Class 10 Math DPP
1. write the value of sin30°, cos60°, and tan45°
2. If sinθ = 1/2 Find θ.
3. Find the value of 1) Sin²30° + Cos²30°
2) 2 tan45° + Cos60°
4. If 8cotA = 15. Find ((1+tan²A))/((1-tan²A)).
5. In any ∆ ABC, If CosA = CosB, what is the nature of ∆.
6. If Sinθ = Cosθ, find the value of θ.
7. If 3tanA = √3, find ((SinA+CosA))/((SinA-CosA)).
8. If SinA + CosA = 1/2 and SinA - CosA = -1/2. Find A.
9. If SinA = 1/3 find cosec²A + 1/( sin²A).
10. If tan(A+B) = √3 and tan(A-B) = 1 find A and B.
also find Sin(A+B), Cot (A+B)
Chapter: Introduction to Trigonometry Angles Only)
Time: 45 Minutes Marks: 25
Section A: Very Short Answer (1 mark each)
1. Write the value of:
(a) sin 60° (b) cos 30° (c) tan 45° (d) sec 60° (e) cot 0°
Section B: Short Answer (2 marks each)
2. Prove that:
sin² 30°+ cos² 30°= 1
3. Find the value of:
tan 30° - cot 60° + sin² 45°
4. If sin A = 1/3 and angle A is acute, find angle A and verify all trigonometric
ratios of angle A A.
Section C: Long Answer (3 marks each)
5. Evaluate: (sin 30° + cos 60°)/(tan 45°)
6. Simplify: (1 + tan² 30°)/(sec² 30°)
7. If cos 4 = √3/2 and A is acute, find angle A and all other trigonometric
ratios.
Bonus (2 marks) Fill in the missing values in the table:
Angle (°) sin θ cos θ tan θ
1. If pth term of AP is ‘q’ and qth term is p then find its nth terms.
2. If mth term of A.P is 1/n and its nth term is 1/m then find mnth term.
3. If 1st and last terms are 8 and 65. and sum of its term(all) is 730. find
common difference.
4. A sum of Rs 1500 is to be used to give 10 cash prizes to student of a school.
If each prize is Rs 20 less than its preceding prize. find the value of each
prize.
5. If 7th term of A.P is 1/9 and its 9th term is 1/7 , find 63rd term
6. Find the sum of all odd integers b/w 1 and 100 which are divisible by 3.
7. The sum of 1st natural number is 5n²-n. Find nth term and sum of 50 terms.
8. Which term of A.P. 52, 48, 44.... will be First Negative term.
9. If X = 1-6+2-7+3-8+ .... to 1000 terms, then find X.
10. If sum of First 'm' terms of A.P is same as the sum of First n terms. then find
the sum of (m+n) terms.
11. If b, c, 2b are 3 terms of A.P, then find the ratio of b and c.
Section(A) (1 mark)
1. Write the value of:
Sin²45 + Cos²45
2. Simplify:
(〖sin〗^2 θ)/(1+cosθ)+ (1+cosθ)/(〖sin〗^2 θ)
Section B (2 marks)
3. Prove:
(1-〖cos〗^2 θ)/(〖sin〗^2 θ)=1
4. Show that
Sec²θ - 1 = tan²θ
5, Proved that
cosθ/(1-sinθ)+ cosθ/(1+sinθ)=2secθ
Section C (3 marks)
6. Prove that
(1+〖tan〗^2 A)/(1+ 〖cot〗^2 A)=〖tan〗^2 A
7. If Secθ + tanθ = P then prove that
secθ=(P^2+1)/2P
Section D (4 mark)
8. (1+cosA)/sinA +sinA/(1+cosA)=2 cosecA
9. Prove that
(sinA+cosA)/sin〖A-cos A〗 +(sinA-cosA)/(sinA+cosA)=2 secA
10. If SinA+CosA = √2 Cos A. Find
SinA - CosA
Co-ordinate
1. Find the distance b/w A(a, b) and
(-a, -b).
2. Find the co-ordinates of points of
trisection of line joining A(4,6)
and B(-2,5).
3. Find the ratio in which x-axis
divides the line (2,8) and (3,6)
1. If the distance b/w the points (x,0) and (0,3) is 5 units. then find the value
of k.
2. Find the distance b/w (10cos30, 0) and (0, 10 cos60°).
3. Find the distance b/w (-8/5, 2) and (2/5, 2).
4. If distance b/w (4,k) and (1,0) is 5 units, then find k.
5. The x coordinate of a point 'P’ is twice its y coordinate. If P is equidistant
from Q (2,-5) and R (-3,6). find P.
6. If P(5,2), Q(2,2) and R(-2,a) are the vertices of right triangle with LQ=90°,
Find a.
7. Find the distance b/w A(cosθ, sinθ), B (sinθ,-cosθ)
8. A circle with centre C (3,5) passes through a Point (-2,4). find the diameter
of circle.
9. Find distance b/w (acosθ, asinθ) from origin.
10. Find k, If Point (0,u) is equidistant from the Point (10,k) and (k,8).
11. Find x and y if O(0,0), A(0,2), B(x,y) and C(3,0) form a rectangle OABC.
12. Find y such that points A(5,4), B(5,2), C(2,2) and D(2,5) forms a square.
13.
1. Find coordinate of Point P, If. P and Q trisect the line segment joining the
Points (5,-3) and (-1,3).
2. The line segment joining the points (2,1) and (5,-8) is bisected at Point P
and Q. If P lies on 2x-y+k=0, find k.
3. Find P. If the distance p from (3,4) is √10 unit and abscissa of P is double of
its ordinate.
4. Find the x if the distance of (0, x) from (3,5) is 5 unit.
5. Find the value of y, If (5,y) (5,5) (1,5) and (1,2) are the vertices of
rectangle.
6. Find Point on x-axis which is equidistant from (-2,5) and (2,-3)
7. Find the ratio in which the line segment joining the P(3,-6) and (5,-3) is
divided by x-axis.
8. If (-1,2) divides the line segment P(2,5) and Q(x,y)in ratio 3:4.
Then find x² + y².
9. Find ratio in which S(u, m) divides P(2,3) and Q(6,-3)
10. Find K. If x axis divides the line segment joining the Points (-4,-6) and (5,2)
in K:1.
11. If end points of diameter of a circle are (2,4) and (-3,-1). find radius.
12. Find x and y
1. Find the value of x, If 8x+9, 6x-2, 2x-7 are 3 consecutive terms of A.P.
2. If AP 5,8,11, ... has 40 terms. find the sum of lost 10 terms.
3. For what value of k will k+9, 2k-1 and 2k+7 are in A.P.
4. Sum of 1st n terms of A.P is 5n²+2n, then find its 2nd term.
5. Find common difference of A.P. 1/p ,(1-p)/p ,(1-2p)/p ……..
6. Find the middle term of 6, 13, 20, ……., -216
7. If 1/(x+2) ,1/(x+3 ) ,1/(x+5) are in A.P. Find x ?
8. Find 5th term of A.P. whose nth term is 3n-5.
9. If 18, a, b, and -3 are in A.P. then find a+b.
10. The 4th term of A.P is 11. The sum of the 5th and 7th term is 34. find
common difference.
11. If the angles of a Δ are in A.P. and smallest is 40°. Find largest.
12. The angle of a quadrilateral in A.P. whose common diff is 10° find the sum
of smallest and largest angle.
13. If sum of First 7 term is 49 and that of 17 terms 289. Find the sum of n
terms.
14. If ratio of the sum of the First m and n terms of A.P. is m²:n² then find the
ratio of mth and nth terms.
