+BF2

The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5 √5 cm. Its surface area is

Question 1 (i) ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that ΔABD≅ΔACD

If the given system of equation is 3x + 2y = 2xy; 6x + 2y = 3xy, then the first step to solve such eqs is

Question 68 Fill in the blanks to make the statements true.​​​​​​​ A regular polygon is a polygon whose all sides are equal and all ___ are equal.

AB and CD are parallel lines. Then,

Find the range of x for the following expression: ∣∣x2−3x+2x2+3x+2∣∣≥1

The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

In the figure below, it is given that chords AB = PQ. The ∠AOB=550, and ∠POQ=x0, find x.

Two dice are thrown simultaneously. The probability of getting a doublet is

The total distance travelled if you start walking along the edge of a shape is known as its:

ABCD is a parallelogram and A1 and B1 are the mid-points of the sides BC and CD respectively. If →AA1+→AB1=λ →AC, then ′λ′ is equal to

The graph of f(x) = x2 lies in:

A circus artist is climbing a 30m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The height of the pole, if the angle made by the rope with the ground level is 30∘ __ m.

After having the straight line 180∘, we should __ this angle to get 90∘

The perimeter of an isosceles right angled triangle having an area of 200 cm2 is

Question 4(iii) Identify the greater number, wherever possible, in each of the following: (iii) 28 or 82

The value of tan63∘+cot23∘tan27∘+cot67∘−tan63∘tan67∘ is

Two points A &amp; B are marked on the number line as shown in figure. A = -7 and distance between them is 10 units. The point B is

The passage given below is followed by four summaries. Choose the option that best captures the author's position?

If A is the set of all xϵR such that x(log x)2−3 log x+1&gt;1000, and A=(a,∞) then √10a will be ___. ( (Base of logx is 10).

In geometry, is the fundamental unit which exists by itself.

The cost of a room in a hotel is partially fixed and partially varying with the number of hours. A person staying for 10 hours paid Rs. 600 and a person staying for 15 hours paid Rs. 840. Find the fixed cost and the variable cost per hour.

Question 5 The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is A) 13 B) 65 C) 875 D) 1750

In the figure given below, if ∠AOP=75∘ and ∠AOB=120∘, the what is ∠AQP?

Draw a histogram for the following data: Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163 Using this histogram, draw the frequency polygon on the same graph

Differentiate the following w.r.t xex[log(a)]+ea[log(x)]+ea[log(a)]

If x = y and y = 8, then find the value of 2x+x2 using Euclid's axioms.20

Question 24 Which of the following is an equiangular and equilateral polygon? a) Square b) Rectangle c) Rhombus d) Right angled Triangle

Question 9 In figure X and Y are the mid - points of AC and AB respectively, QP || BC and CYQ and BXP are straight lines. Prove that ar(ΔABP)=ar(ΔACQ).

if b is not equal to 0 how can we showthat a by b is a rational number

The mid points of an equilateral triangle of side 10 cm are joined to form a triangle. What type of triangle is obtained by joining the mid points?

If ΔABC∼ΔPQR, identify the pairs of corresponding angles.

Question 03. In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?

Question 180(iv) Simplify (15)45×(15)−60−(15)28×(15)−43

Question 68 Fill in the blanks to make the statements true. A regular polygon is a polygon whose all sides are equal and all ___ are equal.

Two points A & B are marked on the number line as shown in figure. A = -7 and distance between them is 10 units. The point B is

If A is the set of all xϵR such that x(log x)2−3 log x+1>1000, and A=(a,∞) then √10a will be ___. ( (Base of logx is 10).