List of practice Questions

Find the intervals in which the following functions are strictly increasing or decreasing:
$(a) x^2 + 2x − 5 $
$(b) 10 − 6x − 2x^2 $
$(c) −2x^3 − 9x^2 − 12x + 1 $
$(d) 6 − 9x − x^2 $
$(e) (x + 1)^3 (x − 3)^3$

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10cm.

If $\sin(sin^{-1}\frac{1}{5}+\cos^{-1}x)=1$ , then find the value of x.

सूची I का सूची II से मिलान कीजिए

	सूची I जल अणुओं की मात्रा सूची		सूची II वर्णन
A	गुरुत्व जल	I	जल का वह भाग जो पादप जड़ों द्वारा आसानी से अवशोषित किया जाता है
B	कोशिकीय जल	II	वह जल जो मृदा के अंदर और बाहर गुरुत्व बल के कारण गति करता है
C	आर्द्रताग्राही जल	III	Water that fills the micropores of the soil
D	उपलब्ध जल	IV	वह जल जो मृदा के कणों से सख्ती से जुड़ा होता है (सक्शन के 31 बार)

निम्नलिखित विकल्पों में से सही उत्तर का चयन कीजिए:

A dip circle is taken to geomagnetic equator. The needle is allowed to move in a vertical plane perpendicular to the magnetic meridian. The needle will stay

If the system of linear equations $ 8 x+y+4 z=-2 $, $ x+y+z=0 $, $ \lambda x-3 y=\mu$ has infinitely many solutions, then the distance of the point $\left(\lambda, \mu,-\frac{1}{2}\right)$ from the plane $8 x + y +4 z +2=0$ is :

What is the term used for chemical secretions of endocrine glands responsible for changes taking place in the body?

What is spectrochemical series? Explain the difference between a weak field ligand and a strong field ligand.

Nitrogen atom of amino group is _______hybridised.

The integrating factor of the differential equation.
$(1-y^{2})\frac{dx}{dy}+yx=ay$$(-1<y<1)$$is$

Two bars ot copper having same length but unequal diameter are heated to the same temperature. The change in length will be

What are the starting materials to get $2$-methylpropene as the major product?

What are the characteristics of the transition elements and why are they called transition elements? Which of the d-block elements may not be regarded as the transition elements?

When a = 0, b = – 1, find the value of the given expressions: (i) 2a+2b (ii) 2a²+b²+1 (iii) 2a²b+2ab²+ab (iv) a²+ab+2

There are 4 letters and 4 directed envelopes. The number of ways in which all the letters can be put in wrong envelope is

How many numbers of 6 digits can be formed from the digits of the number 112233 ?

DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD (Fig 9.15). If the area of the parallelogram is $1470$ $cm^2$ , AB = $35$ $cm$ and AD = $49$ $cm$, find the length of BM and DL.

A slit of width a is illuminated by red light of wavelength $ 6500\, \overset{\text{o}}{\mathop{\text{A}}}\, $ . If the first minimum falls at $ \theta =30{}^\circ , $ the value of $ a $ is

The time period of rotation of the earth around its axis so that the at the objects at the equator become weightless is nearly $(g=9.8m/s^2)$,Radius of earth =6400 km.