`alpha,beta,gammaand delta` are angles in I,II,II and IV quadrants, respectively and none of them is an integral multiple of `pi//2`. They form an increasing arithmetic progression.
Which of the following does not hold?

A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or III or all the three. The probabilities of the Student passing in tests I,II and III are m, n and 1/2 respectively. If the probability of the student to be successful is 1/2 , then which one of the following is correct? (a) m (1+n)=1 (B) n (1+m) =1 (C) m=1 (D) mn=1

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta) y(t)x'(t)dt, S=int_(alpha)^(beta) x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. If the curve given by parametric equation x=t-t^(3), y=1-t^(4) forms a loop for all values of t in [-1,1] then the area of the loop is

Let x be the length of one of the equal sides of an isosceles triangle, and let theta be the angle between them. If x is increasing at the rate (1/12) m/h, and theta is increasing at the rate of pi/(180) radius/h, then find the rate in m^2 / h at which the area of the triangle is increasing when x=12m a n d theta=pi//4.

Let alpha,betaa n dgamma be some angles in the first quadrant satisfying tan(alpha+beta)=(15)/8a n dcos e cgamma=(17)/8, then which of the following hold(s) good? (a) alpha+beta+gamma=pi (b) cotalpha+cotbeta+cotgamma=cotalphacotbetacotgamma (c) tanalpha+tanbeta+tangamma=tanalphatanbetatangamma (d) tanalphatanbeta+tanbetatangamma+tangammatanalpha=1

If alpha,beta,gamma,delta are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity k , then the value of 4sin(alpha/2)+3sin(beta/2)+2sin(gamma/2)+sin(delta/2) is equal to (a) 2sqrt(1-k) (b) 2sqrt(1+k) (c) (sqrt(1-k))/2 (d) none of these

Go through the following statements (i) In chlorophyceae the flagella are 2 in number, unequal in size and lateral in position (ii) In phaeophyceae flagella are 2-8 in number, equal in size and apical in position (iii) Chlorella and Spirullina re rich in proteins and are used as food supplements even by space travellers. (iv) The leaves in pteridophyta are microphylls as in Selaginella or macrophylls as in ferns. Which of these are correct a. i,ii,iii b. ii,iii c. i,ii,iv d. iii,iv

Statement I : The magnetic moment of an electron rotating in an atom is proportional to its angular momentum . Statement II : The electrons in an atom can rotate only if those orbits for which the angular momentum of the electron is an integral multiple of (h)/(2pi) (h - Planck 's constant ).

In which of the following situations, does the list of numbers involved is in the form of a GP? (i) Salary of Sharmila, when her salary is 5,00,000 for the first year and expected to receive yearly increase of 10%. ii) Number of bricks needed to make each step, if the stair case has total 30 steps, provided that bottom step needs 100 bricks and each successive step needs 2 brick less than the previous step. iii) Perimeter of the each triangle, when the mid points of sides of an equilateral triangle whose side is 24 cm are joined to form another triangle, whose mid points in turn are joined to form still another triangle and the process continues indefinitely.

Consider a triangle PQR ,right at R ,in which PQ = 29 units ,QR =21 units and angle PQR =theta , then find the values of (i) cos ^(2) theta + sin ^(2) theta and (ii) cos ^(2) theta -sin ^(2) theta

Statement I: the alternating current lags behind the voltage by a phase angle pi/2 when ac flows through an inductor, Statement II: The inductive reactance increases as the frequency of ac source decreases.