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The equation (m being real), $m{x}^2+2x+m=0$ has two distinct roots if ___.

If the perimeter of a circle is equal to that of square, then the ratio of their areas is:
(A) $22:7$
(B) $14:11$
(C) $7:22$
(D) $11:14$

A bus travelling the first one-third distance at a speed of $10\text{km/h},$ the next one-third at $20\text{km/h}$ and the last one-third at $60\text{km/h}$. The average speed of the bus is

Using section formula, show that the points $A(2,-3,4)B(-1,2,1)$ and $C(0,\frac{1}{3},2)$ are collinear.

Find the value of the constant ‘m’ if :
y = – 1 is a root of the quadratic equation $7+4(m+2)y–y^2$ = 0.

__

Can two numbers have 15 as their H.C.F. and 175 as L.C.M. Give reason

What can you say about the ratio of the coefficients for the lines $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ from the graph ?

1. 3240

When 6 new boys were admitted and 6 girls left from the class,the percentage of boys increased from 60%to 75%.find the original number of boys and girls in class

The incenter of a triangle is given by:

Two pipes running together can fill a tank in 11 one by nine minutes if one pipe takes 5 minutes more than the the other to fill the tank separately find the time in which each pipe would fill the tank separately

A man has 300, Rs 50 shares of a company paying 20 % dividend. Find his net income after paying 3% income tax .

Explained answer of

If (x+a) is a factor of 2x²+2ax+5x+10 find a

If sin A = $\frac{8}{17}$, find the value of sec A cos A + cosec A cos A.

Construct a triangle BCP given BC=5cm,BP=4cm and $\angle$PBC=45${}^{\circ }$. Complete the rectangle ABCD such that:

(1) P is equidistant from AB and BC

(2) P is equidistant from C and D.

Measure and record the length of AB.

The sum of the sides of a right-angled triangle is 36 cm, whose hypotenuse is 15 cm. The difference between the other two sides of this triangle would be:

In the given figure, $△ABC$ is inscribed in a circle. The bisector of $\angle BAC$ meets BC at D and the circle at E. If EC is joined, then $\angle ECD={30}^{\circ }$. Find $\angle BAC$.

Explain the similar triangles

If sin A - cos A is equal to 1/2 then find the value of one upon sin a + cos A

Ram is 5 times as old as Shyam. If their difference of age is 8 years, how old is Shyam?

Which function models the graph below?

X –axis 1 grid = 1 unit

Y –axis 1 grid = 1 unit

Question 6
In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

If the two zeroes of the quadratic polynomial 7x² - 15x - k are reciprocals of each other, the value of k is:

The discriminant of the quadratic equation 2x² – 6x + 3 = 0 is

The value of 5 tan²θ – 5 sec²θ is :

p and q are called coprime integers if _

Suppose that all the terms of an arithmetic progression are natural numbers. If the ratio of thesum of the first seven terms to the sum of thefirst eleven terms is 6:11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is

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

Draw the graphs of the following equations on the same graph paper:

2x + 3y = 12

x - y = 1.

Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis.

A vertical tower is 20 m high. A man standing at some distance from the tower knows that the cosine of a angle of elevation of the top of the tower is 0.53. How far is he standing from the foot of the tower?

If LM $\parallel$ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?

Points A & B have coordinates (7, 3) & (1, –9) respectively. Find

Solve :
(a) Which of the following points lie at a distance of 2 units from the X axis: (1,1), (-1,-2), (2,2), (2,0), (-2,3)
(b) Find a point on 2x + 3y = 10 which is at a distance of 2 units to the right of the Y axis. [3 MARKS]

If $lo{g}_{10}2=0.30103$, then $lo{g}_{10}50=$

The quadratic polynomial in x whose zeros are -a, 2a is:

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ },\angle BAC={30}^{\circ }$ and AB=BC, then find $\angle ECD.$

In the given figure, ABC is an isosceles right angle triangle, right angled at B. The ratio of the sides AB: BC : AC is _________.

At $\theta ={90}^{\circ }$ which of the following trigonometric ratios are not defined?