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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 7401. |
Which of the following statements is true I : If (a+b+c)(a+b-c)=ab then angleC=60^(@) II If sin^(2)A+sin^(2)B+sinC=2 in a DeltaABC then it is right angled |
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Answer» onlyI |
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| 7402. |
If the vertex of a parabola is (0,2), directrix on x-axis then its focus is : |
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Answer» (0,0) |
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| 7403. |
Two unbiased dice are thrown . Find the probability that sum of the numbers on thetwo faces is neither 9 nor 11 , |
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Answer» |
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| 7404. |
Let A=pi/7, B =(2pi)/7, C=(4pi)/7 and cosA cos B cosC=-1//8, then 2sum tan A tan B= |
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Answer» 7 |
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| 7405. |
Find the coordinates of the point which divides the line joining (5, -2) and (9, 9) in the ratio 3 : 1. |
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Answer» |
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| 7406. |
f: N rarr N, where f(x)=x-(-1)^(x). Then f is |
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Answer» one-one and into |
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| 7407. |
(iii) Let y= (x+1) (2x +3)^(3) (5x + 7)^(2) |
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Answer» |
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| 7408. |
If a is the arithmetic mean of b and c, and two geometric means G_(1) and G_(2) are inserted between b and c such that G_(1)^(3)+G_(2)^(3)=lamda abc, then find the value of lamda. |
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Answer» |
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| 7410. |
if the coefficient of rth (r+1) th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P. then correct statements is : |
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Answer» `N^(2)-n(4R+1)+4r^(2)-2=0` |
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| 7411. |
If the sides of a triangle arexy + yz , yz +zx , zx+ xythen inradius of the triangles is |
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Answer» ` xyz ` |
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| 7412. |
If bara, barb, barc are mutually perpendicular unit vectors then [bara barb barc]^(2)+[barb barc bara]^(2)+[barcbarabarb]^(2)+[barabarcbarb]^(2)+[barcbarb bara]^(2)= |
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Answer» 0 |
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| 7413. |
Compare the following statements : p is a sufficient condition for q. |
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Answer» |
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| 7414. |
Which of the following hold (s) good for the function f(x)=2x-3x^(2//3) |
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Answer» f(x)has two POINTS of extremum |
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| 7415. |
Price relative means the ratio of price of a certain item in current year to the price of that item in base year , expressed as a............... |
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Answer» PERCENTAGE |
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| 7416. |
If 'm' and 'b' are real numbers with mbgt0, then the line whose equation is y=mx+b cannot contain the point |
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Answer» (0,2015) |
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| 7417. |
If tanalpha=(m)/(m+1)andtanbeta=(1)/(2m+1) then (alpha+beta) is equal to |
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Answer» `(pi)/(2)` |
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| 7418. |
On one side of a road of width 'd' meters there is a points of observation P at a height 'h'meters from ground. If a tree on the othr side of the road, makes a right angle at P, heigt of the tree in meters is |
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Answer» `(H^(2)-d^(2))/(h)` |
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| 7419. |
r_1^(2)= r_1r_2+r_2r_3 +r_3r_1 triangle is |
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Answer» Equilateral |
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| 7420. |
A gentleman buys every year Banks' certificates of value exceeding the last year's purchase by 25. After 20 years he finds that the total value of the certificates purchased by him is 7,250. Find the value of the certificates purchased by him in the 1st year and in the 13th year. |
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Answer» |
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| 7421. |
Determine whether the following measurements produce one triangle, two triangles or no triangle. angleB=88^(@), a=23, b=2. Solve if solution exists. |
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Answer» |
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| 7422. |
(a) Eliminat theta between the equation: (i)x=h+acostheta,y=k+b"sin"theta (ii)x=a costheta+b"sin"theta,y=a "sin"theta-b costheta (iii)x=a sec theta, y=b tan theta (b) Eliminate A between the equation: (i)sec A +"tan" A=m, secA-"tan"A=n (ii)acosecA+bcotA=x^(2),bcosecA+acotA=y^2 (iii)psecA+q"tan"A=x,p"tan"A+q sec A=y. |
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Answer» (ii) `x^(2)+y^(2)=a^(2)+b^(2)` (III) `((x)/(a))^(2) -((y)/(b))^(2)` =1 (b) (i) mn=1 (ii) `a^(2) -b^(2)=x^(4)-y^(2)` (iii) `p^(2)-Q^(2)=x^(2)-y^(2)`. |
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| 7423. |
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio. |
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Answer» |
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| 7424. |
Find the range of each of the following functions. (i) f(x)=2-3x, x in R, x gt 0 (ii) f(x)=x^(2)+2x, x is a real number. (iii) f(x) = x, x is a real number |
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Answer» |
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| 7425. |
The value of the expession (1- 4 sin 10^(@) sin 70^(@))/(2 sin 10 ^(@)) |
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Answer» `1//2` |
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| 7426. |
Let P_(r )(x_(r ), y_(r ), z_(r )), r = 1,2,3be three points where x_(1), x_(2), x_(3), y_(1), y_(2), y_(3), z_(1), z_(2), z_(3), are each in G.P. with the same common ratio then P_(1), P_(2), P_(3) are |
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Answer» COPLANAR |
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| 7427. |
........... is the eccentricity of ellipse if distance between focii is 6 unit and length of minor axis is 8 unit . |
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Answer» |
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| 7428. |
If sin theta + cos thea = m and sec theta+cosec theta = n, then n (m + 1) (m - 1) = |
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Answer» m |
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| 7429. |
Discuss the continuity of the functionf(x) = [x] + [-x] AA x in R. (where [.] denotes the G.I.F.) |
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Answer» |
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| 7430. |
If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5. Then, find each of the following f((1)/(2)) xx g (14) |
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Answer» |
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| 7431. |
Find the variance and standard deviation for the following data : |
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Answer» |
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| 7432. |
Find the radian measure corresponding to the following degree measures. 25^(@) |
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Answer» (II) ` - (19pi)/(72)` (III) ` (4pi)/(3)` (IV) ` (26 PI)/(9)` |
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| 7433. |
For what values of m will the equation x^(2)-2mx+7m-12=0 have (i) equal roots, (ii) reciprocal roots ? |
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Answer» (II) `m=(12)/(7)` |
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| 7434. |
In a triangle ABC if (cos A)/a=(cos B)/b= (cos C)/c, then Delta ABC is |
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Answer» EQUILATERAL |
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| 7436. |
In a /_\ABC if a^(2)+b^(2)+c^(2)=8R^(2) then show that/_\ABC is a right angled triangle. |
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Answer» |
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| 7437. |
Find the number of ways in which 4 cards can be selected from a pack of 52 cards. In how many ways (i) all 4 cards are from one suit? (ii) all 4 cards are from different suits? (iii) all 4 cards are face cards? (iv) two cards are red and 2 cards are black? (v) all 4 cards are of same colour? |
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Answer» Solution :No. of ways of selecting 4 cards from 52 cards `= .^(52)C_(4)` `= (52 xx 51 xx 50 xx 49)/(1 xx 2xx 3 xx 4)` `= 270725` (i) No opf ways of selecting 4 cards of diamond from 14 cards `= .^(13)C_(4)`. No of ways of selecting 4 cards of club from 13 cards `= .^(13)C_(4)` No of ways of selecting 4 cards of hearts from 14 cards `= .^(13)C_(4)` No of ways of selecting 4 cards of spade from 13 cards `= .^(3)C_(4)` Now from ADDITION principle Required ways `=.^(13)C_(4) +^(13)C_(4) +^(13)C_(4) +^(13)C_(4)` `= 4 xx .^(13)C_(4)` `- 4xx (13 xx 12 xx 11 xx 10)/(1 xx 2 xx 3 xx 4)` `= 2860`. (ii) No. of ways of selecting one cardfrom 13 cards of diamond `= .^(13)C_(1) = 13` No. of ways of selecting one card from 13 cards of clud `= .^(13)C_(1) = 13` No of ways of selecting one card from 13 cards of spade `= .^(13)C_(1) = 13` No of ways of selecting one card from 13 cards of heart `= .^(13)C_(1) = 13` Now from multiplication principle Required ways `= 13 xx 13 xx 13 xx 13` `= 28561` (iii) No of face cards in 52 cards = 12 No of ways of selecting 4 cards from 12 cards `= .^(12)C_(4)` `= (12 xx 11 xx 10 xx 9)/(1 xx 2 xx 3 xx 4)` `= 495`. (iv) No. of ways of selecting 2 cards from 26 RED cards `= .^(26)C_(2)` No of ways of selecting 2 cards from 26 black cards `=.^(26)C_(2)` Now from multiplicarion principle Required ways `= .^(26)C_(2) xx .^(26)C_(2)` `= (26 xx 25)/(1 xx 2)xx (20 xx 25)/(1 xx 2)` `= 105625`. (v) No of ways of selecting4 cards from 26 red `=.^(26)C_(4)` Now from addition principle Required ways ` .^(26)C_(4) +^(26)C_(4)` `= 2 xx^(26)C_(4)` `= 2xx (26 xx 25 xx 24 xx 23)` `(1 xx 2xx 3 xx 4)` `= 29900`. |
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| 7438. |
If f(x) = (ax + b) Cos x +(cx +d) Sin x and f^(1) (x) = x Cosx is an an identity in x then a,b,c ,d are given by |
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Answer» `a = B= C = d ` |
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| 7439. |
A box contain3 identical red balls, 3 identical white balls and 1 black ball. A ball is selected randomly from a bag and then put it in the bag. Aging a ball is drawn. Write the sample space for this experiment. |
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Answer» <BR> ANSWER :`S={R_(1)R_(1),R_(1)R_(2),R_(1)R_(3),R_(1)W_(1),R_(1)W_(2)R_(1)B,R_(2)R_(1),R_(2)R_(2),R_(2)R_(3),R_(2)W_(1),R_(2)W_(2),R_(2)B,R_(3)R_(1),R_(3)R_(2),R_(3)R_(3),R_(3)W_(1),R_(3)W_(2),R_(3)B,W_(1)R_(1),W_(1)R_(3),W_(1)W_(1),W_(1)W_(2),W_(1)B,W_(2)R_(1),W_(2)R_(2),W_(2)R_(3),W_(2)W_(1),W_(2)W_(2),W_(2)B,BR_(1),BR_(2),BR_(3),BW_(1),BW_(2),BB}` |
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| 7442. |
Two equal sides of an isoceles triangle are given by 7x-y+3=0 and x+y-3=0 and the third side passes through the point (1,10) then slope m of the third side is given by |
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Answer» |
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| 7443. |
lim_(yto0^(+))(3sqrt(y)+3sqrt(y^(2))-4sqrt(y^(3)))/(3sqrt(y)+y+4sqrt(y^(3))=……… |
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Answer» -1 |
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| 7444. |
A line is drawn from the point P (1,1,1) and Perpendicular to a line with direction ratios (1,1,1) to intersect the plane x + 2y + 3z = 4at Q. The locus of point Q is |
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Answer» `X/1 = (y-5)/(-2) = (Z+2)/(1)` |
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| 7445. |
If the angles alpha, beta, gamma of a triangle satisfy the relation, sin ((alpha - beta)/(2)) + sin ((alpha - gamma )/(2)) + sin (( 3 alpha )/(2)) = 3/2, then The measure of the smallest angle of the triangle is |
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Answer» `30^(@)` |
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| 7446. |
For any statement,p and q, prove that pimplies q -= (~p vv q). |
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Answer» `(##SCH_OPM_ISC_MAT_XI_C27_E08_009_A01##)` In this table , thecolumns headedp => Q and`~p VV q`COINCIDE , Hence , `(p=>q)-=(~p vv q).` |
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| 7447. |
If L and M are the feet of the perpendiculars from the point (2,4,5) to the planes XY and YZ, then distance LM is : |
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Answer» `9sqrt2` |
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| 7448. |
Express the following expression in the form of a+lb: [((sqrt(5)+i)/(2))(sqrt(5)-2i)]+(6+5i) |
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Answer» |
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| 7449. |
If the coordinate axes are the bisectors of the angles between the pair of lines ax^(2)+2hxy+by^(2)=0, when h^(2) gt ab and a ne b then |
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Answer» `a+B=0` |
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| 7450. |
Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . p vv q |
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Answer» |
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