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A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 CM such that the diameter of the hemisphere is equal to the edge of the cube . Determine the volume and total surface area of the remaining block.

100 surnames were randomly picked up from a local telephone directory & the frequency distribution of the number of letters in the English alphabets in the surname was obtained as follows.

$\begin{array}{ccccccc}\text{Number of letters}& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ \text{Number of surnames}& 6& 30& 40& 16& 4& 4\end{array}$

Determine the median number of letters in the surnames.

1. 8.05

In a triangle the sum of two sides is x and the product of the same sides is y. If $x^2-c^2=y$, where c is the third side of the triangle, then the ratio of the in radius to the circum – radius of the triangle is

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

The image of a point P on reflection in a Line listen p'. Describe the location of the line l and explain the answer.

The equation of a line whose x intercept is 3 and y intercept is -2 is

Pick out the value of ‘y’ from the following

(1) 4 ⊕ y = 0 (mod 5)

(a) 0 (b) 1 (c) 4 (d) 5

(2) 3 ⊕ y = 2 (mod 6)

(a) 4 (b) 2 (c) 5 (d) 6

(3) 2 y = 1 (mod 5)

(a) 2 (b) 5 (c) 6 (d) 3

(4) y ⊗ y = 1 (mod 8)

(a) 6 (b) 3 (c) 8 (d) 4

${\text{sec}}^{4}A(1-{\text{sin}}^{4}A)-2{\text{tan}}^{2}A=$ ___

Which of the following does not satisfy the following property?

A number which divides 542 and 128 and leaves a remainder 2 in both cases.

Given : AB // DE and BC //EF. Prove that :
(i) $\frac{AD}{DG}=\frac{CF}{FG}$
(ii) $\Delta$ DFG~ $\Delta$ ACG.

Find the remainder when $x^3-a{x}^2+6x-a$ is divided by $x-a$. [2 MARKS]

If two cubes of volume $216m^3$ are joined end to end to form a cuboid, then find the volume and total surface area of the cuboid.

Which of the following is/are a measure of central tendency?

If $A^T=\left[\begin{array}{cc}3& 4\\ -1& 2\\ 0& 1\end{array}\right]\text{and}B=\left[\begin{array}{ccc}-1& 2& 1\\ 1& 2& 3\end{array}\right]$,

then find $A^T-B^T$

Define Segment of a Circle.

Joey buys an article at a rebate of $30\%$ on the printed price. He spends Rs.40 on transportation of the article. After charging sales tax at the rate of $7\%$ on the printed price, he sells the article for Rs.856.Find his profit percentage.

The equations $\lambda x-y=2,2x-3y=-\lambda ,3x-2y=-1$ are consistent for

A right triangle is formed by connecting the 3 coordinates A, B and C. Then the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in the figure is

Prove- sin theta/cot theta + cosec theta=2+sin theta/cot theta- cosec theta

Solve for x and y:

$3x-5y-19=0,-7x+3y+1=0.$

If A,B,C are the interior angles of a $\Delta$ ABC, show that:

(i) sin $\frac{B+C}{2}=cos\frac{A}{2}$

(ii) cos $\frac{B+C}{2}=sin\frac{A}{2}$

The probability of getting a perfect square number in a single throw of a dice is ____.

If alpha and beta are the zeroes of the quadratic polynomial f(x)=x^{2-px+q then find the values of (1)alpha}2 + beta²

If $3^{rd}$ term of a G.P is 12 and $6^{th}$ term is 96, find its $7^{th}$ term.

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'R' are ___

Which of the following is true about a quadratic function?

Question 1 (iv)

Solve the following pair of linear equations by the elimination method and the substitution method:

$\frac{x}{2}+\frac{2y}{3}=-1$ and $x-\frac{y}{3}=3$

A can do a piece of work in $x$ days and B can do the same work in $x+16$ days. If both working together can do it in 15 days, find the value of $x$.

In the given below figure CD in the median and DB = 3 cm , CD = 4 cm. the value of BC is

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.