24740 + Interview Questions in Mathematics Page 79 InterviewSolution

3901.	Angles of a triangle are in AP if the smallest angle is 450.Find the largest angle
Answer» Angles of a triangle are in AP if the smallest angle is 450.Find the largest angle

Discussion

3902.	The point at which concurrent lines intersect is called point of ___.
Answer» The point at which concurrent lines intersect is called point of ___.

Discussion

3903.	The circles shown below have the same centre O. Prove that ΔOAB and ΔOPQ are similar.
Answer» The circles shown below have the same centre O. Prove that ΔOAB and ΔOPQ are similar.

3903.

The circles shown below have the same centre O. Prove that ΔOAB and ΔOPQ are similar.

Answer»

The circles shown below have the same centre O.

Prove that ΔOAB and ΔOPQ are similar.

Discussion

3904.	The area in cm2 of a sector of a circle with radius 6 cm if angle of the sector is 60∘ is ___ cm2.
Answer» The area in $c m^{2}$ of a sector of a circle with radius 6 cm if angle of the sector is $60^{\circ}$ is ___ $c m^{2}$ .

Discussion

3905.	A building is in the form of a cylinder surmounted by a hemispherical vaulteddome and contains 41m3 of air. If the internal diameter of dome is equal to itstotal height above the floor, find the height of the building?
Answer» A building is in the form of a cylinder surmounted by a hemispherical vaulteddome and contains 41m3 of air. If the internal diameter of dome is equal to itstotal height above the floor, find the height of the building?

Discussion

3906.	Question 1 (viii)Without actually performing the long division, state whether 615 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Answer» Question 1 (viii) Without actually performing the long division, state whether $\frac{6}{15}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Discussion

3907.	If x = 5+2, then x-1x equals(a) 25(b) 4(c) 2(d) 5
Answer» If x = $\sqrt{5} + 2$ , then $x - \frac{1}{x}$ equals (a) $2 \sqrt{5}$ (b) 4 (c) 2 (d) $\sqrt{5}$

Discussion

3908.	PQRS is a parallelogram, S is the midpoint of line segment PT. Find the ratio of area of ΔPQR and area of ΔPQT.
Answer» PQRS is a parallelogram, S is the midpoint of line segment PT. Find the ratio of area of $Δ P Q R$ and area of $Δ P Q T$ .

Discussion

3909.	Factorise:x2+1x2-3
Answer» Factorise: $x^{2} + \frac{1}{x^{2}} - 3$

Discussion

3910.	Find the area of a quadrilateral ABCD in which AB = 6 cm, BC = 8 cm, CD = 8 cm, DA = 10 cm and AC = 10 cm. [3 MARKS]
Answer» Find the area of a quadrilateral ABCD in which AB = 6 cm, BC = 8 cm, CD = 8 cm, DA = 10 cm and AC = 10 cm. [3 MARKS]

Discussion

3911.	A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
Answer» A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

Discussion

3912.	A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
Answer» A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

Discussion

3913.	X is to the south west of A, Y is to the east of X and L is to the north of Y in line with X and A but not in between them. In which direction of A is L located?
Answer» X is to the south west of A, Y is to the east of X and L is to the north of Y in line with X and A but not in between them. In which direction of A is L located?

Discussion

3914.	Let →a=i+2j+3k if →b is a vector such that →a,→b=\|→b\| and \|→a−→b\|=√7, then \|→b\|= ____________
Answer» Let $\to a = i + 2 j + 3 k$ if $\to b$ is a vector such that $\to a, \to b = \| \to b \|$ and $\| \to a - \to b \| = \sqrt{7}$ , then $\| \to b \| =$ ____________

Discussion

3915.	Question 4Given that HCF (306, 657) = 9, find LCM (306, 657).
Answer» Question 4 Given that HCF (306, 657) = 9, find LCM (306, 657).

Discussion

3916.	The set of natural numbers less than 15 and divisible by 3 in roster form is .
Answer» The set of natural numbers less than 15 and divisible by 3 in roster form is .

Discussion

3917.	Can two angles be supplementary if both of them are acute?
Answer» Can two angles be supplementary if both of them are acute?

Discussion

3918.	If P=√(√12)+12+√(13+2√12))−√12,then find the value of P?
Answer» If $P = \sqrt{(\sqrt{12}) + 12 + \sqrt{(13 + 2 \sqrt{12}))}} - \sqrt{12}$ ,then find the value of P?

Discussion

3919.	The number of value(s) of x satisfying the eqaution x2−6x+8=3+√1+x,x∈(3,∞) is
Answer» The number of value(s) of $x$ satisfying the eqaution $x^{2} - 6 x + 8 = 3 + \sqrt{1 + x}, x \in (3, \infty)$ is

Discussion

3920.	The mean of 25 elements is 36. If the mean of the first 13 elements is 32 and that of the last 13 elements is 39, then 13th element is
Answer» The mean of $25$ elements is $36.$ If the mean of the first $13$ elements is $32$ and that of the last $13$ elements is $39,$ then $13^{th}$ element is

Discussion

3921.	Question 4Write whether the following statement is True or False?The graph given below represents the linear equation x = 3.
Answer» Question 4 Write whether the following statement is True or False? The graph given below represents the linear equation x = 3.

Discussion

3922.	Question 1 (f)State whether true or false.(f) All rhombuses are kites.
Answer» Question 1 (f) State whether true or false. (f) All rhombuses are kites.

3922.

Question 1 (f)State whether true or false.(f) All rhombuses are kites.

Answer»

Question 1 (f)

State whether true or false.

(f) All rhombuses are kites.

Discussion

3923.	Question 53 Fill in the blanks to make the statement true. ___ × (-1) = -35
Answer» Question 53 Fill in the blanks to make the statement true. ___ $\times$ (-1) = -35

3923.

Question 53 Fill in the blanks to make the statement true. ___ × (-1) = -35

Answer»

Question 53

Fill in the blanks to make the statement true.

___ $\times$ (-1) = -35

Discussion

3924.	If f(x) = 3x - 1, what is f(a)?
Answer» If f(x) = 3x - 1, what is f(a)?

Discussion

3925.

Complete the following information about yourselfSURVEY ON THE USE OF COMPUTERS Age: Boy / Girl: Hours spent at the computer: Hours spent playing games and chatting on the computer: Hours spent surfing the Internet/websites for learning: Hours spent per week studying at home: Hours spent for leisure activities: If you reduce your time spent on the computer, how would you spend the extra time? I like to spend my time at the computer because:

Answer»

Complete the following information about yourself

SURVEY ON THE USE OF COMPUTERS

Age:
Boy / Girl:
Hours spent at the computer:
Hours spent playing games and chatting on the computer:
Hours spent surfing the Internet/websites for learning:
Hours spent per week studying at home:
Hours spent for leisure activities:
If you reduce your time spent on the computer, how would you spend the extra time?
I like to spend my time at the computer because:

Discussion

3926.	If x=√5−2√5+2 and y=√5+2√5−2. Find the value of x+y? 18
Answer» If $x = \frac{\sqrt{5} - 2}{\sqrt{5} + 2}$ and $y = \frac{\sqrt{5} + 2}{\sqrt{5} - 2}$ . Find the value of $x + y$ ? 18

Discussion

3927.	The atmosphere at this level of altitude is called Heterospher
Answer» The atmosphere at this level of altitude is called Heterospher

Discussion

3928.	x2+5x−24 can be factorized as .
Answer» $x^{2} + 5 x - 24$ can be factorized as .

Discussion

3929.	if A,B,C are events associated with a random experiment such that P(exactly one of events A or B)=P(exactly one of B OR C)=P(exactly one of A OR C)=p and P(all three events occuring simul†an eously )=p^2 ,then find probability of occurrence of at least one of A ,B, and C
Answer» if A,B,C are events associated with a random experiment such that P(exactly one of events A or B)=P(exactly one of B OR C)=P(exactly one of A OR C)=p and P(all three events occuring simul†an eously )=p^2 ,then find probability of occurrence of at least one of A ,B, and C

Discussion

3930.	Find the remainder when x3 + 4x2 + 4x − 3 is divided by x.
Answer» Find the remainder when x³ + 4x² + 4x − 3 is divided by x.

Discussion

3931.	In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that . ar(ΔAXS)=12ar(PQRS)
Answer» In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that . $a r (Δ A X S) = \frac{1}{2} a r (P Q R S)$

Discussion

3932.	A coin is tossed 700 times and we get head 385 times and tail 315 times. Find the probability of getting a head.
Answer» A coin is tossed 700 times and we get head 385 times and tail 315 times. Find the probability of getting a head.

Discussion

3933.	What length of canvas 3 m wide will be required to make a conical tent of height 8 m and radius of base 6 m? (use π = 3.14)
Answer» What length of canvas 3 m wide will be required to make a conical tent of height 8 m and radius of base 6 m? (use π = 3.14)

Discussion

3934.	Question 7Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm×20 cm×5 cm and the smaller of dimension 15 cm×12 cm×5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs. 4 for 1000cm2, find the cost of cardboard required for supplying 250 boxes of each kind.
Answer» Question 7 Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions $25 c m \times 20 c m \times 5 c m$ and the smaller of dimension $15 c m \times 12 c m \times 5 c m$ . For all the overlaps, $5 %$ of the total surface area is required extra. If the cost of the cardboard is $R s . 4 f o r 1000 c m^{2}$ , find the cost of cardboard required for supplying 250 boxes of each kind.

Discussion

3935.	In the adjoining figure, ABCD is a \|\|gm whose diagonals AC and BD intersect at O. A line segment through O meets AB at P and DC at Q. Prove that ar(APQD) =12ar(ABCD).
Answer» In the adjoining figure, ABCD is a $\| \|^{g m}$ whose diagonals AC and BD intersect at O. A line segment through O meets AB at P and DC at Q. Prove that ar(APQD) $= \frac{1}{2}$ ar(ABCD).

Discussion

3936.	{ One year ago, a man was }7 times as old as his son. The equation of this situation: Take : present age }}{ of father and son }x and }y year respectively)
Answer» { One year ago, a man was }7 times as old as his son. The equation of this situation: Take : present age }}{ of father and son }x and }y year respectively)

Discussion

3937.	Prove that the points (3,0), (4, 5), (-1, 4) and (-2, -1) taken in order form a rhombus. Also, find its area.
Answer» Prove that the points (3,0), (4, 5), (-1, 4) and (-2, -1) taken in order form a rhombus. Also, find its area.

Discussion

3938.	Find the volume of a sphere sphere whose diameter is, (i) 14 cm (ii) 3.5 dm (iii) 2.1 m
Answer» Find the volume of a sphere sphere whose diameter is, (i) 14 cm (ii) 3.5 dm (iii) 2.1 m

Discussion

3939.	Probability of occurrence of an event is defined as ______.
Answer» Probability of occurrence of an event is defined as ______.

Discussion

3940.	In the given circle with diameter AB, find the value of ‘’.
Answer» In the given circle with diameter AB, find the value of ‘’.

3940.

In the given circle with diameter AB, find the value of ‘’.

Answer»

In the given circle with diameter AB, find the value of ‘’.

Discussion

3941.	Draw a rectangle of perimeter 17 cm and sides in the ratio of 5 : 3. Find the measure of the smallest side.3.2
Answer» Draw a rectangle of perimeter 17 cm and sides in the ratio of 5 : 3. Find the measure of the smallest side. 3.2

Discussion

3942.	In △ ABC,it is given that D is the midpoint of BC;E is the midpoint of BD and O is the midpoint of AE.Then,ar(△ BOE)=? (a) 13ar(△ ABC) (b) 14ar(△ ABC) (c) 16ar(△ ABC) (d) 18ar(△ ABC)
Answer» In $△ A B C$ ,it is given that D is the midpoint of BC;E is the midpoint of BD and O is the midpoint of AE.Then,ar( $△ B O E$ )=? (a) $\frac{1}{3} a r (△ A B C)$ (b) $\frac{1}{4} a r (△ A B C)$ (c) $\frac{1}{6} a r (△ A B C)$ (d) $\frac{1}{8} a r (△ A B C)$

3942.

In △ ABC,it is given that D is the midpoint of BC;E is the midpoint of BD and O is the midpoint of AE.Then,ar(△ BOE)=? (a) 13ar(△ ABC) (b) 14ar(△ ABC) (c) 16ar(△ ABC) (d) 18ar(△ ABC)

Answer»

In $△ A B C$ ,it is given that D is the midpoint of BC;E is the midpoint of BD and O is the midpoint of AE.Then,ar( $△ B O E$ )=?

(a) $\frac{1}{3} a r (△ A B C)$

(b) $\frac{1}{4} a r (△ A B C)$

(c) $\frac{1}{6} a r (△ A B C)$

(d) $\frac{1}{8} a r (△ A B C)$

Discussion

3943.	Draw the graphs of the following equations on the same system of co-ordinates. Write the co-ordinates of their points of intersection.x + 4 = 0, y -1 = 0, 2x + 3 = 0, 3y - 15 = 0
Answer» Draw the graphs of the following equations on the same system of co-ordinates. Write the co-ordinates of their points of intersection. x + 4 = 0, y $-$ 1 = 0, 2x + 3 = 0, 3y $-$ 15 = 0

Discussion

3944.	If lines l \|\| m are intersected by lines n \|\| o and ∠1=34∘ then what is ∠8′? 146
Answer» If lines l \|\| m are intersected by lines n \|\| o and $∠ 1 = 34^{\circ}$ then what is $∠ 8^{'}$ ? 146

Discussion

3945.	When x4+x3−2x2+x+1 is divided by x−1, the remainder is 2 and the quotient is q(x). Find q(x).
Answer» When $x^{4} + x^{3} - 2 x^{2} + x + 1$ is divided by $x - 1$ , the remainder is 2 and the quotient is q(x). Find q(x).

Discussion

3946.	Question 5Write True or False and justify your answer:If the side of a rhombus is 10cm and one diagonal is 16 cm, then area of the rhombus is 96 cm2.
Answer» Question 5 Write True or False and justify your answer: If the side of a rhombus is 10cm and one diagonal is 16 cm, then area of the rhombus is 96 $c m^{2}$ .

Discussion

3947.	Question 1 (ii) Solve the following pairs of equations by reducing them to a pair of linear equations: 2√x+3√y=24√x−9√y=−1
Answer» Question 1 (ii) Solve the following pairs of equations by reducing them to a pair of linear equations: $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2 \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = - 1$

Discussion

3948.	The third proportion to (x2−y2) and (x - y), where x and y are unequal, is:
Answer» The third proportion to $(x^{2} - y^{2})$ and (x - y), where x and y are unequal, is:

Discussion

3949.	Point P is the midpoint of seg XY. If XP = 8.5, find l(XY).
Answer» Point P is the midpoint of seg XY. If XP = 8.5, find l(XY).

Discussion

3950.

A die is tossed 250 times and the data is recorded as below:Outcome123456Frequency305050752025The probability of getting an odd number is

Answer»

A die is tossed 250 times and the data is recorded as below:

Outcome	1	2	3	4	5	6
Frequency	30	50	50	75	20	25

The probability of getting an odd number is

Discussion

Explore topic-wise InterviewSolutions in .

Angles of a triangle are in AP if the smallest angle is 450.Find the largest angle

The point at which concurrent lines intersect is called point of ___.

The circles shown below have the same centre O. Prove that ΔOAB and ΔOPQ are similar.

The area in cm2 of a sector of a circle with radius 6 cm if angle of the sector is 60∘ is ___ cm2.

A building is in the form of a cylinder surmounted by a hemispherical vaulteddome and contains 41m3 of air. If the internal diameter of dome is equal to itstotal height above the floor, find the height of the building?

Question 1 (viii)Without actually performing the long division, state whether 615 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

If x = 5+2, then x-1x equals(a) 25(b) 4(c) 2(d) 5

PQRS is a parallelogram, S is the midpoint of line segment PT. Find the ratio of area of ΔPQR and area of ΔPQT.

Factorise:x2+1x2-3

Find the area of a quadrilateral ABCD in which AB = 6 cm, BC = 8 cm, CD = 8 cm, DA = 10 cm and AC = 10 cm. [3 MARKS]

A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

X is to the south west of A, Y is to the east of X and L is to the north of Y in line with X and A but not in between them. In which direction of A is L located?

Let →a=i+2j+3k if →b is a vector such that →a,→b=|→b| and |→a−→b|=√7, then |→b|= ____________

Question 4Given that HCF (306, 657) = 9, find LCM (306, 657).

The set of natural numbers less than 15 and divisible by 3 in roster form is .

Can two angles be supplementary if both of them are acute?

If P=√(√12)+12+√(13+2√12))−√12,then find the value of P?

The number of value(s) of x satisfying the eqaution x2−6x+8=3+√1+x,x∈(3,∞) is

The mean of 25 elements is 36. If the mean of the first 13 elements is 32 and that of the last 13 elements is 39, then 13th element is

Question 4Write whether the following statement is True or False?​​​​​​​The graph given below represents the linear equation x = 3.

Question 1 (f)State whether true or false.(f) All rhombuses are kites.

Question 53 Fill in the blanks to make the statement true. ___ × (-1) = -35

If f(x) = 3x - 1, what is f(a)?

If x=√5−2√5+2 and y=√5+2√5−2. Find the value of x+y? 18

The atmosphere at this level of altitude is called Heterospher

x2+5x−24 can be factorized as .

if A,B,C are events associated with a random experiment such that P(exactly one of events A or B)=P(exactly one of B OR C)=P(exactly one of A OR C)=p and P(all three events occuring simul†an eously )=p^2 ,then find probability of occurrence of at least one of A ,B, and C

Find the remainder when x3 + 4x2 + 4x − 3 is divided by x.

In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that . ar(ΔAXS)=12ar(PQRS)

A coin is tossed 700 times and we get head 385 times and tail 315 times. Find the probability of getting a head.

What length of canvas 3 m wide will be required to make a conical tent of height 8 m and radius of base 6 m? (use π = 3.14)

In the adjoining figure, ABCD is a ||gm whose diagonals AC and BD intersect at O. A line segment through O meets AB at P and DC at Q. Prove that ar(APQD) =12ar(ABCD).

{ One year ago, a man was }7 times as old as his son. The equation of this situation: Take : present age }}{ of father and son }x and }y year respectively)

Prove that the points (3,0), (4, 5), (-1, 4) and (-2, -1) taken in order form a rhombus. Also, find its area.

Find the volume of a sphere sphere whose diameter is, (i) 14 cm (ii) 3.5 dm (iii) 2.1 m

Probability of occurrence of an event is defined as ______.

In the given circle with diameter AB, find the value of ‘’.

Draw a rectangle of perimeter 17 cm and sides in the ratio of 5 : 3. Find the measure of the smallest side.3.2

In △ ABC,it is given that D is the midpoint of BC;E is the midpoint of BD and O is the midpoint of AE.Then,ar(△ BOE)=? (a) 13ar(△ ABC) (b) 14ar(△ ABC) (c) 16ar(△ ABC) (d) 18ar(△ ABC)

Draw the graphs of the following equations on the same system of co-ordinates. Write the co-ordinates of their points of intersection.x + 4 = 0, y -1 = 0, 2x + 3 = 0, 3y - 15 = 0

If lines l || m are intersected by lines n || o and ∠1=34∘ then what is ∠8′? 146

When x4+x3−2x2+x+1 is divided by x−1, the remainder is 2 and the quotient is q(x). Find q(x).

Question 5Write True or False and justify your answer:If the side of a rhombus is 10cm and one diagonal is 16 cm, then area of the rhombus is 96 cm2.

Question 1 (ii) Solve the following pairs of equations by reducing them to a pair of linear equations: 2√x+3√y=24√x−9√y=−1

The third proportion to (x2−y2) and (x - y), where x and y are unequal, is:

Point P is the midpoint of seg XY. If XP = 8.5, find l(XY).

A die is tossed 250 times and the data is recorded as below:Outcome123456Frequency305050752025The probability of getting an odd number is

Question 4Write whether the following statement is True or False?The graph given below represents the linear equation x = 3.