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The surface area of a solid sphere is increased by 21% without changing its shape.Find the percentage increase in its:

(i) radius (ii) volume

The ratio of the length of a rod and its shadow is $1:\sqrt{3}$. The angle of elevation of the sun is _______.

In figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3, the probability that |x| < 2 is

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs 0.35 per $c{m}^2$ . (Use $\sqrt{3}=1.7$) [3 MARKS]

Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.

For the figure shown
What will be the position of point $B$ as observed from point $C$, given that origin is at $O$.

The points A(2, 1), B(3, 4), C(–1, –2) and D(, ) in order, are the vertices of a parallelogram. Find the coordinates of D.

Show that 2 + 7 is a factor of 2³ + 5² – 11 – 14. Hence factorise the given expression completely using factor theorem.

Which of the following is in reduced row Echelon form

Question 107

Solve the following

A steamer goes downstream and covers the distance between two ports in 5 hours, while it covers the same distance upstream in 6 hours. If the speed of the stream is 1km/h, then find the speed of the steamer in still water.

If two or more than two triangles be equiangular and the ratios of their corresponding sides are equal, then the triangles are called___triangles.

Solve for x,
abx²+(b²−ac)x−bc=0

Question 9
Zero of the polynomial p(x) = 2x + 5 is

A) $-\frac{2}{5}$
B) $-\frac{5}{2}$
C) $\frac{2}{5}$
D) $\frac{5}{2}$

If the side of the square is x = 6 cm. then find the area of the square.

ABC is a right angled triangle, right angled at B with AB = 3 cm and BC = 4 cm. A circle which touches all the sides of the triangle is inscribed in the triangle. Calculate the radius of the circle.

The steps involved in dividing a line segment are given below. Arrange them in the correct order.

I. Draw a ray $PM$ making an acute angle with $PQ$

II. Locate m+n points $P_1$, $P_2$, $P_3$......... $P_{m+n}$, such that $P{P}_1$ = $P_1{P}_2$ = $P_2{P}_3$ … = $P_{m+n-1}{P}_{m+n}$.

III. Measure the $\angle$ $P{P}_{m+n}Q$.

IV. Draw a line parallel to $Q{P}_{m+n}$ at $P_m$.

V. Join $Q{P}_{m+n}$.

VI. Draw an angle equal to $\angle$ $P{P}_{m+n}Q$ at $P_m$.

The point Q' at which the line $P_{m}Q\text{'}$ intersects PQ divides the line PQ in the ratio $m:n$

1. 4

In $\Delta$ ABC, if DE $\parallel$ BC, then which of the following is stated by Basic Proportionality Theorem?

Given above is a figure of a dartboard, where the length and the breadth of the rectangle are respectively 7 feet and 6 feet, and the radius of the circle is 2 feet. The probability that a point chosen from the given figure lies inside the circle is:

In the right triangle ABC, which of the following side is termed as "adjacent side" with respect to the angle $\theta$?

The journey of 192 km from Mumbai to Pune text 2 hours less by a superfast train then by an ordinary passenger train .if the average speed of the passenger train is 16 km / hour less than that of the super fast train determine their average speed.

The sum of the first 10 whole numbers and ten highest negative integers be X . Find the value of X .

1. Can two no. have HCF as 19 & LCM as 300

Question: A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48, 60 and 72 km a day, round the field. When will they meet again?

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

On a map, drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and angle ABC = ${90}^{\circ }$. Calculate : (i) the actual lengths of AB and BC in km. (ii) the area of the plot in sq. km.

Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him₹50 per metre and trouser material that costs him ₹90 per metre. For every 3 metres of the shirt material he buys 2 metres of the trouser material. He sells the materials at 12% and 10% profit respectively. His total sale is ₹36,600. How much trouser material did he buy?

Note: Please guide me on selling price and percentage and others.

Sin0=0. Prove

What is the arithmetic mean of the numbers $a$ and $b$?

Fill in the blank with a modal auxiliary showing certainty.
I _______ have submitted the cheque to the bank in the morning.

${\left(\frac{1+\tan \theta }{1+\cot \theta }\right)}^2=$

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

The present age of a father is the sum of the ages of his three sons. Ten years from now his age will be a three quarter of the sum of the ages of his children. How old is the father?

There are ___ numbers that are less than 4 on a die.

Solve the following equation & give your answer up to 2 d. p.: ² – 5 –10 = 0.

Which of the following statement is/are correct for equation 2x - 3y + 5 = 0:

1. Slope of the straight line is $\frac{2}{3}$

2. x-intercept of the straight line is $\frac{-5}{2}$

3. y-intercept of the straight line is $\frac{5}{3}$

If a, b, c are in A.P. then $3^a$, $3^b$, $3^c$ are in ___.

The Face Value (FV) of a share is ₹$150$ while its Market Value (MV) is ₹$200$. If 100 shares are purchased by a person, find the sum he invested in the shares.