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A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is ${30}^{\circ }$ [1 MARK]

Find HCF of 2 consecutive odd numbers.

A parallelogram and a rectangle having same base length and same height .If $P_1$ & $P_2$ be the perimeter of the parallelogram and the rectangle respectively, then which of the following is correct?

What is the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively ?

(a) 13 (b) 9 (c) 3 (d) 585

The value of $\Delta =\left|\begin{array}{cc}\cos {15}^{\circ }& \sin {15}^{\circ }\\ \sin {75}^{\circ }& \cos {75}^{\circ }\end{array}\right|$ is



[2 marks]

Two tangents PA and PB are drawn from an external point P to the circle with centre O, such that $\angle$APB =${120}^{\circ }$what is the relation between OP and AP?

Find out the wrong number in the series given below :

$2,3,5,9,17,35$

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

$\begin{array}{cccccccc}\text{Number of plants}& 0-2& 2-4& 4-6& 6-8& 8-10& 10-12& 12-14\\ \text{Number of Houses}& 1& 2& 1& 5& 6& 2& 3\end{array}$

Which method did you use for finding the mean, and why?

In the given figure,O is the centre of the circle & $\angle ACB={60}^{\circ }$, Find angle OAB.

A lady holds 1800, Rs 100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what is the return she gets as percent on her investment?

Give your answer to the nearest integer.

Question 7 (i)

In a right triangle ABC, B =90^o.

If AB= 6cm, BC= 8cm, find AC.

The price of cooking oil has increased by $25\%$. By what percentage should the consumption be cut down such that the expenditure on purchasing cooking oil remains the same?

Question 126 (b)

Architects design many types of buildings. They draw plans for houses, such as the plant shown in the following figure.

An architect wants to install a decorative moulding around the ceilings in the rooms. The decorative moulding costs ₹ 500/ meter.

The carpet costs ₹ 200 per $m^2$. Find the cast of carpeting each room.

More than One Answer Type

एक से अधिक उत्तर प्रकार के प्रश्न



Which of the following figure(s) has/have more than 15 triangles?



निम्नलिखित में से कौनसे चित्र/चित्रों में 15 से अधिक त्रिभुज है/हैं?

The height of an equilateral triangle is 3$\sqrt{3}$ cm. Its area is

(a) 6$\sqrt{3}c{m}^2$ (b) 27$c{m}^2$ (c) 9$\sqrt{3}c{m}^2$ (d) 27$\sqrt{3}c{m}^2$

Find the equation of the straight line that has a $y-$intercept of 5 and is parallel to the straight line $x-3y=3.$

A___ is a line and a ___ is a line segment.

In the figure given below, PA and PB are tangents to the circle from point P. Which of the following is the correct relation between PA and PB?

If the degree of the divisor g(x) is one then the degree of the remainder r(x) is

Solve the following quadratic equations :- a) $x^2=4x$ b) $x^2=9$

The following table gives, the literacy rate (in percentage) in 40 cities. Find the mean literacy rate, choosing a suitable method. $\begin{array}{cccccc}\text{Literacy rate(\%)}& 45-55& 55-65& 65-75& 75-85& 85-95\\ \text{Number of cities}& 4& 11& 12& 9& 4\end{array}$

If 5tan$\theta$=4, then value of (5sin$\theta$ -4cos$\theta$)/(5sin$\theta$ +4cos$\theta$) is:

Find the sum of the first 18 natural numbers.

Which of the following form an infinite sequence?

(i) Odd positive integers between 1 and 99

(ii) 1.5, 2.4, 3.3, 4.2, 5.1, 6.0, 6.9, 7.5

(iii) Sequence of all integers



(iv)Prime numbers less than 25.

the general form of a polynomial is

Prove the following trigonometric identities:

$\frac{tan\theta }{1-cot\theta }+\frac{cot\theta }{1-tan\theta }=1+tan\theta +cot\theta$

40 men can build a road in 10 days, working 5 hours a day. In how many days will 30 men, working 8 hours a day, complete the road?

If $p=2^a\times 3^b\times 5^c$ and $a>b>c$ are natural numbers, then what is the unit digit of p?

Mr. Navin opened a Savings Bank Account at Union Bank on 1st April 2007. The entries of one year as shown in his pass book are given below.

$\begin{array}{ccccc}Date& Particulars& Withdrawal& Deposit& Balance\\ 1^{st}April2007& Bycash& -& 8550.00& 8550.00\\ {12}^{th}April2007& ToSelf& 1200.00& -& 7350.00\\ {24}^{th}April2007& Bycash& -& 4550.00& 11900.00\\ 8^{th}July2007& Bycheque& -& 1500.00& 1340.00\\ {10}^{th}Sept.2007& Tocheque& -& 3500.00& 16900.00\\ {17}^{th}Sept2007& Bycheque& 2500.00& -& 15200.00\\ {11}^{th}Oct2007& Bycash& -& 800.00& .15200.00\\ 6thJan2008& ToSelf& 2000.00& -& 13200.00\\ 9^{th}March2008& ByCheque& -& 950.00& 14150.00\end{array}$

The bank pays interest of 5% per annum. What will be the interest paid on 1^st April, 2008? The answer should be correct to the nearest rupee.