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If sin $\theta$ = cos $(\theta -{45}^o)$, where $\theta$ is acute, find the value of $\theta$.

Sandeep deposited Rs. 5000 in his saving account. His amount increases by 1/10 times of itself after every two years. What are the maturity amounts (in Rs.) of investment after $2^{nd}$, $4^{th}$, $6^{th}$ and $8^{th}$ years respectively? Are the maturity amounts (in Rs.) after $2^{nd}$, $4^{th}$, $6^{th}$ and $8^{th}$ years the terms of an AP?

If sin (A + B) = sin A cos B + cos A sin B and cos (A - B) = cos A cos B + sin A sin B, find the values of (i) sin ${75}^{\circ }$ and (ii) cos ${15}^{\circ }.$

There is a solid cylinder of base radius 5 cm and height 10 cm. From one of the flat ends of the solid cylinder a hemispherical depression having same radius as cylinder is hollowed out. What is the total surface area (in sq.cm) of this new solid?

In a diary, there are 60 cows and buffalos. The number of cows is twice that of buffalos. Buffalo X ranked seventeenth in terms of milk delivered. If there are 9 cows ahead of buffalo. X, how many buffalos are after in rank in terms of milk delivered?

A pendulum swings through an angle of ${30}^{\circ }$ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.

The marks for Computer Science obtained by 40 students out of 60 is given below:
$\begin{array}{cccccc}\text{Marks}& 43& 55& 40& 30& 60\\ \text{No. of students}& 7& 10& 13& 8& 2\end{array}$ .

Find the mode of the above data.

The quadratic equation which has D = 0 and a root as $\frac{1}{10}$ is

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 an A.P., the sum of first n terms is $\frac{3n^2}{2}+\frac{13}{2}n$. Find its 25th term.

Divide Rs. 1, 290 into A, B and C such that A is $\frac{2}{5}$ of B and B : C = 4: 3.

Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius. [4 MARKS]

Question 32

Fill in the blanks to make each statement true:

The sum of two consecutive multiples of 10 is 210. The smaller multiple is ................

2/√x+3/√y=2

4/√x-9/√y=-1

If primetermof circle is equal to the perimeter of square , then find the ratio of their areas .

Write the value of k for which exercise equal to 2 is a zero of polynomial X square + 2 k x + 2

In the above figure, $\angle CAB={60}^{\circ },\angle CBA={60}^{\circ }$. PQ is a tangent at A. What is the value of $\angle BAQ$.

A vessel in the form of an inverted cone is filled with water to the brim. It's height is 20 cm and diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one third of the water in the original cone overflows. What is the volume of each of the solid cone submerged?

A polynomial of degree of n can have at most ______ number of zeroes.

The total surface area of a right circular cylinder of height 9m is 440 sq. meter.Find the radius of the cylinder. (Take π = 22/7)

prove that ( 1 + cot a - cosec a ) ( 1 + tan a + sec a) = 2

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

If k is any non zero constant and a,b are zeroes of x^2+cx+1,then the polynomial choose zeroes are a^2/b and b^2/a is

cosx + secx =2 ,(0 < x < ${90}^{\circ }$) What is the value of secnx + cosnx if n is an integer?

Question 1 (iv)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

$-x^2+7x-10=0$

How many outcomes have no heads on every coin in a toss of multiples coins as given below?

1 coin - ___

2 coins - ___

3 coins - ___

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

Finding the square root of the polynomial $16x^4-24x^3+25x^2-12x+4.$

If the mean of the data is 60, find the value of p

$\begin{array}{cc}Classmark& frequency\\ 25-35& 12\\ 35-45& 16\\ 45-55& p\\ 55-65& 15\\ 65-75& 8\\ 75-85& 19\\ 85-95& 13\end{array}$

If $3x=2y-2$ is written in the standard form $ax+by+c=0$, what will be the possible values of $a,b$ and $c$?

In an AP, the sum of the first ten terms is $-80$ and the sum of the next ten terms is $-280$. Find the AP.

Question 2 (i)
For which values of ‘a’ and ‘b’ does the following pair of linear equations have an infinite number of solutions?
2x + 3y =7
(a - b)x + (a + b)y = 3a +b - 2

$AB$ and $CD$ are respectively arcs of two concentric circles of radii $21cm$ and $7cm$ and centre $O$. If $\angle AOB={30}^{\circ }$, find the area of the shaded region.

50 bells $B_1,B_2,B_3,.......B_{50}$ start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively.
In a span of 1 day , how many times do bells $B_{10},B_{20},....B_{50}$ ring together?

A parallelogram with longer side being 20 cm makes an angle of ${135}^{\circ }$ with one of the smaller sides. If the area of the parallelogram is $80c{m}^2$ the length of the smaller side is equal to