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If f is an even function defined on the interval (-5,5), then the real values of x, satisfying the equation $f\left(x\right)=f\left(\frac{x+1}{x+2}\right)$ are ___.

Sam is looking at the roof of the adjacent building from top of his flat. His height is 5 feet. He knows that the height of his building and the distance between the two buildings is 50 feet. Sam measures the angle of elevation of his line of sight of the tip of the other building to be ${30}^{\circ }$. Based on the information in the question, find the height of the adjacent building?

There are 6 points in a plane out of which 3 points are collinear. What is the probability if 3 points which are selected form a triangle?

Prove the following trigonometric identities:

$\frac{1-cosA}{1+cosA}=(cotA-cosecA{)}^2$

Question 9

Which of the following equations does not have a solution in integers ?

(a) $x+1=1$

(b) $x-1=3$

(c) $2x+1=6$

(d) $1-x=5$

Someone is asked to take a number from 1 to 100. The probability that the selected number is prime is:

The graph y= p(x) is shown below. How many zeroes does the polynomial p(x) have?

Question 4(a):

Say true or false

Two diameters of a circle will necessarily intersect.

Which term of A. P. 5, 15, 25, ............ will be 130 more than its ${31}^{st}$ term ?

Find a quadratic polynomial for the given numbers as the sum and product of its zeroes respectively.

$\frac{1}{4},-1$

XYZ. Ltd. provided the following information, calculate Net Cash Flow from Financing Activities:

Additional Information:

1.Interest paid on debentures ₹ 19,000.

2. Dividend paid in the year ₹ 50,000.

3. During the year, XYZ Ltd. issued bonus shares in the ratio of 5 : 1 by captialising reserve.

A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:

Fill in the blanks using correct word given in the brackets:−

(i) All circles are __________. (congruent, similar)

(ii) All squares are __________. (similar, congruent)

(iii) All __________ triangles are similar. (isosceles, equilateral)

(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are __________ and (b) their corresponding sides are __________. (equal, proportional)

If cos θ=12/13, show that sinθ(1−tan θ)=35/156

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m. [4 MARKS]

51 + 52 + 53 + ……. + 70

A box contains 3 black balls, 4 red balls and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black or green ball?

If $5x-3\le 5+3x\le 4x+2$, express it as $a\le x\le b$.

If sin B = 1, find the value of B if $0\le B\le 90$.

Find the sum of first 51 terms of an A. P. whose $2^{nd}$ and $3^{nd}$ terms are 14 and 18 respecitively.

Ravi completed of a job the first day and of it on the second. How much of the job did he do in these two days together? How much remains to be done?

O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O a point P is taken. From this point, two tangent PQ and PR are drawn to the circle. Then, the area of quad. PQOR is

(a) 60 $c{m}^2$ (b) 32.5 $c{m}^2$ (c) 65 $c{m}^2$ (d) 30 $c{m}^2$

If $(a − b)$,$a$ and $(a+b)$ are zeros of the polynomial $2x^3-6x^2+5x-7$, write the value of $a$.

The probability of getting a sum of 13 when two dice are thrown simultaneously is___