Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the sum of a] first 10 multiples of 8 b] first 25 multiples of 3 c] first 100 multiples of 2.

Answer»


Answer :a] `=5 [16+ 72] = 5 xx 88 = 440`.
b] `= (25)/(2) [ 6 + 72] = (25)/(2) xx 78 = 975`.
C] `= 50[ 4+198] = 50 xx 202 = 10100.`
Discussion
2.

Which of the following figures correctly represents the relation between:Doctors,Lawyers.Professionals?

Answer»




SOLUTION :Both DOCTORS and LAWYERS are professionals.But both are ENTIRELY DIFFERENT from each other.
Discussion
3.

A solid metalli sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the : (i) radius of the cylinder (ii) curved surface area of the cylinder. (Take pi=3.1)

Answer»


ANSWER :(i) 3 CM (II) `59.2cm^(2)`
Discussion
4.

Solve the following simultaneous equations : x/3 + y/4 = 2 , 3x + 4y = 25

Answer»


ANSWER :`(3,4)`
Discussion
5.

Construct a triangle similar to a given triangle ABC with its sides equal to (6)/(5) of the corresponding sides of the triangle ABC (scale factor (6)/(4)).

Answer»


ANSWER :`(6)/(5)`
Discussion
6.

A man has a choice to invest in hundread rupee shares of two firms at 120rs or at 132rs. The first firm pays a dividend of 5% per annum and the second firm pays a dividend of 6% per annum. Find : (i) which company is giving a better return. (ii) if a man invests 26400rs with each firm how much will be the difference between the annual returns from the two firms ?

Answer»


ANSWER :`(i)` SECOND `(II) 100RS`
Discussion
7.

10 students of Class-X took part in a mathematics quiz. If the number of girls in 4 more than the number of boys then, find the number of boys and the number of girls who took part in the quiz.\

Answer»


ANSWER :NUMBER of girls = 7: NUMBR of BOYS = 3
Discussion
8.

Number of distinct line segments that can be formed out of n- points is…

Answer»

`(N (n - 1))/2`
`n/2`
`(n + 1)/2`
`(n^(2) ( n -1))/2`

ANSWER :A
Discussion
9.

Find the sum of the following Aps: (i) 2, 7, 12, …….., to 10 terms. (ii) -37, -33, -29, …….., to 12 terms. (iii) 0.6, 1.7, 2.8,….., to 100 terms (iv) (1)/(15), (1)/(12),(1)/(10),……,to 11 terms

Answer»


ANSWER :(i) `S_(10) = 245`.
(ii)`S_(12) = -180`
(III) `S_(100) = 5505`.
(IV) `S_(11) = (33)/(20)`.
Discussion
10.

Write the following sets in the set-builder form (i) {3,6,9,12} (ii) {2,4,8,16,32} (iii) {5,25,125,625} (iv) {1,4,9,16,25,....,100}

Answer»


ANSWER :(i) A={x : x is multiple of 3 & less than 13}
(ii) `B={x : x =2^(a), a in N, a lt 6}`
(iii) `C={x : x=5^(a), a in N, a lt 5}`
(iv) D={x : x is a square number and `x le 10, x lt N}`
Discussion
11.

Find True or False: 15 is the mode of the data 16,15,17,16,15,19,17,14,15.

Answer»
Discussion
12.

A closed cylindrical tank, made of thin iron sheet, has diameter = 8.4 m and height 5.4 m. How much metal sheet, to the nearest m^(2), is used in making this tank, if (1)/(15)of the sheet actually used was wasted in making the tank ?

Answer»


ANSWER :`270:34 m ^(2)`
Discussion
13.

Draw a line segment of length 7.6 cm and divide it in the ratio 3 : 2.

Answer»


Answer :`(PA)/( PB) = (A_3 A)/( A_ 3 A_5) = (3)/(2)`
Hence P divides AB in the ratio 3 : 2.
Discussion
14.

Find the mean of the following data . Range of first n natural numbers , range of negative integers from - n to -1 (where -n lt -1) , range of first n positive even integers and range of first n positive odd integers .

Answer»

`(3)/(2) ( n-1)`
`(3n-2)/(2)`
`(3)/(2) (n-2)`
`(4n-3)/(2)`

SOLUTION :Range of the first 'n' NATURAL numbers =n - 1.
Range of the last n negative INTEGERS = `-1 - (-n) = n-1`.
Range of the first 'n' positive even integers = 2n - 2 .
Range of first 'n' positive odd integers = (2n+ 1) - (1) = 2n -2 .
`therefore` Mean of the given data is
`((n- 1) + ( n - 1) + (2n -2) + (2n - 2))/(4)`
`= (6n-6)/(4) = (3n-3)/(2)`
`= (3)/(2) (n-1)`.
Discussion
15.

Who is sitting to the immediate right of Tanisha among five friends sitting around a circle facing the center? I. Ayesha is sitting exactly between Kanak and Sneha and Raj is sitting to the immediate right of Sneha. II. Tanisha is sitting exactly between Kanak and Raj and Ayesha is sitting to the immediate right of Kanak.

Answer»

if the data in statement I alone are SUFFICIENT to ANSWER the question, while the data in statement II alone are not sufficient to answer the question,
if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question,
if the data either in statement I alone or in statement II alone are sufficient to answer the question,
if the data given in both statements I and II together are not sufficient to answer the question,

SOLUTION :From each one of I and II, we obtain the order:

Clearly, Kanak is sittin to the IMMEDIATE right of Tanisha.
Discussion
16.

Point P lies in the exterior of a circle with cnetre O and radius 5 cm. If OP = 13 cm, then what is the length of a tangnet from P to the circle ?

Answer»


ANSWER :12 CM
Discussion
17.

If (1-sinA)(1-sinB)(1-sinC)=(1+sinA)(1+sinB)(1+sinC),then show that each side is equal to +-cosAcosBcosC.

Answer»
Discussion
18.

Draw a DeltaABC in which AB=5 cm, BC= 6 cm and angleABC=60^(@). Construct a triangle similar to ABC with scale factor (5)/(7). Justify the construction.

Answer»

Solution :Steps of construction
1. Draw a LINE segment AB=5 cm .
2. From point B, draw `angleABY=60^(@)` on which take BC= 6 cm.
3. Join AC , `DeltaABC` is the required triangle.
4. From A, draw any ray AX downwards making an acute angle.
5. Mark 7 point `B_(1),B_(2),B_(3),B_(4),B_(5),B_(6) " and " B_(7)` on AX,
Such that `AB_(1)=B_(1)B_(2)=B_(2)B_(3)=B_(3)B_(4)=B_(4)B_(5)=B_(5)B_(6)=B_(6)B_(7)`.
6. Join `B_(7)B` and from `B_(5)` draw `B_(5)M||B_(7)B` intersecting AB at M.
From point M draw MN||BC intersecting AC at N.
Then, `DeltaAMN` is the required triangle WHOSE sides are EQUAL to `(5)/(7)` of the CORRESPONDING sides of the `DeltaABC`.
Justification
Here , `B_(5)M||B_(7)B` ( by construction )
`:. (AM)/(MB)=(5)/(2)`
Now, `(AB)/(AM)=(AM+MB)/(AM)`
`=1+(MB)/(AM)=1+(2)/(5)=(7)/(5)`
Also, MN||BC
`:. DeltaAMN ~DeltaABC`
Therefore, `(AM)/(AB)=(AN)/(AC)=(NM)/(BC)=(5)/(7)`
Discussion
19.

Construct a triangle similar to a given triangle LMN with its sides equal to (4)/(5) of the corresponding sides of the triangle LMN (scale factor (4)/(5)).

Answer»


ANSWER :`DELTA LMN`
Discussion
20.

Chek whether the following are quadratic equation: x^(2)+3x+1=(x-2)^(2)

Answer»


ANSWER :No
Discussion
21.

Determine a point which divides a line segment 7 cmlong, internally in the ratio 2:3

Answer»

Solution :1. Draw a line segment AB=7cm by using a ruler.
2. Draw any ray making an acute `angleBAC` with AB.
3. Along AC, mark off (2+3)=5 point `A_(1),A_(2),A_(3),A_(4) " and " A_(5)` such that
`A A_(1)=A_(1)A_(2)=A_(2)A_(3)=A_(3)A_(4)=A_(4)A_(5)`.

4. Join `BA_(5)`
5. Through `A_(2)` draw a line `A_(2)P` parallel to `A_(5)B` by making an angle equal to `angleAA_(5)B` at `A_(2)` intersecting AB at a point P.
The point P so obtained is the required point.
Justification: In `DELTAA A_(5)B`,
`A_(2)P||A_(5)B` ( construction )
`:. (A A_(2))/(A_(2)A_(5))=(AP)/(PB)` (by. B.P. theorem)
`implies (2)/(3)=(AP)/(PB)`(construction )
`implies AP:PB=2:3`
i.e., P DIVIDES AB internally in the ratio 2:3.
Alternate Method:
We can use ONE more method for this question.
1. Draw the line segment AB=7 cm
2.Draw any ray AC making an acute angle `angleBAC` with AB.
3. Draw a ray BD parallel to AC by making ` angle ABC` equal to angle `angleBAC`.
4. Mark off 2 points `A_(1)` and `A_(2)` on AC and 3 points `B_(1), B_(2), B_(3)` on AD such that
`A A_(1)=A_(1)A_(2)=BB_(1)=B_(1)B_(2)=B_(2)B_(3)`
5. Join `B_(3)A_(2)`, suppose it intersect AB at point P. Then, P is the require point.
Discussion
22.

What is Sumit's position from the right end in a row of children? I. There are 10 children between Sumit and Rajan. II. Rajan is twentieth from the left end of the row of children.

Answer»

if the data in statement I alone are sufficient to answer the QUESTION, while the data in statement II alone are not sufficient to answer the question,
if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question,
if the data either in statement I alone or in statement II alone are sufficient to answer the question,
if the data given in both statements I and II together are not sufficient to answer the question,

SOLUTION :Clearly, neither the NUMBER of CHILDREN in the row is given nor the position of SUMIT relative to Rajan is mentioned in any one of I or II.
Discussion
23.

Water flows at a rate of 10 m per minute through a cylindrical pipe having its diameter as 20 mm. How much time will it take to fill a conical vessel of base diameter 40 cm and depth 24 cm.

Answer»


ANSWER :3 MINUTES 12 SECONDS
Discussion
24.

4th term of an A.P. is equal to 3 times its first term and 7th term exceeds twice the 3rd term by 1. Find the first term and the common difference.

Answer»


ANSWER :a=3 and d=2
Discussion
25.

John and Priya went for a small picnic. After having their lunch Priya insisted to travelin a motor boat. The speed of the motor boat was 20 km/hr. Priya being a Mathematics student wanted to know the speed of the current. So she noted the time for upstream and downstream. She found that for covering the distance of 15 km the boat took 1 hour more for upstream than downstream. Let speed of the stream be x km/hr. then speed of the motorboat in upstream will be

Answer»

`20 km//hr`
`(20+x) km//hr `
`(20-x) km//hr`
`2 km//hr`

SOLUTION :In this case SPEED of the MOTORBOAT in upstream will be (20 - x) km/hr.
Thus (c) is correct OPTION.
Discussion
26.

John and Priya went for a small picnic. After having their lunch Priya insisted to travelin a motor boat. The speed of the motor boat was 20 km/hr. Priya being a Mathematics student wanted to know the speed of the current. So she noted the time for upstream and downstream. She found that for covering the distance of 15 km the boat took 1 hour more for upstream than downstream. What is the relation between speed distance and time?

Answer»

SPEED = (distance )/TIME
distance = (speed )/time
time = speed `xx` distance
none of these

Solution :distance = (speed )/time
THUS (B) is CORRECT option.
Discussion
27.

John and Priya went for a small picnic. After having their lunch Priya insisted to travelin a motor boat. The speed of the motor boat was 20 km/hr. Priya being a Mathematics student wanted to know the speed of the current. So she noted the time for upstream and downstream. She found that for covering the distance of 15 km the boat took 1 hour more for upstream than downstream. Which is the correct quadratic equation for the speed of the current ?

Answer»

`X^(2) +30X -200=0`
`x^(2) +20x -400=0`
`x^(2) +30x -400=0`
`x^(2) -20x-400=0`

Solution :Asper QUESTION,
`(15)/(20-x) =(15)/(20+x) +1`
`15 (20+x)= 15(20 -x)+(20 -x)(20+x) `
`15 x= -15x+ (20^(2)-x^(2))`
` 30 x= -x^(2) +400`
`x^(2) +30x -400=0`
Thus (c) is correct OPTION.
Discussion
28.

John and Priya went for a small picnic. After having their lunch Priya insisted to travelin a motor boat. The speed of the motor boat was 20 km/hr. Priya being a Mathematics student wanted to know the speed of the current. So she noted the time for upstream and downstream. She found that for covering the distance of 15 km the boat took 1 hour more for upstream than downstream. What is the speed of current ?

Answer»

20 km/hour
10 km/hour
15 km/hour
25 km/hour

Solution :We have `x^(2) +30x -400 = 0 `
`x^(2) + 40x -10x-400 = 0`
`x(x+40)-10x (x+40) =0`
`(x+40) (x-10) =0`
`x=10, -40`
Here x = 10 is only possible.
Thus (C) is correct OPTION.
Discussion
29.

John and Priya went for a small picnic. After having their lunch Priya insisted to travelin a motor boat. The speed of the motor boat was 20 km/hr. Priya being a Mathematics student wanted to know the speed of the current. So she noted the time for upstream and downstream. She found that for covering the distance of 15 km the boat took 1 hour more for upstream than downstream. How much time boat took in downstream ?

Answer»

90 minute
15 minute
30 minute
45 minute

Solution :In DOWNSTREAM speed of boat = 20 + 10 = 30 km/hr
TIME take to COVER distance 15 km will be 30 minutes.
Thus (c) is correct option.
Discussion
30.

The sum of the 2nd term and the 7th term of an A.P. is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P.

Answer»


ANSWER :1,5,9,13……
Discussion
31.

Solve the following pair of linear equation by elimination method: 3x = 5y - 4 = 0 and 9x = 2y + 7.

Answer»


ANSWER :`X = 2, y = 3`
Discussion
32.

If X is brother of the son of Y's son, how is X related to Y?

Answer»

Son
Brother
Cousin
Grandson

Answer :D
Discussion
33.

If the following alphabets are written in reverse order: ABCDEFGHIJKLMNOPQRSTUVWXYZ Which will be seventh letter to the right of the twelth letter from the left?

Answer»

G
F
H
S

Answer :C
Discussion
34.

If A(20, 10), B(0, 20) are given, then find the co-ordinate of the point which bisects segment AB into two equal parts.

Answer»
Discussion
35.

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: (i) x^(2) + 3x + 1, 3x^(4) + 5x^(3) - 7x^(2) + 2x+2 (ii) t^(2) -3, 2t^(4) + 3t^(3) - 2t^(2) - 9t -12

Answer»


ANSWER :(i) YES,
(II) yes
Discussion
36.

The radii of the two ends of a pail of height 45 cm ar 28 cm and 7 cm respectively . What will be the volume and the total surface area of the pail ?

Answer»


ANSWER :48510 CC
Discussion
37.

For an A.P., the sum of its terms is 60, common difference is 2 and last term is 18. Find the number of terms in the A.P.

Answer»


ANSWER :4 or 15
Discussion
38.

Cramer's rule, what is the nature of solution if D = 0? Explain with the help of an example.

Answer»


ANSWER :If D = 0, then the two simultaneous equations do not have a unique SOLUTION.
Discussion
39.

Using the Remainder Theorem, factorise each of the following completely: (i) 3x^3+2x^(2)-19x+6 (ii) 2x^(3)+x^2-13x+6 (iii) 3x^(3)+2x^2-23x-30 (iv) 4x^3+7x^2-36x-63 (v) x^3+x^2-4x-4

Answer»


ANSWER :(i) (x-2) (x+3) (3x-1) (II) (2x-1) (x-2) (x+3) (III) (x-3) (x+2) (3x+5) (IV) (x+3) (x-3) (4x+7) (V) (x+1) (x-2) (x+2)
Discussion
40.

The sum of the reciprocals of Rehman's age (in years) 3 years ago and 5 years from now is (1)/(3). Find his present age.

Answer»


ANSWER :7 YEARS
Discussion
41.

Solve the following systems of inequalities for all x in RSolve (|x|-1)(|x|-2)ge0,x in R,x 3 # pm2

Answer»


ANSWER :`[-1, 1]CUP (-INFTY,-2)cup (2,infty)`
Discussion
42.

The radius of a circle is decreased by 10%. Its area is changed by

Answer»

0.12
0.1
0.19
0.81

Answer :C
Discussion
43.

The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6). State the name of the mirror line and write its equation.

Answer»


ANSWER :y - AXIS ; EQUATION is X = 0
Discussion
44.

The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6). State the co-ordinates of the image of (-8,-5) in the mirror line.

Answer»


ANSWER :(8,-5)
Discussion
45.

Find the antilog of 2.421.

Answer»

Solution :STEP 1: In the CHARACTERISTIC is 2, we place the decimal after three DIGITS from the LEFT, i.e., antilog 2.421 = 263.6.
Discussion
46.

How many coins 1.75 in diameter and of thickness 2mm must be melted to form a cuboid of dimensions 5.5cm xx 10cm xx3.5 cm

Answer»


ANSWER :400
Discussion
47.

Draw a circle of radius 3 cm. Draw a tangent to this circle making an angle of 30^@ with a line passing through the centre.

Answer»


ANSWER :`QOP = 60^@`.
Discussion
48.

If two tangents to a circle are inclined at an angle of 75^(@), then the radii through their points of contact are inclined at an angle of ..........

Answer»

`15^(@)`
`75^(@)`
`105^(@)`
`125^(@)`

ANSWER :A
Discussion
49.

Find the area of quadrilateral ABCD, the co-ordinates of whose vertices are A(1, 2), B(6, 2), C(5, 3) and D(3,4).

Answer»


ANSWER :`(11)/(2)` SQ UNITS
Discussion
50.

A pot conical shaped , the radius and heightof which is 6 cm and 8 cmrespectively , is fulfilled with water of this pot in sucha waythat it just touches the two sides of the pot . So , how many part of the waterof the pot will over flow ?

Answer»

Solution :In the figure beside ,
AD = 6 cm and DC = 8 cm
` :. AC = SQRT(CD^(2)+AD^(2))`
` = sqrt(8^(2) + 6^(2)) ` cm
` = sqrt(64 + 36)` cm
10 cm
Now , in the right - angled trinagles `Delta ACD and Delta EOC` , we get
` ANGLE ACD = angle ECO`
Let the radius of the sphere be x cm
` :.` as per figure , AD = AE = 6 cm
` :.EC = (AC- AE) = (10-6)` cm = 4 cm
Again , ` Delta ADS ~ Delta EOC , :. (DC)/(AD) = (EC)/(EO)`
` rArr 8/6 = 4/3 rArr x = (4xx 6)/8 = 3`
` :.` the radius of the sphereis 3 cm
So , the volume of the sphere` = 4/3pi xx 3^(3) ` cc = 36 ` pi` cc
Again, the volume of the CONICAL pot ` = 1/3 xx pi xx 6^(2) xx 8 ` cc = ` 96 pi ` cc
So , the required part ` = (36pi)/(96pi) = 3/8`
Hence `3/8` part of the WATER of the pot will overflow
Discussion