Explore topic-wise InterviewSolutions in Current Affairs.

If $\overrightarrow{a}$ is a vector of magnitude 50 and is collinear with the vector $\overrightarrow{b}=6\hat{i}-8\hat{j}-\frac{15}{2}\hat{k}$ and makes an obtuse angle with the positive direction of z - axis, then $\overrightarrow{a}$ is equal to

$△$ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm.$△$ DEF is similar to $△$ABC. If EF = 4 cm, then the perimeter of $△$DEF is

The ________ of a circle has the major arc as part of its boundary.

The base area of a prism is $40c{m}^2$. What would be the height of the prism if its volume = $200c{m}^3$ ?

The area of a trapezium is 1586 cm² and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, then find the other parallel side.

The area of a rectangle is $A=25a^2-35a+12$. Its length is ($5a-3$), find its width.

(i) Write the points whose abscissa is 0.
(ii) Write the points whose ordinate is 0.
(iii) Write the points whose abscissa is -5.

A circus artist is climbing a 20m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is ${30}^{\circ }$.

Question 1 (h)

Write all the factors of the given number:
23

There is a black bag which contains 100 identical balls. 99 of those balls are red in colour and remaining 1 is white. Now, if you take a ball out of the bag, what can be said about its colour?

Without using trigonometric tables, evaluate:

$\left(i\right)cos{48}^{\circ }-sin{42}^{\circ }$

$\left(ii\right)cosec{31}^{\circ }-sec{59}^{\circ }$

$\left(iii\right)cot{34}^{\circ }-tan{56}^{\circ }$

$\left(iv\right)co{s}^2{13}^{\circ }-si{n}^2{77}^{\circ }$ [4 MARKS]

The inner radius of a hollow iron sphere is $9cm$. If iron is $1cm$ thick, find the volume of iron used to make the ball.

$\frac{\sqrt{3}-1}{\sqrt{3}+1}=a-b\sqrt{3}$ then the values of a and b are

If $x=\sqrt{5}+2$, then find the value of $x-\frac{1}{x}$.

Which of the following is not a chief organ of the United Nations Organisations?

Find the point (x,y) that divides the line joining A(3,6) and B(7,10) in the ratio 3:1.

Ex:7.1 question number 7

Answer given: p is mid point

Angle BAD=angleABE

Angle EPA=Angle DPB

To prove triangle DAP in congruent to triangle EBP

Proof angle EPA+Angle EPD=angle DPB + angle EPD

Angle APD=angle BPE (1)

In triangle DAP and Triangle EBP

Angle BAD = angle ABE(given)

AP=PB (p is mid point of AB)

Angle APD=Angle BPE (frome 1)

So by asa criteria

Triangle DAP is congruent to triangle EBP

Three numbers are in continued proportion whose mean proportional is 12 and the sum of the remaining two numbers is 26, then find these numbers

Simplify (3+√2)(4+√7)

Give possible expression for the length and breadth of each of the following rectangles in which the areas are given

(Sir/Mam in the problem please explain the splitting in a step by step manner)

a) (35y^2+13y--12)

b) ( 25^2-35a+12)

If x=7+√3, find the value of √x+1\√x

The remainder when $x^4-3x^3+2x^2$ is divided by $x-2$ is:

Solve for $x$

$3^{4x+1}={27}^{x+1}$

Question 79

Bachhu Manjhi earns Rs. 24000 in 8 months. At this rate,

a) how much does he earn in one year?

b) in how many months does he earn Rs. 42000?

Diagonals of a rhombus are ________ to each other.

The perimeter of $△ABC$ is 49 cm. The angle bisector of $\angle A$ meets BC at M. BM = 6 cm, MC = 8 cm. Find AC.

A measurement box measures 18 cm × 6 cm × 2 cm. The volume of the packet containing 12 such boxes is

$\text{In}△ABC,\angle B=\angle C.\text{D and E are the mid points of AB and AC respectively.}\text{Then, the value of the ratio}\frac{BE}{CD}\text{is}$ _______.

In ΔPQR, S is any point on the side QR, then

PQ is a line parallel to side BC and passing through vertex A of a triangle ABC. BE || AC and CF || AB meet PQ at E and F respectively. If the base and altitude of ΔABC are 6 cm and 8 cm respectively, the area of ΔACF is ___.

ABCD is a parallelogram, Area(DAB)=

Draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Find the radius of the circle.

If a hemisphere has radius __ cm, then total surface area of the hemisphere is 9.42 ${cm}^2$.

(Take $\pi$ = 3.14)

Which of the following is equal to $4k^2+12km+9m^2$ ?

Question 7 (ii)
AB is a line segment and P is its mid-point. D and E are points on the same side of
AB such that $\angle BAD=\angle ABE\text{and}\angle EPA=\angle DPB$ (See the given figure). Show that
AD = BE
​

The ratio in which the line segment PQ, where P (-5, 2) and Q (2, 3), is divided by the y-axis is

If sin4A = cos(A - 30), where 4A and (A - 30) are acute angles, then the value of A is ___.

The locus of the point, whose chord of contact w.r.t the circle $x^2+y^2=a^2$ makes an angle $2\alpha$ at the centre of the circle is

A line passing through origin can be represented by an equation

Find the point on the y-axis which is equidistant from A (3, - 4) and B (- 5, 9).

A scooter was bought at ₹42000 and its value depreciated at the rate of 8% per annum. Find its value after one year.

Look at the statemets given below:

I.A parallelogram and a rectangle on the same base and between the same parallels are equal area.

II.In a ||gm ABCD,it is given that AB=10 cm.The altitudes DE on AB and BF on AD being 6 cm and 8 cm respectively,then AD=7.5 cm.

III.Area of a ||gm=$\frac{1}{2}\times base\times altitude$.

Which is true?

(a) I only

(b) II only

(c) I and II

(d) II and III