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In which of the following quadrilaterals, diagonals bisect each other?

i) Parallelogram

ii) Rhombus

iii) Rectangle

iv) Square

v) Kite

Arrange the heights of the given students in a grouped distribution with a class interval of 5 and find the number of students whose height is more than 169cm.

Heights (in cm): 150, 153, 162, 170, 186, 153, 162, 180, 165, 150, 178, 156, 184, 176, 173, 186, 159, 183, 150, 156.

If $f\left(x\right)=$$\{\begin{array}{c}|x|-3,x<1\\ |x-2|+a,x\ge 1\end{array},$ $g\left(x\right)=\{\begin{array}{c}2-|x|,x<2\\ \text{sgn}\left(x\right)-b,x\ge 2\end{array}$ and $h\left(x\right)=f\left(x\right)+g\left(x\right)$ is discontinuous at exactly one point, then which of the following values of $a$ and $b$ are possible

Mark the correct option:

The number of pairs positive integers (m, n) such that mⁿ = 25 is

A. 0

B. 1

C. 2

D. more than 2

The number of sides of the polygon in which all the interior angles sums to ${1980}^o$ is

Question 51

In the following question, fill in the blanks to make the statements true.

By multiplying ${\left(\frac{5}{3}\right)}^4$ by ___ we get $5^4$.

Identify which is/are not a linear function.

Select the smallest triangle.

In the figure of a cube,

i) Which edge is the intersection of faces EFGH and EFBA?

ii) Which faces intersect at edge FB?

iii) Which three faces from the vertex A?

iv) Which vertex is formed by the faces ABCD, ADHE and CDHG?

v) Give all the edges that are parallel to edge AB

vi) Give the edges that are neither parallel nor perpendicular to edge BC.

vii) Give all the edges that are perpendicular to edge AB.

viii) Give four vertices that do not all lie in one plane.

Let $g\left(x\right)=1+x-\left[x\right],$

$f\left(x\right)=\{\begin{array}{cc}-1,& x<0\\ 0,& x=0\\ 1,& x>0\end{array}.$

Then for all $x$, $f\left(g\left(x\right)\right)$ is

(where $[.]$ is greatest integer function)

The sum of first 5 consecutive odd numbers is:

Question 112(i)

Sonia picks up a card from the given cards



Find the probability of getting An odd number ?

Question 143(iii)

Use the propeties of exponents to verify that each statement is true.

$25\left(5^{n-2}\right)=5^n$

By selling a bicycle at 1334 rupees a shopkeeper would suffer a loss of 8 percent. At how much amount should he sell it to make a profit of 25/2 percent

Find the cube root of each of the following numbers by prime factorisation method.

(i) $64$

(ii) $512$

(iii) $10648$

(iv) $27000$

(v) $15625$

(vi) $13824$

(vii) $110592$

(viii) $46656$

(ix) $175616$

(x) $91125$

Construct a rhombus with side 6 cm and one diagonal 8 cm. Measure the other diagonal.

Which of the letters have both horizontal and vertical line of symmetry?

(a) If two cubes of dimensions 3 cm by 3 cm by 3 cm are placed side by side, then what is the resulting dimension(length (l), breadth (b) and height (h)) of the cuboid? Find the value of l+b+h (in cm).

(b) A metallic cylinder with volume $1331c{m}^3$ is melted and is transformed into a cube. What will be the length of the sides of the cube formed? (Volume of a cube with side length $a$ is given as $a^3$)
[3 MARKS]

Shopkeeper gains $20\%$ by selling a video game for $\text{Rs.}15000.$ If the profit is increased to $60\%,$ then the selling price is

A ______ is described as the numeric value separating the higher half of a sample.

Find angle x if line l is parallel to line m and line n is a transversal.

Find the value of x for which ${\left(\frac{5}{3}\right)}^{-4}\times {\left(\frac{5}{3}\right)}^{-5}={\left(\frac{5}{3}\right)}^{3x}$

Meena needs to serve mango juice to her guests in cylindrical tumblers of radius 7 cm and height 10 cm. If she wants to serve 25 guests, how much juice does she need to prepare? [Assume that the juice is filled up to the brim]

Question 8(b)
A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold.
What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags?

The factors of $4x^3+12x^2+6x+18$ are:

(i)1 micron $=\frac{1}{1000000}$m. Express it in standard form.

(ii)Size of a bacteria =0.0000004 m. Express it in standard form.

(iii)Thickness of a papaer =0.03 mm. Express it in standard form.

If set A and set B have 3 and 6 elements respectively, then which of the following can be the minimum number of elements in $(A\cup B)$?

In a division problem, if dividend = 23 and quotient = 4, which of the following is correct?

Question 9

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

The reciprocal ( Multiplicative inverse) of $\frac{3}{5}$ $\times$ $\frac{15}{5}$ is ________-