Explore topic-wise InterviewSolutions in .

If point P lies on the line y = 2, then what is its x-coordinate?

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^2-4x-1=0$

In the figure, PQ || AB, CQ = 4.8 cm, QB = 3.6 cm and AB = 6.3 cm. If AP = x, length of AC in terms of x is .

If a ladder makes an angle of elevation of 30° with the top of a 10 m high wall, then the length of of the ladder is ___m.

A tree 32 m tall broke due to a gale and its top fell at a distance of 16 m, from its foot. At what height above the ground did the tree break?

$\text{In the following figure, triangle AXY}\text{is isosceles with}\angle AXY=\angle AYX.$



$\text{If}\frac{BX}{AX}=\frac{CY}{AY},\text{then prove that}\text{triangle ABC is an isosceles triangle.}$

Two pillars of equal heights stand on either side of a road which is 100 m wide. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are ${60}^{\circ }$ and ${30}^{\circ }$. Find the height of each pillar and position of the point on the road. [Take $\sqrt{3}$=1.732] [3 MARKS]

In a triangle ABC, $\angle A={60}^{\circ }$ and the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively.

Solve for x and y where $x\ne 0,y\ne 0:$

$\frac{1}{2(x+2y)}+\frac{5}{3(3x-2y)}=\frac{-3}{2}\frac{5}{4(x+2y)}-\frac{3}{5(3x-2y)}=\frac{61}{60}$

Among the following, the terminating rational number is .

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level fo water is raised by 6.75 cm.What is the radius of the ball ?

What is the solution of the equations √2x - √3y = 0 and √5x + √2y = 0?

If the $5^{th}$ and ${11}^{th}$ term in an A.P are 11 and 5. Find the ${16}^{th}$ term.

Question 24

Factorise

(i) $2x^3–3x^2–17x+30$



(ii) $x^3–6x^2+11x–6$



(iii) $x^3+x^2-4x-4$



(iv) $3x^3–x^2-3x+1$

4 focus lights are to be fixed on a square aluminium plate of side 28 inches. Circles are cut in the plate to accommodate the lights. After the required alterations, the aluminium plate looks similar to the figure shown below. What is the area of the aluminium portion after alterations?

Question 6

Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

Given $l=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$ Find $l^2$

The common tangents AB and CD to two circles with centers O and O' intersect at E between their centers. Prove that the points O, E and O' are collinear,

Question 5
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

AB is the diameter and AC is a chord of a circle with centre O such that angle BAC = ${30}^o$. The tangent to the circle at C intersects AB produced in D. Show that : BC = BD.

Reena bought a washing machine for ₹ 9800 including tax of 10%. Find the price of the washing machine before VAT was added.

Which of the following equations are quadratic?

Prove that x − 1 is a factor of xⁿ − 1 for every natural number n.

Find the product of the rational expressions 2xyz/(x + y) and $x^2$ + $y^2$ + 2xy)/5xz

Angles of inclination of line XY with $AB,CD,EF$ and $GH$ are respectively are $\alpha$, $\beta$, $\varphi$ and $\theta$. Identify the angle of inclination of $EF$ with respect to $XY$.

The diameter of a circular pond is 17.5 m. It is surrounded by a path of width 3.5 m. Find the area of the path in $m^2$.

__