24740 + Interview Questions in Mathematics

1.	Question 3 (iii) On comparing the ratios a1a2, b1b2 and c1c2 find out whether the following pair of linear equations are consistent, or inconsistent. 32x+53y=7;9x−10y=14
Answer» Question 3 (iii) On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the following pair of linear equations are consistent, or inconsistent. $\frac{3}{2} x + \frac{5}{3} y = 7; 9 x - 10 y = 14$

Discussion

2.	Question 1 (i) In the following figure (i), DE \|\| BC. Find EC.
Answer» Question 1 (i) In the following figure (i), DE \|\| BC. Find EC.

Discussion

3.	3√−a6×b3×c21c9×a12=
Answer» $\sqrt[3]{\frac{- a^{6} \times b^{3} \times c^{21}}{c^{9} \times a^{12}}} =$

Discussion

4.	The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination are 71, find the ratio of the number of boys to the number of girls.
Answer» The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination are 71, find the ratio of the number of boys to the number of girls.

Discussion

5.	Factorise: 13x2−2x−9
Answer» Factorise: $\frac{1}{3} x^{2} - 2 x - 9$

Discussion

6.	Find the area of the region in red colour.
Answer» Find the area of the region in red colour.

6.

Find the area of the region in red colour.

Answer»

Find the area of the region in red colour.

Discussion

7.	In the figure, AC = 10cm, PC = 15cm, PQ = 12 cm, then PB = __ cm .
Answer» In the figure, AC = 10cm, PC = 15cm, PQ = 12 cm, then PB = __ cm .

Discussion

8.	Find the cost of sinking a tube-well 280 m deep , having a diameter 3m at the rate of Rs 15 per cubic metre. Find also the cost of cementing its inner curved sufrace at Rs 10 per square metre.
Answer» Find the cost of sinking a tube-well 280 m deep , having a diameter 3m at the rate of Rs 15 per cubic metre. Find also the cost of cementing its inner curved sufrace at Rs 10 per square metre.

Discussion

9.	Factorize : x2−1−2a−a2.
Answer» Factorize : $x^{2} - 1 - 2 a - a^{2} .$

Discussion

10.	If each edge of a cube is increased by 50%, the percentage increase in its surface area is
Answer» If each edge of a cube is increased by $50 %$ , the percentage increase in its surface area is

Discussion

11.	In the figure, if AB⊥BC, then x=
Answer» In the figure, if $A B ⊥ B C$ , then x=

11.

In the figure, if AB⊥BC, then x=

Answer»

In the figure, if $A B ⊥ B C$ , then x=

Discussion

12.	Find three rational numbers lying between 35 and 78 How many rational numbers can be determined between these two numbers?
Answer» Find three rational numbers lying between $\frac{3}{5}$ and $\frac{7}{8}$ How many rational numbers can be determined between these two numbers?

12.

Find three rational numbers lying between 35 and 78 How many rational numbers can be determined between these two numbers?

Answer»

Find three rational numbers lying between $\frac{3}{5}$ and $\frac{7}{8}$

How many rational numbers can be determined between these two numbers?

Discussion

13.	In the given figure, O is the centre of the circle. If ∠ACB=50∘, find ∠OAB.
Answer» In the given figure, O is the centre of the circle. If $∠ A C B = 50^{\circ}$ , find $∠$ OAB.

13.

In the given figure, O is the centre of the circle. If ∠ACB=50∘, find ∠OAB.

Answer»

In the given figure, O is the centre of the circle. If $∠ A C B = 50^{\circ}$ , find $∠$ OAB.

Discussion

14.	1. Is −3+√6 irrational 2. Is −3×√8 irrational 3. 4√3 irrational 4. √10 multiply √40
Answer» 1. Is $- 3 + \sqrt{6}$ irrational 2. Is $- 3 \times \sqrt{8}$ irrational 3. $\frac{4}{\sqrt{3}}$ irrational 4. $\sqrt{10}$ multiply $\sqrt{40}$

Discussion

15.	A __ connects a vertex of a triangle to the midpoint of the opposite side.
Answer» A __ connects a vertex of a triangle to the midpoint of the opposite side.

Discussion

16.	Ravi asked suresh about his age. Suresh replied to him the value of the following expression is my age, Then, Suresh's age is 15[sin222∘+sin268∘cos222∘+cos268∘+sin263∘+cos63∘sin27∘]
Answer» Ravi asked suresh about his age. Suresh replied to him the value of the following expression is my age, Then, Suresh's age is $15 [\frac{s i n^{2} 22^{\circ} + s i n^{2} 68^{\circ}}{c o s^{2} 22^{\circ} + c o s^{2} 68^{\circ}} + s i n^{2} 63^{\circ} + c o s 63^{\circ} s i n 27^{\circ}]$

Discussion

17.	D, E and F are respectively the mid-points of the sides BC, CA and AB of a △ABC. Show that (i) BDEF is a parallelogram.(ii) ar (△DEF) = 14 ar (△ABC). [4 MARKS]
Answer» D, E and F are respectively the mid-points of the sides BC, CA and AB of a $△$ ABC. Show that (i) BDEF is a parallelogram.(ii) ar ( $△$ DEF) = $\frac{1}{4}$ ar ( $△$ ABC). [4 MARKS]

Discussion

18.	All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is (i) a red card, (ii) a face card, (iii) a card of clubs [4 MARKS]
Answer» All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is (i) a red card, (ii) a face card, (iii) a card of clubs [4 MARKS]

Discussion

19.	How do you represent 0.3125 in the form of pq where p and q are integers?
Answer» How do you represent $0.3125$ in the form of $\frac{p}{q}$ where $p$ and $q$ are integers?

Discussion

20.	Find 5 rational numbers between 3 and 4 using x(n+1)n+1,y(n+1)n+1 [4 MARKS]
Answer» Find 5 rational numbers between 3 and 4 using $\frac{x (n + 1)}{n + 1}, \frac{y (n + 1)}{n + 1}$ [4 MARKS]

Discussion

21.	If CD = 9 m, then find the perimeter of the △ BCD.
Answer» If CD = 9 m, then find the perimeter of the $△$ BCD.

21.

If CD = 9 m, then find the perimeter of the △ BCD.

Answer»

If CD = 9 m, then find the perimeter of the $△$ BCD.

Discussion

22.	In the given figure, if ∠OAB=40∘, then ∠ACB = ___.
Answer» In the given figure, if $∠ OAB = 40^{\circ}$ , then $∠ ACB$ = ___.

Discussion

23.	Explain Euclid Postulates.
Answer» Explain Euclid Postulates.

Discussion

24.	In the given figure, ABC is an equilateral triangle; PQ\|\|AC and AC is produced to R such that CR = BP. Prove that QR bisects PC.
Answer» $In the given figure, ABC is an equilateral triangle; P Q \| \| A C and AC is produced to R such that CR = BP. Prove that QR bisects PC.$

24.

In the given figure, ABC is an equilateral triangle; PQ||AC and AC is produced to R such that CR = BP. Prove that QR bisects PC.

Answer»

$In the given figure, ABC is an equilateral triangle; P Q | | A C and AC is produced to R such that CR = BP. Prove that QR bisects PC.$

Discussion

25.	Let D, E, F be the middle points of the sides BC, CA, AB respectively of a ΔABC. Then,−−→AD+−−→BE+−−→CF equals
Answer» Let D, E, F be the middle points of the sides BC, CA, AB respectively of a $Δ A B C$ . Then, $- - \to A D + - - \to B E + - - \to C F$ equals

Discussion

26.	If A = {x:x²+5x+6,x€N} then n(P(A))=____ what is meaning of n(P(A))?
Answer» If A = {x:x²+5x+6,x€N} then n(P(A))=____ what is meaning of n(P(A))?

Discussion

27.	is one of the factors of ab−2b+a2−2a
Answer» is one of the factors of $a b - 2 b + a^{2} - 2 a$

Discussion

28.	Question 3 (iii) In the given figure, ABD is a triangle right angled at A and AC⊥BD. Show that (iii)AD2=BD×CD
Answer» Question 3 (iii) In the given figure, ABD is a triangle right angled at A and $A C ⊥ B D$ . Show that $(i i i) A D^{2} = B D \times C D$

Discussion

29.	If I draw two circles of radius 3 cm and 5 cm with common centre and draw a line AB such that it is chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.
Answer» If I draw two circles of radius 3 cm and 5 cm with common centre and draw a line AB such that it is chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.

29.

If I draw two circles of radius 3 cm and 5 cm with common centre and draw a line AB such that it is chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.

Answer»

If I draw two circles of radius 3 cm and 5 cm with common centre and draw a line AB such that it is chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.

Discussion

30.	In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I and 3 read all three newspapers, find (i) the number of people who read atleast one of the newspapers. (ii) the numbers of people who read exactly one newspaper.
Answer» In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I and 3 read all three newspapers, find (i) the number of people who read atleast one of the newspapers. (ii) the numbers of people who read exactly one newspaper.

30.

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I and 3 read all three newspapers, find (i) the number of people who read atleast one of the newspapers. (ii) the numbers of people who read exactly one newspaper.

Answer»

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I and 3 read all three newspapers, find

(i) the number of people who read atleast one of the newspapers.

(ii) the numbers of people who read exactly one newspaper.

Discussion

31.	If the mean of 5 observations x,x+2,x+4,x+6 and x+8 is 11, find the value of x.
Answer» If the mean of $5$ observations $x, x + 2, x + 4, x + 6$ and $x + 8$ is $11,$ find the value of $x .$

Discussion

32.	In the figure given below, state which lines are parallel and why?
Answer» In the figure given below, state which lines are parallel and why?

32.

In the figure given below, state which lines are parallel and why?

Answer»

In the figure given below, state which lines are parallel and why?

Discussion

33.	In th figure, AB \|\| DE, find ∠ACD.
Answer» In th figure, AB $\| \|$ DE, find $∠ A C D$ .

33.

In th figure, AB || DE, find ∠ACD.

Answer»

In th figure, AB $| |$ DE, find $∠ A C D$ .

Discussion

34.	Simple interest on a sum of money for 2 years at 4 % is rupees 450. find compound interest on the same sum at the same rate for 2 years.
Answer» Simple interest on a sum of money for 2 years at 4 % is rupees 450. find compound interest on the same sum at the same rate for 2 years.

Discussion

35.	Factorize (ax+by)² + (ay-bx)²
Answer» Factorize (ax+by)² + (ay-bx)²

Discussion

36.	Find the mode for the following series: 7.5,7.3,7.2,7.2,7.3,7.3,7.4,7.5,7.5,7.3,7.2,7.6,7.2
Answer» Find the mode for the following series: 7.5,7.3,7.2,7.2,7.3,7.3,7.4,7.5,7.5,7.3,7.2,7.6,7.2

36.

Find the mode for the following series: 7.5,7.3,7.2,7.2,7.3,7.3,7.4,7.5,7.5,7.3,7.2,7.6,7.2

Answer»

Find the mode for the following series:

7.5,7.3,7.2,7.2,7.3,7.3,7.4,7.5,7.5,7.3,7.2,7.6,7.2

Discussion

37.	ABCD is a quadrilateral such that diagonal AC bisects that angles ∠A and ∠C. Prove that AB = AD and CB = CD.
Answer» $ABCD is a quadrilateral such that diagonal AC bisects that angles ∠ A a n d ∠ C . Prove that AB = AD and CB = CD.$

Discussion

38.	In the given figure, ABCD and ABEF are two cyclic quadrilateral. If ∠BCD=110∘ then ∠BEF=? (a) 55∘ (b) 70∘ (c) 90∘ (d) 110∘
Answer» In the given figure, ABCD and ABEF are two cyclic quadrilateral. If $∠ B C D = 110^{\circ} t h e n ∠ B E F = ?$ (a) $55^{\circ}$ (b) $70^{\circ}$ (c) $90^{\circ}$ (d) $110^{\circ}$

38.

In the given figure, ABCD and ABEF are two cyclic quadrilateral. If ∠BCD=110∘ then ∠BEF=? (a) 55∘ (b) 70∘ (c) 90∘ (d) 110∘

Answer»

In the given figure, ABCD and ABEF are two cyclic quadrilateral. If $∠ B C D = 110^{\circ} t h e n ∠ B E F = ?$

(a) $55^{\circ}$

(b) $70^{\circ}$

(c) $90^{\circ}$

(d) $110^{\circ}$

Discussion

39.	The mean weight of 25 students of a class is 52 kg. If the mean weight of the first 13 students of the class is 48 kg and that of the last 13 students is 55 kg, find the weight of the 13th student.
Answer» The mean weight of 25 students of a class is 52 kg. If the mean weight of the first 13 students of the class is 48 kg and that of the last 13 students is 55 kg, find the weight of the 13th student.

Discussion

40.	Find the following using the identity a) 160×94 b) 0.99×1.01
Answer» Find the following using the identity a) $160 \times 94$ b) $0.99 \times 1.01$

Discussion

41.	In a triangle ABC, ∠B = 35∘. What type of angle is this ?
Answer» In a triangle ABC, $∠$ B = 35 $^{\circ}$ . What type of angle is this ?

Discussion

42.	The ratio of height to the base radius of a cylinder is 1:2. The ratio of total surface of cylinder to curved surface of cylinder is:
Answer» The ratio of height to the base radius of a cylinder is 1:2. The ratio of total surface of cylinder to curved surface of cylinder is:

Discussion

43.	What is the value of 8a3+27b3+c3 if 2a+3b+c=0?
Answer» What is the value of $8 a^{3} + 27 b^{3} + c^{3}$ if $2 a + 3 b + c = 0$ ?

Discussion

44.	6x2+17x+5=? (a) (2x+1) (b) (2x+5)(3x+1) (c) (6x+5)(x+1) (d) None of these
Answer» $6 x^{2} + 17 x + 5$ =? (a) $(2 x + 1)$ (b) $(2 x + 5) (3 x + 1)$ (c) $(6 x + 5) (x + 1)$ (d) None of these

44.

6x2+17x+5=? (a) (2x+1) (b) (2x+5)(3x+1) (c) (6x+5)(x+1) (d) None of these

Answer»

$6 x^{2} + 17 x + 5$ =?

(a) $(2 x + 1)$

(b) $(2 x + 5) (3 x + 1)$

(c) $(6 x + 5) (x + 1)$

(d) None of these

Discussion

45.	\|A3×3\|=3,\|B3×3\|=−1 and \|C2×2\|=+2 then \|2ABC\|=
Answer» $\| A_{3 \times 3} \| = 3, \| B_{3 \times 3} \| = - 1$ and $\| C_{2 \times 2} \| = + 2$ then $\| 2 A B C \| =$

Discussion

46.	Find four rational numbers between 37 and 57.
Answer» Find four rational numbers between $\frac{3}{7}$ and $\frac{5}{7}$ .

Discussion

47.	Find two rational numbers between 0.232332333...&0.212112111...
Answer» Find two rational numbers between 0.232332333...&0.212112111...

Discussion

48.	A tank 72 cm long,60 cm wide ,36 cm high, contains water to a depth of 18cm .A metal block 48 cm by 36 cm by 15 cm is put into the tank and totally submerged.Find in cm the amount the water level rises?
Answer» A tank 72 cm long,60 cm wide ,36 cm high, contains water to a depth of 18cm .A metal block 48 cm by 36 cm by 15 cm is put into the tank and totally submerged.Find in cm the amount the water level rises?

Discussion

49.	If the cost of 12 pens is Rs.75 then the cost of 1 pen is:
Answer» If the cost of 12 pens is Rs.75 then the cost of 1 pen is:

Discussion

50.	A circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, the radius of the circle is
Answer» A circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, the radius of the circle is

50.

A circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, the radius of the circle is

Answer»

A circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, the radius of the circle is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 3 (iii) On comparing the ratios a1a2, b1b2 and c1c2 find out whether the following pair of linear equations are consistent, or inconsistent. 32x+53y=7;9x−10y=14

Question 1 (i) In the following figure (i), DE || BC. Find EC.

3√−a6×b3×c21c9×a12=

The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination are 71, find the ratio of the number of boys to the number of girls.

Factorise: 13x2−2x−9

Find the area of the region in red colour.

In the figure, AC = 10cm, PC = 15cm, PQ = 12 cm, then PB = __ cm .

Find the cost of sinking a tube-well 280 m deep , having a diameter 3m at the rate of Rs 15 per cubic metre. Find also the cost of cementing its inner curved sufrace at Rs 10 per square metre.

Factorize : x2−1−2a−a2.

If each edge of a cube is increased by 50%, the percentage increase in its surface area is

In the figure, if AB⊥BC, then x=

Find three rational numbers lying between 35 and 78 How many rational numbers can be determined between these two numbers?

In the given figure, O is the centre of the circle. If ∠ACB=50∘, find ∠OAB.

1. Is −3+√6 irrational 2. Is −3×√8 irrational 3. 4√3 irrational 4. √10 multiply √40

A __ connects a vertex of a triangle to the midpoint of the opposite side.

Ravi asked suresh about his age. Suresh replied to him the value of the following expression is my age, Then, Suresh's age is 15[sin222∘+sin268∘cos222∘+cos268∘+sin263∘+cos63∘sin27∘]

D, E and F are respectively the mid-points of the sides BC, CA and AB of a △ABC. Show that (i) BDEF is a parallelogram.(ii) ar (△DEF) = 14 ar (△ABC). [4 MARKS]

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is (i) a red card, (ii) a face card, (iii) a card of clubs [4 MARKS]

How do you represent 0.3125 in the form of pq where p and q are integers?

Find 5 rational numbers between 3 and 4 using x(n+1)n+1,y(n+1)n+1 [4 MARKS]

If CD = 9 m, then find the perimeter of the △ BCD.

In the given figure, if ∠OAB=40∘, then ∠ACB = ___.

Explain Euclid Postulates.

In the given figure, ABC is an equilateral triangle; PQ||AC and AC is produced to R such that CR = BP. Prove that QR bisects PC.

Let D, E, F be the middle points of the sides BC, CA, AB respectively of a ΔABC. Then,−−→AD+−−→BE+−−→CF equals

If A = {x:x²+5x+6,x€N} then n(P(A))=____ what is meaning of n(P(A))?

is one of the factors of ab−2b+a2−2a

Question 3 (iii) In the given figure, ABD is a triangle right angled at A and AC⊥BD. Show that (iii)AD2=BD×CD

If I draw two circles of radius 3 cm and 5 cm with common centre and draw a line AB such that it is chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.

If the mean of 5 observations x,x+2,x+4,x+6 and x+8 is 11, find the value of x.

In the figure given below, state which lines are parallel and why?

In th figure, AB || DE, find ∠ACD.

Simple interest on a sum of money for 2 years at 4 % is rupees 450. find compound interest on the same sum at the same rate for 2 years.

Factorize (ax+by)² + (ay-bx)²

Find the mode for the following series: 7.5,7.3,7.2,7.2,7.3,7.3,7.4,7.5,7.5,7.3,7.2,7.6,7.2

ABCD is a quadrilateral such that diagonal AC bisects that angles ∠A and ∠C. Prove that AB = AD and CB = CD.

In the given figure, ABCD and ABEF are two cyclic quadrilateral. If ∠BCD=110∘ then ∠BEF=? (a) 55∘ (b) 70∘ (c) 90∘ (d) 110∘

The mean weight of 25 students of a class is 52 kg. If the mean weight of the first 13 students of the class is 48 kg and that of the last 13 students is 55 kg, find the weight of the 13th student.

Find the following using the identity a) 160×94 b) 0.99×1.01

In a triangle ABC, ∠B = 35∘. What type of angle is this ?

The ratio of height to the base radius of a cylinder is 1:2. The ratio of total surface of cylinder to curved surface of cylinder is:

What is the value of 8a3+27b3+c3 if 2a+3b+c=0?

6x2+17x+5=? (a) (2x+1) (b) (2x+5)(3x+1) (c) (6x+5)(x+1) (d) None of these

|A3×3|=3,|B3×3|=−1 and |C2×2|=+2 then |2ABC|=

Find four rational numbers between 37 and 57.

Find two rational numbers between 0.232332333...&amp;0.212112111...

A tank 72 cm long,60 cm wide ,36 cm high, contains water to a depth of 18cm .A metal block 48 cm by 36 cm by 15 cm is put into the tank and totally submerged.Find in cm the amount the water level rises?

If the cost of 12 pens is Rs.75 then the cost of 1 pen is:

A circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, the radius of the circle is

Find two rational numbers between 0.232332333...&0.212112111...