Explore topic-wise InterviewSolutions in Current Affairs.

A flagstaff 6 metres high throws a shadow 2$\sqrt{3}$ m long on the ground. The angle of elevation (in degree) of the top of the flagstaff from the point where the shadow ends.

Verify :

x^{​​​​​​3} + y^{​​​​​​3} = (x + y) (x^{​​​​​​2} + y^{​​​​​​2} – xy)

Plot the points A (4, 0), B (4, 4) and C (0, 4) on the graph. Join OA, AB, BC, and CO, where O is the origin. Name the figure so formed and measure its sides.

What will be the diameter of a circle whose radius is 15 cm?

Imagine a picture of a scoop of ice-cream in a cone. Consider the cone to be in equilateral shape and the scoop to fit at the top of the cone. What would be the area of the picture if the side of the equilateral triangle is, a = 6 cm?

(i) Given two points P and Q, find how many line segments do they deter-mine.

(ii) Name the line segments determined by the three collinear points P, Q and R.

If $x+2y+3z=0$ then $x^3+8y^3+27z^3$ = _____________

What is the area of the right-angled triangle $\Delta MNO$, right angled at N.

105×106 without multiplying. Which identity we use in this tricky question??

Evaluate the following using suitable identities:

${\left(998\right)}^3$ [2 MARKS]

Solutions of the equation 2x + 5y = 0 is:

In an experiment with 15 observations on $x$, the following results were available: $\sum x^2=2830,\sum x=170$ One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. The corrected variance is

An army camp of 250 men has provision for 350 days. After 25 days, 50 men died due to epidemic. The food will last for

The graph x + 3 = 0 is a line

(a) making an intercept - 3 on the x - axis

(b) making an intercept - 3 on the y - axis

(c) parallel to the y - axis at a distance of 3 units to the left of y - axis

(d) parallel to the x - axis at a distance of 3 units below the x - axis

$\text{AD is an altitude of an isosceles}\Delta ABC\text{in which AB = AC.}\text{Show that (i) AD bisects BC,}\text{(ii) AD bisects}\angle A.$

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

$\begin{array}{cc}Assertion\left(A\right)& Reason\left(R\right)\\ \text{The diagonals of a}||gmdivideit& \text{A diagonal of a}||gmdividesitinto\\ \text{into four triangles of equal area.}& \text{two diagonals of equal area.}\end{array}$

The correct answer is :(a) /(b) /(c) /(d)

In $△ABC$, if D and E are midpoints of BC and AD respectively such that $ar\left(△AEC\right)=4c{m}^2$, then $ar\left(△BEC\right)$ =

The area of a rectangle is x² + 9x + 14, what are the dimensions of rectangle if x = 2.

In a given figure, BE is a median of $△ABD$. If the area of parallelogram ABCD is $24c{m}^2$. Then the area of $△ABE$ is:

Question 2
Visualize $4.\overline{26}$ on the number line, up to 4 decimal places.

Any line of the type y = mx ha to pass through origin, hence the answer

A line y = mx passes through the origin So m takes

Things which are double of the same things are _____ to one another.

Question 2 (v)
Write the abscissa of the point D.

Which of the following equations have $x=4\text{and}y=2$ as a solution?

Let $f:(4,6)\to (6,8)$ be a function defined by $f\left(x\right)=x+\left[\frac{x}{2}\right]$ (where [.] denotes the greatest integer function),
then $f^{-1}\left(x\right)$ is equal to

In Fig. AB > AC. Show that AB > AD. [4 MARKS]

In a triangle ABC, D is mid-point of BC; AD is produced upto E so that DE = AD. Prove that :

(i) $\Delta$ ABD and $\Delta$ ECD are congruent.

(ii) AB = EC.

(iii) AB is parallel to EC.

If $3^{4x}=(81{)}^{-1}$ and $(10{)}^{\frac{1}{y}}=0.0001$, find the value of $2^{-x}\times {16}^y$

Class mark of a particular class is 10.5 and class size is 7, then class interval is

What is the area of this triangle? [2 MARKS]

$Themagnitudeoftheprojectionof2\hat{i}+3\hat{j}+4\hat{k}onthevector\hat{i}+\hat{j}+\hat{k}willbe\underset{–}{}$

Solve the following pair of linear equations:
$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$
$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$
(Where $x>0,y>0)$

If $x=2\sqrt{2}+\sqrt{7}$, identify the value of $\frac{1}{2}(x+\frac{1}{x})$.

Find which of the following are the pair of like fractions:

In a right angled triangle, as shown below, if AB=3 cm, BC=4 cm then what is the value of cos A?

Question 01.
Following are the car parking charges near a railway station up to:

$\begin{array}{cc}4hours& Rs.60\\ 8hours& Rs.100\\ 12hours& Rs.140\\ 24hours& Rs.180\end{array}$

Check if the parking charges are in direct proportion to the parking time.

A question was asked in a class
”The points A(5, 5), B(4, 4) and C(3, 3) form which triangle?”.
Unfortunately, no student could get it right.
What type of triangle will be formed if the points are joined ?

Two angles $a\text{and}b$ form a linear pair. If $2a-3b={60}^{\circ }$ then $5b=$____ degrees.

Refer to the figure below, which of the given options is correct.

Any point on the y - axis is of the form

(a) (x, y)

(b) (0, y)

(c) (x, 0)

(d) (y, y)

Which of the following is/are true?

ABCD is a cyclic quadrilateral, in which \(\angle DBC = 80^\circ\) and \(\angle BAC = 40^\circ\). __ is the $\angle BCD$.

The unit vector which is orthogonal to the vector $3\hat{i}+2\hat{j}+6\hat{k}$ and is coplanar with the vectors $2\hat{i}+\hat{j}+\hat{k}and\hat{i}-\hat{j}+\hat{k}$

What is the area of a right angled triangle if its base is given as 6 cm and Hypotenuse is 10 cm.

Which of the following statements is incorrect?