32581 + Interview Questions in Mathematics

1.	Identify the number in place of ‘?’
Answer» Identify the number in place of ‘?’

Discussion

2.	Find the roots of the following equations: (ii) 1x+4−1x−7=1130,x≠−4,7
Answer» Find the roots of the following equations: (ii) $\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}, x \neq - 4, 7$

Discussion

3.	In Fig. 7.223, D is the mid-point of side BC and AE⊥BC. If BC = a AC=b, AB=c, ED=z, AD = p and AE =h, prove that: (i) b2=p2+ax+a24 (ii) c2=p2+ax+a24 (iii) b2+c2=2p2+a24
Answer» In Fig. 7.223, D is the mid-point of side BC and $A E ⊥ B C$ . If BC = a AC=b, AB=c, ED=z, AD = p and AE =h, prove that: (i) $b^{2} = p^{2} + a x + \frac{a^{2}}{4}$ (ii) $c^{2} = p^{2} + a x + \frac{a^{2}}{4}$ (iii) $b^{2} + c^{2} = 2 p^{2} + \frac{a^{2}}{4}$

3.

In Fig. 7.223, D is the mid-point of side BC and AE⊥BC. If BC = a AC=b, AB=c, ED=z, AD = p and AE =h, prove that: (i) b2=p2+ax+a24 (ii) c2=p2+ax+a24 (iii) b2+c2=2p2+a24

Answer»

In Fig. 7.223, D is the mid-point of side BC and $A E ⊥ B C$ . If BC = a AC=b, AB=c, ED=z, AD = p and AE =h, prove that:

(i) $b^{2} = p^{2} + a x + \frac{a^{2}}{4}$
(ii) $c^{2} = p^{2} + a x + \frac{a^{2}}{4}$
(iii) $b^{2} + c^{2} = 2 p^{2} + \frac{a^{2}}{4}$

Discussion

4.	In Fig. 7.144, ΔABC is right angled at C and DE⊥AB. Prove that ΔABC∼ΔADE and hence find the lengths of AE and DE.
Answer» In Fig. 7.144, $Δ A B C$ is right angled at C and $D E ⊥ A B$ . Prove that $Δ A B C \sim Δ A D E$ and hence find the lengths of AE and DE.

4.

In Fig. 7.144, ΔABC is right angled at C and DE⊥AB. Prove that ΔABC∼ΔADE and hence find the lengths of AE and DE.

Answer»

In Fig. 7.144, $Δ A B C$ is right angled at C and $D E ⊥ A B$ . Prove that $Δ A B C \sim Δ A D E$ and hence find the lengths of AE and DE.

Discussion

5.	In ΔABC (Fig 7.60), if ∠1=∠2, prove that ABAC=BDDC.
Answer» In $Δ A B C$ (Fig 7.60), if $∠ 1 = ∠ 2$ , prove that $\frac{A B}{A C} = \frac{B D}{D C}$ .

5.

In ΔABC (Fig 7.60), if ∠1=∠2, prove that ABAC=BDDC.

Answer»

In $Δ A B C$ (Fig 7.60), if $∠ 1 = ∠ 2$ , prove that $\frac{A B}{A C} = \frac{B D}{D C}$ .

Discussion

6.	In △ ABC, D is a point on BC such that BD: DC = 1 : 3. If area △ ABC = 60 sq cm, then area of △ ABD = ____ sq cm.
Answer» In △ ABC, D is a point on BC such that BD: DC = 1 : 3. If area △ ABC = 60 sq cm, then area of △ ABD = ____ sq cm.

Discussion

7.	A line segment AB, we want to divide it in the ratio m : n, where both m and n __ integers.
Answer» A line segment AB, we want to divide it in the ratio m : n, where both m and n __ integers.

Discussion

8.	If the area of a circle with radius r is equal to the curved surface area of a cone with radius r1 and slant height l then the value of r1 in terms of r and l is:
Answer» If the area of a circle with radius r is equal to the curved surface area of a cone with radius $r_{1}$ and slant height l then the value of $r_{1}$ in terms of r and l is:

Discussion

9.	△ ABC is right angled at B and the perpendicular drawn to the opposite side bisects it at D. BD = ___ cm if AD = DC = 5 cm.
Answer» $△$ ABC is right angled at B and the perpendicular drawn to the opposite side bisects it at D. BD = ___ cm if AD = DC = 5 cm.

Discussion

10.	A, B are two events with positive probabilities. If P(A)=0.4, P(B/A)=0.9, P(¯B/¯A)=0.6 then
Answer» A, B are two events with positive probabilities. If $P (A) = 0.4$ , $P (B / A) = 0.9$ , $P (¯ B / ¯ A) = 0.6$ then

Discussion

11.	what is the expression of sec θ in the given triangle?
Answer» what is the expression of sec θ in the given triangle?

11.

what is the expression of sec θ in the given triangle?

Answer»

what is the expression of sec θ in the given triangle?

Discussion

12.	A copper wire of diameter 6 mm is evely wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cu-cm, find the weight of the wire.
Answer» A copper wire of diameter 6 mm is evely wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cu-cm, find the weight of the wire.

Discussion

13.	A coin is tossed once. What is the probability of getting tail?
Answer» A coin is tossed once. What is the probability of getting tail?

Discussion

14.	The sum of two natural numbers is 15 and the sum of their reciprocals is 310. Find the numbers.
Answer» The sum of two natural numbers is 15 and the sum of their reciprocals is $\frac{3}{10}$ . Find the numbers.

Discussion

15.	A solid is in the shape of a frustum of a cone. The diameters of the two circular ends are 60 cm and 36 cm and the leight is 9 cm. Find the area of its whole surface and the volume.
Answer» A solid is in the shape of a frustum of a cone. The diameters of the two circular ends are 60 cm and 36 cm and the leight is 9 cm. Find the area of its whole surface and the volume.

Discussion

16.	A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1,2,3,...,12 as shown in the figure. What is the probability that it will point to (i) 6 ? (ii) an even number? (iii) a prime number ? (iv) a number which is a multiple of 5?
Answer» A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers $1, 2, 3, . . ., 12$ as shown in the figure. What is the probability that it will point to (i) $6$ ? (ii) an even number? (iii) a prime number ? (iv) a number which is a multiple of $5$ ?

16.

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1,2,3,...,12 as shown in the figure. What is the probability that it will point to (i) 6 ? (ii) an even number? (iii) a prime number ? (iv) a number which is a multiple of 5?

Answer»

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers $1, 2, 3, . . ., 12$ as shown in the figure. What is the probability that it will point to
(i) $6$ ?

(ii) an even number?

(iii) a prime number ?

(iv) a number which is a multiple of $5$ ?

Discussion

17.	Find the area of both the segments of a circle of radius 42 cm with central angle 120∘. [ Given, sin 120∘=√32and√3 = 1.73. ]
Answer» Find the area of both the segments of a circle of radius 42 cm with central angle $120^{\circ}$ . [ Given, sin $120^{\circ} = \frac{\sqrt{3}}{2} a n d \sqrt{3}$ = 1.73. ]

Discussion

18.	If the mean of the set of number x1,x2...xn is ¯x ,then the mean of the number xi+2i,1≤≤n is
Answer» If the mean of the set of number $x_{1}, x_{2} . . . x_{n}$ is $¯ x$ ,then the mean of the number $x_{i} + 2 i, 1 \leq\leq n$ is

Discussion

19.	The total surface area in m2 of a cuboid with dimensions of 26m, 14m and 6.5m respectively is ___ m2.
Answer» The total surface area in $m^{2}$ of a cuboid with dimensions of 26m, 14m and 6.5m respectively is ___ m $^{2}$ .

Discussion

20.	Question 1 Find the mean marks of students for the following distribution MarksNumber of students0 and above 8010 and above 7720 and above 7230 and above 6540 and above 5550 and above 4360 and above 2870 and above 1680 and above 1090 and above 8100 and above 0
Answer» Question 1 Find the mean marks of students for the following distribution $\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s 0 a n d a b o v e & 80 10 a n d a b o v e & 77 20 a n d a b o v e & 72 30 a n d a b o v e & 65 40 a n d a b o v e & 55 50 a n d a b o v e & 43 60 a n d a b o v e & 28 70 a n d a b o v e & 16 80 a n d a b o v e & 10 90 a n d a b o v e & 8 100 a n d a b o v e & 0 \end{matrix}$

Discussion

21.	Check whether 6n can end with the digit 0 for any natural number n.
Answer» Check whether $6^{n}$ can end with the digit 0 for any natural number n.

Discussion

22.	The equation of the straight line which passes through the point P (3, 4) and whose intercept on y-axis is twice of that on x-axis, is .
Answer» The equation of the straight line which passes through the point P (3, 4) and whose intercept on y-axis is twice of that on x-axis, is .

Discussion

23.	The equation of circle with centre (1,1) and radius 4 is given by ________ .
Answer» The equation of circle with centre $(1, 1)$ and radius 4 is given by ________ .

Discussion

24.	If a and b are distinct real numbers, show that the quadratic equation 2(a2+b2)x2+2(a+b)x+1=0 has no real roots.
Answer» If a and b are distinct real numbers, show that the quadratic equation $2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0$ has no real roots.

Discussion

25.	Question 36 State whether the following statement is true (T) or false (F). Sum of the ages of Anjuand her mother is 65 years. If Anju's pesent age is y years, then her mother's age before 5 years is (60-y) years.
Answer» Question 36 State whether the following statement is true (T) or false (F). Sum of the ages of Anjuand her mother is 65 years. If Anju's pesent age is y years, then her mother's age before 5 years is (60-y) years.

25.

Question 36 State whether the following statement is true (T) or false (F). Sum of the ages of Anjuand her mother is 65 years. If Anju's pesent age is y years, then her mother's age before 5 years is (60-y) years.

Answer»

Question 36

State whether the following statement is true (T) or false (F).

Sum of the ages of Anjuand her mother is 65 years. If Anju's pesent age is y years, then her mother's age before 5 years is (60-y) years.

Discussion

26.	Write down the decimal expansions of : 2323.52
Answer» Write down the decimal expansions of : $\frac{23}{2^{3} {.5}^{2}}$

Discussion

27.	Angle between the hour and minute hand of a clock at 11:15 is -
Answer» Angle between the hour and minute hand of a clock at 11:15 is -

Discussion

28.	Question 1 (ii) 4+78
Answer» Question 1 (ii) $4 + \frac{7}{8}$

Discussion

29.	State the co-ordinates of the followingpoints under reflection in origin : (i) (-2, -4) (ii) (-2, 7) (iii) (0, 0)
Answer» State the co-ordinates of the followingpoints under reflection in origin : (i) (-2, -4) (ii) (-2, 7) (iii) (0, 0)

29.

State the co-ordinates of the followingpoints under reflection in origin : (i) (-2, -4) (ii) (-2, 7) (iii) (0, 0)

Answer»

State the co-ordinates of the followingpoints under reflection in origin :

(i) (-2, -4) (ii) (-2, 7) (iii) (0, 0)

Discussion

30.	In Fig. 8.67, two tangents AB and AC are drawn to a circle with centre O such that ∠BAC=120∘. Prove that OA =2AB.
Answer» In Fig. 8.67, two tangents AB and AC are drawn to a circle with centre O such that $∠ B A C = 120^{\circ}$ . Prove that OA =2AB.

Discussion

31.	Three coins are tossed simultaneously. What is the probability of getting exactly two heads? (a) 12 (b) 14 (c) 38 (d) 34
Answer» Three coins are tossed simultaneously. What is the probability of getting exactly two heads? (a) $\frac{1}{2}$ (b) $\frac{1}{4}$ (c) $\frac{3}{8}$ (d) $\frac{3}{4}$

Discussion

32.	Anita buys a new salt cellar in the shape of a cylinder topped by a hemisphere as shown below. The cylinder has a diameter of 6 cm and a height of 10 cm. She pours the salt into the salt cellar, so that it takes up half the total volume of the cellar. Find the depth of the salt, marked with x in the diagram
Answer» Anita buys a new salt cellar in the shape of a cylinder topped by a hemisphere as shown below. The cylinder has a diameter of 6 cm and a height of 10 cm. She pours the salt into the salt cellar, so that it takes up half the total volume of the cellar. Find the depth of the salt, marked with x in the diagram

Discussion

33.	Question 5 Two identical cubes each of volume 64 cm3 are joined together end to end. What is the surface area of the resulting cuboid?
Answer» Question 5 Two identical cubes each of volume $64 c m^{3}$ are joined together end to end. What is the surface area of the resulting cuboid?

Discussion

34.	Given that x−√5 is a factor of the cubic polynomial x3−3√5x2+13x−3√5 find all the zeroes of the polynomial.
Answer» Given that $x - \sqrt{5}$ is a factor of the cubic polynomial $x^{3} - 3 \sqrt{5} x^{2} + 13 x - 3 \sqrt{5}$ find all the zeroes of the polynomial.

Discussion

35.	In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10 cm, find the length of PB up to one place of decimal.
Answer» In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10 cm, find the length of PB up to one place of decimal.

35.

In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10 cm, find the length of PB up to one place of decimal.

Answer»

In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10 cm, find the length of PB up to one place of decimal.

Discussion

36.	An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 14 of the radius of the original ball, how many such balls are made ? Compare the surface area, of all the smaller balls combined together with that of the original ball.
Answer» An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is $\frac{1}{4}$ of the radius of the original ball, how many such balls are made ? Compare the surface area, of all the smaller balls combined together with that of the original ball.

Discussion

37.	Show that: (i) x−2isafactorof5x2+15x−50 (ii) 3x+2isafactorof3x2−x−2
Answer» Show that: (i) $x - 2 i s a f a c t o r o f 5 x^{2} + 15 x - 50$ (ii) $3 x + 2 i s a f a c t o r o f 3 x^{2} - x - 2$

Discussion

38.	A car moves a distance of 2592 km with uniform speed. The number of hours taken for the journey is one-half the number representing the speed, in km/hour. Find the time taken to cover the distance.
Answer» A car moves a distance of 2592 km with uniform speed. The number of hours taken for the journey is one-half the number representing the speed, in km/hour. Find the time taken to cover the distance.

Discussion

39.	There are two temples, one on each bank of a river, just opposite to each other. One temple is 50 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30∘ and 60∘ respectively. Find the width of the river and the height of the other temple.
Answer» There are two temples, one on each bank of a river, just opposite to each other. One temple is 50 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are $30^{\circ}$ and $60^{\circ}$ respectively. Find the width of the river and the height of the other temple.

Discussion

40.	The 9th term of an A.P. is twice its 10th term. Show that its 72nd term is 4 times is 15th term .
Answer» The 9th term of an A.P. is twice its 10th term. Show that its 72nd term is 4 times is 15th term .

Discussion

41.	The sum of -3491 and 4567 is ___
Answer» The sum of -3491 and 4567 is ___

Discussion

42.	Find the perimeter and area of the figure given below:
Answer» Find the perimeter and area of the figure given below:

Discussion

43.	Simplify (1+1x)(1+1x+1)(1+1x+2)(1+1x+3)
Answer» Simplify $(1 + \frac{1}{x}) (1 + \frac{1}{x + 1}) (1 + \frac{1}{x + 2}) (1 + \frac{1}{x + 3})$

Discussion

44.	I have 2 road rollers. These road rollers are joined end to end along the flat surfaces to form a combined longer road roller. What are the surfaces present in the new road roller?
Answer» I have 2 road rollers. These road rollers are joined end to end along the flat surfaces to form a combined longer road roller. What are the surfaces present in the new road roller?

Discussion

45.	In △ABC, the medians BE and CF intersect at G. AGD is a line meetin BC in D. If GD is 1.5 cm, then AD is equal to -
Answer» In $△$ ABC, the medians BE and CF intersect at G. AGD is a line meetin BC in D. If GD is 1.5 cm, then AD is equal to -

45.

In △ABC, the medians BE and CF intersect at G. AGD is a line meetin BC in D. If GD is 1.5 cm, then AD is equal to -

Answer»

In $△$ ABC, the medians BE and CF intersect at G. AGD is a line meetin BC in D. If GD is 1.5 cm, then AD is equal to -

Discussion

46.	Find the discriminant of the quadratic equation x2 + 5 x – 3 = 0
Answer» Find the discriminant of the quadratic equation $x^{2}$ + 5 x – 3 = 0

Discussion

47.	A two digit number is 4 times the sum of its digit and twice the product of the digits find the number.
Answer» A two digit number is 4 times the sum of its digit and twice the product of the digits find the number.

Discussion

48.	If[αβγ−α]is the square root of second order unit matrix, Then α,β and γ should satisfy the relation
Answer» $I f [\begin{matrix} α & β γ & - α \end{matrix}] is the square root of second order unit matrix, T h e n α, β a n d γ should satisfy the relation$

Discussion

49.	A sum of money is to be distributed among A, B, C, D in the proportion of 3:5:10:4. If C gets Rs. 600 more than D, what is A's share?
Answer» A sum of money is to be distributed among A, B, C, D in the proportion of 3:5:10:4. If C gets Rs. 600 more than D, what is A's share?

Discussion

50.	Question 16 The sum of first 16 terms of the AP 10, 6, 2, … is A) -320 B) 320 C) -352 D) -400
Answer» Question 16 The sum of first 16 terms of the AP 10, 6, 2, … is A) -320 B) 320 C) -352 D) -400

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Identify the number in place of ‘?’

Find the roots of the following equations: (ii) 1x+4−1x−7=1130,x≠−4,7

In Fig. 7.223, D is the mid-point of side BC and AE⊥BC. If BC = a AC=b, AB=c, ED=z, AD = p and AE =h, prove that: (i) b2=p2+ax+a24 (ii) c2=p2+ax+a24 (iii) b2+c2=2p2+a24

In Fig. 7.144, ΔABC is right angled at C and DE⊥AB. Prove that ΔABC∼ΔADE and hence find the lengths of AE and DE.

In ΔABC (Fig 7.60), if ∠1=∠2, prove that ABAC=BDDC.

In △ ABC, D is a point on BC such that BD: DC = 1 : 3. If area △ ABC = 60 sq cm, then area of △ ABD = ____ sq cm.

A line segment AB, we want to divide it in the ratio m : n, where both m and n __ integers.

If the area of a circle with radius r is equal to the curved surface area of a cone with radius r1 and slant height l then the value of r1 in terms of r and l is:

△ ABC is right angled at B and the perpendicular drawn to the opposite side bisects it at D. BD = ___ cm if AD = DC = 5 cm.

A, B are two events with positive probabilities. If P(A)=0.4, P(B/A)=0.9, P(¯B/¯A)=0.6 then

what is the expression of sec θ in the given triangle?

A copper wire of diameter 6 mm is evely wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cu-cm, find the weight of the wire.

A coin is tossed once. What is the probability of getting tail?

The sum of two natural numbers is 15 and the sum of their reciprocals is 310. Find the numbers.

A solid is in the shape of a frustum of a cone. The diameters of the two circular ends are 60 cm and 36 cm and the leight is 9 cm. Find the area of its whole surface and the volume.

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1,2,3,...,12 as shown in the figure. What is the probability that it will point to (i) 6 ? (ii) an even number? (iii) a prime number ? (iv) a number which is a multiple of 5?

Find the area of both the segments of a circle of radius 42 cm with central angle 120∘. [ Given, sin 120∘=√32and√3 = 1.73. ]

If the mean of the set of number x1,x2...xn is ¯x ,then the mean of the number xi+2i,1≤≤n is

The total surface area in m2 of a cuboid with dimensions of 26m, 14m and 6.5m respectively is ___ m2.

Question 1 Find the mean marks of students for the following distribution MarksNumber of students0 and above 8010 and above 7720 and above 7230 and above 6540 and above 5550 and above 4360 and above 2870 and above 1680 and above 1090 and above 8100 and above 0

Check whether 6n can end with the digit 0 for any natural number n.

The equation of the straight line which passes through the point P (3, 4) and whose intercept on y-axis is twice of that on x-axis, is .

The equation of circle with centre (1,1) and radius 4 is given by ________ .

If a and b are distinct real numbers, show that the quadratic equation 2(a2+b2)x2+2(a+b)x+1=0 has no real roots.

Question 36 State whether the following statement is true (T) or false (F). Sum of the ages of Anjuand her mother is 65 years. If Anju's pesent age is y years, then her mother's age before 5 years is (60-y) years.

Write down the decimal expansions of : 2323.52

Angle between the hour and minute hand of a clock at 11:15 is -

Question 1 (ii) 4+78

State the co-ordinates of the followingpoints under reflection in origin : (i) (-2, -4) (ii) (-2, 7) (iii) (0, 0)

In Fig. 8.67, two tangents AB and AC are drawn to a circle with centre O such that ∠BAC=120∘. Prove that OA =2AB.

Three coins are tossed simultaneously. What is the probability of getting exactly two heads? (a) 12 (b) 14 (c) 38 (d) 34

Question 5 Two identical cubes each of volume 64 cm3 are joined together end to end. What is the surface area of the resulting cuboid?

Given that x−√5 is a factor of the cubic polynomial x3−3√5x2+13x−3√5 find all the zeroes of the polynomial.

In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10 cm, find the length of PB up to one place of decimal.

Show that: (i) x−2isafactorof5x2+15x−50 (ii) 3x+2isafactorof3x2−x−2

A car moves a distance of 2592 km with uniform speed. The number of hours taken for the journey is one-half the number representing the speed, in km/hour. Find the time taken to cover the distance.

The 9th term of an A.P. is twice its 10th term. Show that its 72nd term is 4 times is 15th term .

The sum of -3491 and 4567 is ___

Find the perimeter and area of the figure given below:

Simplify (1+1x)(1+1x+1)(1+1x+2)(1+1x+3)

I have 2 road rollers. These road rollers are joined end to end along the flat surfaces to form a combined longer road roller. What are the surfaces present in the new road roller?

In △ABC, the medians BE and CF intersect at G. AGD is a line meetin BC in D. If GD is 1.5 cm, then AD is equal to -

Find the discriminant of the quadratic equation x2 + 5 x – 3 = 0

A two digit number is 4 times the sum of its digit and twice the product of the digits find the number.

If[αβγ−α]is the square root of second order unit matrix, Then α,β and γ should satisfy the relation

A sum of money is to be distributed among A, B, C, D in the proportion of 3:5:10:4. If C gets Rs. 600 more than D, what is A's share?

Question 16 The sum of first 16 terms of the AP 10, 6, 2, … is A) -320 B) 320 C) -352 D) -400​​​​​​​

Question 16 The sum of first 16 terms of the AP 10, 6, 2, … is A) -320 B) 320 C) -352 D) -400