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A man invests a certain sum in buying 15% Rs 100 shares at 20% premium. Find :

(i) his income from one share.

(ii) the number of shares bought to have an income, from the dividend, Rs 6,480.

(iii) sum invested.

If α and β are the zeros of polynomial f(x)=x^2-p(x+1)-c, then (α+1)(β.+1)=

In the figure, ABC is a triangle in which $\angle BAC={30}^{\circ }$. Show that BC is equal to the radius of the circumcircle of $\Delta ABC$, whose centre is O.
[3 MARKS]

The median of a distribution divides it into

The two zeroes are √2+3 and √2-3 . What is the sum of zeroes ?

Solve the following systems of linear equations graphically:

3x + y - 11 = 0, x - y - 1 =0.

Shade the region bounded by these lines and y-axis. Also, find the area of the region bounded by the these lines and y-axis

Two dice are thrown at a time. Find the probability of one of the values being a multiple of the other. [3 MARKS]

A ladder reaches a window 12 m above the ground and its foot is at distance of 5 m from a wall, then the length of the ladder is __ m.

Find the value of 'k', for which the points (8, 1), (k, -4), (2, -5) are collinear.

Find the median of the following data.

$\begin{array}{cc}No.ofPlants& No.ofhouse\\ 0-2& 1\\ 2-4& 3\\ 4-6& 2\\ 6-8& 4\\ 8-10& 5\\ 10-12& 3\\ 12-14& 2\end{array}$ [3 MARKS]

Question 1 (ii)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: $p\left(x\right)=x^4-3x^2+4x+5,g\left(x\right)=x^2+1-x$

The diagonal of a rectangle is 20 cm and it makes an angle of ${40}^{\circ }$ with one of its sides.The perimeter of the rectangle will be equal to $[sin{40}^{\circ }=1.64,cos{40}^{\circ }=0.76]$

In the figure given below, sides PB and QA are perpendiculars drawn to the line segment AB.

If PO = 6 cm, QO = 9 cm and area of $\Delta POB=120c{m}^2$, then the area of $\Delta QOA$ is

From a point P, two tangents PA and PB are drawn to a circle with center O as shown.
If angle AOB = ${100}^{\circ }$, then find the value of $\angle APB.$

In figure, find $\angle E$.

Find the trigonometric ratio equivalent to the following:

$sin{55}^{\circ }+cos{20}^{\circ }+cot{70}^{\circ }+cosec{85}^{\circ }$

The given table shows the salaries of 81 people in thousands. Calculate the Median from the data given.

$\begin{array}{cc}\text{Salary(in thousands)}& \text{No. of people}\\ 5-10& 7\\ 10-15& 12\\ 15-20& 15\\ 20-25& 8\\ 25-30& 11\\ 30-35& 18\\ 35-40& 10\end{array}$

The difference between the outside and inside surface of a cylindrical metallic pipe 14 cm long is $44c{m}^2$. If the pipe is made of 99 $c{m}^3$ of metal, find the outer and inner radii of the pipe. [4 MARKS]

Question 62

Solve the following:

$\frac{x}{2}-\frac{1}{4}(x-\frac{1}{3})=\frac{1}{6}(x+1)+\frac{1}{12}$

If a circle is drawn with centre 'C' (0,8) and radius 10 cm as shown in figure then the coordinates of R and S are___

Prove (cosecA - sinA) (sec A - cos A) = $\frac{1}{tanA+cotA}$

Which of the following statements is true?

Question 2 (c)

What is the HCF of two consecutive odd numbers?

Question 81

In the following question, state whether the given statements are true (T) or false (F).

$a^p\times b^q=(ab{)}^{pq}$

If P(E) and P(E’) are the probabilities of two complementary events, then which of the following is always true?

Select the statements that hold true for the figure given below:

$\text{In the given figure, PT is a tangent of a}\text{circle, with centre O, at point R. If}\text{diameter SQ is produced, it meets with}\text{PT at point P with}\angle SPR=x\text{and}\angle QSR=y,\text{then find the value of}x+2y.$

Construct $\Delta$PQR with QR = 6.5 cm, PQ= 5.5 cm, PR = 5 cm. Construct and find the radius of incircle of the $\Delta$PQR

Identify the null matrix from the given list

Question 2
Prove that $3+2\sqrt{5}$ is irrational.

Obtain all the zeros of 2 x^ 4 - 3 x^3 - 3 x^2 + 6 x- 2 if two of its zeros are √2 and- √2.

1. 25

Mr. Tiwari invested Rs 29040 in $15\%$ Rs 100 shares quoted at a premium of $20\%$. Calculate the number of shares he bought and his income from the investment.

How many excenters does a triangle have? ___

A number increased by 15% becomes 391. Find the number

If the distance between the points A (4, p) and B(1, 0) is 5 then p =

You spin a spinner that has 8 equal-sized sections numbered 1 to 8. Find the theoretical probability of landing on the given section(s) of the spinner.
(i) section 1 (ii) odd-numbered section (iii) a section whose number is a power of 2. [4 MARKS]

In the given figure, two circles touch each other externally at point, P. AB is the direct common tangent of these circles. Select the statements that are true.

Find the value of |x+b| + |x + a| + |a-b| ___

Question 6
Value(s) of k for which the quadratic equation $2x^2$ - kx + k = 0 has equal roots is/are
(A) 0 only
(B) 4
(C) 8 only
(D) 0, 8​​​​​​