Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

Prove that:\frac{1-\tan 2 \theta \tan \theta}{1+\tan 2 \theta \tan \theta}=\frac{\cos 3 \theta}{\cos \theta}

Answer»
2.

m2-129 If tanntan B and sinA msinB, prove that cos AI1

Answer»
3.

average of runs in the three mulllies u10. Sudhir's present age is s more than three times the age of Viru. Anil!'sage is half the age of Sudhir. If the ratio of the sum of Sudhir's and:Viru's age to three times Anil's age is 5:6 , then find Viru's age.ActivityΔ ABC on a tracing paperthat point A coincides wpoint Q and point C witthe trigngles c

Answer»

Let Viru 's present age = x yrs then Sudhir's present age = (5 + 3x) yrs Anil's present age = (5 + 3x)/2 yrs

Ratio of the sum of Sudhir's and Viru's age to three times Anil's age is 5 : 6

e.g., (5 + 3x + x)/3(5 + 3x)/2 = 5/6 => 2(5 + 4x)/3(5 + 3x) = 5/6 => 12(5 + 4x) = 15(5 + 3x)=> 4(5 + 4x) = 5(5 + 3x) => 20 + 16x = 25 + 15x => x = 5

Vinu's age is 5 years.

4.

\left. \begin{array} { l } { \frac { 1 + \operatorname { sin } 2 \theta + \operatorname { cos } 2 \theta } { 1 + \operatorname { tan } 2 \theta + \operatorname { cos } 2 \theta } = } \\ { 1 + \operatorname { tan } \theta - \operatorname { cos } 2 \theta } \\ { ( 1 ) \frac { 1 } { 2 } \operatorname { tan } \theta ( 2 ) \frac { 1 } { 2 } \operatorname { cot } \theta ( 3 ) \operatorname { tan } \theta ( 4 ) \operatorname { cot } \theta } \end{array} \right.

Answer»
5.

24. A curve is traced by a point P(x, y) which moves such that its distance from the point A(-1,1) isthree times its distance from the point B(2,-1). Determine the equation of the curve.

Answer»
6.

Plot the points A (2,8),B (-3,3), C (2 ,3) andfind the area of the regionenclosed by the figure ABC

Answer»
7.

84. The area of the region enclosed by the curvesy = x, x = e, y = 1/x and the positive x-axis is

Answer»
8.

Construct a square of side equal to 7.5 cm.

Answer»
9.

i1+ (7(कण (¢1+i(1-0) (€ I+(1+u) (1iuu""" +IEEHITTHIUT+1J03nEANYY -y

Answer»
10.

What are homogeneous and heterogeneous system

Answer»

Asystemof linear equations ishomogeneous if all of the constant terms are zero: Ahomogeneous systemis equivalent to a matrix equation of the form. where A is an m × n matrix, x is a column vector with n entries, and 0 is the zero vector with m entries.

A heterogeneous systemis denned as one consisting of two or morehomogeneousbodies.

11.

(i1) (2x+1)* + (x+1)* = 6x+47

Answer»
12.

1. Find the area of a circle whose radius is(1) 21 cm(i1) 3.5 m.

Answer»
13.

17. The side of a square is equal to the side of an equilateral triangle. Theratio of their areas is

Answer»
14.

:13, A labourer earns1980 in 12 days.(1) How much does he earn in 7 days?(i1) In how many days will he earn 2640?

Answer»
15.

Find the values of the following:tan-(1)+ cosi12

Answer»

We know that the range of principal values of tan^-1, cos^-1 and sin^-1 are (−π/2,π/2) , (0,π) and (−π/2,π/2) respectively,

Let tan^-1(1) = θ1. Then, tanθ1 = 1 = tanπ/4 ⇒θ1 = π/4 ∈[0, π].

Let cos^−1(−1/2)=θ2. Then,cos θ2=−1/2 = −cos π/3=cos(π− π/3)=cos 2π/3So θ2 =2π/3∈[0 , π].

Let sin^−1(−1/2)=θ3. Then, sin θ3=−1/2 = −sin π/6 =sin (−π/6)So θ3 =−π/6∈[−π2 , π2].

So, tan^−1(1)+cos^−1(−12)+sin^−1(−12)= π/4+ 2π/3−π/6=3π/4

16.

oL 1774)?30° + sin? 60° - 3 cos? 60°2 tan’ 45° (ICSE 1993)

Answer»
17.

6. Find LillFind the solution of the pair11-0, 1+1IY-15=U.the solution of the pair of linear equation 3x - 5y - 4 = 0 and 9x = 2y + 7.

Answer»
18.

8. The graph of the linear equation 3x +2y6 cuts the y-axis at the point

Answer»
19.

11. The length of the intercept made by parabola x?-7x+ 4y + 120on x-axis is(A) 4(B) 3(C) 1(D)2

Answer»
20.

2. List the points of differencesbetween homogeneous andheterogeneous mixtures.

Answer»

homogeneous_a homogeneous mixtures has the same uniform appearanceand composition throughout.many homogeneous mixtures are refferd as solutions for

heterogeneous-a heterogeneous mixture consist of visibly different substances or phases.they are not refferd as solutions

Ahomogeneous mixtureis a solution that has equal proportions of its components throughout any givensample. Conversely, aheterogeneous mixturehas components whose proportions vary throughout thesample. "Homogeneous" and "heterogeneous" are not absolute terms but depend on context and the size of thesample.

Homogeneous mixture

1. A mixture in which different constituents are mixed uniformly.2. They cannot have physically distinct parts.

Heterogeneous mixture

1. A mixture in which different constituents are not mixed uniformly.2. They have physically distinct parts.

Ahomogeneous mixtureis a mixture where the components that make up the mixture are uniformly distributed throughout the mixture. The composition of the mixture is the same throughout. There is only onephase of matterobserved in a homogeneous mixture. So, you wouldn't observe both a liquid and a gas or a liquid and asolidin a homogeneous mixture.

Aheterogeneous mixtureis a mixture where the components of the mixture are not uniform or have localized regions with different properties. Different samples from the mixture are not identical to each other. There are always two or more phases in a heterogeneous mixture, where you can identify a region with properties that are distinct from those of another region, even if they are the same state of matter (e.g., liquid, solid).

A homogeneous mixture is a solution that has equal proportions of its components throughout any given sample. Conversely, a heterogeneous mixture has components whose proportions vary throughout the sample. "Homogeneous" and "heterogeneous" are not absolute terms but depend on context and the size of the sample.

21.

Use identity, find (b+7)^2

Answer»

b²+49+14b will be the answer for this

22.

use suitable identy to get each of the following product (2y+5)(2y+5)(6×+7)(6×-7)

Answer»
23.

If the perimeter of a protractor is 72 cm, calculate its area. | Use7-22)

Answer»

From which book have you taken this question? Please tell us so that we can provide you faster answer.

24.

spindi ogradius2gmentofthecirde(Use,s314|NCERT EXEMPLARI7) A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. Find the areaof the corresponding major segment of the circle. (Use π = 3.14)

Answer»

r = 20cm¤ = 90°Area of sector = theta/360 * π * r2

= 90/360 * 22/7 * 20 * 20

= 1/4 * 22/7 * 20 * 20

= 2200/7314.2 cm2

Area of triangle = 1/2 * base * height

= 1/2 * 20 *20 (base and height both are r ) = 200 cm2

Area of minor segment = 314.2 - 200 = 114.2 cm2

major segment = area of circle - 114.2

= π * r2- 114.2

=22/7 * 20 * 20 -114.2

= 1142 .94 cm2

hai

25.

(x) The length of latus rectum of the parabola 3x2 = 8y is

Answer»
26.

4. In figure, find the area of the shaded region, enclosed between twoconcentric circles of radii 7 cm and 14 cm where ZAOC 40[All India](Use π22)

Answer»

Like if you find it useful

27.

| C. I1+]1+6= |d 6+ 2+2= _

Answer»

c.8 answer. D. 10 answer

28.

5. Prove that each of the following numbers is irrational:2(i1) 7

Answer»

Let as assume to the contrary that 1/√3 is rational number 1/√3= P/Q { where p and Q are co-prime and Q not equal to 0}√3 P =Q .1 √3 = Q/P √3 = Irrational numberQ/P =RationalIrrational not equal to rational this is a contradiction has arisen by the wrong assumption because of our incorrect assumption that 1 / √3 is rational.hence, 1/ √3 is irrational .{proved}

29.

If P(-3, 2) is one end of the focal chord PQ of the parabola y +4x +4y 0, then the slope of thenormal at Q is(B) 2(D) -2

Answer»

The parabola is (y+2) ^2 = -4(x-1)

A=

The point P has t = -2 as (at^2,2at) gives (-4,4) and on shifting the origin (x-1) = -1

X= -3

And (y+2) = 4y = 2

As PQ is focal chord and t at Q would be +½ (t1,t2 = -1)

Slope of thenormatis –t

Therefore slope of normal at Q would be -½

30.

23· The abscissae of the two points A and B are the roots of theequation x2 +2ax-b2 0 and their ordinates are the rootsof the equation x2 +2px- 0. Find the equation and theradius of the circle with AB as diameter.

Answer»
31.

14. The equation of the parabola with focus) and directrix y3 is

Answer»
32.

5. In the given figure, findthe area of the shadedregion, enclosed betweentwo concentric circles ofradii 7 cm and 14 cm when22鷹,B40°LOC = 40° (π =-)7

Answer»
33.

gram ofown the14) A ladder rests against a vetical wall at a height of12 m from the ground with its foot at a distancef2 BCICSE)9 m from the wall on the ground. If the foot of theladder is shifted 3 m away from the wall, how muchlower will the ladder slide down ?

Answer»
34.

In fig. 6, find the area of the shaded region, enclosed between two concentriccircles of radii 7 cm and 14 cm where 2AOC18.12= 40°. (Use π3す)A.p:Figure 619

Answer»

Area of shaded region =22/7*14*14*40/360-22/7*7*40/360=51.33cm

35.

3x-4y=18—4x - 6y=10

Answer»

Multiplying (1) by 4,12x-16y= 72 (3)Multiplying (2) by 3,-12x-18y=30 (4)Adding 3 and 4,-34y=102y=-3x=18-12/3 =2So the value of x is 2 and y is -3.

36.

13. The value of the expression ſcosec (75° + ) - sec (15° - 0) - tan (55° + ),cot (35° - 0) is0-1Boo,B)D?

Answer»

Answer will be 0all will be cancelled outOption B

answer is zero... so option is B

answer is 0 means option B is right answer

37.

10.If the lines 3x -4y+4-0 and 6x -8y-7-0tangents to a circle, then the radius of the circle isare

Answer»
38.

ORnig APB and AQP are semi-dirdes, and AO- OB If the perimeter of the following igure is 47 cm, findthe area of the shaded region. | Use7

Answer»
39.

The vertex of the parabola x^2-4x-3y+7=0 is ......

Answer»
40.

Find the value of K, if the pair of linear equation 3x + 4y Kand 9x +12y 6 has infinite many solutions.

Answer»
41.

\begin{array} { l } { \text { Find the locus of poles of normal chord of the parabola } y ^ { 2 } = 4 a x \text { . } } \\ { \text { Find the locus of poles of normal chord of the parabola } y ^ { 2 } = 4 a x \text { . } } \\ { \text { (P.U. } 2017 ) } \end{array}

Answer»

Bhai booster kansa hai Tere pass

42.

The line joining the midpoint of one diagonal to one of the other two vertices is 70 cm.What is the length of other diagonal?

Answer»
43.

ABCD is a rhombus with one diagonal cqual to 18cm. &lengtinof endhside equal to 15 cm. Find the length of the other diagonal and area ofrhombus.1Sem

Answer»

Like my answer if you find it useful!

44.

25. निम्नलिखित समीकरणों के तीन-तीन हल लिखिए :1.2x +y=72x+4yअथवा

Answer»

x=1y=52(1)+5=7this is the correct answer your doubt

this is correct or not

x=1y=5z=7 is the right answer

25. 1. X=0,y=7, x=1,y=5, x=-2,y=11.

Here is your answer

12 is the correct answer me to

x=1y=5it is the correct answer

x = 1y=5z=7 is the correct answer me to

1. (1,5),(2,3),(0,7)

45.

Show that root of the equation X2+px-q2=0 are real for all values of p & q

Answer»

please help me in this also....Out of a no. of saras bird, one fourth of the number are moving about in lot one ninth coupled with one fourth as well as 7 times the square root of no. move on a hill of bird remain in vakula tree. What is the total number of birds?

46.

x ^2 +y= 6x-14 shifted parabola .

Answer»
47.

10. Find the area of the region enclosed by the parabola x-y, the line y=x + 2 andthe x-axis.

Answer»
48.

A windew in a building is at a height ef 10 m rom the greund the sngle of depressian of spoiat P on the ground from the windew is 30 The angle ef elévatien of the top of the buildingivom the point P is 60% Find the height ef the buildinglAns 30 ml

Answer»
49.

9. Find x and y from the parallelograms given below :(0253x18104y-3B

Answer»
50.

Find the number of solutions of the following pair of linear equations:2x 3y + 174y + 6r + 1500

Answer»