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How many outcomes does the experiment "drawing two balls from a bag" have if the bag contans 4 black balls, 4 white balls and 1 red ball?

A person standing at some distance from a tower sees the top of the tower, making an angle of elevation of ${50}^{\circ }$. When he moves 10 m towards the tower the angle of elevation changes to ${70}^{\circ }$. Find the height of the tower.

$[tan{70}^{\circ }=2.74,tan{50}^{\circ }=1.2]$

What is the smallest number by which √5-√2 to be multiplied to make it a rational number? Also, find the number so obtained.

Mike works in a grocery store. He was assigned to segregate and arrange items into their respective aisles.



Which of the following Venn diagrams accurately represents notebooks, fruits, and berries?

1. 6

Find the area of a parallelogram $ABCD$ in which $AB=3cm,BC=7cm$ and $AC=8cm$ using Heron's formula.

Question 1

If the radius of a sphere is 2r, then its volume will be:



A) $\frac{4}{3}\pi r^3$

B) $4\pi r^3$

C) $\frac{8}{3}\pi r^3$​​​​​​​

D) $\frac{32}{3}\pi r^3$​​​​​​​

Solve: $3-\frac{12}{5}$.

The three angles of a quadrilateral are ${40}^{\circ },{80}^{\circ },{90}^{\circ }$. The fourth angle is:

Which of the following option is correct?



S1 : Total surface area of a cuboid is the sum of areas of 4 faces excluding top and bottom faces.

S2 : Lateral surface area of a cuboid is the sum of areas of 4 faces excluding top and bottom faces.

S3 : Area of a face of a cuboid is of the form xy, where x and y are length and breadth respectively.

The parallel sides of a trapezium are 25 cm and 11 cm. The perpendicular distance between the parallel sides is 13 cm. Find the area of the trapezium.

What do you mean by triangle

ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). From the figure, which of the following can be deduced?

In a $△ABC,$ $BM$ and $CN$ are perpendiculars from $B$ and $C$ respectively on any line passing through A. If $L$ is the mid-point of $BC,$ prove that $ML=NL.$

If the circum-radius of a right-angled triangle is $20cm$, then the length of the hypotenuse will be ___ (in cm)

Without performing actual computations, find the quotient when 94+49 is divided by 11

The volume of a square pyramid of base edge 12 cm and height 18 cm is:

In a carton of 120 fruits, 24 are rotten. The probability that a fruit taken at random will be good is ___.

Two angles of a quadrilateral are ${36}^{\circ }$ and ${72}^{\circ }$ and other two angles are in the ratio 3:4 , then the measure of other two angles are

1. 2

Question 2

Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

A triangle in which each angle is less than 90 degrees is called ___.

Which of the following should be the SECOND sentence after rearrangement?

A line whose equation is given as $px+qy=20$ is plotted on the graph below. What would be the values of $p$ and $q$?

The altitude AD of a ΔABC, in which ∠A is obtuse and AD = 10cm. If BD = 10√3cm, then ∠A = ?

A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remainig circles (Fig.). In the shaded region she writes a message 'Save Energy'. Find the area of the shaded region. (Use $\pi =\frac{22}{7}$)

Express this statement as an equation:
My age is 3 years less than twice the age of my brother. Assume that my brother’s age is x and my age is y.

ABC and DBC are two isosceles triangle on the same base BC and vertices A and D are on the same side of BC if AD is extended to intersect BC at P show that triangle ABD is congruent to triangle ACD and triangle ABD is congruent to triangle ACP and AP bisects angleA as well as angleD and AP is the perpendicular bisector of BC